Portrait perspective: Quiz and two questions

[Jerry Fusselman]

I hope someone's answer to questions #1 and #2 in boldface below will help me to choose great perspective for portraits in 4x5 and 8x10. I want a careful answer that I can understand, so I introduce some math. The quiz is supposed to be a fun way to introduce my questions :), and I think it can help us avoid the pointless arguments and inadequate rules of thumb that usually dominate this kind of subject.

To keep things simple, assume no movements (and no rise, fall, or shift). The lens is rectilinear, and possibly a telephoto.

Recall from photography kindergarten that when we focus a particular lens, that determines the distance from the lens to the plane of sharp focus and the magnification achieved there. Furthermore, any line segment centered in the plane of sharp focus is imaged as a line segment centered in the film plane, and the line segment in the plane of sharp focus determines an angle from the front nodal point. Here are some variables we can measure:

f = lens focal length;
u = distance from the front nodal point to the plane of sharp focus;
v = distance from the rear nodal point to the film plane corresponding to u;
m = image magnification;
s = length of a line segment centered in the plane of sharpest focus (in the subject);
z = length of the line segment centered in the film plane corresponding to s;
a = angle that the line segment of length s forms from the front nodal point.

What I said about photography kindergarten can be restated in terms of these seven variables. That is, if we know f, u, and z, then we can deduce v, m, s, and a---provided the data is logical and consistent.

In this post, assume that the numbers we are given are logical and internally consistent, meaning, for example, that we never have a situation that assumes or implies u < f or v < f. Another way to say this is that the data we are given is measured with perfect accuracy. We may as well assume that f, u, v, s, and z are all measured in mm. And to sidestep a few unnecessary complications, assume that all of the numbers are positive and finite: In particular, we are not focusing at infinity.

It looks like there must be four equations relating my seven variables, because assigning three values determines the other four. We have seven equations in seven unknowns. The seven equations here are three variable assignments (f, u, and z) plus four other equations needed to deduce v, m, s, and a.

Quiz problem A: Write out four equations that allow us to determine v, m, s, and a from known values of f, u, and z.

Quiz problem B (optional): Of the seven variables I listed above, some combinations of three variables suffice to deduce the other four. But some do not: For examle, f, u, and v determine m, but not z, s, or a. List all of the combinations of three variables for which the values of the remaining four variables can be uniquely determined. We already know that (f, u, z) is yes, but (f, u, v) is no. There are 35 possible combinations of three variables (7 choose 3 equals 35), so the question is which of these 35 combinations of three allow deducing the other four variables?

Question #1: What distance to the subject determines the perspective with a print of a three-dimensional subject that fills the frame? I am guessing that the subject-to-film-plane distance is only an approximation, and that the exactly correct distance that defines this perspective is the subject-to-front-nodal-point distance.

I should be more specific. Suppose my 8x10 portrait print was shot with a particular lens on 35mm film. It is an enlargement from a 24 mm by 30 mm area on the film. And suppose that I want to match that perspective with large-format film. My question becomes this: What distance should I hold constant to duplicate that perspective with an 8x10 camera? (This will define what focal length we should use.)

I think the answer is to keep the subject-to-front-nodal-point distance the same between formats, but I am not sure. Keeping this distance constant as I vary formats, it seems to me, will keep the relative positions and sizes of the nose and ears unchanged in the images. It will also keep visible precisely what was visible before. Can anyone say for sure, or maybe even offer some proof?

My next question makes sense only if my guess for the answer to question #1 is correct.

Question #2: I want great perspective for head-and-shoulders portraits. In the world of 35mm, a 50 mm lens for this kind of portrait is considered terrible---too short. An 85 mm lens is okay, but many pros prefer 300 mm. In summary, some 35mm pros say that 50 mm is terrible, 85 mm is okay, and 300 mm is great (for shooting a head-and-shoulders portrait).

Still assuming that my guess for question #1 is correct, you can see that the 35mm pro advice for great head-and-shoulders portraits can be restated as advice on the proper subject-to-front-nodal-point distance.

Using your answers to quiz problem A or B, you will see that their counsel is that for head-and-shoulders portraits, a subject-to-front-nodal-point distance of 2.4 feet is terrible, 4 feet is okay, and 14 feet is great. To arrive at these distances, I assumed that 16 inches in the plane of sharp focus corresponds to 30mm in the film plane, i.e. z = 30 and s = 16*25.4 (because 25.4 mm = 1 inch).

In 8x10, matching these three subject-to-front-nodal-point distances require focal lenghts of approximately 280 mm, 480 mm, and 1680 mm. (I used z = 10*25.4 and the three I values computed above.) Using our hypothetical 35mm pro's appraisals, this means that 280 mm is terrible, 480 mm is okay, and 1680 mm is great.

I think modern 8x10 portrait shooters ignore this advice. So here is my question: Shooting portraits with 8x10 film, are we, without good reason, accepting generally poor and unflattering perspective?

Few 4x5 portrait shooters heed the 35mm pro's advice either, for it becomes this: 180 mm is terrible, 300 mm is okay, and 1040 mm is great.

Does anybody shoot 4x5 portraits with lenses anywhere near the recommended 1000 mm? Does anybody shoot 8x10 portraits with lenses anywhere near the recommended 1600 mm?

[Jay DeFehr]

Jerry,

I hope you'll forgive me for opting out of your math quiz, and consider the role of the film format in reproduction magnification and optimum viewing distances as clues to the reasons perspective rules that apply to 35mm format do not necessarily translate to larger formats. For what it's worth, my favorite portrait lens in 35mm is a 58mm f 1.2, which produces results roughly analogous to my 14 1/2" f4 Verito, which is one of my favorite portrait lenses for 8x10. Good luck with your calculations.

Jay

[Neal Wydra]

Dear Jerry,

"...some 35mm pros say that 50 mm is terrible, 85 mm is okay, and 300 mm is great..."

Two questions: Why all the math? What do the "other pros" say?

[Phong]

"(For 35mm) 50 mm is terrible, 85 mm is okay, and 300 mm is great (for shooting a head-and-shoulders portrait). "

I consider this one of those "inadequate rules of thumb that usually dominate this kind of subject". :-)

As a counterpoint, I offer the Kodak book "The Portrait", which recommends a 75mm lens in 35mm and 14 to 16 inches (355-400mm) for 8x10 head-and-shoulders portraits. Perhaps not ideal (I prefer slightly longer myself), but certainly adequate, and far from producing "generally poor and unflattering perspective".

Of the working professionals I know, there is not one who uses a 300mm as their main lens to do head-and-shoulders portraits on a regular basis. Sure, I have tried it myself, but any focal length say above 85mm is very adequate (and even much shorter, but that would require a lot more skills from the photographer). The problem with a very long focal length is that the working distance becomes terrible in communicating with the model. I consider this communication vital in getting a good expression with the subject, which in turn is what makes a good portrait. 300mm is great for candids though.

By the way, I noticed the "best" perspective are a bit further away with Caucasian than with Asian subjects, for my taste, generally speaking; it still depends on the specific subject. 90mm (in 35mm format) works reasonably well to achieve a more traditional/standard head-and-shoulder portrait with most subjects.


Cheers,

- Phong

[David Beal]

There's an empirical, if not mathematic basis for 300 mm 4x5 portraits. The diagonal of a 35 mm negative is 43 mm; twice the diagonal is 86 mm. 85 mm is a very popular portrait lens for that format. The diagonal of a 4x5 is 150 mm; by analogy, 300 mm is the "optimum" portrait lens.

Occasionally I will use a 135 mm lens for 35 mm head shots, but I think it's a bit much for my style.

HOWEVER: this is just me; or as the younger generation would say, "YMMV." Anyone can take my advice, and a twenty dollar bill, and buy a cup of coffee at Starbucks.

Good shooting.

/s/ David

[Mark Sampson]

When I was a portrait photographer we used 210mm lenses on the 6x7cm format. Which equals 105mm on 35mm, 360mm on 4x5. Now I prefer 90mm on 35- but that's because it's the lens that fits the camera I like best for portraits. Plenty of people shoot portraits on 8x10 but I'd guess that few use a 600mm lens (the approximate equivalent). That may be due to the logistical and d-o-f problems with such a long lens. But it really comes down to what works- and that's most often, a slightly longer than 'normal' focal length.

[Henry Ambrose]

"Perspective" is determined by camera to subject distance and nothing else.

As an example, any camera and any lens at five feet from a subject will produce the same perspective. Framing may change, perspective will not.

[Ernest Purdum]

It's perhaps less applicable to formal portraits than to other photographs, but I have noticed that very old books often offer "horrible" perspective examples that to contemporary eyes don't look all that awful. Apparently, our eyes have now become more accepting of images produced by wider lenses. Perhaps this has come about over the years by seeing so many news and television images made with quite short lenses at close distances.

[David Hempenstall]

Henry has it exactly right.

No need for maths and all the craziness.

Stand at a distance that you find the rendering of the subject to your liking. Choose a lens that provides the cropping that you want.

It is no more complicated than that.

It is also a mistake to get stuck into the idea that a certain lens/focal length/aperture/camera/film/filter (blah blah blah) must be used to accomplish something photographically.

something about skinning a cat.....

Look through the camera. When you see something that excites you, make a picture.

D.

[jnantz]

hi jerry -

sorry, when it comes to photography, i rarely do math.
(i even cheat when it comes to computing bellows compensation)

i just stick a lens on the camera, and take the picture, otherwise i'd have to get a pad and paper and do long computations, and by the time i was done with the math, my subject would have fallen asleep. :)

why make things more complicated than you have to ...

-john

[Patrik Roseen]

I have glanced through alot of photobooks lately, including head,half height and fullheight body pictures. Some of these included data about filmformat and size of lens...and it is very hard to see any pattern in which lens is the one to use for certain pictures. What I did learn however, is that the lens is very much chosen based on the appropriate distans to the subject due to e.g. how the lighting is composed not to interefere by creating shadows, not being able to step away from the subject, avoiding unnecessary background information etc.

[Frank Petronio]

I bet if you could calculate the focal length of many famous paintings, they'd be wide enough to surprize you. I tend to go wider for roundness and volume. But I also narrow most faced 5% or so in Photoshop because I am a fashion victim and don't want my faces looking fat.

Frankly, I think long lens portraits are far easier, almost to the point of cheating. I much prefer the classic Avedon/Penn portraits done with the 80mm on the 6x6 Rolleiflex. I have shot 4x5 with everything from a 127 to a 300, and I like my 8x10s done with the 300 as well as the 360.

[Ted Harris]

Frank is right on point with is brief discussion of faces. There are many variables in addition to the lens that need to be considered ... the size and shape of the face of your subject, the effect you wish to achieve, the available lighting, your finesse (or the subject's) with makeup, etc. All of these need to work together.

Having said all that for formal sittings I generally use a 300mm Apo Symmar or a 250mm Imagon for 4x5 depending on the final effect I am after. I prefer to work with controlled lighting so I can use it to 'model' the planes of my subject's face and bone structure.

[Mike H.]

Jerry, I bet you and Leonard Evans would get along just great! :) I could sit there and watch the two of you talk just as though I was watching at a verbal tennis match, and although I would really, truly, greatly admire your skills at math and lens dynamics, I wouldn't have a clue what was being said. I make my images by sticking closely to a prescribed procedure given to me by my large format instructor and never worry about the rest of it. My mind is all on seeing and composing the image. And I'm comfortable with that.

[Jim Galli]

Thank goodness understanding all that math is not really requisite to portraiture or I'd be left out in the cold. I'll make a guess that 99.8% of portraits are done by photogs that simply learn what works by trial and error. 8X10 and larger portraiture becomes something of a special case though. Since a human head can roughly fill an 8X10 frame, an 810 shooter that's doing busts is always working somewhere near 1:1 or a little less. To get to 1:1 with a 1680mm lens would require 3360mm of bellows. To get 1:1 with a 480mm lens requires 960mm bellows. I've found by my seat of the pants method that you really don't need anything longer than 12 - 16" (sorry to break your mm rule but history wins here) for 810 portraiture, and 1000's of old time studios would bear this out.

Here are a couple done with my 13" P&S Series IV.

http://tonopahpictures.0catch.com/Jason.jpg

Done with a 13" lens at roughly 25+" bellows for a near 1:1 head. So was my 13" lens a 13" or a 25" ?

http://tonopahpictures.0catch.com/Don.jpg

Same lens but this time the bellows was more like 18" or 19"
(forgive the dirty scans).

A 15" lens on an 8X10 with a 30" bellows is manageable for most things. The old timers with their big Century Bi Centennial camera stands and their Century 9A cameras knew exactly what they were doing.

