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

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.