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Concepts from Optics
The optical quality of an imaging system is limited partly by the quality of its optics. The point spread function (PSF) describes how a column of light is spread out after passing through the optics. The PSF is shown in the first figure below. The bright central region is called the Airy Disc. A cross section of the Airy Disc is shown in the second figure. This function can be approximated as a Gaussian G(x, σ^{2}_{psf}). The effect of jitter motion on image quality can be determined by how it affects the PSF. Lineofsight jitter motion can generally be modeled by as a Gaussian random error with variance σ^{2}_{j}. The effective PSF is given by the convolution of the Gaussian PSF and the Gaussian jitter, which is simply G(x, σ^{2}_{psf} + σ^{2}_{j}). In effect, the jitter motion widens the PSF. The jitter affects the image only during an exposure time of T seconds, so the jitter variance is computed over a window of T seconds.
Point Spread Function with Airy DiscAiry function and Gaussian approximation
