Lens viewing angles

[swmcl]

Hi all,

I'm new to LF and doing some sums ...

I take the data available for the 80mm Super Symmar and find this ...
It has an image circle (@ f22) of 212mm at which point the lens will be 80mm from the film. The lens has a stated field of view of 105 degrees. Simple geometry indicates the useable data on the 'input' side of the lens (the side where the subject is !) is in the same 'angle of view' as the 'output' side of the lens. Both being at 105 degrees.

Is it possible for a lens to have a 105 degree 'input' side and say an 80 degree 'output' side ?

This would mean a 150mm lens might have a image circle of 212mm and a field of view of 105 degrees yet also have a focus distance of say 120mm ... (YES! - I can fit the thing on a camera !) [I also get a little worried by the light striking my film at such an oblique angle ...]

Does anyone know of such technology ? I have put numerous lens data through my spreadsheet and they're all looking the same in that the angle of view on one side of the lens is the same angle of view on the other side. The final element on my 35mm 17mm lens is no closer to the film plane than the final element of my 200mm lens !

Cheers,
Steve

[Ron Marshall]

Have a look at this thread:

http://www.largeformatphotography.info/forum/showthread.php?t=20698

[Sheldon N]

Hi all,
Is it possible for a lens to have a 105 degree 'input' side and say an 80 degree 'output' side ?

This would mean a 150mm lens might have a image circle of 212mm and a field of view of 105 degrees yet also have a focus distance of say 120mm ... (YES! - I can fit the thing on a camera !)

No, at infinity I do not believe it is possible for a lens to have an 'input' of 105 degrees and an 'output' of 80 degrees. If the lens has an output (angle of coverage) of 80 degrees it is not a super wide angle design and must therefore be used on a smaller format (when compared to a ultra wide design). On the smaller format it would be closer to a semi-wide at best.

If you focus close enough, any lens will eventually have enough coverage. You do see very short focal lengths for ultra macro lenses. However, the extra extension will alter the effective focal length, and the drastic reduction in depth of field at such close focus really makes the angle of view ('input' side) irrelevant.

[swmcl]

Thanks guys,

I appreciate your comments. In a discussion about it here at my workplace I likened it to 35mm photography. In 35mm, many of the lenses have their last element at a similar distance from the film plane. So a 35mm lens and a 70mm lens and a 135mm lens all have the same lens-film distance (pretty much). Not so the case in LF.

If lens manufacturers for LF were to make all their lenses have say a 100mm distance from film to last lens element (for infinity focus) then all LF cameras (for a given size like 4x5) would only need bellows that extended from say 100mm to 200mm. Easy !

I reckon its got something to do with optics or shifts. It may be that to allow a lens to shift it needs to be of a certain design and the one I'm thinking would be nice wouldn't allow shifts because it would need to be central to the film area.

Any other thoughts welcome !

[robc]

does your spreadsheet take into consideration the design of each lens you are doing the calculation for, or are you just assuming that your formulas will work for all lens designs just because you have used the generic formulas printed in some publication?

If it's the latter, which I suspect, then you are wasting your time except for learning that since you don't have the design parameters for each individual lens design, you can't do what you are trying to do with any accuracy.

[Leonard Evens]

Hi all,

I'm new to LF and doing some sums ...

I take the data available for the 80mm Super Symmar and find this ...
It has an image circle (@ f22) of 212mm at which point the lens will be 80mm from the film. The lens has a stated field of view of 105 degrees. Simple geometry indicates the useable data on the 'input' side of the lens (the side where the subject is !) is in the same 'angle of view' as the 'output' side of the lens. Both being at 105 degrees.


The angle of view is the same on both sides of the lens. But you don't want to confuse the angle of coverage with the angle of view. The latter is determined by the format size and the distance of the frame from the lens. The former is determined by the design of the lens and relates to light fall off and loss of resolution as you move from the center to the peripherry. For a 4 x 5 frame, which has a diagonal of about 153 mm, the angle of view of an 80 mm lens when focused at infinity is about 87 degrees. As you extend the bellows, the angle of view decreases, although until you are in the close-up range, the change is negligible. The figures you give for the angle of coverage---105 degrees---and the diameter of the circle of coverage---212 mm---are consistent with one another. As you extend the bellows, the angle of coverage stays roughly the same, and the circle of coverage increases. Again, this increase is negligible until you are in the close-up range.




