I wrote that the lens was still actually 8mm and f/2.8, and became like something else, as far as the image is concerned when you cropped. IOW, a 2x digital zoom will give the same image as a sensor of the same size with 1/4 the pixels, double the f-number (double the diffraction blur, double the analog DOF, and 1/4 the photons), and double the focal length.
I disagree with part of that- any diffraction is still the same. The number of photons hitting the pixels in a digital zoom is still the same because the pixels don't change size. Using a digital zoom doesn't mean you need four times the exposure time to saturate the pixels in bright light. The f-number is still the same.
This "equivalence" is just a sometimes-convenient model for comparing systems. It does not mean that it isn't also just a 2x crop from a 8/2.8 lens; that's another model. You can't mix and match parameters between models. The "equivalence" model makes it vividly clear how much digital zoom erodes maximum image quality potential, for those who can't appreciate the losses of cropping directly, such as those stuck on "pixel level views" who see no losses in cropping, compared to using the entire frame for the same composition, with the same optics.
No models needed. It doesn't matter where I perform the crop, the image was taken with a certain exposure and aperture.
That's what I meant by "more pixels on subject".
Ok, I understand that.
Are you talking about geometrical clipping from the edges of the sensor with 200mm, or total subject light with the 100mm, or something else?
Nope. You get the same total light, but it is spread over 4 times the area. As the sensor doesn't expand, you are going to only get a portion of the total light on the sensor. Think about your earlier comment "More pixels on subject"- the subject is providing the same illumination. That illumination is spread over more pixels. This is where "1/4 the photons" comes into play, when doubling the focal length.
Is the latter a problem? You would only zoom so far as to not clip part of your desired composition away. There may be some practical reasons to not zoom as tight (in case you need to rotate, or the tracking shifts, or AF is better with that lens when you zoom out).
I never indicated it was a problem, just commenting on the math involved to maintain f/4 from 100 to 200 mm.