On 11X14, I'm just scratching the surface, but 19" - 22" seems "logical" to an old 'seat-of-the-pants' photog. You can actually make a human head bigger than lifesize with the 1114.

http://tonopahpictures.0catch.com/JohnColeS.jpg

The above was done with a Voigtlander 22" Petzval and bellows at perhaps 47".

[Jason Greenberg Motamedi]

A useful discussion here sans math:
http://www.apug.org/forums/showthread.php?t=15090

[Bruce E. Rathbun]

All math factors aside I find that a 14" lens seems to be ideal for portraits on 8"x10" and a 19" for 11"x14". Assuming of course that the subject is framed from the waist up.

[Steve J Murray]

I've shot many many fine portraits, even "head and shoulders" with 35mm format with the 50mm lens and the 105mm lens. I think some fashion photogs use longer lenses to flatten perspective and blur backgrounds. The 50mm gives a more intimate feel to a portrait, and you are closer to the subject and can interact more intimately and capture nuance in expression more easily. I like the 105 too, but it flattens the features more, but gives a nice bokeh. Translating to 4x5 those would be fairly normal lenses. I agree with the other posts here: you really have to go by look and feel and not worry about the math.

[Bob Gentile]

All this "technical" math stuff reminds me of an interview with a musician -- an ol' blues legend. When asked if he was familiar with all the "technical" stuff (chord construction, progressions, etc.) he replied, "Oh, yeah! Sure! But... not enough to hurt my playing."

When it comes to portraits, forget the math. It's all about the expression!

[Jerry Fusselman]

Henry and David,

One quick question. Did you two give an answer to my question #1? Is it u, u+v, or something else? That is, are you two asserting that perspective is determined by the subject to front-nodal-point distance in agreement with my guess, or is it the subject-to-film-plane distance in disagreement with my guess, or is something else entirely?

[Jerry Fusselman]

The old timers with their big Century Bi Centennial camera stands and their Century 9A cameras knew exactly what they were doing.

Jim, would you be willing to please expound on this a little as to format, focal length, and magnification?

[Jerry Fusselman]

Frank,

Thanks for responding! (And that goes for everyone, even those, unlike Frank, who insist that my questions are stupid and could not possibly benefit anyone.)


I bet if you could calculate the focal length of many famous paintings, they'd be wide enough to surprise you.

Hmm..., how would you go about calculating the focal length of a painting?


I also narrow most faced 5% or so in Photoshop because I am a fashion victim and don't want my faces looking fat.

I wonder what focal length we would calculate your images with the 5% Photoshop narrowing. The entire program you describe for calculating focal lengths for unreal images sounds almost hopelessly impossible to me, but I am willing to learn otherwise.

[Bob Younger]

For your math questions, go download a copy of VadeMecum. http://www.bobwheeler.com/photo/ .
It runs on a variety of small devices (handhelds) and has calculations for virtually every photographic requirement. Most of which you'll never use because few landscape or other photographs are actually made of flat planes; there always seems to be a tree or rock that intrudes and messes up the calculations.
But they are helpful in mentally envisioning what you're trying to do, and in defining the limits of what you can do. It's saved me from exposing film that would have been just wasted.

[Henry Ambrose]

Jerry,

Your original post began:

"I hope someone's answer to questions #1 and #2 in boldface below will help me to choose great perspective for portraits in 4x5 and 8x10. I want a careful answer that I can understand, so I introduce some math. The quiz is supposed to be a fun way to introduce my questions , and I think it can help us avoid the pointless arguments and inadequate rules of thumb that usually dominate this kind of subject."

Its the difference in magnification between the tip of the nose and the ears. (for instance) Get too close and the person looks strange - we're outside of our "normal view of the world". The nose being closer to the camera it is magnified more than things farther away. As we move away from the subject the difference between magnification of the parts of the subject (nose and ears in this example) lessens, as we move closer the "magnification ratio difference"(?) increases.

So if we get too close to a portrait subject we may get a "big nose" look because the nose is magnified more than the other parts of the object. Setting up the camera farther away "flattens" the look - decreases the difference in magnification between the parts of the subject.

Now if we want to "avoid pointless arguments" then its very simple that perspective is determined by:
1) where you stand
2) how far you set up the camera from the subject
3) the distance from the object being photographed to the film plane
4) object distance to the rear principal point of the lens

All being esentially the same location stated differently and in increasing levels of precision. Number 4 becomes difficult because the values change for different lens types and anyway are way beyond the precision needed for a portrait.

For that matter, precision higher than number 1 is probably not needed. If it were we'd all be using exactly the same focal length for portraits. We don't because we all know that effective portraits can be made lots of different ways, from varying distances. But still the one rule that stands is distance to the subject. Perspecitive is contolled only by how far we are from the subject. I think dressing it up past that point is needless. Unless it makes the 'light bulb" of realization come on over someone's head (but I can't see that labored complication does that - but it might for some).

[Henry Ambrose]

How about a formula that goes like this:

1) I want to be X inches from my subject
2) My film is X inches tall
3) I want the chin to top of head to be X inches tall on my film.
4) What focal length gives that result?

[Jim Galli]

Jim, would you be willing to please expound on this a little as to format, focal length, and magnification?

The big century stands and cameras are designed for 2 things that are extremely needful in LF 8X10 and larger portraiture. First, they are a sturdy platform for giant heavy lenses. When you get into 16" f3.8 lenses you get into very large very heavy glass. The Century (and others like Ansco) portrait cameras were simply a giant billboard size front standard with 9X9 lensboards. They facilitated lenses like 19" f4 Sigmar's (street car headlamps) with ease. The big front also made it easy to have BIG packard shutters inside with apertures large enough to facilitate a 19" f4. Then with bellows draws like 36" (necessary to get a bust with a 19" lens) the camera had the capacity for that, and by design it simply sits flat on a table platform. No tripods when you get into the big stuff.


http://tonopahpictures.0catch.com/Century9A_1.jpg
9a Set up for a macro of indian rice grass with a 16" Beach Multifocal lens.

http://tonopahpictures.0catch.com/Century9A_2.jpg
This is an 11X14 Bausch & Lomb Tessar Ic mounted in a universal aperture holder.

I've divided my portrait lens collection into groups. Portable and NON. The portable lenses like the 13" P&S can travel in the field and work well on a Kodak 2D. The giants like an 18" Hyperion f4 are confined to the 9a / Studio. The big 9a with it's stand makes using the giants easy though.

The big Universal Aerture lens holder with a packard behind becomes a versatile test stand for a host of lenses that find their way to Tonopah Nevada.

[Henry Ambrose]

Jerry wrote:
"Thanks for responding! (And that goes for everyone, even those, unlike Frank, who insist that my questions are stupid and could not possibly benefit anyone.)"

Just to be sure you know --- I don't think your questions are stupid.

I don't exactly understand "where you're coming from" but I sure don't think bad of you and I'm not here for an argument. I am trying to help.

[vijayn]

Finally a math problem on this otherwise dull and mundane forum (sarcasm alert) ... but no Jerry, your math is surely wrong - a 280 on 8x10 cannot equal 180 on 4x5 - for you see, 8x10 is exactly 2x of 4x5 in dimensions.

And coming from an engineer, your problem has simpler solutions if you solve for angles instead of linear dimensions. So ask yourself this: what angle of view gives you a portrait that you find most flattering; and what lens focal length will yield this angle of view on the format that you want to use. Simple trigonometry will work instead of lens equations.

And having done this exercise I can tell you that as you go up in format size, you have to live with larger angles of view for the same task. Obviously you cannot use an 1800mm lens (300/50 * 300; 300mm on 35mm is 300/50 = 6x the standard focal length which would be 6x of 300mm on 8x10, since 300mm is the standard focal length on 8x10), so the next question becomes what focal length is acceptable.

As for the math, we can take it offline if you want.

[Maris Rusis]

If there is no time for calculations an alternative approach is to put the camera lens at the distance you would be if you were relating to your portrait subject in a respectful, interested, and engaged way. Too close is no good. It invades personal space. Too far seems aloof and cool. When the distance feels right it is pretty sure to look right.

Different cultures have different personal spacings. For average "western" subjects 1.5 metres is a typical friendly (but not too friendly) distance for all cameras, lenses, and formats. If you want more coverage use a shorter lens: want tighter framing, go for a longer focal length but leave the distance the same.

[Jerry Fusselman]

Sorry, vijayn, I believe yours is a common mistake, and since you expressed yourself so clearly, it is easiest to address it here. You were right in all respects except one. Let me first try to summarize what I think you are saying with an example.

In brief, I think you are forgetting that back focus increases more than you expect when focusing closer than infinity and shifting to a larger format. This is just intuition, and my upcoming example is more careful.

Suppose we are shooting 4x5 with a 300 mm lens and we focus on a 15-inch tall subject in portrait orientation. This is a head-and-shoulders portrait, if you like. The magnification is 1/3 (5 inches of film/15 inches of subject), the subject-to-front-nodal-point distance is 1.2 meters, and the distance to the film plane is 400 mm (meaning we focus 100 mm out). All of these numbers make sense. You can either use the lens equation or set it up and measure it. Do whichever is easier for you.

I think you say two things now about shifting to a 600mm lens:

1. When you change to a 600mm lens, you get the same perspective as before provided the subject-to-front-nodal-point distance stays at 1.2 meters. I hope we agree that this is true!

2. You say that when you change to a 600mm lens and use 8x10 film at that distance, you get the same percentage of the face on the film as before. Or stated another way, if you switch to 600mm and keep the same perspective as before, the correct film for capturing the entire image is 8x10.

But I say it ain't so---#2 is wrong. To keep that 1.2 meter distance in focus with a 600mm lens, you know that you must move the distance from the lens (rear nodal point) to the film from 400 mm to 1200 mm, and the magnification becomes exactly 1. Because of that magnification, what you need to get the face framed as before is not 10 inches, but 15 inches of film.

Not convinced? OK, instead of going from 300 mm to 600 mm, go from 300 mm to 3000 mm. I.e., let us be more extreme. Imagine using 40x50 inch film to focus this image, but everyone knows that one cannot focus 1.2 meters away with a 3 meter lens. Now I hope you are convinced!

Of course, I have to agree with your logic in all respects when focusing at infinity.

This was all described without math. You can measure it. My key point is that doubling the focal length to match the perspective when moving from 4x5 to 8x10 makes sense only when focusing near infinity (with m near zero).

By the way, the correct answer for 8x10 with matching perspective is a 480 mm lens for a magnification of 2/3 and a back focus distance of 800 mm. Again, use either the lens equation or measure it, whichever is easier for you.

For those who did my problem 1 in the original post for this thread, a more-general answer is easy: If we like the perspective with a 300 mm lens with 4x5 film at magnification m, then the proper lens to match that perspective with 8x10 film is 300 x (2m+2)/(2m+1). In the case I gave, m = 1/3, which is why we get that a 480 mm lens matches the perspective.

Vijayn, you are right about doubling the focal length only when m = 0.

This analysis assumes that my answer to my question #1 is correct. It is so odd to me that nobody has yet answered my bold-faced question #1! However, I am becoming more and more confident in my guess, and here is why. Ignoring gravity and diffraction, light moves in straight lines in air. Because light moves in straight lines, moving the rear standard back has no effect on perspective at all, so it must be the front nodal point that determines perspective. Or if you do not like to think of nodal points, imagine a thin lens and say the the lens location relative to the subject determines the perspective. Imagine a standard ray diagram, which seems to bolster my position. Anyone disagree with this? Does anyone agree or disagree with my answer to original bold-faced question #1?

[David Hempenstall]

Sorry, but reading all this I'm getting to the point of pouring gasoline all over myself and striking a match.

[Walter Calahan]

"Sorry, but reading all this I'm getting to the point of pouring gasoline all over myself and striking a match." LOL

Who cares what the math says, it's what feels correct. I've made portraits with 12mm to 600mm lenses in 35mm format. It doesn't matter which lens I use, as long as the lenses works with the situation.

For my Carroll County project (http://www.walterpcalahan.com) I use a Nikkor 240mm on an 10-8 camera to make full length portraits of farmers. Seems right to me. But what do I know?

Simply never been good at math in the field. Never been good a pop quizzes either. Grin.

Now where's my match?

[Frank Petronio]

Those Carroll County farmers sure have big feet! ;-) Nice shots

[Henry Ambrose]

Jerry,
I answered your question number 1. Go back and read what I wrote.

And again, if you want the same perspective, you have to have the same distance from the camera to the object being photographed.

[Jerry Fusselman]

Yes, you came the closest to answering my original boldfaced question in your post (post #7). If you view this topic in threaded mode, then you will see that I already responded to your post. This is what I wrote (post #20):


Henry and David,

One quick question. Did you two give an answer to my question #1? Is it u, u+v, or something else? That is, are you two asserting that perspective is determined by the subject to front-nodal-point distance in agreement with my guess, or is it the subject-to-film-plane distance in disagreement with my guess, or is something else entirely?

