Information-theoretic analyses of a birefringent blur filter

Area of Science:

• Optical Engineering
• Information Theory
• Image Processing

Background:

• Undersampled imaging systems often face limitations in information density.
• Birefringent blur filters offer a unique approach to manipulating point-spread functions.
• Optimizing filter design is crucial for enhancing image quality.

Purpose of the Study:

• To perform an information-theoretic analysis of an undersampled imaging system with a birefringent blur filter.
• To determine optimal parameters for the birefringent blur filter to maximize information density.
• To investigate the combined effects of defocus aberration and birefringent blur.

Main Methods:

• Information-theoretic analysis was employed.
• The spacing between point-spread function replicas was systematically varied.
• A comprehensive search across blur and defocus parameters was conducted.

Main Results:

• The optimal spacing for the birefringent blur filter was identified, yielding maximum information density.
• The optimized birefringent filter design outperformed conventional qualitative designs.
• Combined blur and defocus aberrations created local peaks in information density exceeding individual optimizations, particularly at low fill factors.

Conclusions:

• Adjusting birefringent blur filter replica spacing is key to maximizing information density in undersampled systems.
• Synergistic effects of blur and defocus can significantly enhance information density beyond individual component optimization.
• The findings are especially relevant for imaging systems with low photodetector fill factors.