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Rumors Panasonic 100-500mm f5-7.1 announcement soon

Yes, it's basically the same.

Initial exposure, yes. But light captured, not. If you crop, you are literally cutting light away. If you would do the process analog, you would actually see it getting darker, when magnifying the picture, if you don't adjust for it. In digital, your computer, camera or whatever, does the adjustment for you in the background.
It would be good to get to some agreement on this (and I accept I may be wrong)...

- Cropping keeps the same image brightness so the exposure remains the same. But you crop away 50% of the pixels (APSC) so the "total light" is halved. This matters if you upscale to the original dimensions because you'll introduce noise.

- Using a TC reduces the image brightness so you need to up the ISO to keep the SS and f-stop the same. This also introduces noise.

I think in principle the end result for a given image size is probably the same in terms of noise, but of course there is also the option to increase the exposure using a TC rather than up the ISO which will get back what you lose in "total light" terms. You don't have this option with cropping of course.

But of course, all this discussion is paying no attention to fancy NR techniques which will potentially level the field.
 
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