Phase retrieval based on the vectorial model of point spread function

Abstract

We present an efficient phase retrieval approach for imaging systems with high numerical aperture based on the vectorial model of point spread function. The algorithm is in the class of alternating minimization methods and can be adjusted for applications with either known or unknown amplitude of the field in the pupil. The algorithm outperforms existing solutions for high numerical aperture phase retrieval: (1) the generalisation of the method of Hanser et al. based on the extension of the scalar diffraction theory by representing the out-of-focus diversity applied to the image by a spherical cap and (2) the method of Braat et al. which assumes through the use of extended Nijboer-Zernike expansion the phase to be smooth. The former is limited in terms of accuracy due to model deviations while the latter is of high computational complexity and excludes phase retrieval problems where the phase is discontinuous or sparse. Extensive numerical results demonstrate the efficiency, robustness, and practicability of the proposed algorithm in various practically relevant simulations.

Differentiable model-based adaptive optics for two-photon microscopy

“…The dynamic range could for example be extended by combining multiple fluorescence images recorded with different integration times [31]. Additional improvements in performance are expected from using a model approximation that is more accurate for high numerical aperture objectives than the one used here [32]. Together, such improvements will more accurately reflect the physical setup and aberrations and therefore improve optimization results.…”

Adaptive optics for optical microscopy [Invited]

“…Hanser et al use a scalar model of the PSF which will affect the accuracy for high NA systems. This work has been extended to a vectorial PSF model which reduces the residual wavefront error by a factor of 2 to 3 [ 158 ]. Compared to measurements of the wavefront by a Shack-Hartmann wavefront sensor or inferred through sensorless AO, phase retrieval can provide a much more detailed measurement of the wavefront.…”

Projection methods for high numerical aperture phase retrieval

“…In this section, the algorithms applied to (17) will be indicated by the additional ' + ' sign in their names (for example, RAAR + ) to distinguish with themselves for solving (12). We analyze the performance of the VAM + [56] (equivalently, AP + ), DR + , KM-DR + , HPR + , RAAR + , RRR + and DRAP + algorithms for solving (17). For the same reason as for solving (12), we chose to skip the phase retrieval results of DR + , KM-DR + , HPR + and RRR + for brevity.…”

“…This paper considers the same setting of high-NA phase retrieval as in [56]. For an unknown phase aberration Φ ∈ R n×n , let r d ∈ R n×n + be the measurement of m PSF images I(A, Φ, φ d ) generated by (7) with phase diversities φ d (d = 1, 2, .…”

“…For high-NA optical systems, the vector nature of light cannot be neglected and point-spread-functions (PSFs) are formed according to a more involved imaging formulation [34,42,43,49], which is called the vectorial PSF to be distinguished from the scalar one according to the Fresnel diffraction equation. In contrast to low-NA settings, only few solution algorithms have been proposed for phase retrieval in high-NA settings [9,23,56].…”