Maximum resolution per lens size

Question

This question is more practical than theoretical, but I am interested in the theoretical considerations as well.

My wife just bought a Samsung S3 phone with a 8 MP image sensor hiding behind a tiny lens. In daylight the pictures come out fine, but it suffers horribly in low-light conditions. Is there a theoretical limit as to how fine an image sensor can be behind a lens of a specific aperture, given a reasonable amount of ambient light and a reasonable shutter speed? Will increasing the sensor resolution beyond this limit decrease the actual resolution (the ability to resolve two points as individual points) of the final image?

Thanks.

Answer 1

The resolution is controlled by diffraction at the smallest part of the lens system. The Wikipedia article on angular resolution goes into this in some detail. To quote the headline from this article, for a camera the spatial resolution at the detector (or film) is given by:

$$ \Delta \ell = 1.22 \frac{f\lambda}{D} $$

where $f$ is the distance from the plane of the lens to the detector, $\lambda$ is the wavelength of the light and $D$ is the camera aperture. Making the pixel size smaller than $ \Delta \ell$ won't do any harm, but it won't make the pictures any sharper.

I don't know if smartphone cameras contain a variable aperture. With conventional cameras larger apertures produce less diffraction so the picture quality should actually improve in low light. However larger apertures expose a larger area of lens and optical aberration dominates the quality. The end result is that there is an optimum aperture below which diffraction dominates and above which optical aberration dominates.

Incidentally, the poor performance at low light probably isn't due to diffraction. I'd guess it's just that the signal to noise ratio of the detected light falls so far the pictures get very noisy.