We have applied a combination of blind deconvolution and deep learning to the processing of Shack–Hartmann images. By using the intensity information contained in spot positions, and the fine structure of the separate images created by the lenslets, we have increased the sensitivity and resolution of the sensor over the limit defined by standard processing of spot displacements only. We also have demonstrated the applicability of the method to wavefront sensing using extended objects as a reference.

We investigate the general adjustment of projection-based phase retrieval algorithms for use with saturated data. In the phase retrieval problem, model fidelity of experimental data containing a non-zero background level, fixed pattern noise, or overexposure, often presents a serious obstacle for standard algorithms. Recently, it was shown that overexposure can help to increase the signal-to-noise ratio in AI applications. We present our first results in exploring this direction in the phase retrieval problem, using as an example the Gerchberg-Saxton algorithm with simulated data. The proposed method can find application in microscopy, characterisation of precise optical instruments, and machine vision applications of Industry4.0.

In theory of optical aberrations, an aberrated wavefront is represented by its coefficients in some orthogonal basis, for instance by Zernike polynomials. However, many wavefront measurement techniques implicitly approximate the gradient of the wavefront by the gradients of the basis functions. For a finite number of approximation terms, the transition from a basis to its gradient might introduce an aliasing error. To simplify the measurements, another set of functions, an “optimal basis"with orthogonal gradients, is often introduced, for instance Lukosz-Braat polynomials. This paper first shows that such bases do not necessarily eliminate the aliasing error and secondly considers the problem of finding an alias-free basis on example of second-moment-based indirect wavefront sensing methods. It demonstrates that for these methods any alias-free basis should be formed by functions simultaneously orthogonal in two dot-products and be composed of the eigenfunctions of the Laplace operator. The fitness of such alias-free basis for optical applications is analyzed by means of numerical simulations on typical aberrations occurring in microscopy and astronomy. © 2020 World Scientific Publishing Company.

We present an efficient phase retrieval approach for imaging systems with high numerical aperture based on the vectorial model of the 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 generalization of the method of Hanser et al., based on 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.

A methodology for retrieving the unknown object distribution and point-spread functions (PSFs) from a set of images acquired in the presence of temporal phase aberrations is presented in this paper. The method works by finding optimal complimentary linear filters for multi-frame deconvolution. The algorithm uses undemanding computational operations and few a priori, making it simple, fast and robust even at low signal-to-noise ratios. Results of numerical simulations and experimental tests are given as empirical proof, alongside comparisons with other algorithms found in the literature. © 2017 Optical Society of America.

Wanneer licht zich door een turbulent medium voortplant, produceertzelfs de meest nauwkeurige optische meetapparatuur onscherpeafbeeldingen. Dit effect kan worden gecompenseerd door een combinatievan een golffrontsensor en een deformeerbare spiegel. De laatsteontwikkelingen in hardware en software hebben deze technologietoegankelijk gemaakt, wat ons zowel op extreem kleine als grote schaalgedetailleerde beelden kan bieden.

A model-based wavefront sensorless (WFSless) adaptive optics (AO) system with a 61-element deformable mirror is simulated to correct the imaging of a turbulence-degraded extended object. A fast closed-loop control algorithm, which is based on the linear relation between the mean square of the aberration gradients and the second moment of the image intensity distribution, is used to generate the control signals for the actuators of the deformable mirror (DM). The restoration capability and the convergence rate of the AO system are investigated with different turbulence strength wave-front aberrations. Simulation results show the model-based WFSless AO system can restore those images degraded by different turbulence strengths successfully and obtain the correction very close to the achievable capability of the given DM. Compared with the ideal correction of 61-element DM, the averaged relative error of RMS value is 6%.The convergence rate of AO system is independent of the turbulence strength and only depends on the number of actuators of DM. © 2015 Optical Society of America.