This puzzling business of "35mm lens equivalent"

[Rob C]

Of course it will. The nose remains the same as long as the lens is wide enough to capture it. What changes with the angle of view, as you change the zoom lens to wide, without altering your position, is the perspective, ie. the relationship between the size of the nose and other objects that come into view as you zoom to wide.

Without those other objects, ears, eyes, people standing behind the head, houses, trees etc, there is little sense of perspective. I wouldn't claim there's no sense of perspective. The nose itself, even though divorced from its background, still has a certain perspective, from tip to base.

However, when the nose is placed in a different context of smaller than expected eyes and ears and pathetically small back ground objects, as a result of the zoom moving to wide mode, the perspective of the nose as a whole changes. It then appears as an exceedingly large nose. Got it?

Ray, I think you've just talked yourself in to my corner! Having got there by yourself, then perhaps you'll now accept the basic truth of what some of us have been saying all along?

Thank God for that; the world can rest easy!

Extend your new credo a smidgen: imagine that neither the camera nor lens has moved, but imagine that the very same lens is now covering a different sensor (smaller or, conversely, larger) at the focal plane inside the camera. There you are: exactly the same perspective and depth of field, but a larger or smaller area of the scene covered.

So, using that very same focal length on any size of sensor at the same image size returns an identical image except for what’s cut off by the smaller section of the circle covered. Or, of course, the other way around if you are starting your experiment on a sensor that’s smaller than the one with which you are making the comparison. Naturally, you need to do this with a lens that covers the area of the larger sensor.

Perspective has not been altered at all; in the case of the larger sensor (for the sake of example and clarity, assume a 50mm lens on FF 135) the lens is seen to be whatever it says on the barrel or the box (50mm); when used with the smaller sensor, the lens is the same lens and you can believe the box. But, it is acting in a manner that makes it seem a longer lens (a 75mm on cropped format). But, it really is the same old 50mm can of worms it always was.

But, try to cover the same subject area with both sensors, and you will then have to get closer or further away than when using the other sensor size; that change in distance is what controls perspective, and not the focal length which, as we have just seen, is the same as ever it was. Whew, I feel I'm back in my back row at last! For which delusion, many thanks!

;-)

Rob C

[AlfSollund]

Of course it will. The nose remains the same as long as the lens is wide enough to capture it. What changes with the angle of view, as you change the zoom lens to wide, without altering your position, is the perspective, ie. the relationship between the size of the nose and other objects that come into view as you zoom to wide.

My final post in this, I promise .

Make up your mind, do the nose remains the same or not? Since the nose itself is a object its proportions either stays the same or changes by zooming. I claim that the proportions at the 2-D photo stays the same. This is also called perspective. You claim that its proportions stays the same and do not stay the same.


Please fell free to approach the Nobel institute with groundbreaking news on the physical world view.

[ejmartin]

I don't know why this subject causes so much consternation every time it comes up; it's really just basic geometry.  Well, OK, maybe that's why  

To see the effect of crop factor, focal length, etc, it is useful to ask what one needs to do to take the same image using different formats.  This establishes a baseline; once you know what scaling of each image parameter is required to take the same image, one can examine how the image will differ when the parameters are changed away from those equivalent values.

Imagine taking a 35mm format camera/lens and shrinking everything by a factor of two in every linear dimension:

1.  The sensor is now 18mm x 12 mm, the focal length is half, the aperture is half (so the f/ratio, which is the ratio of focal length/aperture diameter, remains the same).  The angle of view remains the same -- we went wider in focal length but then cropped to a smaller portion of the image, and the two effects exactly compensate.
2.  Because the f/ratio is the same, the physical depth of field of the image is the same.  But the imager is twice smaller; we need the depth of field to be half of what it was in order to get the same image on our shrunken platform.  Therefore we need to open up the aperture, and make the f/ratio half what it was for 35mm, so that the DoF is shrunk in the same proportion to the camera.  In other words, objects at the edge of the DoF are focused a small distance in front or behind the sensor plane, and this distance should be shrunk by the same factor as the camera so that everything about the imaging process is in proportion to the smaller format.
3.  If we want the same degree of motion blur in the image, we want objects that move across some angle relative to the angle of view during the exposure to traverse the same angle; since nothing has changed about the angle of view, using the same shutter speed will result in the same amount of motion blur.
4.  With half the f/ratio and the same shutter speed, the sensor receives four times the light during the exposure; the ISO should be dropped by a factor of four to to keep the raw data in the same range of values (in particular to avoid blowing out highlights).