Is it possible for a lens to have a 105 degree 'input' side and say an 80 degree 'output' side ?



No.




This would mean a 150mm lens might have a image circle of 212mm and a field of view of 105 degrees yet also have a focus distance of say 120mm ... (YES! - I can fit the thing on a camera !)



It is not clear what you mean by that. The angle of view of a 150 mm lens at infinity is always about 52 degrees, but its angle of coverage and its image circle at infinity would depend on the design of the lens. The distance of the lens to the film must always be not less than the focal length. But that distance has to be measured from what is called the rear principal plane. The position of that plane for most lenses is pretty close to the front of the lensboard, but for some lenses, e.g., those of telephoto design, it could be elsewhere, including some considerable distance in front of the front element of the lens. The actual distance of the lensboard from the film when you are focused at infinity is called the rear flange focal length and is usually specified in the lens specifications. If you know that and the focal length, you can calculate the position of the principal plane. None of this affects the angle of view at infinity, which is determined by the focal length and the frame size.




Does anyone know of such technology ? I have put numerous lens data through my spreadsheet and they're all looking the same in that the angle of view on one side of the lens is the same angle of view on the other side. The final element on my 35mm 17mm lens is no closer to the film plane than the final element of my 200mm lens !



But you can be sure the rear principlal plane for your 17 mm lens is 17 mm from the film when focused at infinity and that for your 200 mm lens it is 200 mm from the film when focused at infinity. Your 200 mm lens is almost certainly a telephoto lens and its rear principal plane is considerably in front of the rear element of the lens and may in fact even be in front of the lens entirely. Your 17 mm lens is probably of inverted telephoto design and its rear principal plane is probably in back of the inside lens element. Its rear flange focal length would be greater than its focal length. That is typically the case for wide angle lense for 35 mm SLRs because room has to be left for the mirror.

[James E Galvin]

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".

[Helen Bach]

...These have different input and output angles...

How are you defining 'angle' in those cases?

Thanks,
Helen

[James E Galvin]

I am using the terms as Steve originally used them. The angle of coverage is the input angle, the output angle is the angle between the lens and film. These are the same for most lenses, but different for telephoto and retrofocus lenses. Consider the wide angle and telephoto converter lenses that screw onto the front of lenses for 35. They change the input angle (the angle of coverage), but not the output angle. It would be nice to have retrofocus lenses for LF, no bag bellows or recessed lensboards, no need for center filter! But looking at the size of very wide lenses for 35, our lenses would be huge.

[Helen Bach]

Sorry, I was wondering which part of the lens you were measuring the 'output angle' from. You do not appear to be measuring from the rear node to the film plane.

Best,
Helen

[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,

[James E Galvin]

I had seen the concept of the nodal points and been puzzled by it. From Kingslake, Lens Design Fundamentals, the nodal points coincide with the principal points if the lens is in air. There is a paraxial ray such that it passes through one nodal point and emerges from the other at the same angle with the optical axis. But consider the refracting telescope. The principal points are in the objective, and just behind the eyepiece. Starlight enters as a parallel bundle, and exits the eyepiece as a parallel bundle, but at an angle than is the telescope magnification times the entrance angle. The only rays with an exit angle equal to the entrance angle are parallel to the optical axis. So I think Kingslake's definition applies only to a single thin lens.
I set up a cradle to hold a lens, about 5 feet from a wall. I put a mark A on the wall. I set a lens on the cradle, optical axis aimed at A. I aim a laser pointer through the lens. The laser pointer was about 1 1/2 feet from the lens. The light went through the lens in the usual direction: the film side of the lens was toward the wall. I stopped the lens to f/45. The lens defocussed the laser beam a bit, but the spot on the wall was less than 1/2 inch in diameter. I could easily sight from the laser to the reflected spot on the lens to the spot on the wall. Now I swing the lens so that its optical axis points to a spot B on the wall, the swing near the lense's maximum. If entrance and exit angles are equal, the spot will still move a small distance because the principal planes have some separation, the light does a dogleg. Guestimating where the planes are in the lenses this move should be less than an inch. For most of my LF lenses the laser spot on the wall was within an inch of A. But for 12 and 14 inch Commercial Ektars, a 203 Ektar, and a 90/6.8 Grandagon the spot was 3-4 inches from A, in the opposite direction from B: the exit angle is larger than the entrance. For a 190 Wide Field Ektar the spot was 3-4 inches toward B: the exit angle is a little less than the entrance angle. The differences are perhaps 10%.
Next I got out my 35mm kit and tried a 28m Vivatar, a retrofocus lens. I aimed it at point B about 4 feet from A. The laser spot was about midway between A and B, that is 2 feet from A. The exit angle is about half of the entrance angle. Finally I tried a 135mm Topcor, a telephoto. With point B about 1 1/2 feet from A, the laser spot was about 3 feet from A, the exit angle about twice the entrance angle.
Finally I note that 35mm very wide lenses don't seem to need a center filter, explained if the exit angle is 1/2 or so of the entrance angle.

