Statistical analysis of achievable resolution in incoherent imaging

Morteza Shahram; Peyman Milanfar

doi:10.1117/12.505150

5 January 2004 Statistical analysis of achievable resolution in incoherent imaging

Morteza Shahram, Peyman Milanfar

Proceedings Volume 5204, Signal and Data Processing of Small Targets 2003; (2004) https://doi.org/10.1117/12.505150
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

The present paper concerns the statistical analysis of limits to achievable resolution in a so-called "diffraction-limited" imaging system. The canonical case study is that of incoherent imaging of two closely-spaced sources of possibly unequal intensities. The objective is to study how far beyond the classical Rayleigh limit of resolution one can reach at a given signal to noise ratio. We consider the definition of resolution limit from a statistical point of view as the ability of the imaging system to distinguish two closely-located sources in presence of additive noise. This problem can be stated in a hypothesis testing framework where the hypotheses consider whether one or two point sources are present. In terms of signal detection/ estimation, this leads to composite detection/estimation problem where a deterministic signal with unknown parameters is being sought. To solve this problem, we use locally optimal statistical tests with respect to a desired range of (small) separations between the point sources. Specifically, we will derive explicit relationships between the minimum detectable distance between two point sources, and the required SNR. For a specific point spread function, the required SNR can be expressed as a function of probabilities of detection and false alarm and the distance between point sources.

Citation Download Citation

Morteza Shahram and Peyman Milanfar "Statistical analysis of achievable resolution in incoherent imaging", Proc. SPIE 5204, Signal and Data Processing of Small Targets 2003, (5 January 2004); https://doi.org/10.1117/12.505150

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