I answer over your text:
Very brave!
2) If we crop the wide-angle shot to the same FoV as the telephoto shot, we have effectively changed the focal length of the lens, thus demonstrating the principle that different lenses on different format cameras can have the same effective focal length. I've always argued that it's the effective focal length that counts, not the lens per se.
Incorrect. The focal length of a lens is a physical optical parameter, measured in mm. By cropping you only change the FOV. Different lenses on different formats can have the same FOV, not the same focal length. The term 'effective focal length' is incorrect, there is not such thing. There is just a FOV produced by the combination of a given focal length + sensor format. The term 'equivalent focal length' could be acceptable IMO, even if it doesn't refer to a focal length but to the FOV the lens would produce in a 35mm format.
Guillermo, you will find that the terms "effectively the same" and "equivalent" are used interchangeably in the English language when referring to similarities in the focal length of lenses and other matters. The terms are synonymous. "Effectively the same" means "equivalent". If you disagree, I would describe that as a semantic quibble.
Here's one definition of equivalence from the Encarta Dictionary.
equivalence | equivalency:
The fact of being the same, effectively the same, or interchangeable with something else.
It is understood that two lenses of different 'actual' focal length, but equal 'effective' or 'equivalent' focal length as a result of cropping, are not necessarily equivalent in other respects, such as maximum F/stop, nearest focussing distance, vignetting, MTF response and a whole lot of distortions such as barrel distortion and volume anamorphosis.
It should also be understood, when attempting to compare the perspective in shots taken from the same position with different 'equivalent' focal lengths of lens, one should remove as far as possible such lens distortions from each shot in order not to prejudice the findings. The lens modules in ACR in CS5 do a pretty good job of removing or reducing many distortions, but don't appear to have any effect on volume anamorphosis. To fix
that, one needs the sort of converter and lens modules provided by DXO Labs, or do it manually with Photoshop's free transform and warp.
Having successfully removed such distortions before the comparison of the perspective issue, one cannot prove that perspective is not affected by differences in 'equivalent' focal length, or FoV, by making the equivalent focal length the same in both images through cropping.
That would almost be like claiming that 2 = 5, and to prove it I'll remove 3 from the 5. So, whilst it's not true that 2 = 5, it
is true that 2 = 5 - 3.
The analogy here is that 2 = the shot with the long lens, and 5 = the shot with the shorter lens. The perspective in 2 is not equal to the perspective in 5, but it is equal if you subtract all the additional objects in the wider field of 5.
Your demonstration that FoV does not affect perspective, using the 10mm shot of your microwave oven, with overlay crop marks for 17mm and 22mm equivalence, is merely a tautology. You are basically stating the obvious that 2 (22mm) = 5 (10mm) minus 3 (cropping).
Let's consider again the example of the person with the big nose. I take a portrait with a standard lens that is not flattering but is accurately realistic because the big nose is very apparent. I decide to take another shot from a much greater distance which is more flattering, but I have only the one standard lens. However, my camera is an IQ180 with 60mp, and I reckon with the high quality pixels of the IQ180 I can make a reasonable A3 portrait from a crop consisting of 2 or 3 mp.
Now you are claiming that it makes no difference to the perspective distortion of the nose whether I use a 400mm lens or an 80mm lens to capture the head and shoulders portrait, whereas I'm suggesting that without the cropping and magnification of the 80mm shot, the perspective will not look distorted.
In other words, if the field size (how much of the subject and its surrounding area is visible) is different, then the sense of perspective in the image from the viewpoint of the viewer will be different. The perspective distortion will not be apparent when the subject is surrounded by similarly distorted and distant background objects.
If one crops a distant object, divorces it from its surroundings then enlarges it, the perspective that was seen as being natural for that object when viewed at a distance in a photo taken with a standard lens, will then become unnatural, although more flattering in our example.
There is also an obvious contradiction in your methodology of examing perspective based on identical distance from subject to viewer. In order to determine that the perspective of distant small objects in a narrow field cropped from a wide-angle shot is the same as another shot with a longer lens that encommpasses the same narrow field, you have to break the condition of equal distance. You have to get closer to the small crop to peer at it with a magnifying glass.
In other words, you are 'effectively' saying, "The perspective in shots taken with different 'actual' and different 'equivalent' focal lengths of lenses, from the same position, can be demonstrated as being the same,
provided I convert both images to the same 'equivalent' focal length, and
provided I change my viewing distance to the smaller crop from the wider-angle shot.
What a balls-up! What sort of a scientific method is this!
I'll repeat. The proper way to examine this issue is to eliminate
all variables as far as possible. Keep the distance from the scene the same in all shots. Keep the camera the same and the print sizes the same. Don't 'doctor' the evidence by cropping in post-processing, which is tantamount to 'selection bias'. Don't make different size prints of the images being compared, and don't view such prints from different distances.
If you follow this sound scientific procedure, I think you will find that FoV does indeed influence the sense of perspective in a scene, in the mind of the viewer.
However, divorced from the viewer, the perspective does not change. But that's Alice in Wonderland stuff.
