Every digital photographer soon discovers that there are three main sources of visible random noise that affect pictures taken in normal conditions: Shot, pixel response non-uniformities (PRNU) and Read noise.[1]
Shot noise (sometimes referred to as Photon Shot Noise or Photon Noise) we learn is ‘inherent in light’; PRNU is per pixel gain variation proportional to light, mainly affecting the brighter portions of our pictures; Read Noise is instead independent of light, introduced by the electronics and visible in the darker shadows. You can read in this earlier post a little more detail on how they interact.
However, shot noise is omnipresent and arguably the dominant source of visible noise in typical captures. This article’s objective is to dig deeper into the sources of Shot Noise that we see in our photographs: is it really ‘inherent in the incoming light’? What about if the incoming light went through clouds or was reflected by some object at the scene? And what happens to the character of the noise as light goes through the lens and is turned into photoelectrons by a pixel’s photodiode?
Fish, dear reader, fish and more fish.
values recorded in the raw data in the center of the image plane in units of Data Numbers per pixel – by a digital camera and lens as a function of absolute spectral radiance 
at the lens – can be estimated as follows:
indicating absolute-referred units and 
the three system Spectral Sensitivity Functions. In this series of articles 
is wavelength by wavelength multiplication (what happens to the spectrum of light as it progresses through the imaging system) and the integral just means the area under each of the three resulting curves (integration is what the pixels do during exposure). Together they represent an inner or dot product. All variables in front of the integral were previously described and can be considered constant for a given photographic setup. 
twice in sequence.
space to a Fast Fourier Transform routine and, presto, it produces MxN numbers representing the amplitude of the PSF on the 
sensing plane. Figure 1a shows a simple case where pupil function 
arrives at the front of the lens. It goes through the lens being partly blocked and distorted by it as it arrives at its virtual back end, the Exit Pupil, we’ll call this blocking/distorting function 
. Other than in very simple cases, the Exit Pupil does not necessarily coincide with a specific physical element or Principal surface.
as shown below (not to scale, the product of the two arrays is element-by-element):
), that is the individual MTFs of the perfect lens PSF, the perfect square pixel and the delta grid; 
represents two dimensional convolution.
here indicating normalization to one at the origin). I used Matlab to generate the examples below but you can easily do the same with a spreadsheet. ![\[ MTF_{2D} = \left|\widehat{ PSF_{lens} }\cdot \widehat{PIX_{ap} }\right|_{pu}\ast\ast\: \delta\widehat{\delta_{pitch}} \]](https://i0.wp.com/www.strollswithmydog.com/wordpress/wp-content/ql-cache/quicklatex.com-3409f065a49bb47fd4618ed595be72fc_l3.png?resize=320%2C37&ssl=1 "Rendered by QuickLaTeX.com")
![\[ DR = \frac{Maximum Signal}{Minimum Signal} \]](https://i0.wp.com/www.strollswithmydog.com/wordpress/wp-content/ql-cache/quicklatex.com-f89166dae7cfbfc1a37b1ef0f536dd7e_l3.png?resize=194%2C41&ssl=1 "Rendered by QuickLaTeX.com")
![\[ DR = log_2(\frac{Maximum Acceptable Signal}{Minimum Acceptable Signal}) \]](https://i0.wp.com/www.strollswithmydog.com/wordpress/wp-content/ql-cache/quicklatex.com-c691db4feaf1e0b8c2cf50cb84b5b7bf_l3.png?resize=321%2C41&ssl=1 "Rendered by QuickLaTeX.com")
the signal in photoelectrons and 
the 
independently of format. Ignoring noise, lenses and aspect ratio for a moment and assuming the same camera gain and number of pixels, they will produce identical raw files. 
. 