The rotating point spread function (PSF) is an effective tool with a various applications in the modern optics. In the optical system with the established rotating PSF, a point-like object is imaged as a rotationally asymmetrical diffractive spot and the longitudinal object translation is transformed to the image rotation. The rotating PSF can be implemented to a standard imaging system by a specially designed mask composed of annular apertures with a spiral phase modulation and the resulting rotation effect is achieved by a superposition of generated optical vortices. Obviously, a numerical algorithm enabling evaluation of the PSF angular orientation plays the key role in the digital processing of the detected rotating PSF. The aim of this work is an analysis of selected numerical methods for the rotating point spread function evaluation.
In the phase retrieval applications, the Gerchberg-Saxton (GS) algorithm is widely used for the simplicity of implementation. This iterative process can advantageously be deployed in the combination with a spatial light modulator (SLM) enabling simultaneous correction of optical aberrations. As recently demonstrated, the accuracy and efficiency of the aberration correction using the GS algorithm can be significantly enhanced by a vortex image spot used as the target intensity pattern in the iterative process. Here we present an optimization of the spiral phase modulation incorporated into the GS algorithm.
In recent years, optical microscopy has been enriched by a wide range of modern techniques enabling exploration of volume samples. One of the preferred ways for reaching a depth estimation required in three-dimensional (3D) imaging is based on utilization of optical systems working with a point spread function (PSF) that rotates under defocusing. Here, the method of axial localization of microparticles is examined that is based on the evaluation of the PSF rotation caused by interference of the vortex nondiffracting beams (VNBs). For generation of the VNBs, a special complex mask is used, modulating both amplitude and phase of the spatial spectrum of the specimen. The main attention is focused on examination of the optical performance of the method and analysis of the effects that occur, when the mask is implemented using a spatial light modulator (SLM).
We demonstrate the vortex point spread function (PSF) whose shape and the rotation sensitivity to defocusing can be controlled by a phase-only modulation implemented in the spatial or frequency domains. Rotational effects are studied in detail as a result of the spiral modulation carried out in discrete radial and azimuthal sections with different topological charges. As the main result, a direct connection between properties of the PSF and the parameters of the spiral mask is found and subsequently used for an optimal shaping of the PSF and control of its defocusing rotation rate. Experiments on the PSF rotation verify a good agreement with theoretical predictions and demonstrate potential of the method for applications in microscopy, tracking of particles and 3D imaging.
Spiral phase contrast imaging is one of the modern methods of optical microscopy applicable to edge contrast
enhancement of amplitude and phase samples. The method is based on a spatial spectrum filtering realized by a spiral
phase element at the focal plane of the Fourier lens. In this paper, the results of a paraxial wave model of the spiral
imaging are presented which allow to calculate the point spread function for real parameters of the spiral filtering and to analyze defocusing effects. A particular attention is given to the analysis of the spiral imaging implemented by a phase mask with a finite number of discrete phase levels. As the main result, a defocusing-induced rotation of the point spread function is discovered and analyzed in detail. Theoretical predictions are verified in experiments using a spatial light modulator for generation of the discrete spiral phase mask.