Angle of View

thuggins · Jul 21, 2020

There didn't seem a good place to post this, so it is being awkwardly shoe-horned in here.

We are all familiar with comparing focal lengths for various formats, in order to get an "equivalency". This is usually referred to as the "crop factor" in dealing with d!&!+@l cameras. The practical intent is to be able to frame the same image in say 35mm and 6x9.

I had always used a direct ratio. So given that a normal 35mm lens is ~43mm and a normal 6x9 lens is ~108mm, an 80mm lens on 6x9 would give 80/108*43 = 31.9. So a moderately wide lens sitting right between 35mm and 28mm.

While playing with the baby Graphic it became apparent that the fields of view were not aligning correctly. I broke out my OM-1 for a direct comparison. At all focal lengths the field of view on the Graphic was less than a ratio would indicate. That 80mm lens on the Graphic was closer to a 38mm on the OM. This was across the board with all lenses. The field of view was notably smaller for the 6x9 than a ratio comparison to a 35mm frame would indicate. The 101mm Optar was just shy of 50mm on the OM, rather than the 40mm the calculation gives. I double checked this with a Tewe viewfinder, and the Tewe and the OM lined up exactly.

As can be seen by the examples above, the difference is significant and noticeable. It is certainly more than can be ascribed to a "rounding error". More confusing, one would expect the error to go the other direction, as the OM viewfinder has a slight crop.

Sirius Glass · Jul 21, 2020

You are missing the point that press cameras used wide angle lenses so that

They had a wider depth of field, thus making them easier to focus in a hurry.
The larger negative allowed generous cropping when needed.

The press did not use the "normal" 150mm for 4"x5", but the shorter 128mm and 135mm lenses.

grain elevator · Jul 21, 2020

6x9 isn't usually the full 90mm wide. Measure your ground glass, it's probably only around 82mm wide.

thuggins · Jul 21, 2020

grain elevator said:
6x9 isn't usually the full 90mm wide. Measure your ground glass, it's probably only around 82mm wide.

If we're going to go there, then there is invariably going to be some small variation from camera to camera. The Graphic measures a skosh over 3-1/4" wide, which is pretty typical for full frame cameras. I initially assumed the frame was 2" x 3" (i.e. not metric), but that is not the case. This is not some tiny amount of difference; it is quite noticeable. And as I pointed out above, the OM screen is (very slightly) cropped. So the effect should be the opposite of what is actually seen.

mmerig · Jul 21, 2020

Field (or angle) of view is non-linear, so a linear interpolation, as done in post #1, will give incorrect results.

wiltw · Jul 22, 2020

Consider using the ratio of the FL vs. the short dmention of the frame as the comparison for 'equialency' between different formats!
I present these comparisons for consideration

135 format has 24mm frame, with 24mm lens it captures 53 degree AOV in the short direction
645 format has 42-43mm frame, with 42mm lens it captures 53 degree AOV in the short direction
6x7 format has 56mm frame, with 56mm lens it captures 53 degree AOV in the short direction4x5
4x5 format has 93mm frame opening, with 93mm lens it captures 53 degree AOV in the short direction

BTW, too many calculators of captured image area (FOV) or angle of view (AOV) assume the nominal dimensios, so 645 is assumed to be 45mm x 60mm, when reality is 43-43mm x 55-56mm actual image area. 4x5 is assumed to be 90mm x 120mm opening, but when you measure film holders, actually 93mm is exposed to the image presented by the lens!

Assuming a 45mm 'normal' on 135 (rather than the overlong normals, typically 50-58mm that have been presented over the years as 'noirmal' FL lens on 135 SLRs, that is a multiple of 45/24 or 1.875x, so for other formats the same AOV is captured with

28mm on APS-C
79mm on 645
105mm on 6x7
174mm om 4x5

and all would capture the same AOV along the short dimension of the frame.

thuggins · Jul 22, 2020

mmerig said:
Field (or angle) of view is non-linear, so a linear interpolation, as done in post #1, will give incorrect results.

That's pretty much my question. What is the relationship?