I asked a question directly to you and the poster who agreed with you about perspective. I can rephrase my question: When you say "camera" do you mean "film plane" or "lens" or some other point? Probably if you say "lens," you mean the front nodal point---is this right? It makes a difference to me, because I am shooting near 1:1. When I first read what you wrote, I thought you meant film plane, but now I am less sure as to which location you mean.

[Jerry Fusselman]

Jim, do you recall some details of how you shot these? Any movements? Do you recall the taking apertures approximately?

[Henry Ambrose]

Jerry,

I wrote:
............... perspective is determined by:
1) where you stand
2) how far you set up the camera from the subject
3) the distance from the object being photographed to the film plane
4) object distance to the rear principal point of the lens

All being esentially the same location stated differently and in increasing levels of precision. Number 4 becomes difficult because the values change for different lens types and anyway are way beyond the precision needed for a portrait.

So, its:

4) object distance to the rear principal point of the lens

[Jerry Fusselman]

I see which post you mean now, and I see what you mean now, thanks! You are saying the exact answer to my question #1 is "object distance to the rear principal point". Thanks so much for being specific. But why the rear nodal point? That cannot be right, can it?

Let us look at an example. My 360mm Telomar has its rear nodal point about 130mm in front of its front nodal point, due to its strong telephoto design. There is just air there. A person inserting his eye at that point would see a quite different perspective than what is embodied in the rays of light hitting the front of the lens. It would be easy to construct an example with some object visible from the rear nodal point in front of the lens that is invisible to anyone standing at the lens. Do you see what I mean? This is why I do not think the rear principal (or nodal) point is correct.

[vijayn]

Jerry - let us define perspective first: Take two objects (for simplicity, two lines of the same length suffice) of the same size at two different distances from the image plane. Perspective is simply the ratio of the length of the images of the lines. This has nothing to do with the absolute magnification of each line; but rather is the ratio of those two magnifications.

Now, the important thing to remember is that every lens offers the exact same perspective, regardless of focal length, since the ratio of the magnifications cancels out the 'v' (or is it 'u'?) in the equation; thus the ratio of the images will be the ratio of the distances of the two objects from the lens plane, or more specifically from the front nodal point.

That is counterintuitive, I know, but true nonetheless. Thus, if you have an object at 100m from your lens and another at 200m, and both are of the same height (as in the optical term for linear size) then every lens, regardless of focal length, will form an image (assuming enough covering power etc) wherein the further object is half the height of the nearer.

So now I ask you this: if every lens yields exactly the same perspective, all that matters is the ratios of the distances of different objects from the lens, and the lens has no idea of what format is sitting behind it, why do we have to care about anything other than angle of view?

In other words, when you talk of "perspective" of an image, you are not talking of the mathematical definition of perspective, because that does not depend on either the focal length of the lens or the image format. You are, in reality, talking about angles of view to begin with. When you talk of angles of view, then you do have to double focal lengths as format size doubles.

Your fallacy is that you are trying to calculate perspective for two objects that are very close. However, remember that you cannot focus on two objects at different distances simultaneously; meaning that magnification can be calculated for one of the objects but not the other, out of focus object. This makes the issue of perspective irrelevant unless the distance of the objects is such that they are relatively close together and far away from the lens (mathematically, u>>f and u'>>f and u ~ u' i.e., u is approximately equal to u').

1. When you change to a 600mm lens, you get the same perspective as before provided the subject-to-front-nodal-point distance stays at 1.2 meters. I hope we agree that this is true!

Yes, this is exactly true, but it is true for all focal lengths, not only 600mm, and the idea of perspective is meaningful only when the objects are far away from the lens.

2. You say that when you change to a 600mm lens and use 8x10 film at that distance, you get the same percentage of the face on the film as before. Or stated another way, if you switch to 600mm and keep the same perspective as before, the correct film for capturing the entire image is 8x10.

This is approximately true for front-nodal-point to subject distances much larger than the focal length of the lens, much larger means at least 10 times larger. Thus for all distances above 3m this is more or less true. And you are correct that it is exactly true only when the lens is focused at infinity.

Hopefully this makes it clearer.

[John Berry]

Let's put another shovelful in the wheelbarrow. Lens choice MUST also take into consideration print size and viewing distance. ( If were going to jump in to the Nth degree, might as well go for Nth squared) Perspective envisioned in the shot will only be realized when the print is view at the right distance. Vijayn said much better than I, what I was thinking. Any lens will do when viewed at it's proper distance. I've shot the same head shot with a 24 and a 105 on 35mm. When viewed at 5 ft we can see how bad a choice the 24 was. Now take the 24 shot and put it 1" away from your nose. Perspective will appear much more acceptable. As for 8x10, Jim proves it very well, some of these rules of thumb are made to hit with a hammer once in a while. Other factors are How far in front of the backdrop do you need for the lighting you want and how much too small did you make said backdrop, forcing you into a longer lens.

[Jerry Fusselman]

As a counterpoint, I offer the Kodak book "The Portrait", which recommends a 75mm lens in 35mm and 14 to 16 inches (355-400mm) for 8x10 head-and-shoulders portraits. Perhaps not ideal (I prefer slightly longer myself), but certainly adequate, and far from producing "generally poor and unflattering perspective".

Of the working professionals I know, there is not one who uses a 300mm as their main lens to do head-and-shoulders portraits on a regular basis. Sure, I have tried it myself, but any focal length say above 85mm is very adequate (and even much shorter, but that would require a lot more skills from the photographer).

Phong, (or anyone else who can contribute) for me this brings up three questions:


What is this you are saying about requiring a lot more skill from the photographer? Are you saying that a short perspective is rather poor and therefore takes some work to fix? But how can too-close perspective be fixed? You are still close---there is no way undo that except by moving back, I would think.
I agree that 85mm is adequate, sure it's okay, but 300mm really looks better to me. When you and others call shorter focal lengths "adequate," that does not sound like a ringing endorsement to me. It almost sounds like you are agreeing with my point, and saying the best head-and-shoulders portrait perspective is taken with longer lenses than are commonly used. Am I misreading you?
Do you think a 35mm professional who favors 300mm when he is trying to get the most beautiful look possible might read the Kodak book and decide to switch to 75mm?

[Jerry Fusselman]

How about a formula that goes like this:

1) I want to be X inches from my subject
2) My film is X inches tall
3) I want the chin to top of head to be X inches tall on my film.
4) What focal length gives that result?

In terms of the variables in my initial post and also my paper (attached), Part 1 is u, part 2 is not relevant, and part 3 is z. I guess the chin from the top of the head in the subject is a distance something like 9 or 10 inches, so maybe s = 10. The formula you seek is this: How do we find f when given u, s, and z?

The answer is given in line 23 of table 1 (on p. 3): You first compute m = z/s, then you compute f = u/(1+1/m). The answer is in inches. There you go.

[Jerry Fusselman]

All this "technical" math stuff reminds me of an interview with a musician -- an ol' blues legend. When asked if he was familiar with all the "technical" stuff (chord construction, progressions, etc.) he replied, "Oh, yeah! Sure! But... not enough to hurt my playing."

Interesting example. I used to teach music at the University of Nebraska. Anyone who cannot do any of the technical stuff would flunk the first year. The best musicians I know have a solid foundation in the technical stuff. They have other skills, of course, that set them apart. But we did not teach a ton of jazz.

[Jerry Fusselman]

Frankly, I think long lens portraits are far easier, almost to the point of cheating.

Like Mae West said, well,


I generally avoid temptation, except when I can't resist it.

I can't resist asking, Frank or anyone else who understands, could you devote a paragraph or two explaining this point for me? The almost-cheating point, not the temptation point.

It sounds to me like a odd aesthetic is behind it. As if, it sounds to me, with a rainbow on your right and something mundane on your left, you would choose to shoot to your left because including the rainbow would be far easier, almost to the point of cheating. If I am way off on your meaning, I apologize, but I still want to know what you really mean.

[Juergen Sattler]

Jerry, do you ever get to taking a picture? This post blows my mind - do you REALLY worry about this stuff? And what's with this quiz-idea? Do WE have to take a test to fullfill your need for mathematical precision which IMHO does not matter one bit when you are taking photographs? I am sorry, but I have no idea where you are coming from!

[Bob Salomon]

We were taught both at the USAF Photo School and in portrait seminars that you need a lens and aperture that ensures that the tip of the nose to the base of the ear are within the area of focus on a head and shoulders portrait. It was far easier to see that on the ground glass then trying to figure it out on paper and then check it on the ground glass.

[Bob Salomon]

We were taught both at the USAF Photo School and in portrait seminars that you need a lens and aperture that ensures that the tip of the nose to the base of the ear are within the area of focus on a head and shoulders portrait. It was far easier to see that on the ground glass then trying to figure it out on paper and then check it on the ground glass.


And, we were taught to focus on the bridge of the nose.

[Paul Fitzgerald]

HI Jerry,

"I can't resist asking, Frank or anyone else who understands, could you devote a paragraph or two explaining this point for me? The almost-cheating point, not the temptation point. "

IF you change to percentage value it's easy to understand. With a shorter lens and focus the iris of the eyes (100%) the tip of the nose is (85%?) and the tips of the ears (115%?). With a longer lens and longer distance to the sitter the eyes are 100%, nose 95%, ears 105%. The longer the lens and distance, the smaller the apparent difference, making it easier to get correct focus at wider apertures. In other words it's telephoto compression, too much is a bad thing.

Just a thought.

[Leonard Evens]

I can answer all your mathematics questions, but it would take some time, so let me just address some of the points you raise. If you want to know more, you can contact me privately so as not to bother all the "math is irrelevant" people.

In this connection it is worth pointing out that the behavior of photographic lenses is a matter of physics, not pure mathematics. That means that there are various physical theories which can be brought to bear. The one we use for the sort of things you are interested in is called geometric optics. It is not absolutely accurate, but it is close enough to descrbing real behavior in practical situations that you can ignore real world departures from predictions. In this case, not only can we calculate the values of the various variables from others, but we can also estimate the errors in those calculations when compared with reality.

First, you are right that it is the distance from the front nodal point that should be used in determining the distance to the plane of exact focus. For most lenses this is very close to the center of the lens, but for lenses of telephoto design it may be well in front of the lenses. But even for such lenses, it is usually close enough to the center of the lens, so that it won't make a significant difference in any calculations for subjects at normal distances for portraiture. But it is possible that for some long large format lenses of telephoto design that the nodal point is far enough in front of the lens to make a practical difference.

Second, it is the position of the lens (or as above the front nodal point) relative to the subject that determines perspective. Also, it is certainly possible to produce identical prints, ignoring issues like resolution, from different formats. The relevant factors are the magnifcation in the print relative to the subject, the degree of enlargement to produce the print, and the distance of the subject relative to the lens. Given those numbers, you can calculate the magnification in the film plane and from that the lens to film distance and the needed focal length.

But there is one additional point which you didn't consider. When you view a print, you will only see the image with the proper perspective at one point. Without movements, that point will be centered in the image and at a distance determined by the lens to fim distance and the degree of enlargement. (Actually you would use the distance from the rear nodal point to the film.)

For example, suppose you are using 8 x 10 format, with a 600 mm lens, and the plane of exact focus at two meters. The lens to film distance would be about 857 mm, and the degree of enlargement for an 8 x 10 print would be 1, so, you should view the print from 857 mm. Suppose instead you use 35 mm format (24 x 36 mm) and enlarge 8 times (which would involve cropping a couple of inches in the long dimension) to yield an 8 x 10 print. If you wanted the same degree of magnifcation in the print relative to the subject, you would have to reduce the lens to film distance by a factor of 8. That would give you 857/8 ~ 107 mm. With the subject at the same 2 meters, that means the focal length would have to be about 100 mm., and then you could use the same point to view the identical print.

Notice, however, that you don't usually view 8 x 10 prints from 857 mm ~ 34 inches. You are likely to view such a print from about 12 to 14 inches. Since you are viewing the print closer than the center of perspective, that "distorts" the perspective to your visual system. The effects here are a bit complicated because the eye-brain visual system doesn't follow the simple laws of geometric optics. But the net result is that the perspective is flattened, and the portrait appears to be more natural.

The reason generally for using longer lenses for portraiture is that for shorter focal length lens, your eye would be too close to the print in normal viewing. For wide angle lenses, the center of perspective would be closer than the normal viewing distance in any case. For a normal focal length (defined as the diagonal of the format), the proper viewing point would be close to the normal viewing point for the print size, but to get a sufficient magnification in the print for portraiture, you would need to place the subject too close to the lens. The problem doesn't arise from the geometric optics of the lens, but rather from the characteristics of the eye brain system. Within a certain range of distances from your eye, your view of a face is adjusted by a phenomenon called size constancy. That is, a face viewed at 3 feet looks much the same as one viewed at six feet. But the camera lens just records (to a high degree of accuracy) what the laws of geometric optics say it must. So the resulting image in the print will look distorted.

