A three-dimensional point spread function for phase retrieval and deconvolution.

Area of Science:

• Optics and Photonics
• Image Processing
• Computational Imaging

Background:

• The accurate modeling of the optical point spread function (PSF) is crucial for image deconvolution and phase retrieval.
• Existing methods, such as the extended Nijboer-Zernike approach, offer analytic expressions but can lack flexibility.
• Advanced computational imaging techniques require robust and adaptable PSF formulations.

Purpose of the Study:

• To present a novel formulation of the optical point spread function (PSF).
• To offer a more flexible representation compared to existing analytic methods.
• To demonstrate the efficacy of the proposed formulation in phase retrieval and deconvolution tasks.

Main Methods:

• The formulation is based on a scaled three-dimensional Fourier transform of the focal field distribution.
• It incorporates the expansion of a generalized aperture function.
• A phase diversity algorithm with a regularization strategy was developed and analyzed.

Main Results:

• The proposed PSF formulation provides an equivalent yet more flexible representation.
• The phase diversity algorithm effectively utilizes the new formulation for phase retrieval.
• Deconvolution performance is enhanced by the presented approach, as confirmed by experiments.

Conclusions:

• The novel PSF formulation offers significant advantages in flexibility and applicability.
• The developed phase diversity algorithm demonstrates the practical utility of the formulation.
• The findings validate the effectiveness of the proposed method for advanced optical imaging applications.