It appears the nonlinearity comes in once you get into wide angle lenses. Zuiko lenses show a linear relationship from 50mm to 400mm, with the angle of view halved with each doubling of the focal length. But this does not hold when going down to 24mm, which is substantially less than twice the 50mm angle of view.

I wonder if this is related to the relation between the focal length, perspective compression and cropping, that I've kicked around for quite a while. For 35mm, a 28mm lens is fairly wide and a 200mm lens is fairly long. There is a very obvious compression in the perspective as one goes from the 28mm to 200mm. But assume you had a "perfect" film with no grain and infinite resolution, such that the lens was the limiting factor of the image. If you cropped the 28mm image to the field of view of the 200mm image, would they look the same? Or would you still see the difference in perspective of the lenses?

wiltw · Jul 22, 2020

thuggins said:
That's pretty much my question. What is the relationship?

It appears the nonlinearity comes in once you get into wide angle lenses. Zuiko lenses show a linear relationship from 50mm to 400mm, with the angle of view halved with each doubling of the focal length. But this does not hold when going down to 24mm, which is substantially less than twice the 50mm angle of view.

I wonder if this is related to the relation between the focal length, perspective compression and cropping, that I've kicked around for quite a while. For 35mm, a 28mm lens is fairly wide and a 200mm lens is fairly long. There is a very obvious compression in the perspective as one goes from the 28mm to 200mm. But assume you had a "perfect" film with no grain and infinite resolution, such that the lens was the limiting factor of the image. If you cropped the 28mm image to the field of view of the 200mm image, would they look the same? Or would you still see the difference in perspective of the lenses?

Consider this

12.5mm lens on 135 format sees 87.66 degrees on the short dimension of the film
25mm lens on 135 format sees 51.3 degrees on the short dimension of the film
50mm lens on 135 format sees 26.99 degrees on the short dimension of the film
100mm llens on 135 format sees 13.69 degrees on the short dimension of the film
200mm llens on 135 format sees 6.87 degrees on the short dimension of the film
400mm llens on 135 format sees 3.44 degrees on the short dimension of the film

the focal length progression in that series is a doubling, but the AOV in the series is not always 'half' of the previous lens, as you have noted. To your question, there is NO CHANGE OF PERSPECTIVE when the camera position is not changed. Period. The AOV of the uncropped shots taken with various WA might not be invresely proportional to the FL change, but the camera position is the only thing that changes 'perspective'

reddesert · Jul 22, 2020

For a dimension d (whether short side, long side, or diagonal), angle of view = 2 * arctangent (d/2 / focal length).
Equivalently, d/2 / focal length = tangent(angle of view /2).
This iswhere the non-linearity comes from. It's close to linear for small angles (long lenses).

The diagonal of "6x9" (really 2.25 x 3.25") is about 100mm, this explains some of the discrepancy in the first post.

wiltw · Jul 22, 2020

reddesert said:
For a dimension d (whether short side, long side, or diagonal), angle of view = 2 * arctangent (d/2 / focal length).
Equivalently, d/2 / focal length = tangent(angle of view /2).
This iswhere the non-linearity comes from. It's close to linear for small angles (long lenses).

The diagonal of "6x9" (really 2.25 x 3.25") is about 100mm, this explains some of the discrepancy in the first post.

To turn the math into something understandable for a mere mortal who cannot infer what is happening...

Imagine the face of a clock. the angle formed by 12:00 vs 1:00 is identical to the angle formed by 2:00 to 3:00 (360 degrees divided by 12, or 30 degrees. But if you instead consider the HORIZONTAL DISTANCE formed by that angle (30 degrees), the horizontal distance from 12:00 to 1:00 is a greater distance than the horizontal distance from 2:00 to 3:00...the distance change is a 'circular function', as evidenced by the equation using the Tangent function or circular function.

thuggins · Jul 28, 2020

The tangent function explains the non-linearity that comes in with wide lenses. The tangent is essentially linear for small angles but loses this relationship as angles approach 45 degrees.

reddesert said:
The diagonal of "6x9" (really 2.25 x 3.25") is about 100mm, this explains some of the discrepancy in the first post.