Because of the factors I just described, you are better off with longer lenses. When comparing 8 x 10 to 35 mm, if you end up with 8 x 10 prints, as the calculations above indicated, a factor of about 8 is appropriate in comparing focal lengths. (For larger prints, the same calculations apply if the prints are viewed at the normal distance for the print size.) The usual recommendation is that the focal length should be about 2 to 3 times the normal focal length. For 35 mm, the diagonal of the format is about 43 mm, so that puts us in the range 85 - 135 mm. (50 mm is considered "normal" for 35 mm only by historical accident. It is actually a bit long.) But as you say, some people prefer even longer focal lengths. For 8 x 10, the normal focal length is about 300 mm (very close to the diagonal of the exposed film area), so the "proper" focal lengths for portraiture would be in the range 600 - 900 mm. For something in 8 x 10 roughly equivalent to 300 mm in 35 mm, using a multiplier of 8 would yield 2400 mm. (This is only an approximation. One would have to use actual film to lens distances as I did before to get a more accurate value.)

Note that there is a real problem. As we saw, with a final image in mind, it is possible to calculate which focal length lenses in 35 mm and 8 x 10 will produce identical prints. But there aren't many very long focal lenth lenses available for 8 x 10 cameras. In addition, there is another problem. For the same subject distance and the same magnification of print relative to subject, you get significantly less depth of field in the larger format at the same relative aperture. In fact you would have to multiply the f-number roughly by a factor of 8. Because diffraction is less of an issue with less enlargement, you can use those smaller apertures, but then subject movement becomes a problems because of the long exposure times needed. Because of both these factors, it doesn't make sense to do the same kind of portraiture with large format cameras that you would do with 35 mm or even medium format cameras. You tend to do more full figure and environmental portraits.

I hope this clarifies some of the points you raise. If you need more information, feel free to contact me.

[Jerry Fusselman]

With a shorter lens and focus the iris of the eyes (100%) the tip of the nose is (85%?) and the tips of the ears (115%?). With a longer lens and longer distance to the sitter the eyes are 100%, nose 95%, ears 105%. The longer the lens and distance, the smaller the apparent difference, making it easier to get correct focus at wider apertures.

Hi Paul,

The percentages you quote are relevant to perspective, but they are largely irrelevant to depth of field. To a first order of approximation, depth of field is determined by aperture number and magnification. (If the reader thinks it is important to keep the format constant, assume so here.) In this thread, the subject is head-and-shoulders portraits, so magnification is fixed as you try different focal lengths. The long lens and the short lens have essentially the same depth of field if they use the same aperture number.

The main second-order effects, which make no big difference here, are two: The longer lens will have less diffraction, and the traditional approach to depth of field says you get a tad more depth on the close end and a tad less on the far end when you use the shorter lens. But these effects are small and can be ignored here, I think.

In fact, if you follow Merklinger's analysis of object-field resolution in The Ins and Outs of Focus, you will see that the depth of field measured his way is exactly the same in these two cases. (Keep format, aperture number, subject size, and plane of sharpest focus the same as you vary focal length, and ignore diffraction. You get similar triangles that imply the exact same spot sizes.)

Merklinger covers this issue in his book. Contributors to LF Forums have also discussed it.

My main point is that a longer lens hardly affects depth of field when you keep magnification unchanged, and that means that the reason for Frank's statement cannot be a depth-of-field consideration. It might be something about perspective, I don't know. I think it unlikely that his statement has anything to do with diffraction.

[Jerry Fusselman]

Jerry, do you ever get to taking a picture?

Nice of you to ask. I took pictures three nights so far this week. I am thrilled with my pictures from Monday. I am going to scan some of them---my first 6x24 scanning.


Do WE have to take a test to fulfill your need for mathematical precision which IMHO does not matter one bit when you are taking photographs?

You misunderstood me entirely. No one requires that you find every topic interesting. No one requires you to read all posts. No one requires that you answer posts. As I said in paragraph 1, the quiz was supposed to fun; if not, no one requires you to do it. If you were shocked and appalled that a quiz appeared in my post, I suggest you read titles of posts a little more closely.

I was hoping the word "quiz" in the title would bring the kind of poster who thinks a little quiz on perspective might be fun. Paraphrasing Scarlett O'Hara, "Quiz fun?!? Fun for teachers, you mean."

Maybe I should have included the word "math" in the title? Would that have helped you steer clear?

Here is another confusion of yours, but it is shared by many others: I never said I worry about mathematical precision while taking pictures. As it happens, I do no math worth mentioning while taking pictures. The math in my post is for camera design and lens choices almost exclusively. Math sometimes helps me figure out what to build, buy, or bring. When I am out there shooting, I use what I brought and do the best I can. At that point, math is too late.

The reason for math is that is often faster and easier for me than trial and error. I also enjoy it. But the amount of math we are talking about here is about five orders of magnitude less than what appears in some photography books, so I am just a math dabbler by comparison to some of the heavyweights.

[Helen Bach]

Well, I think that I've read through every post and nobody has pointed out that the entrance pupil is the centre of perspective of a lens, not the front nodal point. That is why when you use a fixed-lens camera to take a panorama with multiple shots you should rotate the camera about the entrance pupil. Apologies if I have missed a post that has already pointed this out.

Best,
Helen

[Jerry Fusselman]

Well, I think that I've read through every post and nobody has pointed out that the entrance pupil is the centre of perspective of a lens, not the front nodal point. That is why when you use a fixed-lens camera to take a panorama with multiple shots you should rotate the camera about the entrance pupil. Apologies if I have missed a post that has already pointed this out.

Helen, yours is definitely the first to make this point. Thanks. Do you remember any reference to this idea of rotating the camera about the entrance pupil and that being the location that determines perspective? I seem to recall that there was some intelligent disagreement about the best rotation point for panoramas, but I cannot recall that it was well resolved anywhere.

[Ralph Barker]

. . . Do WE have to take a test to fullfill your need for mathematical precision . . .

Juergen - the test is being conducted on Sunday afternoon at my place in Rio Rancho. But, you have to bring the tequilla for the pre-test margaritas. ;)

[Phong]

What is this you are saying about requiring a lot more skill from the photographer? Are you saying that a short perspective is rather poor and therefore takes some work to fix? But how can too-close perspective be fixed? You are still close---there is no way undo that except by moving back, I would think.


I was alluding to non camera/lens related stuff like communicating with your subjects, establishing a rapport with them, getting the right expressions, etc. Sometimes these issues dictate subject distance, hence lens choices. Yousuf Karsh is recognized as one of the great masters of portrait photography (I certainly think so); yet in analyzing his photos I often find the lens choice too short, making the hands looming in the foreground in some cases. My guess is that he wanted to be close enough to his subjects, hence forego a more "ideal" focal length. Communicating with the subject is the number one skill in a portrait photographer in my opinion.



I agree that 85mm is adequate, sure it's okay, but 300mm really looks better to me. When you and others call shorter focal lengths "adequate," that does not sound like a ringing endorsement to me. It almost sounds like you are agreeing with my point, and saying the best head-and-shoulders portrait perspective is taken with longer lenses than are commonly used. Am I misreading you?


You may be. Perhaps I should have said "more than good enough" rather "adequate".
Aside from the issues I mentioned above, 300mm on 35mm film is a terrible perspective in my view; it flattens the face too much, and also gives the look from a distance (like what we see on newspapers of say presidents and heads of state). My taste goes for 90-105mm for heads and shoulders; as heads and shoulders make up a very small percentage of my portraits, I use wider lenses much more often. On 8x10, my current favorite focal length for portraits is 240mm (I have 4 different 240mm lenses at the moment). 4 240mm's and a 450mm. No 300mm (tried that), no 360mm (tried that too).



Do you think a 35mm professional who favors 300mm when he is trying to get the most beautiful look possible might read the Kodak book and decide to switch to 75mm?


???? You were quoting some unnamed "pros", so I offered the Kodak book as a counterpoint. In both cases, my reaction is "so what?", or perhaps more politely, "uhm, interesting, but that's not me". Anyway, even if 300m was my favorite focal length on 35mm, I wouldn't want to use a 1800mm lens on a 8x10 camera because it would be so unwieldy.

Regards,

- Phong

[Leonard Evens]

Panoramas and nodal point:

I did a google search, and everything I found suggested that for panoramic photos, you rotate about the nodal point. They don't say which nodal point, but it is fairly clear it must be the front nodal point.

[Jerry Fusselman]

Juergen - the test is being conducted on Sunday afternoon at my place in Rio Rancho. But, you have to bring the tequilla for the pre-test margaritas. ;)

Great! Can I come to Rio Rancho too? I already finished my answer to the test---it appears in post 42 as well as the thread with the super-exciting title "Computing seven lens variables from three inputs." Since I have answered the quiz already, can I have two margaritas? For extra credit, if you like, I can bring my latest camera that required table 1 for its construction.

[Ralph Barker]

Great! Can I come to Rio Rancho too? . . .

Of course! Anyone who brings tequilla (or fresh chilis [red and green]) is welcome. :cool:

[Helen Bach]

Panoramas and nodal point:

I did a google search, and everything I found suggested that for panoramic photos, you rotate about the nodal point. They don't say which nodal point, but it is fairly clear it must be the front nodal point.

It's a very common error, and the internet is full of unreliable information. I'm not at home at the moment, so can't quote Sidney Ray. I can't find the Zeiss document(s) that my memory pictures so vividly*, but here (http://www.zeiss.com/C12567A8003B8B6F/EmbedTitelIntern/Verzeichnungsmessgeraet_e_PDF/$File/VMG_e_Version_030716.pdf)is another.

It isn't difficult to demonstrate that it should be the entrance pupil.

Best,
Helen

*later edit: found an example (http://www.hasselblad.co.uk/Archive/documents/Downloads_files/Productsheets/CFE40if.pdf) "The entrance pupil position is the correct position of the axis of rotation when making a panorama image by combining individual images of a scene." Will you trust Zeiss? Better to understand why by working it out than take it on trust, no matter how reliable the source. The fact that it is the centre of the entrance pupil makes it quite easy to find the correct point by parallax when looking into the front of the lens.

[Leonard Evens]

Helen appears to be right about something, but I'm still not sure what.

It does appear to be true that it is the center of the entrance puil which should be over the axis of rotation when doing panoramic photography. When you rotate about that position, you don't have any parallel errors. According to several sources which appear to know what they are talking about, this is commonly miidentified as the front nodal point. Be that as it may, the methods recommended for finding the proper point rely on checking for parallax and in fact find it whatever it is called.

It also seems clear that the entrance pupil need not be centered on the front nodal point, although Jacobson, who presumably is the ultimate expert, suggests in his lens FAQ that the distance from the entrance pupil to the front nodal point is often negligible.

The other thing which seems to be clear is that the variables in the various formulas we have been discussing, which are all based on the lens equation, are measured from the principal planes, which are the planes centered on the nodal points and perpendicular to the lens axis. Also ray tracing is done using the principal planes and nodal points.

I am not sure how to make sense of all of this. In particular, just where is the center of perspective? It seems that one can make arguments for either the center of the entrance pupil or for the front nodal point. Parallax arguments suggest the former, while ray tracing and lens formulas suggest the latter. The parallax arguments seem convincing, but then we need an explanation for why the nodal point is wrong.

To add to the confusion, it would seem that the arguments used in deriving DOF formulas use the distance from the exit pupil to the film plane. If this distance is different than the distance to the rear principal plane, there seems to be a problem.

I will keep looking, but if someone else can clarify all this and provide a reference, I would appreciate it.

[Juergen Sattler]

Juergen - the test is being conducted on Sunday afternoon at my place in Rio Rancho. But, you have to bring the tequilla for the pre-test margaritas. ;)
I can always be convinced of a good margarita - how many bottles Tequilla should I bring? I am sure all this math is much easier after the first 5 or 6 margaritas and maybe it'll even make sense.

[Alan Davenport]

The math discussed is extremely important when dealing with the science and craft of optics, and can provide and interesting diversion when one has time to kill. It has little to do with photography, IMO.

[Jerry Fusselman]

Can anyone make an intelligent guess as to how well Ansel Adams would do on my quiz?

[Helen Bach]

"I will keep looking, but if someone else can clarify all this and provide a reference, I would appreciate it."
Leonard,
What specifically do you want a reference for?