So, the same photo results on the half-size format using the same shutter speed, half the f/ratio, half the focal length and one quarter the ISO (if available).  Change any one of these parameters, and a different image results.  So for instance if one doesn't halve the f/ratio, the DoF will be deeper and the sensor receives less light, increasing the appearance of noise.  Differences between the formats most often arise at the limits of the available range of parameters; for instance the 35mm format image taken at a base ISO of 100 will have no equivalent in the half-size format unless the camera goes down to ISO 25, which such cameras typically do not.  And sufficiently wide angle, wide aperture lenses may not be available relative to their 35mm equivalents, etc.

[Rob C]

ejmartin -

See two post above: Snap!

Rob C

[John Camp]

One interesting thing about this argument -- okay, maybe it's not *that* interesting -- is that it could have been settled for anyone with a camera and two different lenses in less time than it took to type out some of the contrary arguments.

[Rob C]

John, that would never do; what would be left about which to argue?

Rob C

[Ray]

So, using that very same focal length on any size of sensor at the same image size returns an identical image except for what’s cut off by the smaller section of the circle covered.

There are many images of very different scenes, Rob, which are identical, except for the parts that are different. If there are parts that are different, the scenes are not identical, period. Almost everything has something in common. Even you have a few genes which are identical to mine, but don't worry about it. 

In digital photography, the degree of commonality is far greater. Most digital images, whether portraits, or landscapes with distant mountain views, will have certain components that are identical, such as pixels with the same value, such as R=50, G=150, B=79.

One could argue that a particular 'head-and-shoulders' portrait is identical to a particular mountain scene, except for the parts that are different.

You should have noticed throughout this thread that I've always argued that it's the 'equivalent' or 'effective' focal length that affects perspective. The Wikipedia article quoted by Mouse was correct in the sense that it stated, 'it's not the 'lens per se' that influences perspective'. However, the Wikipedia article should have added, 'It's the effective focal length that has a bearing on perspective'.

If I could attribute a single cause of confusion in this thread, it's the failure to understand that 'effective' focal length is what counts. Nominal focal length (as stated on the lens) does not necessarily have any effect of perspective, but real world effective focal length does.


Ciao!

[mediumcool]

I don't know why this subject causes so much consternation every time it comes up; it's really just basic geometry.  Well, OK, maybe that's why  

To see the effect of crop factor, focal length, etc, it is useful to ask what one needs to do to take the same image using different formats.  This establishes a baseline; once you know what scaling of each image parameter is required to take the same image, one can examine how the image will differ when the parameters are changed away from those equivalent values.

Imagine taking a 35mm format camera/lens and shrinking everything by a factor of two in every linear dimension:

1.  The sensor is now 18mm x 12 mm, the focal length is half, the aperture is half (so the f/ratio, which is the ratio of focal length/aperture diameter, remains the same).  The angle of view remains the same -- we went wider in focal length but then cropped to a smaller portion of the image, and the two effects exactly compensate.
2.  Because the f/ratio is the same, the physical depth of field of the image is the same.  But the imager is twice smaller; we need the depth of field to be half of what it was in order to get the same image on our shrunken platform.  Therefore we need to open up the aperture, and make the f/ratio half what it was for 35mm, so that the DoF is shrunk in the same proportion to the camera.  In other words, objects at the edge of the DoF are focused a small distance in front or behind the sensor plane, and this distance should be shrunk by the same factor as the camera so that everything about the imaging process is in proportion to the smaller format.
3.  If we want the same degree of motion blur in the image, we want objects that move across some angle relative to the angle of view during the exposure to traverse the same angle; since nothing has changed about the angle of view, using the same shutter speed will result in the same amount of motion blur.
4.  With half the f/ratio and the same shutter speed, the sensor receives four times the light during the exposure; the ISO should be dropped by a factor of four to to keep the raw data in the same range of values (in particular to avoid blowing out highlights).

