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Cramer-Rao bound and phase-diversity blind deconvolution performance versus diversity polynomials.

Jean J Dolne¹, Harold B Schall

¹Boeing Company, 6633 Canoga Avenue, MS WB63, P.O. Box 7922, Canoga Park, California 91309, USA. jean.j.dolne@boeing.com

|October 22, 2005

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This study analyzes information theoretic bounds for Zernike coefficients using phase diversity. Defocus diversity can offer higher bounds, and the phase diversity algorithm achieves the Cramer-Rao lower bound (CRLB) for known and unknown objects.

Area of Science:

Optical imaging and signal processing.
Information theory and estimation theory.

Background:

Accurate estimation of Zernike coefficients is crucial for optical system aberration correction.
Phase diversity techniques are employed to estimate phase aberrations.
Information theoretic bounds provide a benchmark for estimation performance.

Purpose of the Study:

To present information theoretic bounds on Zernike coefficient estimation for different phase diversity functions.
To compare the performance of defocus diversity against other diversity functions.
To evaluate the performance of a phase diversity algorithm using simulated images.

Main Methods:

Derivation of information theoretic bounds, specifically the Cramer-Rao lower bound (CRLB).
Simulation of images using various diversity phase functions.

Related Experiment Videos

Evaluation of a phase diversity algorithm's performance against the CRLB.

Main Results:

Defocus diversity can result in a higher CRLB compared to other diversity functions in certain scenarios.
The phase diversity algorithm achieves the CRLB for known objects with extended scenes and defocus diversity.
The algorithm achieves approximately twice the CRLB for unknown objects.

Conclusions:

Defocus diversity is a viable and effective phase diversity function.
The phase diversity algorithm demonstrates near-optimal performance for aberration estimation.
The findings have implications for improving imaging system accuracy and performance.