The first principal plane goes through the first principal point, not the first nodal point, though they may be coincident. Remember that the two principal planes and the two nodal planes are only coincident when the lens is in a single medium. They need not be coincident for the Nikonos underwater lenses, for example (but they would be coincident for the amphibian lenses, because those are really all-air lenses).

Zeiss have a lot of information on their website if you want some examples of the locations of the various planes. For example the 60 mm f/3.5 CFi:
Entrance pupil position 32.2 mm behind the first lens vertex
Position of principal plane H 53.8 mm behind the first lens vertex.

Where is the quote that says "that the distance from the entrance pupil to the front nodal point is often negligible"?

"Helen appears to be right about something, but I'm still not sure what." Would it be easier to start with what I'm wrong about?

Best,
Helen

[Jerry Fusselman]

In Ray, third edition, p. 123, I found this: "The centre of the entrance pupil is the centre of perspective of the lens." I had missed it because it is in the index under "center" instead of "perspective." I too am also puzzled by this, because I thought I had worked out a demonstration that it had to be the front nodal point.

[Leonard Evens]

Helen,

I was aware that the nodal points and the principal points might be different, but I assumed the medium was the same on both sides of the lens, thus, as you point out excluding underwater photography. I don't know anyone who does large format underwater photography, but I suppose it is possible.

I don't know of anything you are wrong about. I just don't understand the signficance of the difference between the principal planes and the entrance/exit pupils, so although you are certainly right in what you said, I don't fully see what its implications are beyond panoramic photography. The only thing that makes any sense is that there is some sort of shift in the position of the image when computed using the principal planes, but I don't understand what that might mean. I've looked at the Leitz tables and some others, and they do in fact confirm that these differences do exist for many lenses. But despite some extensive searching and some time spent in NU's Science Engineering Library, I don't understand how these things relate and just which of them you use to calculate which parameters.

As to Jacobson, I can't find the original source of my statement, but if you look at his Lens Tutorial at

www.photo.net/learn/optics/lensTutorial

you will find the statement "It can be shown that zE = f*(1-1/p)" where "zE is the distance the entrance pupil is in front of the front principal point." Here p is the pupil magnification. He then goes on to say "For all symmetrical lenses and most normal lenses the aperture appears the same from front and rear, so p~=1", which means that zE ~= 0. So the main exceptions for large format photography would be long lenses of telephoto design and perhaps some wide angle lenses of reverse telephoto design. I wish I could see that derivation. It might be enlightening.

[vijayn]

Wow Jerry - TeX and pdfTeX on this forum - I thought few outside the scientific/engineering community ever used it.

Anyway, with all this talk about nodal points and entrance pupils, could we go back somewhat and define "perspective"? What does the statement "The centre of the entrance pupil is the centre of perspective of the lens." mean? I mean really - what is the definition of "centre of perspective" and to take another step backwards, what is "perspective", or at least what does Ray mean by it?

To point out a few things in your paper - in example 2, the hint is "For the same perspective we need the same u"; however what you then proceed to compute is magnification, not perspective. To get 2x the magnification, there is no reason to assume a constant u, therefore there are infinite solutions to the equation. In other words, I could triple the focal length and increase u and still end up with the same magnification; or I could halve the focal length and decrease u and again end up with the same magnification etcetera.

If you want a constant u, then you are talking about "real" perspective, i.e., the ratios of the magnifications, and then the focal length does not matter, provided u>>f and u'>>f and u ~ u' as I pointed out in my last post. For close distances and u !~ u', you cannot get the two magnifications M and M' without refocusing (i.e., changing u' or v') thereby making the question of the ratio M/M' invalid. Remember M is defined only when the lens equation is solved (i.e., the lens is focused). M is undefined when the lens is not focused, i.e., when u and v are such that the relation 1/u + 1/v = 1/f is not met.

I hope I am being clear enough - if not I can write up all this in a TeX document as well ;-)

[Helen Bach]

I have a sneaking suspicion that the flaw in the apparently bulletproof front-nodal-point-as-the-centre-of-perspective analysis is that it is based on the properties of in-focus objects.

When you are considering perspective you are considering objects that are brought to perfect focus in the film plane and objects that aren't. A single ray from a point that is in perfect focus can define the location of the image of that point, because it is where that ray intersects the film plane.

Suppose that there is a coincident ray coming from a point further away - ie from an object that is (almost) in line. This object is not imaged as a point, but as a small circle. The coincident ray from the distant object arrives at the film plane at the same point as the ray from the focussed point, but that does not have to be where the centre of the circle is located. One ray alone cannot define the apparent location of the image of a point that is not in perfect focus. The circle is defined by the whole bundle of rays entering the lens.

Without going to the lengths of a full explanation (hey, it's 11:45 on a Saturday night and time to go out), is that enough to make it clearer why the entrance pupil is the centre of perspective? Perspective in this case being about how things in three dimensions appear to line up to an observer.

Best,
Helen

[Leonard Evens]

Vijay,

Remember M is defined only when the lens equation is solved (i.e., the lens is focused). M is undefined when the lens is not focused, i.e., when u and v are such that the relation 1/u + 1/v = 1/f is not met.

Keep in mind that in principle every point in the subject (object) space is imaged by some point in focus in the image space. The distances of those points are what satisfy the lens equation. Now consider what happens if you consider a subject plane closer than the plane of exact focus. The corresponding image plane is further away than the negative plane. Let u and v be the subject and image distances for the plane of exact focus and u' and v' the corresponding diistances for the closer subject plane. Each pair satisfies the lens equation. The respective magnifications are m v/u and v'/u'. Now consider a distance h' in the closer plane. It exact image (not in the film plane) will be of size v'/u' x h'. But if we pull this back to the film plane, we have to reduce it by a factor of v/v', so the size of the (slightly blurred) image in the film plane will be v/v' x v'/u' x h' = v/u' x h'. u' is smaller than u, so v/u' is larger than v/u. In other words, objects closer than the plane of exact focus will be magnfied in the negative plane more than than objects of the same size in the plane of exact focus, but by not as much as you might expect by comparing magnications for the two image planes. Similarly, objects further away than the plane of exact focus will appear to be magnfied less than the naive calculation would suggest.

Note, however, that in most situations the correction v'/v for magnification, in either case is going to be pretty close to 1.

Helen,

I haven't really absorbed your argument, but I think there is something not quite right in what you say. Any image point is the apex of a cone with base the exit pupil. It intersects the film plane, as you say, in a small disc, and the center of that disc is on a line from the apex of the cone, the image point, to the center of the exit pupil. There is no decentering. (It gets somewhat more complicated iin case of tilsts or swings.)

I don't see why your argument tells us anything about the center of perspective in any case, but let me think about it.

[Helen Bach]

Leonard,

It was a mistake for me to write half an explanation in a rush on a Saturday night. I'll re-write it with a clearer head.

Best,
Helen

[vijayn]

Leonard, explain then why the image of anything that is out of focus is larger than the image when the object is in focus, regardless of which side of the plane of sharp focus the object lies.

Something is incorrect with your argument; by your logic, if I bring the film plane closer to the lens, the size of all images would get smaller as they went further out of focus. That is precisely the opposite of what happens; images grow as they go further out of focus. Lens cone, point becomes disk etcetera.

The point still remains. Magnification is defined only for an object whose image is in focus. That is, for a given v, only those objects at a distance u that satisfy the lens equation have a magnification defined. For other objects, it is not possible to compute the magnification (which point in the blur do you define as the edge of the image?)

[Leonard Evens]

Vijay,

You are right that defocused objects have fuzzy boundaries, but as long as you are in the DOF region, the fuzziness will be small enough that you can ignore it. Consider for example a line segment parallel to the plane of exact focus but closer to the lens. Its image is a line segment further from the lens that the image (negative) plane. That line projects back to the film plane to a shape consisting of a long narrow rectangle with semicircles stuck on either end. So there is a certain amount of ambiguity is how you should go about measuring its length in order to compare it with the length of the original object line segment. But, if the original object line segment is in the DOF region, the thickness of the rectangle and the radii of the circles are very small, less than the maximal allowable circle of confusion. For an 8 x 10 camera, that would be something like 0.2 mm.
So, within the limits of accuracy set by the coc, it does make sense to talk of magnification for that line segement. Of course, if you are well outside the DOF region, the cocs will be quite large, and it won't really make sense to talk about magnfication the same way,

With all that kept in mind, if you stay within the DOF region, objects closer than the plane of exact focus are imaged in the film plane with greater magnfication that objects in the plane of exact focus. Objects further than the plane of exact focus are imaged in the film plane with less magnification than objects in the film plane. If you consider real photographs, this is obvious. Suppose you are photographing a group of people all the same height, and they are standing at different distances. Suppose you focus on someone in the middle distance and choose your aperture so everyone is in adequate focus. Do you doubt that those nearer the camera will look larger and those further away will look smaller?

[Leonard Evens]

I've been studying a book on geometric optics, and I think it is beginning to make sense. Let's assume that the medium is the same on both sides of the lens; indeed assume it is just air. That means, according to Jacobson that the nodal points will be where the lens axis intersects the principal planes. Also, the lens equation 1/u + 1/v = 1/f does apply, where the distances are measured from the appropriate principal planes. Concepts such as magnification, based on the lens equation, would then refer to those distances. On the other hand, the center of perspective is definitely the center of the exit pupil. A consequence is that if you rotate about that point, images will line up properly as in panoramic photography. I believe it also means that it is the center of persepctive in the ordinary sense of geometric perspective as in art theory, but I want to think about that a bit more. In addition, in depth of field and depth of focus calculations, you should use distances to the entrance and exit pupils, which generally will be different from distances to the principal planes. For anything done entirely on the image side of the lens, this seems not to make any real difference. The only thing which would change is that you might need to use the distance from the exit pupil to the focal point instead of the distance from the rear principal plane to the focal point (which I believe is the normal focal length) in some calculations. However, in translating DOF information to the object side of the lens, you would have to adjust. I think this is the reason why Jacobson's DOF formulas include a factor depending on the pupil magnification, which is something I never understood before.

Finally, if the pupil magnification is close to 1, you don't go far wrong by assuming that the entrance and exit pupils are in the principal planes. According to Jacobson, that is usually the case for large format lenses.

[vijayn]

Now I agree with you fully, Leonard. The relations I had put forward earlier for the concept of perspective to make sense are implied by your explanation.

[Gregory Gomez]

Jerry,

I don’t mean to be disrespectful, but after reading your original post, some of which I found confusing, and all the responses to it, especially your attached paper, it’s clear that you might already know the answers to your questions. So what is the real reason for your inquiry?

I don’t know which photographic professionals you have consulted to form your assumptions about 35mm lens choice for head-and-shoulder portraits, but from what I have read over the past 25 years and from my own experience, a photographer can use ANY camera and ANY lens to make a portrait. I cannot emphasize this observation enough. Making a portrait is a creative act, assuming of course that there are no commercial constraints that might dictate format and lens choice.

In 35mm photography, 70mm through 105mm focal length lenses are often used to make standard head-and-shoulder portraits. This is common knowledge. (In my own work, I prefer the 70mm lens, but will often use the 105mm focal length.)

Using lenses shorter than 70mm on a 35mm camera can introduce an unflattering scale of depth. Some facial features in the foreground, like the nose, may become more prominent than desired if the photographer is not careful with camera and subject placement. If a wide angle lens (e.g., a 28mm focal length) is used, “wide angel distortion” may appear, which will exaggerate the near-to-far relationship of facial elements even more so. And foreground facial features, like the nose, may become bulbous in quality. If one wishes to create a caricature, or if some other photographic intent is sought, then such an exaggeration may be welcome. It’s really a matter of personal preference and photographic style.

When lenses longer than 105mm are used in portrait work, the resulting image may lack adequate depth perspective, and a slight pincushion effect may also appear, even if highly corrected ED glass has been used. Facial elements in the foreground may appear slightly smaller than real, and the distance between the foreground facial elements, like the nose, and the background elements, like the ears, is made smaller, more compressed, and two-dimensional. Such an effect might be desirable if the photographer wants to de-emphasize the nose and make the face more compact overall. The longer lens also makes it easier to throw the background out of focus, making the subject’s face standout from any distracting elements. In this regard, the 300mm is often used on location, like the beach.

To say that the 50mm lens is “terrible,” the 85mm is “only okay,” and the 300mm is “best” is biased. Many fine photographs of people have been taken with the 50mm lens on a 35mm camera, so it’s far from terrible. As for the 85mm, that would be my lens of choice for head-and-shoulder portraits, with the 300mm used on special occasions when shooting on location, as mentioned above. Thus, the 70mm through 105mm, at least for 35mm work, will give you the “great perspective” you seek. If you disagree and like the angle of view and depth perspective created by a 300mm lens, then use it. However, you will not find an equivalent lens for an 8x10 camera.

