Portrait perspective: Quiz and two questions

[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.