Portrait perspective: Quiz and two questions

[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:

1. 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.
2. 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?
3. 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.