It’s my impression that you may have confused angle of view – what the lens “sees” (or the angle of subject area projected on the film) – with perspective – the distance from subject to the lens rear nodal plane, or “v” in commonly used lens formulas. (Perspective is also and more commonly referred to as the appearance of depth when viewing a two- or three-dimensional object.) Angle of view is related to lens focal length, and is usually expressed in degrees measured along the film diagonal or the longest film border. When a longer focal length lens is used, less of the scene is included, but perspective remains unchanged. When a shorter lens is used, more of the scene is included, but again perspective remains constant, at least according to Ansel Adams.

Ansel Adams asserts (Adams, 1980; The Camera, p. 98) that perspective is a function of camera-to-subject distance. We can change perspective by moving closer to or farther away from our subject. When we move closer, the subject appears larger within our picture format; when we move farther away, the subject appears smaller. Adams also says that “moving closer to or farther away from a scene will have a different effect on those parts of the subject that are at different distances from us. The apparent size of subject areas close to the camera will increase or decrease more than distant ones as we change the camera-to-subject distance” (Adams, 1980; The Camera, p. 98).

Stroebel (Stroebel, 1999; View Camera Technique, p. 130) defines perspective “as the appearance of objects with respect to their distance and position. Perspective is the quality that creates the illusion of three dimensions in two-dimensional photographs.” Stroebel goes on to say that it’s best to select camera position first based on the perspective desired, and then choose the lens focal length that will produce the appropriate image size. (I agree with this assertion.) If the camera position is close to the subject, a “strong perspective” is created. Conversely, when the camera position is at a longer than “normal” position from the subject, a weak perspective occurs, which is true for portraiture. Thus, if a photographer chooses a 300mm lens on a 35mm camera, and even if he or she fills the frame with the subject, a relatively weak perspective will be created, according to Stroebel.

According to Adams (Adams, 1980; The Camera, p. 45) all lenses of a given focal length (e.g., 100mm) produce images of the same size for a given subject and subject distance regardless of film size or camera format. If the subject size is 25.4mm, for example, the image will nearly fill a 35mm frame, but it will only fill about one quarter of the 4x5 film. Thus, the subject will be isolated from its background on a 35mm camera, but not on a 4x5.

Adams asserts that image size is proportional to focal length (Adams, 1980; The Camera, p. 45). For a given format, if the focal length doubles, image size also doubles and the total image area is cut in half. But if the format size also doubles, then the image size and image area remain the same. Thus, a 150mm lens on a 4x5 produces the same image area and image size as does a 300mm lens on an 8x10 camera.

However, focal length and perspective are not mutually exclusive, according to Stroebel. “Substituting lenses with different focal lengths, with the camera remaining in the same position, changes the size of the images of near and far objects at the same rate with no change in the relative sizes of the objects…It is not correct, however, to say that focal length has no effect on perspective. Even though the relative sizes of near and far objects remain identical with different focal length lenses, the angles of view and overall image sizes will be different and can create different impressions of depth in the photographs” (Stroebel, 1999; View Camera Technique, p. 132).

To be continued...

[Gregory Gomez]

When comparing lenses across film formats, I use the film diagonal to include the effects of both the horizontal and vertical angles of view. With this in mind, a 300mm lens on a 35mm camera would be roughly equivalent to a 1,065mm lens on a 4x5 and a 2,130mm lens on an 8x10. But keep in mind that the aspect ration between the 35mm and the 4x5/8x10 is not the same, as you already know. So any direct comparison will only be an approximation. However, cropping 35mm film to 24mm x 30mm to match the aspect ratio of a “trimmed” 4x5 negative (3.8125 x 4.75 inches) permits a direct comparison. In this situation, using the film diagonal, a 1,208mm lens for the 4x5 and a 2,416mm lens for the 8x10 would be needed to match the angle of view created by a 300mm lens on a 35mm camera.

Note that there are few long focal length lenses available for 4x5 and 8x10 cameras. Schneider offers an 800mm and 1,100mm; Nikon, at one time, offered an 800mm and 1’200mm, respectively.

Personally, I would never use such lenses for a 4x5 or 8x10. I think many would agree. My lenses of choice for portraiture for the 4x5 would be the 240mm, 250mm, or 300mm. For the 8x10, it would be the 355mm, 360mm, 420mm, 450mm, or 480mm. Using these focal lengths would not cause “unacceptable compromises” in my opinion.

The formulas you have listed in your attached paper are useful when a photographer wants to know how much bellows draw will be required when a given lens focal length is used and what will be the camera to subject distance so that there will be enough room between subject and camera in the studio.

Adams (Adams, 1980; The Camera, p. 191) lists two fundamental lens formulas:

1/u + 1/v = 1/f

I/O = v/u = M

Where

f = lens focal length

O = object (subject) size

I = image size on ground glass or in view finder

u = distance from object (subject) to the lens rear nodal plane

v = distance from the rear nodal plane to the image (I)

M = magnification of the image in relation to the subject size

The derived formulas include the following:

v = (M + 1) f

u = (1/M =1) f

This information is also included in your paper.

In a portrait setting, for example, using an 85mm lens on a 35mm camera with an image size (I) of 25.5mm in the view finder, which is 85% of the cropped vertical dimension (i.e., 85% of 30mm) and an object size of 432mm (head-and-shoulder’s shot), the resulting magnification (M), using the formula M = I/O, would be 0.059. The “u” and “v” measurements would be 1,526mm and about 90mm, respectively. (Note that using the cropped vertical dimension (30mm) allows direct comparisons across formats because the aspect ratios would be maintained.)

Applying the above information to a 4x5 camera and duplicating the same diagonal angle of view (i.e., if an unlimited lens selection existed, then a 342mm lens on a 4x5 would be about equal to an 85mm lens on a cropped 35mm negative), the following values would result for a 4x5, provided that “I” were to occupy about 85% of the ground glass vertical dimension, which was the case above for the 35mm:

f = 342mm

O = 432mm

I = 103mm

u = 1,779mm

v = 423mm (bellows draw required for a non-telephoto lens)

M = 0.238

For an 8x10, the following values would result:

f = 685mm

O = 432mm

I = 205mm

u = 2,127mm

v = 1,010 mm (bellows draw required for a non-telephoto lens)

M = 0.475

From my calculations, it would appear that if the same diagonal angle of view is maintained across formats, then lens focal length increases proportionally as film size increases, an observation made by Ansel Adams and others. In all three examples, object size remains constant, which is what one would expect. If image size in the view finder/ground glass is maintained as a percentage of a format’s vertical dimension, then image size (I) increases proportionally as format size increases. However, what I find interesting is that “u,” the distance from the subject to the rear lens nodal plane, actually increases as lens focal length increases, provided angle of view is held constant. The increase is somewhat small but significant. Also, “M” does not increase proportionately as format and focal length increase. It’s important to point out that perspective will change slightly across formats due to the different “u” values noted.

If we want to maintain a constant “u” value (i.e., a constant distance from subject to the lens rear nodal plane) between 35mm and 4x5, for example, focal length would have to change from 342mm to 293mm for the 4x5 camera. However, angle of view would also change, but not by much. Here are the new values for the 4x5 when 35mm and 4x5 “u” values match:

f = 293

O = 432mm

I = 102.6mm

u = 1,526mm

v = 363mm (bellows draw required for a non-telephoto lens)

M = 0.238

In this new set of values, the quantities for “O,” “I,” and “M” remain unchanged, as one would expect, and “u” equals 1,526mm, the distance from subject to the lens rear nodal plane for the 35mm camera. Values for “v” and “f” need to be calculated as follows:

u = (1/M +1) f

1,526 = (1/0.238 + 1) f

f = 293mm


v = (M+1) f

v = (0.238 + 1) 293

v = 363mm

In view of the foregoing discussion and all that has been contributed to this thread, it’s my guess, Jerry, you are no closer to finding the “perfect” portrait lens for the 4x5 or 8x10, right? I don’t think lens selection can be done deductively, but is an outcome of simple empiricism. To use an epithet of Fred Picker, “Try it!” That is, you will have to gain the necessary experience, directly and vicariously, in order to make the right lens choice for your 4x5/8x10. Attempting to do so using lens formulas alone, while entertaining, will not help you much. I know that what I say may not be logically satisfying to you, but photography is not a mathematical proof waiting to be solved; it’s a creative process waiting to be lived.

Good luck!

[Helen Bach]

Leonard wrote:

"On the other hand, the center of perspective is definitely the center of the exit pupil."

Don't you mean the entrance pupil?

Gregory wrote: "However, what I find interesting is that “u,” the distance from the subject to the rear lens nodal plane,...""

Gregory, it is usual practice to refer to the front (first) planes and points for object-space calculations ('object' being synonymous with 'subject' in this case), and the rear (second) planes and points for image-space calculations. An obvious exception is the use of film plane to object distance markings on lenses in focussing mounts.

Best,
Helen.

[Leonard Evens]

en,

"On the other hand, the center of perspective is definitely the center of the exit pupil."

Don't you mean the entrance pupil?

Yes, I meant entrance pupil.

[Henry Ambrose]

I've been following this as best I can, and have a couple of observations and/or questions.

A couple of things y'all seem to be missing is that the calculations you're making have to be done again everytime the camera is focused at a different distance. You would also have to know the EXACT locations of the pricipal points/nodes for each lens at each focus distance. So every lens is different and every focus distance with any given lens is a different set of values -- Yes?

So what Helen wrote about ray tracing seems very important to the discussion. I think each "set-up" of camera, lens and object distance is its own set of numbers.

Earlier I wrote:
1) where you stand
2) how far you set up the camera from the subject
3) the distance from the object being photographed to the film plane
4) object distance to the rear principal point of the lens

All being esentially the same location stated differently and in increasing levels of precision. Number 4 becomes difficult because the values change for different lens types and anyway are way beyond the precision needed for a portrait.

I'm still thinking that my answer number four is not too far from wrong as a general statement using measurements that are more or less available to one while standing there at the camera. Isn't that point (rear principal point ) going to be where the rays begin to spread to recreate the image at the image plane? Isn't that where we'd measure from if we had the ability to do such a thing?

[Leonard Evens]

You would also have to know the EXACT locations of the pricipal points/nodes for each lens at each focus distance.

I could be entirely wrong---this whole discussion has convinced me I knew less than I thought I did----but I believe the principal planes for large format lenses don't change when you focus. It is often claimed that the entrance and exit pupils may change as you focus. I don't see how that can happen if the lens elements remain fixed in relation to the physical stop, but let's suppose it can happen. Since the center of perspective is the center of the entrance pupil, if you need to know that accurately for some reason, then you would indeed have to determine it for your specific focusing configuration. The center of the entrance pupil can be determined by the parallax methods which are used for panoramic photography. Also, in principle, you might be able to find published information on the position of the entrance and exit pupils for selected focusing distances, and interpolate, but I must admit I haven't been able to find it for one telephoto lens i was interested in.

But how often is any of this going to be a problem for large format photography? As I've repeated several times, according to Jacobson, for most lenses, the pupil magnification is very close to 1, so the entrance and exit pupils are going to be very close to the principal planes. In addition, all the cardinal points are going to be very close to the front of the lensboard, so you can take take that to be the center of perspective, and all measurements can be made relative to that. The exception would be lenses of telephoto or reverse telephoto design. For a telephoto lens, the rear principal plane may be well in front of the lens. I presume the same is true for the front principal plane and the entrance pupil. In most photography, with the subjects at some distance from the lens, this is not going to make a significant difference. But it certainly is going to for close-up hotography and in some circumstances at portrait distances. Since you may have to use a telephoto lens, because of bellows extension issues, in head and shoulders portraiture, it would seem that this could be something you have to worry about in certain cases.

If anyone can give a source of information about the relevant parameters for interesting large format lenses, it would help make things more concrete. I haven't been able to find anything of that nature about pupil magnification except for 35 mm lenses.

[Gregory Gomez]

Leonard wrote:

Gregory, it is usual practice to refer to the front (first) planes and points for object-space calculations ('object' being synonymous with 'subject' in this case), and the rear (second) planes and points for image-space calculations. An obvious exception is the use of film plane to object distance markings on lenses in focusing mounts.


Hi Helen,

I am not an engineer; I used the nomenclature in Adams book, The Camera. He used the definition, "the distance from the object to the lens rear nodal plane," in reference to "u."

I would consider Adam's treatment of the subject matter somewhat superficial and perhaps overly simplified for the lay reader like myself. In his discussion, Adams used a simple, not a compound, lens. Nevertheless, I take responsibility for what I posted.

