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Lensless matched filter: operating principle, sensitivity to spectrum shift, and third-order holographic aberrations.

M J Bage, M P Beddoes

|February 19, 2010

Summary

Synthesizing a Fresnel zone plate into a Vander Lugt matched filter creates a lensless matched filter (LLMF). This LLMF maintains space-invariance and its performance is not degraded by unfocused components.

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Area of Science:

Optical Engineering
Holography
Signal Processing

Background:

Vander Lugt matched filters (MF) are crucial for optical pattern recognition.
Integrating Fresnel zone plates offers potential for lensless filter designs.
Understanding aberrations is key to filter performance.

Purpose of the Study:

To investigate the properties of a lensless matched filter (LLMF) created by synthesizing a Fresnel zone plate within an MF.
To analyze the space-invariance and signal-to-noise ratio (SNR) performance of the LLMF.
To compare holographic aberrations, specifically root-mean-square (RMS) astigmatism, between MF and LLMF.

Main Methods:

Synthesizing a Fresnel zone plate within a Vander Lugt matched filter to create the LLMF.
Analyzing the impact of unfocused output components on the LLMF's SNR.
Simulating LLMF displacement to observe filter and lens component shifts.
Generating computer plots to compare third-order holographic aberrations and RMS astigmatism of MF and LLMF.

Main Results:

The synthesized LLMF exhibits space-invariance concerning vignetting apertures.
Unfocused output components do not practically degrade the LLMF's SNR.
LLMF displacement results in a combined shift of its filter and lens elements.
Computer-generated plots reveal comparisons of third-order holographic aberrations and RMS astigmatism.

Conclusions:

The lensless matched filter (LLMF) offers a viable, space-invariant alternative to traditional matched filters.
LLMFs demonstrate robustness against SNR degradation from unfocused components.
Aberration analysis indicates specific differences in holographic performance between MF and LLMF configurations.