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Consider hypothetical camera with pinhole (in mathematical sense) lens and is sensor, like in below image. Is it the case that the central region of the sensor will receive more light (pixels will be brighter) than the pixels closer to the border?

Will the darkening be proportional to the cosine of the sensor normal and the direction which the light comes from?

Is this phenomenon occurring in digital cameras, is it corrected digitally?

enter image description here

EDIT:

I mostly interested in case of idealized film. Digital cameras exhibit this effect due to light attenuation caused be some participating media. I'm asking about pure geometrical effect like in Lambertian law.

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    $\begingroup$ You will see circles, due to diffraction $\endgroup$ – Milo Lu Mar 24 '17 at 1:46
  • $\begingroup$ What if we assume infinitesimal pinhole and classic optics (no diffraction). $\endgroup$ – ciechowoj Mar 24 '17 at 20:41
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This effect is called vignetting. The cases you talk about are specifically natural and pixel vignetting as explained on the wiki page. Digital cameras compensate these effects, but optical vignetting has to be done in image software for DSLR's with interchangeable lenses. For example if you import an image to Lightroom, there's "lens correction" option, which removes vignetting, distortion and chromatic aberration caused by the lens based on the lens profile.

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  • $\begingroup$ Yeah, I've read that article. But does this phenomenon occur if we consider idealized film? Where there is no shadowing by the pixel sensor edges and no attenuation due to nonzero color filers thickness. I'm asking about phenomenon caused just be geometry. $\endgroup$ – ciechowoj Mar 24 '17 at 20:08
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    $\begingroup$ Yes, that's the "natural vignetting" on the wiki page $\endgroup$ – JarkkoL Mar 27 '17 at 3:26

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