Stroebel states more correctly, as you have pointed out, "u," or object distance, should be measured, in direction parallel to the lens axis, from the object to the lens front nodal plane, and "v" (image distance) should be measured from the lens rear nodal plane to the in-focus image (presumably on the ground glass, although Stroebel does not elaborate to that level of specificity). He goes on to say, however, that for most photographic situations in which conventional view camera lenses are used measuring from the lens center (i.e., lens board) will not introduce significant errors. My experience agrees with Stroebel's assessment.

Stroebel suggests that one can determine the lens rear nodal plane by focusing the camera on infinity, and then measuring "one focal length forward (e.g., 210mm for a 210mm focal length lens) from the ground glass. The location of the front nodal plane can be determined by turning the lens around and repeating the process.

Although Ansel Adams book, The Camera, is very useful, I find Stroebel's View Camera Technique more complete and precise, and I recommend it highly to anyone interested in learning more about using the view camera.

Best regards,

Greg

[Helen Bach]

Thanks for explaining that Gregory. It all makes sense now. Adams' The Camera is the only one of the three that I haven't read.

Best,
Helen

[Jim Galli]

Jim, do you recall some details of how you shot these? Any movements? Do you recall the taking apertures approximately?

Sorry, just returned to the discussion after a week away. I doubt anything I might add would be useful. Both of the photos I shared in post # 15 that were done on 8X10 with the 13" Pinkham & Smith lens were done very near f7. DOF is so shallow that I often try a little back tilt to get a little more tip of nose to eyes in focus if possible. No other movements. When I say f7, I mean that is what the scale is pointing at. But since the bellows is at 20 + or - inches I calculate true aperture for my exposure. I do find it interesting that lenses like the P&S IV that were designed to cause an effect between f4 and f8 will have the same effect between those apertures at infinity as it will at 1:1. ie. at a true f4 at infinity it is just as fuzzy as it is at 1:1 f4 indicated which is really f8. Maybe we can chatter on for 5 or 10 more pages about that phenomenon.

The big 22" voigtlander has a single waterhouse stop that would bring it to around f11 at infinity. DOF is so extremely shallow that I've used it in every exposure so far. With bellows draw it usually lands somewhere around f19-f22. Same minor movements at the back of the 11X14.

My sitters usually are intolerant of yellow 8.5X14.5 legal tablets filled with calculations, but might in fact crack a curious smile for me if I whip out the old Keuffel & Esser slide rule.

[Jerry Fusselman]

Gregory,

You wrote, "I don't mean to be disrespectful, but after reading your original post, some of which I found confusing, and all the responses to it, especially your attached paper, it's clear that you might already know the answers to your questions. So what is the real reason for your inquiry?"

Which parts did you find confusing? Sorry about that! I always want to learn how to write better. You (and anyone else) can send writing improvement ideas to me privately, if you prefer. It is very interesting for a writer to find where the reader got lost.

As for my real reason for my inquiry, since others seem confused by this too, I guess I better reveal it---though you will be disappointed.

Where I went to school, the person who gives a quiz thinks he already knows the answers. For the quiz I gave, I knew, or thought I knew, the answers. At the time, I had thought that everyone agreed this is what quiz means. Many of you must have gone to schools where the teacher gave quizzes with no idea as to the answers. :)

I originally thought that some better writer than me might grace the thread with the answers, but since that did not happen, I was required by custom to submit my answers.

After the quiz in my original post came my questions. Those are the things I did not know the answers to. Clear? The quiz has parts A and B. The questions are numbered 1 and 2. The things I labelled questions were my questions---not the quiz. To me, it is really quite simple why I asked the questions. The real reason I asked the questions 1 and 2 was the reason I stated.

[Jerry Fusselman]

Gregory,

You bring up several issues.

You, and several others, wonder, Does any 35mm-portrait photographer really think that a 300mm focal length can be clearly superior to 85mm? I never said most 35mm portrait shooters think so. My task is only to show that some do.

Please recall from my initial post that a 14-foot shooting distance corresponds to a 35mm photographer's 300mm lens, and a 4-foot shooting distance corresponds to an 85mm lens. (More accurately, the numbers are 14.32 and 4.06 feet.) For the upcoming quote, please remember 14 feet and 4 feet as distances that determine two quite different perspectives.

For my demonstration about 300mm lenses for 35mm portrait photographers, I start with quotes from a photo.net article called "Portrait Photography":


"If you want to flatter your subject, you'll probably want to deemphasize his nose. That means you want to stand at 10 or 15 feet away from him so that his nose isn't significantly closer to you than the rest of his face. However, at such a large distance from the camera, if you want to fill the frame with just your subject's face, then you need a high magnification ( i.e., telephoto) lens. . . . Many professional fashion photographers use 300mm or 600mm lenses"

And here are two examples from the photo.net thread "300f4 as a portrait lens":


"I watched a fashion photographer in Miami doing his stuff with a 300mm f2.8 lens on a F5."

"Most of my family members who are by no means "model types" like the thinning effect the longer lens shots. They don't know why, but they usually pick them as keepers..."

Even if someone has signed affidavits of one thousand 35mm portrait pros who despise 300mm lenses, even if so, I have now established all that I want to about 300mm for the purpose of my questions.

Actually, what other photographers do matters very little to me when their "common knowledge" leads to inferior practice. And I generally like my images more than other photographers', so why should I copy others? My attitude is not that unusual, is it? (Galen Rowell's wife, Barbara, generally liked her own images best at locations also photographed by her husband.)

Then why am I personally interested in 300mm? Well, I noticed in my own 35mm portrait shots that my 300mm images seemed especially pleasing. I had used that huge, heavy lens almost by accident---only to keep my equipment safe and out of the water for a special location on a Lake Michigan beach. My sitter and I thought the resulting perspective strikingly good compared to the various shorter focal lengths I used for a couple thousand other shots. The 300mm images really seemed somehow more beautiful and glamourous. That is how I got the idea of trying for more resolution in a larger format---but with that same perspective!

Some may say, well, 300mm shots (on 35mm) look better just because you had extra control over the background with the longer lens. But my answer is that that is a major benefit of the longer perspective, so if the better background is the 35mm pro's reason for the longer lens, then I probably want that with large format too.

You admit, "The longer lens also makes it easier to throw the background out of focus, making the subject's face standout from any distracting elements. In this regard, the 300mm is often used on location, like the beach."

The longer lens allows more control over what parts of the background show, but it does not materially affect depth of field if you hold image magnification and f/stop constant, as I explained earlier in this thread. I hope you agree with this. Many posters think focal length materially affects depth of field in this context, but it doesn't. Remember, we are talking about head-and-shoulders portraits in a given format, so we take magnification as given. It is easy to check the numbers if you doubt it: Focal length has no material affect on depth of field for this image.

First you assert, "When a longer focal length lens is used, less of the scene is included, but perspective remains unchanged," and several posters in this thread agree with you, but later you quote Stroebel, who says the exact opposite: "It is not correct, however, to say that focal length has no effect on perspective." I cannot tell which position you agree with, but personally, I agree with Stroebel.

Stroebel defines the terms weak perspective and strong perspective, but he does not mean any value judgement by the terms. The fact that a longer focal length gives you a weaker perspective does not mean longer focal lengths necessarily give inferior results.

This leads to the question, Does it makes any sense to choose your perspective first if you want an excellent result? Many posters on this thread seem to say "no" when it comes to portraits. And your post contradicts itself on this issue. First you say, "a photographer can use ANY camera and ANY lens to make a portrait. I cannot emphasize this observation enough." This is the lens-first, framing-second, perspective-last school. You say one should choose the lens, "ANY lens", choose the desired image size, and then accept the resulting perspective.

My preferred alternative to this thinking can be called the perspective-first school. Here, you choose the lens only after deciding on your desired perspective. These two schools are opposites from the standpoint of perspective, because one has your perspective chosen last, and the other has it chosen first. It is crucial to see the difference.

You started by endorsing school #1, the perspective-last school, but your post later inexplicably shifts to endorse school #2 (the perspective-first school) by saying, "Stroebel goes on to say that it's best to select camera position first based on the perspective desired, and then choose the lens focal length that will produce the appropriate image size. (I agree with this assertion.)" You go back to school #1 in your closing paragraph of your part 2 (which ironically rejects using math immediately after listing more than 30 equations).

This paragraph from Stroebel (p. 130), even though you cited part of it, clarifies what I just tried to say:

"Inexperienced photographers usually select the camera position on the basis of factors other than perspective. The tendency is to adjust the distance between the camera and the subject to obtain the desired image size and angle of view or to select the most convenient location for the camera without giving consideration to the perspective. . . . Professional photographers learn to control perspective to obtain the desired effect. To do this, it is first necessary for the photographer to be aware of the subtle as well as obvious perspective effects. The camera position is then selected on the basis of the perspective desired, and finally, the focal length lens that will produce the appropirate image size is used."

Do you see? Your endorsment of "ANY lens" (your caps) matches the way inexperienced photographers do it. The fully professional way is to think about perspective first, and only after satisfying your perspective goals do you choose your focal length. Someone asked, "Why all the math?"---the answer is simply that I want to see how to achieve a certain perspective.

Why discuss angle of view? Actually, I think angle of view should be ignored, but you wrote this: "It's my impression that you may have confused angle of view – what the lens "sees" (or the angle of subject area projected on the film) – with perspective – the distance from subject to the lens rear nodal plane, or "v" in commonly used lens formulas."

I offer three corrections: Perspective does not equal that distance, but it may be determined by that distance. And that distance is determined by a point closer to the front nodal point than the "rear nodal plane." And it is u, not v, that measures that distance in the commonly-used lens formulas (such as formulas used by Ansel Adams, Leslie Stroebel, Sidney Ray, Leonard Evens, Jeff Conrad, and me). More fundamentally, in this thread I never said that any angle must be duplicated when switching to a larger format. Indeed, my point was that a certain distance to the subject must be duplicated to match the perspective between formats, and that requirement defines the focal length needed in the new format. I discussed determining focal length to satisfy a perspective requirement, not angle of view. Angle of view played no role in my argument, so how could I have confused angle of view with something else?

The computations of angle of view in part 2 seem a red herring to me. In examples 1 and 2 of my paper, there is a demonstration that a 300mm lens on 4x5 captures the same 15-inch-tall subject as a 480mm lens on 8x10 captures---provided we match the distance u in both cases. That 300mm for 4x5 gives the same perspective as 480mm for 8x10 (this time for a 16-inch-tall head-and-shoulders-sized subject) also appears in question 2 of my original post. Doubling the focal length when going from 4x5 to 8x10 gives you the wrong answer (except when focusing at infinity). The numbers in your part 2 end up with different values for u, so they do not answer my original question. You are changing perspective when you change formats, and my wish was to hold perspective constant.

The right answer if you want to match u as you change formats, as readers of my paper should be able to verify, was given in my original post: An 85mm lens in 35mm (assuming an 8x10 target print so the image size is 24mm by 30mm) corresponds to 300mm in 4x5 and 480mm in 8x10. If you like a significantly weaker perspective than this, then you have to go to significantly longer than these focal lengths.

[Phong]

"Which parts did you find confusing? Sorry about that! I always want to learn how to write better. You (and anyone else) can send writing improvement ideas to me privately, if you prefer. It is very interesting for a writer to find where the reader got lost."


Too verbose.
:-)

- Phong


Gregory,

You wrote, "I don't mean to be disrespectful, but after reading your original post, some of which I found confusing, and all the responses to it, especially your attached paper, it's clear that you might already know the answers to your questions. So what is the real reason for your inquiry?"

Which parts did you find confusing? Sorry about that! I always want to learn how to write better. You (and anyone else) can send writing improvement ideas to me privately, if you prefer. It is very interesting for a writer to find where the reader got lost.

As for my real reason for my inquiry, since others seem confused by this too, I guess I better reveal it---though you will be disappointed.

Where I went to school, the person who gives a quiz thinks he already knows the answers. For the quiz I gave, I knew, or thought I knew, the answers. At the time, I had thought that everyone agreed this is what quiz means. Many of you must have gone to schools where the teacher gave quizzes with no idea as to the answers.

I originally thought that some better writer than me might grace the thread with the answers, but since that did not happen, I was required by custom to submit my answers.

After the quiz in my original post came my questions. Those are the things I did not know the answers to. Clear? The quiz has parts A and B. The questions are numbered 1 and 2. The things I labelled questions were my questions---not the quiz. To me, it is really quite simple why I asked the questions. The real reason I asked the questions 1 and 2 was the reason I stated.



Gregory,

You bring up several issues.

You, and several others, wonder, Does any 35mm-portrait photographer really think that a 300mm focal length can be clearly superior to 85mm? I never said most 35mm portrait shooters think so. My task is only to show that some do.