So, the same photo results on the half-size format using the same shutter speed, half the f/ratio, half the focal length and one quarter the ISO (if available).  Change any one of these parameters, and a different image results.  So for instance if one doesn't halve the f/ratio, the DoF will be deeper and the sensor receives less light, increasing the appearance of noise.  Differences between the formats most often arise at the limits of the available range of parameters; for instance the 35mm format image taken at a base ISO of 100 will have no equivalent in the half-size format unless the camera goes down to ISO 25, which such cameras typically do not.  And sufficiently wide angle, wide aperture lenses may not be available relative to their 35mm equivalents, etc.

I agree that it’s to do with geometry. To bring in aperture size, though, merely confuses the issue, with so many already confused from the outset!

[mediumcool]

I have never read so much crap and confusion.

Perspective is dependant on distance. Period.

Lens focal length, combined with camera imaging area, permit greater or smaller parts of the scene before the camera to be recorded.

And why some posters introduce aperture into this discussion I do not understand.

Geometry may be used to compare lens focal length on different formats; by area, by diagonal or by formats adjusted for aspect ratio. This is the only way, in my view, to consider the subject in a practical, real-world manner.

[Ray]

I agree that it’s to do with geometry. To bring in aperture size, though, merely confuses the issue, with so many already confused from the outset!

The sense of perspective, and the factors that influence it, are many. There's no doubt that DoF contributes to the appearance of perspective.

Consider two scenes of a huge rock against a background of palm trees on a distant shore. One image has the foreground rock in total focus, but the distant shore blurred.

The other image has the foreground rock blurred, but the distant shore as sharp as a tack. Is there really no difference in perspective between the two images?

I get a sense in this thread there's a confusion between the geometricaly theoretical and abstract definition of perspective, and the 'real-world' experience and perception of perspective using our very round eyeballs.

It seems that some people will stick to the abstract, geometrical definition of perspective come what may. Maybe it's a type of religion.

[j-land]

You're close, but a more accurate statement would be: "Perspective is dependent only on the relative position in 3-dimensional space between the observer and subject" You can move spherically around the subject and always be the same distance from it, but the perspective between you and the subject will change (assuming only you, the observer is moving), so more variables than distance alone are needed to define perspective.

If you are Ray, who is swinging his camera around, he should be swinging it around the nodal point of his lens, so that the points in the 3-dimensional scene retain their relative positions when they hit his sensor in his many images taken for stitching. The "stretching" of objects towards the periphery of the image are simply the result of "projection" onto a flat imaging plane, but "perspective" or relative position of points within the scene translated to the imaging surface will remain the same. This is what will allow him to stitch the images together later, stretching and compressing them to match up the points in different images and form various types of "projections" - i.e. pretending that his sensor was spherical or his lens was not rectilinear, and so on.

I have never read so much crap and confusion.

Perspective is dependant on distance. Period.

Lens focal length, combined with camera imaging area, permit greater or smaller parts of the scene before the camera to be recorded.

And why some posters introduce aperture into this discussion I do not understand.

Geometry may be used to compare lens focal length on different formats; by area, by diagonal or by formats adjusted for aspect ratio. This is the only way, in my view, to consider the subject in a practical, real-world manner.

[j-land]

The sense of perspective, and the factors that influence it, are many. There's no doubt that DoF contributes to the appearance of perspective.

Consider two scenes of a huge rock against a background of palm trees on a distant shore. One image has the foreground rock in total focus, but the distant shore blurred.

The other image has the foreground rock blurred, but the distant shore as sharp as a tack. Is there really no difference in perspective between the two images?

I get a sense in this thread there's a confusion between the geometricaly theoretical and abstract definition of perspective, and the 'real-world' experience and perception of perspective using our very round eyeballs.

It seems that some people will stick to the abstract, geometrical definition of perspective come what may. Maybe it's a type of religion.

Ha, ha, well, the perspective will change a bit if you refocus your lens  . Far from being "religion", the geometrical definition of perspective is very important, as it relates to the design of imaging devices, software and production of images at various times during the past millenium. Your "sense" of perspective is subjective and is itself a perspective on perspective, so to speak, so I wouldn't expect everyone to have the same opinion and lively discussion should ensue. Whenever the subject of perspective comes up, though, a lot of misconceptions about the math stuff get thrown around and bog down the discussion about the subjective. False statements about the objective don't make for good arguments about the subjective, IMO.

[BJL]

I have never read so much crap and confusion.

You must be new around here!

Against my better judgement, let me give a brief summary of what people like me mean when they say that perspective depends on distance only, and does not change in the way that some people fear when using a smaller format and proportionately shorter focal length.

