Varis Karitans

The performance of the human eye is limited not only by optical factors but also capabilities of signal processing. The maximum spatial frequency that can be reliably processed depends on the sampling rate. If this frequency is exceeded, spatial aliasing occurs. In this study, we investigate the optimum amount of defocus and spherical aberration needed to avoid spatial aliasing. Measurements are carried out using a simple model eye with the optical and geometrical parameters close to those of a living human eye. A checkerboard pattern with the spatial frequency of 60 cycles/degree is used as a stimulus. A deformable mirror was used to control the amount of defocus and spherical aberration from 0 µm to 0.50 µm in steps of 0.05 µm. If the amount of aberrations is low, fringes of aliased signals are visible along the direction 35.5 degrees relative to the vertical edge of the image. This direction is close to the diagonal direction along which the sampling rate is the lowest. When the amount of aberrations reaches 0.45 µm, spatial aliasing is not observed. The results suggest that low amount of ocular aberrations is desired.

In this study, we address the question of whether a waveguide with absorbing sidewalls can be considered pseudo free space and if the free-space transfer function is valid in such a medium. We test this hypothesis by applying a phase retrieval algorithm based on the free-space transfer function. First, optical measurements are carried out to measure the optical properties of a stack of thin films and select the parameters of simulations. Next, the propagation of light in a waveguide was simulated in COMSOL, and the phase of a wave was retrieved in MATLAB. Analysis was performed both for free-space conditions, and for a waveguide with absorbing sidewalls. The cross-correlation between the distributions of intensity under both conditions was about 0.40. The RMS error of the wave retrieved under free-space conditions was 0.378 rad, while that in the case of absorbing sidewalls was 0.323 rad, indicating successful retrieval. The successfully recovered phase of the input wave suggests that a waveguide with absorbing sidewalls can be approximated as pseudo free space and the free-space transfer function may be valid. These results may be used in future studies on how to shorten the phase retrieval of two-dimensional objects.

In the current study, we address the phase retrieval of one-dimensional phase objects from near-field diffraction patterns using the multiple-plane Gerchberg–Saxton algorithm, which is still widely used for phase retrieval. The algorithm was implemented in a low-cost digital signal processor capable of fast Fourier transform using Q15 arithmetic, which is used by the previously mentioned algorithm. We demonstrate similarity between one-dimensional phase objects, i.e., vectors cut out of a phase map of the tertiary spherical aberration retrieved by the multiple-plane Gerchberg–Saxton algorithm, and these vectors are measured with a non-contact profiler. The tertiary spherical aberration was induced by a phase plate fabricated using grayscale lithography. After subtracting the vectors retrieved by the algorithm from those measured with the profiler, the root mean square error decreased, while a corresponding increase in the Strehl ratio was observed. A single vector of size 64 pixels was retrieved in about 2 min. The results suggest that digital signal processors that are capable of one-dimensional FFT and fixed-point arithmetic in Q15 format can successfully retrieve the phase of one-dimensional objects, and they can be used for applications that do not require real-time operation, i.e., analyzing the quality of cylindrical micro-optics.

In many fields of science, it is often impossible to preserve the information about the phase of the electromagnetic field, and only the information about the magnitude is available. This is known as the phase problem. Various algorithms have been proposed to recover the information about phase from intensity measurements. Nowadays, iterative algorithms of phase retrieval have become popular. Many of these algorithms are based on modulating the object under study with several masks and retrieving the missing information about the phase of an object by applying mathematical optimization methods. Several of these algorithms are able to retrieve not only the phase but also the magnitude of the object under study. In this study, we investigate the effect of the range of modulation of a mask on the accuracy of the retrieved magnitude and phase map. We conclude that there is a sharp boundary of the range of modulation separating the successfully retrieved magnitude and phase maps from those retrieved unsuccessfully. A decrease in the range of modulation affects the accuracy of the retrieved magnitude and phase map differently.

We simulate vitreous floaters in a model eye and apply a phase retrieval algorithm to recover the structure of the vitreous floaters. The algorithm requires modulating the object under study by a relatively small number of masks. The modulating masks are generated by a spatial light modulator. The retrieved phase of the vitreous floaters is compared to that measured with a surface profiler. It can be concluded that the phase of the vitreous floaters can be retrieved in presence of speckles, however, the high computational load is one of the most significant drawbacks of the algorithm. In order to apply the proposed method for real-time correction of the vitreous floaters, the speed of the algorithm must be increased and second-order tracking of the vitreous floaters must be ensured.

In the current study, we investigate the effect of uniform white noise, Poisson noise and a constant background on the phase retrieval of pure phase objects. We also study the influence of the aforementioned factors on phase retrieval at different bit depths of intensity measurements. An algorithm called PhaseLift is used for phase retrieval as it requires a small number of modulating masks and can retrieve the phase of an object from sparse intensity measurements of low bit depth. A test object is modulated by eight random masks generated from a single mask and the phase of the object is retrieved from coded diffraction patterns. Different levels of uniform white noise, Poisson noise and constant background are superimposed on the diffraction patterns and the root-mean-square error (RMSE) of the retrieved object is calculated at each level. The results suggest that Poisson noise and a constant background at the same level cause similar RMSE compared to uniform white noise. Lowering the bit depth from 18-bits to 14-bits resulted in the decrease of the RMSE caused by Poisson noise and a constant background. We conclude that the effects of noise and constant background can be reduced by lowering the bit depth.

We investigate experimentally the phase retrieval of a Kolmogorov phase screen from very sparse data by modulating its amplitude with four binary masks and compare the retrieved phase screen to the ground truth measured with a surface profiler. Previously, we have shown in simulations that this kind of modulation can be successfully used for the phase retrieval of a Kolmogorov phase screen. After subtracting the ground truth from the retrieved phase screen, the root-mean-square error decreased from 0.14 µm to 0.10 µm. We conclude that a Kolmogorov phase screen can be recovered using simple modulation and very sparse data.