As I mentioned previously this is not an issue of nominal vs actual frame size, for multiple reasons. Even if we take 100mm as the "normal" focal length for 6x9 vs the ~108mm calculated from the nominal dimensions, it still does not work out. The 101mm Optar on the Graflex was noticeably narrower than the 40mm Zuiko prime, the 28mm-48mm Zuiko zoom set at 43mm or the Tewes finder set at 43mm.

I believe the culprit is the perspective changes associated with different focal lengths and the fact that an equivalent field of view would only happen at infinity. In order to mark out edge targets, I was framing a scene only about 10' away. Since longer lenses compress perspective, it makes sense that a "long" lens would have a smaller field of view at a finite distance than a "short" lens with the same angle of view on a smaller format.

mmerig · Jul 28, 2020

wiltw said:
To turn the math into something understandable for a mere mortal who cannot infer what is happening...

Imagine the face of a clock. the angle formed by 12:00 vs 1:00 is identical to the angle formed by 2:00 to 3:00 (360 degrees divided by 12, or 30 degrees. But if you instead consider the HORIZONTAL DISTANCE formed by that angle (30 degrees), the horizontal distance from 12:00 to 1:00 is a greater distance than the horizontal distance from 2:00 to 3:00...the distance change is a 'circular function', as evidenced by the equation using the Tangent function or circular function.

This is not a correct analogy.

mmerig · Jul 28, 2020

thuggins said:
The tangent function explains the non-linearity that comes in with wide lenses. The tangent is essentially linear for small angles but loses this relationship as angles approach 45 degrees.

As I mentioned previously this is not an issue of nominal vs actual frame size, for multiple reasons. Even if we take 100mm as the "normal" focal length for 6x9 vs the ~108mm calculated from the nominal dimensions, it still does not work out. The 101mm Optar on the Graflex was noticeably narrower than the 40mm Zuiko prime, the 28mm-48mm Zuiko zoom set at 43mm or the Tewes finder set at 43mm.

I believe the culprit is the perspective changes associated with different focal lengths and the fact that an equivalent field of view would only happen at infinity. In order to mark out edge targets, I was framing a scene only about 10' away. Since longer lenses compress perspective, it makes sense that a "long" lens would have a smaller field of view at a finite distance than a "short" lens with the same angle of view on a smaller format.

As mentioned in post #8, perspective changes with camera position (where you are standing in the scene), not focal length. Focal length acts as a cropping mechanism.

Here is a graph showing the relationship between film distance (by film format, along the long dimension) and angle of view.

Your measurements make sense, if 4 degrees difference is noticeable. In any event, the 101 mm should give a narrower angle of view than the 40 mm on their respective cameras The angle of view for a 101 mm lens on a 6 by 9 (82 mm on the long side), is 44.2 degrees. The angle of view for a 40 mm lens across 36 mm is 48.5 degrees.

Nodda Duma · Jul 28, 2020

Distortion comes into play as well, btw.

mmerig · Jul 28, 2020

Nodda Duma said:
Distortion comes into play as well, btw.

How much? In well-designed lenses that are not extreme wide angles, especially, could the difference be more than a degree?

Vaughn · Jul 28, 2020

mmerig said:
As mentioned in post #8, perspective changes with camera position (where you are standing in the scene), not focal length. Focal length acts as a cropping mechanism.
...

True when looked from the direction you are looking, but from a different point of view; to capture a specific scene, the image's perspective will change depending on the focal length of the lens chosen. Classic example, if one wants a head and shoulder portrait, each focal length lens chosen will present a different perspective to the image. All much of a muchness, as an Aussie I was once married to use to say.

People with very wide lenses for their format are just in the habit of sticking their lens very close to things...

wiltw · Jul 29, 2020

Vaughn said:
T, the image's perspective will change depending on the focal length of the lens chosen. Classic example, if one wants a head and shoulder portrait, each focal length lens chosen will present a different perspective to the image.