If you take several photographs of the same subject from the same position (with all the subjects in the same positions too!), each photograph using a combination of focal length and format size that records the same field of view, then the relationships of size and position between objects in the scene will be the same, even if the focal lengths are very different.

(And for extra credit, if the effective aperture diameter (focal length divided by aperture ratio) are equal, then out--of-focus effects will be very close to equal, deviating only in some extremes like for objects that are very close to the camera --- that enters the other even more hotly debated part of "equivalency", or "when and how can I reproduce in one format the compositional details that I know how to achieve in another format?")


Using different definitions of the terms involved can of course change the truth of a statement by changing its meaning, so I wanted to clarify what people mean when they talk about perspective depending on distance, not focal length.

[ejmartin]

And why some posters introduce aperture into this discussion I do not understand.

Forgive me, but it seemed that much of the to and fro seemed to revolve around whether different formats took different images.  If one establishes what shooting parameters in two different formats take the same image, then that question is answered, and one can move on to the next bone of contention.  In particular, it shows that cameras with different formats can achieve images with the same perspective when the image is taken from the same point.*

Since aperture is part of the answer to that question, I included it in the discussion.

* Unless, as BJL states, there are objects so close to the lens that it substantially affects the ray paths that make up the images in the two formats.  When the subject distance is much larger than the entrance pupil of the lens, that is not an issue; otherwise it might be.

[Eric Myrvaagnes]

One interesting thing about this argument -- okay, maybe it's not *that* interesting -- is that it could have been settled for anyone with a camera and two different lenses in less time than it took to type out some of the contrary arguments.

Indeed. It reminds me of a scene from the Sesame Street kid's TV program of many years ago. The two-headed monster was arguing with itself about why it was so cold in the room (the windows and dorrs were all open and snow was flying in). But eventually the two heads came up with the brilliant idea of cooperating, and once they did, they figured out that they should close the windows and doors.

 

Eric

[Ray]

One interesting thing about this argument -- okay, maybe it's not *that* interesting -- is that it could have been settled for anyone with a camera and two different lenses in less time than it took to type out some of the contrary arguments.

Not necessarily, John. After performing the required experiments with different lenses, the results have to be interpreted. It's frequently the case that the same data can be interpreted in different ways. This is a very common problem in science.

Having carried out such experiments myself many times, there's is no confusion in my mind about perspective. I will summarise my findings.

The conditions for identical perspective in two or more photographic images of the same scene are dependent primarily on 3 factors.

(1) Equal distance to the same subject.

(2) Use of equal, or effectively equal (or equivalent), focal length of lenses.

(3) Use of appropriate settings on each lens to ensure equal DoF and equal focussing.

If one changes any one of those 3 factors, one will change to some degree the sense of perspective that the viewer of the photographs will experience. By viewer I mean a subjective human being, rather than a robot that has been programmed to see only the parts that two or more images have in common.

I say that these are the primary factors, but I believe there are other perhaps more subtle factors such as light, shade, color and contrast which can affect our sense of perspective.

This issue is noted in the following article at: http://csmt.uchicago.edu/glossary2004/perspective.htm

Leonardo da Vinci, writing soon after the invention of scientific perspective, dismissed it as perspectiva accidentalis, and in his work Trattora della Pittura noted the distortive effects of perspective in wide angles and the various visual manipulations and elisions that occur from arbitrarily moving the constructed vanishing point in a painting. Leonardo encouraged painters instead to focus on parallel developments in aerial perspective – gradations in color, shadow, and texture to denote three-dimensional relations.

Elsewhere in the article the differences between the linear perspective of photography and our own vision are also addressed as follows:

This discrepancy between camera and physical eye is accounted for in part by the fact that in our eyes, light projects not onto a flat surface, but the curved inner surface of our eyeballs. Furthermore, a large portion of our perception comes from having two eyes that can triangulate relative depth (known as stereopsis, which is a form of parallax), and the ability to move our heads to accrete multiple views of a single object.

Parallels exist between the functioning of our vision and photography or linear perspective, but because our vision exists not only in the light that enters our eyes, but also the passage of time, and the interweaving of binocular pictures of the world by our brains in conjunction with our mental image of what we expect to see, the parallel becomes problematic. Artistic practice that developed contemporaneously with photography, such as impressionism and cubism, in many ways reflects this difference.