I think it does, yes. Cropping 25% of the center of a 35mm F/2.0, you'd get the equivalent of a 70mm F/4.0, but with only 25% of the pixels obviously.

I expect depth of focus to be different.

Yes, depth of focus will be larger, as signified by the larger f-number.

It will not, I specifically included the F-stops for that reason.

The depth of field is determined by the focus distance and the aperture of the lens. Both remain unchanged.

Note that 35mm F/2.0 is the same aperture as 70mm F/4.0. Both lenses have an aperture of 17.5mm. (35/2.0 == 70/4.0)

You can easily verify this with your favorite zoom lens. If you have an 24-70 F/2.8 available to you, you can verify by taking 2 pictures; one at 35mm F/2.8 and one at 70mm F/5.6. Crop the 35mm one to 25% area (half the width, half the height). Render both images to the same size (print, fill screen, whatever) and see for yourself.

> assuming infinite resolution

this is an assumption that goes against the concept of "f-number" so if one does it, they should not expect to get to anything sensible.

I just meant sensor pixels, because you’re obviously losing those when cropping, but you get the same perspective as from larger focal length (since you’re not moving).

I agree that the images correspond to the same region in object space. Further assumptions on optical resolution don't work well, as the optical resolution depends on the f-number.

The angular resolution depends purely on the aperture diameter, not the f-number. There should be no difference between capturing the image in high resolution, and blowing it up for a lower resolution sensor. All that should be needed is a 200mpx sensor that can output the entire frame in 12mpx, and 12mpx of the central area in full resolution. It's similar to how our eyes work.

I think it's not the same. Changing focal length changes the perspective warping, right? That's why fisheye lenses look crazy, and telephoto lenses "compress" depth. This might be a function of the sensor geometry too, though.

Cropping the centre of a fisheye photo will look the same as a normal or telephoto lens if they are taken at the same distance (the crop will have less resolution of course)

After looking it up, yes you are right, they are the same. I was thinking of changing the distance to subject instead.

Fisheye lenses look crazy because they are deliberately made that way. Rectilinear lenses don't do it.