NOT true!
This linked post is mine, on another forum. In this post, I have ONE camera position, and I take photos with three FL, from 55mm to 97mm to 200mm. Then I crop the images in postprocessing to obtain three shots with similar framed area...and you can see ONE 'perspective' (relationship of the main subject to its surroundings) is presented by ALL THREE FL.

https://photography-on-the.net/forum/showthread.php?p=7667313

The changing 'perspective' is due to the camera position used, to make a head fill the frame the same amount. It is CAMERA POSITION which changes the perspective. This point is proven by another post of mine, all taken with ONE FL, but different distances altering the relative size of my two hands. The perspective' of one hand vs. the other changes due to camera distance, not because I changed my hand positions relative to one another.

https://photography-on-the.net/forum/showthread.php?p=17967126

Nodda Duma · Jul 29, 2020

mmerig said:
How much? In well-designed lenses that are not extreme wide angles, especially, could the difference be more than a degree?

It depends on the lens, and — considering a reasonable 2% distortion of 50 degree FOV is 1.0 degrees — yes.

Deleted member 88956 · Jul 29, 2020

Wondering if I'm reading this thread right as it appears a lot of talk about nothing. The so-called standard focal length is just an approximation of what was determined to be similar to human eye field of view. Still differed from one camera to another in actual production, in 35 mm from 43 to 58 mm FL, for various reasons. No human eye is the same anyways, so it was an approximation no matter how we slice it. Going farther, a lot of photographers, pro and not, expressed their disdain at this approximation. But let's call this normal and leave it at that.

Anything that moves away from that "standard" becomes either wide or tele. Are w trying to figure how to change a lens on another film format in order to "see" the same field? If so, what exactly is the point of trying to figure this out? How does this affect image taking?

Perspective is purely affected by camera to subject distance, irrespective of focal length of the lens, this is as old as photography itself.

While I can see some merit to doing a "COVID exercise" and mathematical photography here, I will say this: hardly have I ever seen much correlation between snapping the same scene with identical view (from same camera position, the apparent premise of this thread) when switching film formats. Even, if I were to shoot the same scene with different cameras at the same time, I still "see" it differently depending on the film size, hence never try (or see reason to) to copy same thing on different film size.

It's empirical photography, unbeknown to me as creative.

Each film size gives physical area to record a scene, hence ought to be used to it's advantage based on image's final destination.

mmerig · Jul 29, 2020

Witold said:
Wondering if I'm reading this thread right as it appears a lot of talk about nothing. The so-called standard focal length is just an approximation of what was determined to be similar to human eye field of view. Still differed from one camera to another in actual production, in 35 mm from 43 to 58 mm FL, for various reasons. No human eye is the same anyways, so it was an approximation no matter how we slice it. Going farther, a lot of photographers, pro and not, expressed their disdain at this approximation. But let's call this normal and leave it at that.

Anything that moves away from that "standard" becomes either wide or tele. Are w trying to figure how to change a lens on another film format in order to "see" the same field? If so, what exactly is the point of trying to figure this out? How does this affect image taking?

Perspective is purely affected by camera to subject distance, irrespective of focal length of the lens, this is as old as photography itself.

While I can see some merit to doing a "COVID exercise" and mathematical photography here, I will say this: hardly have I ever seen much correlation between snapping the same scene with identical view (from same camera position, the apparent premise of this thread) when switching film formats. Even, if I were to shoot the same scene with different cameras at the same time, I still "see" it differently depending on the film size, hence never try (or see reason to) to copy same thing on different film size.

It's empirical photography, unbeknown to me as creative.

Each film size gives physical area to record a scene, hence ought to be used to it's advantage based on image's final destination.

As often happens, a simple question explodes into many directions. The OP's simple question was "The practical intent is to be able to frame the same image in say 35mm and 6x9.", and he was having some trouble figuring it out, using flawed math. Some later posts confused the issue with perspective effects, and some folks had trouble seeing the relationship between focal length and angle of view by looking at an equation. Other details clouded the issue. Most photographers tend to be visual, so I posted a graph, mainly because my earlier post about nonlinearity was not enough. Sure, it's empirical photography, but the main question had an empirical nature, so the responses headed in that direction. Why would anyone want to switch formats and keep the same angle of view? Just now, I can think of three answers to that, and the OP probably had one of them in mind, perhaps the last sentence quoted above.

