HW6 - Sensors Section 14.6

[louiseschul]

I suggest expanding the section for statistics of the photoelectric effect (14.6). Here are some ideas:

• It might help to specify that the shot noise is the square root of the variance. The ‘statistical fluctuation in the number of electrons’ could be confusing.

• The text already explains that the Poisson distribution approaches the Gaussian distribution for large lambda. Some additional discussion about the difference between Poisson and Gaussian distributions could be insightful. Specifically you could mention that Poisson describes discrete independent events while Gaussian arises from the aggregate of many small events (and is therefore continuous in the limit). This concept connects to the idea that photons are quantized.

• I would be interested in learning how lambda is related to sensor parameters. It would be nice to include calculations for how the aperture, exposure time, and pixel area affect the distribution. I would be especially interested to see what conditions lead to small lambda vs large lambda and when a Gaussian approximation is appropriate. This could be connected to the visual quality of the resulting image, i.e., SNR increases as the distribution becomes more Gaussian.

• This is an idea that I find interesting but might fit better elsewhere in the book. We talked about the advantages of burst photography in class, but it doesn’t actually improve noise. The sum of Poisson distributions produces a new Poisson distribution with lambda tot = sum(lambda i). This means that for both 10 short exposure images and one long exposure that is 10x longer, lambda tot = 10 * lambda i and so the shot noise is identical. In contrast, read noise is associated with the electronic circuitry and is therefore constant regardless of exposure time. Since burst photography involves 10 separate measurements, the read noise is 10x that of the long exposure image. This means that burst photography can actually increase noise, but the benefit of limiting saturation is worth the tradeoff in high dynamic range situations.