The General Image Quality Equation and the Structure of the Modulation Transfer Function
Formal rept., 1 Jan 2004-6 Jan 2005
NAVAL RESEARCH LAB WASHINGTON DC
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Sparse aperture systems, despite their promise of lower weight or larger size, produce images that are noisier and more blurred when compared to images produced by a full aperture. Previous work by Hindsley and Mozurkewich 2001 showed that analysis of the Modulation Transfer Function MTF demonstrated the proportionality of signal-to-noise in a sparse aperture to the fill factor of the aperture. Analysis of the MTF also could enumerate the noise amplification characteristics of particular sparse apertures. However, such image quality metrics as the General Image Quality Equation GIQE also include edge effects, basically due to ringing and reduction in the edge sharpness. Here we report on our analysis of the MTF in order to quantify the relationship between the other terms in the GIQE and the structure of the MTF for high signal-to-noise ratio SNR imaging. We find that, for a fixed amount of optical surface, the image quality will improve with decreasing fill fraction due to an increase in resolution. Apodization of the Wiener Filter used to restore the image, as advocated by Hindsley and Mozurkewich, does not result in an improved image quality use of the traditional unapodized Wiener Filter does improve the image quality. While the GIQE does not appear very sensitive to input SNR so long as SNR is high, the input SNR does limit the ability to successfully reconstruct the image and is the ultimate limiting constraint on reducing the fill fraction. The efficacies of different strategies for tweaking an optical system to improve the GIQE are present. The onset of the failure to satisfactorily reconstruct the edges in an image depends on the particular type of array and MTF, as well as the SNR.
- Numerical Mathematics