Vaughn · Jul 29, 2020

wiltw said:
NOT true!

It is true. Focal length will determine camera placement (distance) for any particular image...and as you correctly stated, distance from the subject affects perspective. Applying logic, therefore, focal length determines perspective for any particular image.

Cropping has nothing to do with it. That is all after-the-fact.

mmerig · Jul 29, 2020

Vaughn said:
It is true. Focal length will determine camera placement (distance) for any particular image...and as you correctly stated, distance from the subject affects perspective. Applying logic, therefore, focal length determines perspective for any particular image.

Cropping has nothing to do with it. That is all after-the-fact.

The focal-length-first approach, as explained above, is not the only way to go about framing an image (I rarely if ever do it this way). So the assumption that it determines placement for any particular image is not true, so the logic falls apart there.
Someone may want a geoemtric/compositional arrangement of features in front of them, and move around until they get it. Then. they choose a lens, if necessary, to adjust the angle of view, so cropping is not always after-the-fact.

Vaughn · Jul 29, 2020

Yeah...sitting outside with a cup of tea, I thought that my cropping comment was too specific to the way I work.

In the head and shoulder portrait, I made the assumption that a photographer would want to use as much of the negative area as they could, considering all the other constraints. In this case, one would choose the focal length that gave the perspective one wishes to achieve. If the desired focal length is not in one's bag, but a shorter one is, then cropping can be planned.

I think the same holds for your example. And I agree, in the landscape, once one has chosen the spot to photograph a subject from, perspective is relatively fixed. What causes the photographer choose that spot varies, so my logic does fall apart...my bias. For the first few decades I used one lens per format, usually in the 'normal' range, and habits from that have extended into using multiple lenses. So when I am looking for images, lens focal length is one of my main factors in mentally composing the image and determining where I set up the tripod, if possible. Seems that where I tend to photograph often has limited options on where one can set up large format camera.

Deleted member 88956 · Jul 29, 2020

Vaughn said:
It is true. Focal length will determine camera placement (distance) for any particular image...and as you correctly stated, distance from the subject affects perspective. Applying logic, therefore, focal length determines perspective for any particular image.

Cropping has nothing to do with it. That is all after-the-fact.

I see hardly any logic in what you said. Perspective is nothing but it. And discussion about it is comparing FL to the view shown in the frame. To get the same with different FL, position of the camera must change, inducing new perspective. No need trying to get cute about it.

mmerig · Jul 29, 2020

Vaughn said:
Yeah...sitting outside with a cup of tea, I thought that my cropping comment was too specific to the way I work.

In the head and shoulder portrait, I made the assumption that a photographer would want to use as much of the negative area as they could, considering all the other constraints. In this case, one would choose the focal length that gave the perspective one wishes to achieve. If the desired focal length is not in one's bag, but a shorter one is, then cropping can be planned.

I think the same holds for your example. And I agree, in the landscape, once one has chosen the spot to photograph a subject from, perspective is relatively fixed. What causes the photographer choose that spot varies, so my logic does fall apart...my bias. For the first few decades I used one lens per format, usually in the 'normal' range, and habits from that have extended into using multiple lenses. So when I am looking for images, lens focal length is one of my main factors in mentally composing the image and determining where I set up the tripod, if possible. Seems that where I tend to photograph often has limited options on where one can set up large format camera.

Well, although I disagreed somewhat, I really appreciate learning about how other people work things out. For portraits, focal length has a lot to do with perspective -- most people choose a long-ish lens to allow for a more flattering perspective while filling the frame -- that comes first, then the place to stand comes next, which actually determines the perspective. Of course you know all of this.
This approach could work for landscapes, etc. too, as you explain, and its worth being aware of.

Angle of View

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