Please recall from my initial post that a 14-foot shooting distance corresponds to a 35mm photographer's 300mm lens, and a 4-foot shooting distance corresponds to an 85mm lens. (More accurately, the numbers are 14.32 and 4.06 feet.) For the upcoming quote, please remember 14 feet and 4 feet as distances that determine two quite different perspectives.

For my demonstration about 300mm lenses for 35mm portrait photographers, I start with quotes from a photo.net article called "Portrait Photography":



And here are two examples from the photo.net thread "300f4 as a portrait lens":



Even if someone has signed affidavits of one thousand 35mm portrait pros who despise 300mm lenses, even if so, I have now established all that I want to about 300mm for the purpose of my questions.

Actually, what other photographers do matters very little to me when their "common knowledge" leads to inferior practice. And I generally like my images more than other photographers', so why should I copy others? My attitude is not that unusual, is it? (Galen Rowell's wife, Barbara, generally liked her own images best at locations also photographed by her husband.)

Then why am I personally interested in 300mm? Well, I noticed in my own 35mm portrait shots that my 300mm images seemed especially pleasing. I had used that huge, heavy lens almost by accident---only to keep my equipment safe and out of the water for a special location on a Lake Michigan beach. My sitter and I thought the resulting perspective strikingly good compared to the various shorter focal lengths I used for a couple thousand other shots. The 300mm images really seemed somehow more beautiful and glamourous. That is how I got the idea of trying for more resolution in a larger format---but with that same perspective!

Some may say, well, 300mm shots (on 35mm) look better just because you had extra control over the background with the longer lens. But my answer is that that is a major benefit of the longer perspective, so if the better background is the 35mm pro's reason for the longer lens, then I probably want that with large format too.

You admit, "The longer lens also makes it easier to throw the background out of focus, making the subject's face standout from any distracting elements. In this regard, the 300mm is often used on location, like the beach."

The longer lens allows more control over what parts of the background show, but it does not materially affect depth of field if you hold image magnification and f/stop constant, as I explained earlier in this thread. I hope you agree with this. Many posters think focal length materially affects depth of field in this context, but it doesn't. Remember, we are talking about head-and-shoulders portraits in a given format, so we take magnification as given. It is easy to check the numbers if you doubt it: Focal length has no material affect on depth of field for this image.

First you assert, "When a longer focal length lens is used, less of the scene is included, but perspective remains unchanged," and several posters in this thread agree with you, but later you quote Stroebel, who says the exact opposite: "It is not correct, however, to say that focal length has no effect on perspective." I cannot tell which position you agree with, but personally, I agree with Stroebel.

Stroebel defines the terms weak perspective and strong perspective, but he does not mean any value judgement by the terms. The fact that a longer focal length gives you a weaker perspective does not mean longer focal lengths necessarily give inferior results.

This leads to the question, Does it makes any sense to choose your perspective first if you want an excellent result? Many posters on this thread seem to say "no" when it comes to portraits. And your post contradicts itself on this issue. First you say, "a photographer can use ANY camera and ANY lens to make a portrait. I cannot emphasize this observation enough." This is the lens-first, framing-second, perspective-last school. You say one should choose the lens, "ANY lens", choose the desired image size, and then accept the resulting perspective.

My preferred alternative to this thinking can be called the perspective-first school. Here, you choose the lens only after deciding on your desired perspective. These two schools are opposites from the standpoint of perspective, because one has your perspective chosen last, and the other has it chosen first. It is crucial to see the difference.

You started by endorsing school #1, the perspective-last school, but your post later inexplicably shifts to endorse school #2 (the perspective-first school) by saying, "Stroebel goes on to say that it's best to select camera position first based on the perspective desired, and then choose the lens focal length that will produce the appropriate image size. (I agree with this assertion.)" You go back to school #1 in your closing paragraph of your part 2 (which ironically rejects using math immediately after listing more than 30 equations).

This paragraph from Stroebel (p. 130), even though you cited part of it, clarifies what I just tried to say:

"Inexperienced photographers usually select the camera position on the basis of factors other than perspective. The tendency is to adjust the distance between the camera and the subject to obtain the desired image size and angle of view or to select the most convenient location for the camera without giving consideration to the perspective. . . . Professional photographers learn to control perspective to obtain the desired effect. To do this, it is first necessary for the photographer to be aware of the subtle as well as obvious perspective effects. The camera position is then selected on the basis of the perspective desired, and finally, the focal length lens that will produce the appropirate image size is used."

Do you see? Your endorsment of "ANY lens" (your caps) matches the way inexperienced photographers do it. The fully professional way is to think about perspective first, and only after satisfying your perspective goals do you choose your focal length. Someone asked, "Why all the math?"---the answer is simply that I want to see how to achieve a certain perspective.

Why discuss angle of view? Actually, I think angle of view should be ignored, but you wrote this: "It's my impression that you may have confused angle of view – what the lens "sees" (or the angle of subject area projected on the film) – with perspective – the distance from subject to the lens rear nodal plane, or "v" in commonly used lens formulas."

...

The right answer if you want to match u as you change formats, as readers of my paper should be able to verify, was given in my original post: An 85mm lens in 35mm (assuming an 8x10 target print so the image size is 24mm by 30mm) corresponds to 300mm in 4x5 and 480mm in 8x10. If you like a significantly weaker perspective than this, then you have to go to significantly longer than these focal lengths.

[Jerry Fusselman]

I bet if you could calculate the focal length of many famous paintings, they'd be wide enough to surprize you. I tend to go wider for roundness and volume.

Frank,

In Applied Photographic Optics (third edition, 2002), Sidney Ray gives a way to compute the taking focal length of a photograph, if you know the following:

enlargement magnification;
location (distances) of left- and right-hand vanishing points of a two-point perspective;
there are orthogonal vertical surfaces.


It is really pretty simple to compute; he explains how in the last paragraph of p. 243.

However, this exercise applied to a painting with two-point perspective seems unlikely to prove your point, because, as he says on p. 238,


A painting or drawing may appear to follow exact rules of perspective as obeyed by the technical draughtsman, but usually true perspective is only used for the broad masses of the subject, and detail is subtly altered to give a more pleasing perspective.

Your mention of roundness is interesting too. You say the shorter focal length gives more of a feeling of roundness, but Ray briefly discusses very long focal lengths providing more roundness in this quote from p. 239:


When portrait lenses for large formats were of very long focus, up to 1 m or more, a working aperture of f/16 gave an entrance pupil diameter comparable to the human interocular distance (IOD) of 63.5 mm. This pupil area provides a large number of different viewpoints which integrate in the film plane to give a diffused image. This effect of stereo parallax is therefore not a true plane perspective but gives a psychological effect of `roundness' or `plasticity' which many people consider to be more natural than an acurate central perspective of the sitter.

(There is a typo on that page that confused me for a while---he wrote k + ku when he meant u + ku.)

[Gregory Gomez]

Jerry,

My confusion over what you had originally posted could also be a result of my limited understanding of mathematics and optics engineering. With such subject matter, it’s very important for me that it be extremely well organized and very clear, with every step included. Your attached paper is a good example of a well-thought-out and well written piece. Your e-mail post was not quite up to the same standard. When I read your attached paper, however, I understood everything. Perhaps I should have read your attachment first before posting.

I could send you an e-mail about technical writing, but it would be a tad long and tedious to read. It’s time consuming to give meaningful writing feedback; perhaps that’s why so few English teachers bother to do so. I have spent the last 30 years learning to write reasonably well, and thousands of hours writing and rewriting sentences and paragraphs so that my written work may have some degree of clarity and precision. I’m sorry to say that I’m still learning and that I still make mistakes.

I have taken class work in which there were no right or wrong answers per se. We were graded upon the quality of our work and the thoroughness of our preparation, reasoning, and summation. It was extremely important to show how we derived our conclusions, provided, of course, that our conclusions were not completely absurd.

Perhaps it was the way in which I read your original post that led me to believe that you were providing a quiz for the rest of us because you did not precisely know the answers to the questions you were asking and that you were uncertain as to which lens to use, or better yet, which aesthetic philosophy you should follow in regards to head-and-shoulder portraits. Once again, however, I feel that you know exactly what you want to do so why not just do it? Why bother with the quiz? This is not a forum on mathematics or optics engineering, although it’s my understanding that some of the members of this group are either engineers, or scientists, or hold college degrees in these disciplines.

If you want to duplicate the angle of view (and the “weaker perspective,” as defined by Stroebel”) that is created by a 300mm lens on a 35mm camera using a 4x5, then you will need a 1200mm lens for the 4x5. (But you don’t seem to care about angle of view.) If you use a 300mm lens on the 4x5, then the angle of view and perspective (as defined by Stroebel) would be about equal to an 85mm on a 35mm camera. Nikon once made a lens of this focal length. You can probably buy one used if you are lucky. To duplicate the same conditions for an 8x10, you will need about a 2400mm lens. All I can say is, “Good Luck!” A 480mm lens on an 8x10 will match the same angle of view and “Stroebel’s perspective” as a 68mm lens on a 35mm. But, again, you don’t care about angle of view. I say that angle of view will have some influence upon the image captured by the lens, especially in how the near-to-far details of the subject are rendered, and that includes head-and-shoulders portraits.

Your quote from Photo.net is interesting, and the suggestions given might be useful for subjects that want you, the photographer, to de-emphasize their nose. Would you use the same technique on someone whose nose is too small? Maybe not.

Using a 300mm lens on a 35mm camera for portraits is a personal selection, and cannot be argued as being the lens of choice by using mathematics or citing articles in Photo.net. If you like the look of a "Poparazzi Grab-Shot," then do it. Why seek justification for your photographic style by engaging in endless polemics? If you really believe your approach to portraiture is superior, then there is no need to argue it, right? Or do you like to argue more than taking pictures?

Stroebel’s comments about the perspective created by a given lens are by no means universally accepted. He is also suggesting that focal length has some affect upon perspective, but it does not determine perspective in its entirety or in the same way as camera position does in relationship to the subject. In other words, camera position will have a greater impact upon perspective than focal length. He stresses that differing focal lengths give different impressions of depth in a photograph. That’s an important distinction, for an impression is purely subjective.

How does using any camera with any lens negate a perspective first ideology? That is, establish camera position first, and then choose the lens? It does not. When I made this statement, it was meant to be all inclusive; it was not meant to argue one camera, one lens, or even one photo technique over any other. One can literally use any camera he or she chooses, even a pinhole device, or any lens for that matter. In photography, like art, there are no absolutes, no immutable laws, no required ways of working. If I want to use a panoramic camera with a wide-angle lens to do head-and-shoulders portraits, that’s my business. Conversely, if I want to use an 8x10 camera with a 1200mm lens, that would be my business too. Not everyone will agree with me in either case. There may be as many approaches to portraiture as there are photographers interested in do such work. So my statement stands, and in my opinion, it posses no contradiction at all.

Incidentally, you misread my post. I do not endorse any photographic school of thought. You and Stroebel do, and that’s your right. Does it bother you that I can see both sides of an argument and argue both positions without choosing one side over another?

Here’s a question for you to solve since you brought up Galen Rowell, one of the finest mountaineering photographers of the 20th Century. Let’s assume you and your climbing partner are doing an ascent of El Capitan. What lens would you use on a Nikon FM-3A and why would you use it to photograph you and your buddy? Would it be your beloved 300mm lens or a 24mm wide angle?

And lastly, if you wish to ignore angel of view, again, that’s your business. You can do anything you like, really. You don’t need anyone’s endorsement here, mine least of all.

[Jerry Fusselman]

I will try to be brief.

No, I do not know exactly what I am going to do about LF portraits.

Ansel Adams's book is not a book on mathematics, yet he has lots equations. Some of the responders in this thread would no doubt want to kindly ask him if he ever takes pictures. You see, math is a tool that can help photographers sometimes. Math is not the subject. Math is a language; it may help, just like an English or French article on photography may help.

I am only interested in matching u across formats, so your numbers 1200 mm and 2400 mm are way too high. You might try rereading example #2 in my paper and ask yourself why the answer I gave was 480 mm even though 300 x 2 = 600. Or look at today's post by Leonard Evens in Center of Perspective and Nodal Point that also comes up with 480 mm. I have also discussed these exact numbers twice earlier in this thread.

There is more to perspective than the size of a nose.

I guess I can never tell what you mean to endorse. Personally, when I say "X", I mean that "I believe that X is true." I thought you were endorsing your own sentences, but OK, sometimes not.

Galen Rowel isn't likely to want a head-and-shoulders portrait in that situation, but I seem to remember he published an image in Mountain Light of Ron Kalk (or similar name) free soloing at or near Half Dome taken with a working distance of at least 50 feet, which is plenty sufficient for good perspective. I have seen other shots of his friends climbing, and his working distance is generally more than 20 feet. The point is not to demand a certain focal length for all images. The point is to have correct working distance for the perspective you want.