Lens viewing angles

[James E Galvin]

Yes, the rear node to the film plane. Think of a pinhole. The entrance and exit angles, equal for a pinhole or "ordinary" lens. Not equal for telephoto or retrofocus lenses.

[Helen Bach]

Equal by definition, surely?

[James E Galvin]

For the pinhole, yes. For a lens system, no. Consider putting a telescope in front of the lens. The relationships behind the lens are unchanged, but the entrance angle is smaller, by the magnification of the telescope. Telephoto and retrofocus lenses have some telescope built in. The telephoto has a positive group at the front, negative (with some space) at the rear. This is a Galilean telescope.

[Leonard Evens]

A "normal" lens has the same angle input and output. But there are telephoto lenses and inverted telephoto or retrofocus lenses, which have positive and negative sections with a large spacing. These are common on 35, the retrofocus for wide angle lenses where room behind the lens for the mirror is required, and telephoto to keep the lens short. These have different input and output angles. Think of the telephoto as a normal lens with a built in telextender, and the retrofocus with the reverse. Telephotos are available for large format, the retrofocus as far as I know not. Most LF lenses are "normal".

This presumably refers to the angles as measured from the rear lens element and front lens element. Those need not be equal for the reasons I gave previously. I think those angles are not the relevant ones to look at. The appropriate points from which to measure the two angles are where the two principal planes intersect the lens axis. If you take any line out in the scene which lies in a plane parallel to the gg, and look at the corresponding image line and then measure the angles subtended by the subject and image lines from those two references points, the two should be equal. The largest such lines in the scene which can appar in the image are those which yield a diagonal on the gg, and it is the corresponding angle that you call the angle of view.

Of course, this only refers to normal lenses used in air, which do not distort the image. Fisheye lenses, of course are very different, as are lenses used under water.

[James E Galvin]

Yes, angles should be measured from the intersection of the principal planes and the axis. For a pinhole, and a symmetrical lens, entrance and exit angles are the same. They are not the same for a telescope, that is the point of a telescope. A telescope used as a camera lens by refocussing the eyepiece (eyepiece projection) has different entrance and exit angles, they are different by the magnification of the telescope. Telephoto and retrofocus lenses have some telescope built in. I think a conservation law is being questioned, it is not the angles that are conserverd, but the etendu, the product of the angle and the aperature.

[Struan Gray]

I speak from a position of repeatedly proven ignorance, but here is how I think about this.

The angle of view is defined by lines from the edge of the frame to the rear nodal point. The angle of the projected rear light cone is defined by lines from the edge of the frame to the center of the exit pupil. In asymmetrical lenses the nodal points and pupils do not necessarily lie on the same planes, so the two angles can be different.

I have a 36" LF telephoto from an aerial camera. When focussed at infinity the rear element is only 18" or so away from the film plane, and the exit pupil about six inches in front of that. The light cone 'behind' the lens is substantially shorter and fatter than that from a 36" focal length pinhole.

Then there are telecentrics, where the light cone has zero angle and the pupil is at infinity. Some lenses are only telecentric on one side, giving a radical difference between the angles on the object side and the image side.

[James E Galvin]

Hopefully Steve stopped reading sometime back, or I've helped confuse him more. For "ordininary", that is not telephoto or retrofocus, the angles are the same or nearly so. This would be true for almost all LF lenses.

[Helen Bach]

I agree with Leonard.

Here's my understanding, and I'd be grateful to anyone who explains my error:

If you are talking about the angles at the nodal points of rectilinear lenses, then the 'input angle' equals the 'output angle' for telephotos and for retrofocus lenses just like 'normal' lenses. This is a basic property of the nodal points - in fact it is a condition of the definition of the nodal points. A ray from a point on the object travelling towards the front nodal point appears to emerge from the rear nodal point parallel to its original direction. This is a simple rule of Gaussian optics.

"Consider putting a telescope in front of the lens. The relationships behind the lens are unchanged, but the entrance angle is smaller, by the magnification of the telescope."

If you add a converter or a telescope to the front of a lens, then the rear nodal point does move, and the 'output angle' changes.

If you are considering the angle of view of a recilinear lens for a given film format, and comparing the object plane in focus with the image plane, then the angle of view is always equal to the angle the relevant film dimension subtends at the rear nodal point.

A 90 mm lens has the same angle of view for a given format, whether it is a telephoto, a retrofocus or a 'normal' lens. For a given object distance, the rear nodal point will always be at the same distance from the image plane for all three types of lens.

As Struan points out, the exit pupil may not be at the rear nodal point, but that doesn't alter the angle of view in the plane of focus.

Best,
Helen

[Leonard Evens]

Needless to say I agree with Helen's analysis, since she agrees with me.

Let me just comment on the issue of the principal point vs. the entrance pupil. For most lenses used in large format photography, it was my impression that these are the same. But they could be different and in a previous discussions of this issue, several examples were given, mainly for small formal lenses, where they are. If I understand correctly, the entrance pupil is the correct position to use to determine point of view because it preserves line of sight relations. That is, if you put your eye at the entrance pupil and two objects are along the same line of sight, then in the resulting photograph, they will also be along the same line of sight. So, from that perspective, you could argue that you should use the entrance pupil rather than the front principal point. For, if you took a pair of points, one near and one far, with the near point obscuring the far point, and a similar pair elsewhere, and traced back the rays corresponding to these pairs, they would intersect at the front entrance pupil, and so the angle between the rays should be measured from there. On the other hand, as Helen pointed out, any calculations of relations of subject sizes (or distances) to image sizes (or distances) in (to) the plane of focus, would be done using the principal point.

Be that as it may, for normal subjects, the difference between the entrance pupil and front principal point would be negligible compared to the subject distance. In specifying angles of view, the issue would be irrelevant except for some cases of close-up photography. (But, even for distant subjects, the difference can be important when parallax issues enter the discussion as in panoramic photography involving rotating the camera.)

[swmcl]

Hi guys,

Back after the weekend ...

Thanks James, you've answered my thoughts very well. LF photography is dominated by 'normal' lenses. I didn't know this was the definition of 'normal' and I reckon its a pity there are not more of the other types available especially in the wide angles. I'm stuggling to find a 5x7 field camera (an old one) that will accept some of the new wider angle lenses.

Thanks again,