Hadamard circular masks: high focal depth with high throughput

Area of Science:

• Optics and optical engineering
• Image processing and analysis

Background:

• Optical systems often suffer from reduced performance due to focus errors.
• The Strehl ratio and Modulation Transfer Function (MTF) are key metrics for evaluating image quality.
• Defocus can significantly degrade the MTF, impacting imaging system fidelity.

Purpose of the Study:

• To introduce a novel class of binary masks for enhancing optical system performance.
• To investigate the impact of these masks on Strehl ratio and MTF under defocus conditions.
• To demonstrate the effectiveness of binary masks in mitigating focus-related aberrations.

Main Methods:

• Encoding Hadamard matrix values into binary masks using polar coordinates.
• Analyzing the Strehl ratio as a function of focus error for different mask orders (N).
• Evaluating the MTF's sensitivity to focus error with and without the binary mask (N=16).
• Assessing Fisher information variations with respect to defocus.

Main Results:

• Binary masks increase the Strehl ratio versus focus error by a factor of N (for N ≥ 2).
• The masks achieve the highest possible light throughput.
• For N=16, the binary mask demonstrably reduces the impact of focus error on the MTF.
• The binary mask exhibits low variations in Fisher information with defocus.

Conclusions:

• Binary masks offer a significant improvement in optical system tolerance to focus errors.
• The proposed masks enhance both Strehl ratio and MTF robustness against defocus.
• This approach provides a practical method for improving imaging system performance in the presence of aberrations.