[Helen Bach]

I had seen the concept of the nodal points and been puzzled by it. From Kingslake, Lens Design Fundamentals, the nodal points coincide with the principal points if the lens is in air. There is a paraxial ray such that it passes through one nodal point and emerges from the other at the same angle with the optical axis. But consider the refracting telescope. The principal points are in the objective, and just behind the eyepiece. Starlight enters as a parallel bundle, and exits the eyepiece as a parallel bundle, but at an angle than is the telescope magnification times the entrance angle. The only rays with an exit angle equal to the entrance angle are parallel to the optical axis. So I think Kingslake's definition applies only to a single thin lens.
...

Well, it isn’t just Kinglake’s definition, and it applies to compound lenses, including telephoto and retrofocus lenses but it doesn't apply to an afocal system, though it can apply to elements within an afocal system.

The key thing about a telescope is that it is an afocal combination, so you can’t apply the general relationships of Gaussian optics to the combination – you can apply them to the separate groups making up the combination, and you would find that the groups obey the nodal point relationship. You can also apply the relationship when the telescope is combined with another lens such that an image is formed – ie the combination is no longer afocal.

I think that your experimental results show that you are referring to the angles at the entrance and exit pupils, not the angle at the nodal points. As we’ve already discussed, these can be different and nobody is arguing with that. The angle of view of an in-focus system is determined by the angle at the nodal points, not the angles at the entrance and exit pupils. If you were to re-do your experiment, it might be better to establish the positions of the principal planes and the pupils as accurately as you can.

Best,
Helen

[James E Galvin]

I see that Conrady, Applied Optics and Optical Design, treats the cases of separated lens pairs, and states that one of the principal planes becomes virtual. I will need to read some more to see what is meant, Conrady is not easy reading. I think the front principal plane is inside of the 28mm Vivitar, the rear principal plane just behind the lens, taking 1 fl from the infinity focus. If the nodal points are on the axis at the principal planes, then the input and output angles are clearly very different. I can't visualize any pair of planes that cures this, unless perhaps the glass is imagined to be much larger in diameter (perhaps a couple of feet).

[Helen Bach]

Consider your 28 mm Vivitar focussed at infinity. The rear nodal point is 28 mm from the image plane, on the optical axis. The angle subtended by the film diagonal (43.27 mm) is

2 arctan (43.27/(28x2)) = 75.4°

You say that the output and input angles are different. What is the ‘input’ angle of view?

Your remark about the diameter of the lens: The ray that would pass through the two nodes does not have to exist – in fact it often doesn’t with retrofocus lenses because they aren’t large enough. Here is an example, the 35 mm f/3.5 Distagon for the Contax 645, showing an image point at the corner of the 41.5 x 56 mm frame, object at infinity.

Notice the large difference in angle between the axis and the ray heading for the entrance pupil, and between the axis and the ray appearing to leave the exit pupil.

Best,
Helen

http://gallery.photo.net/photo/5171390-md.jpg