Showing papers on "Zernike polynomials published in 2022"
TL;DR: In this paper, a monocular vision-based method is investigated to measure the plane motion, which can get the displacement and angle as well as orbit simultaneously by using the Zernike moment method with sub-pixel accuracy and decoupling model.
13 citations
TL;DR: In this paper , a compact optical-electronic module based on multi-layered diffractive neural networks printed on imaging sensors is proposed to directly retrieve Zernike-based pupil phase distributions from an incident point spread function.
Abstract: Retrieving the pupil phase of a beam path is a central problem for optical systems across scales, from telescopes, where the phase information allows for aberration correction, to the imaging of near-transparent biological samples in phase contrast microscopy. Current phase retrieval schemes rely on complex digital algorithms that process data acquired from precise wavefront sensors, reconstructing the optical phase information at great expense of computational resources. Here, we present a compact optical-electronic module based on multi-layered diffractive neural networks printed on imaging sensors, capable of directly retrieving Zernike-based pupil phase distributions from an incident point spread function. We demonstrate this concept numerically and experimentally, showing the direct pupil phase retrieval of superpositions of the first 14 Zernike polynomials. The integrability of the diffractive elements with CMOS sensors shows the potential for the direct extraction of the pupil phase information from a detector module without additional digital post-processing.
11 citations
TL;DR: The mean lag of accommodation in emmetropes is approximately equal to the previously reported depth of focus, and accommodation lag increased with the accommodation stimulus, but only for methods using a fixed small pupil diameter.
11 citations
TL;DR: In this article , a sparse Zernike fitting method was introduced for LAS tomography, where the temperature in real physical reality is smoothly distributed and the distributions of total absorbance were sparsely fit as finite Zernke polynomials, and the coefficients were mostly zero or about zero.
Abstract: Laser absorption spectroscopy (LAS) tomography yields cross-sectional images of flame temperature and gas molar concentration in combustions. The total laser absorbance of a specific gas, such as water vapor at each point in the region of interest, was obtained from local normalized second harmonics on limited detectors. These detectors restrict the spatial resolution during image reconstructions through typical iterative methods. A sparse Zernike fitting method was introduced for LAS tomography, as the temperature in real physical reality is smoothly distributed. The distributions of total absorbance were sparsely fit as finite Zernike polynomials, and the coefficients were mostly zero or about zero. The number of coefficients was much smaller than that of pixels, i.e., unknowns in iterative methods. The underdetermined inverse problem was effectively alleviated, and a higher spatial resolution was achieved. A fast convergence and effective method for optimal step selection was also introduced for the iterative solution of the sparse model. The effectiveness of the proposed method was validated by both simulated and experimental data for temperature and concentration imaging. Performance comparisons were made with the typical iterative methods, such as SART and Landweber methods; temporal variations of reconstructed distributions for dynamical flames were captured with higher signal-to-noise ratios. Both the fundamental frequencies of 8.797 Hz without acoustic excitation and 12.7 Hz in the case of 150-Hz excitation were successfully captured, and tomographic images agreed well with the dynamical flame evolutions.
7 citations
TL;DR: In this paper , an adaptive weighted quaternion Zernike moments (AWQZM) method was proposed, which can adaptively set weights for each pixel in the neighborhood, which not only can flexibly search for homogeneous regions of HSIs, but also can strengthen the similarity of pixels from the same class and the distinctiveness of pixels of different classes.
Abstract: Hyperspectral image classification (HSI) has been widely used in many fields. However, image noise, atmospheric conditions, material distribution and other factors seriously degrade the classification accuracy of HSIs. To alleviate these issues, a new approach, namely adaptive weighted quaternion Zernike moments (AWQZM), is proposed, which extracts effective spatial-spectral features for pixels in HSI classification. The main contributions and novelties of the method are as follows: 1) the AWQZM can adaptively set weights for each pixel in the neighborhood, which not only can flexibly search for homogeneous regions of HSIs, but also can strengthen the similarity of pixels from the same class and the distinctiveness of pixels from different classes; 2) the AWQZM can be constructed in a small subset of bands through a grouping strategy, thereby reducing the computational complexity; and 3) the introduction of quaternions can preserve the spatial correlation among bands and reduce the loss of data information, and the use of quaternion phase information makes the extracted features more informative and discriminative. Moreover, the spectral features and spatial features are combined to achieve better HSI classification results. Experimental results on three benchmark data sets demonstrate that the proposed approach achieves better classification performance than other related approaches.
6 citations
TL;DR: Zhang et al. as mentioned in this paper proposed a theoretical method for determining the optimal defocus distance (OPDD) according to AO system parameters instead of numerous tests, and the correction accuracy at the theoretical OPDD is no less than 98% of the highest accuracy in experiments.
6 citations
13 Jun 2022
TL;DR: In this article , the effect of mask absorber properties (n, k, bias, bias and target size) on best focus shifts was investigated. But, the authors focused on lines and spaces with pitch = 5× target size and presented a correlation between the BF shifts and Zernike phase offset.
Abstract: We investigate the induced best focus shifts by the mask absorber. The effect of n, k, bias and target size on BF shifts is studied. We consider lines and spaces with pitch = 5× target size. We present a correlation between the BF shifts and Zernike phase offset and the fourth-order Zernike coefficient that represents defocus. When no mitigation strategies are applied, low n absorber materials can show stronger BF shifts and stronger phase variation versus target size. The knowledge gained from this study will help to identify combinations of absorber properties (n, k, thickness) and biasing strategies, which provide high NILS, and threshold to size and enable proper focus control.
6 citations
TL;DR: This work proposes a method that combines deep learning and Zernike moment algorithms, which provides a new method for the automatic detection of damaged insulators in catenary and even other scenarios.
Abstract: The intelligent damage detection of catenary insulators is one of the key steps in maintaining the safe and stable operation of railway traction power supply systems. However, traditional deep learning algorithms need to train a large number of images with damage features, which are hard to obtain; and feature-matching algorithms have limitations in anti-complex background interference, affecting the accuracy of damage detection. The current work proposes a method that combines deep learning and Zernike moment algorithms. The Mask R-CNN algorithm is firstly used to identify the catenary insulators to realize the region proposal of the insulators. After image preprocessing, the Zernike moment algorithm is used to replace the existing Hu moment algorithm to extract more detailed insulator contour features, then the similarity value and its standard deviation are further calculated, so as to complete the damage detection of the catenary insulator. The experimental results show that the mean average precision of insulator identification can reach 96.4%, and the Zernike moment algorithm has an accuracy of 93.36% in judging the damage of insulators. Compared with the existing Hu moment algorithm, the accuracy is increased by 10.94%, which provides a new method for the automatic detection of damaged insulators in catenary and even other scenarios.
5 citations
TL;DR: In this paper , a novel approach using deep learning-assisted wavefront correction in beam rotation holographic tomography to acquire three-dimensional images of native biological cell samples is described, where a Res-Unet scheme is developed to segment the cell region from its background aberration and a deep regression network for the representation of the aberration on Zernike orthonormal basis.
5 citations
TL;DR: Wang et al. as discussed by the authors proposed a novel approach by eliminating GLCM based features with an improved local Zernike moment and color components of intensity, which is clubbed with the orientation based features extracted from angle co-occurrence matrices (ACMs) to model the background.
5 citations
TL;DR: In this paper , a PD diagnosis method of gas-insulated switchgear (GIS) based on the Zernike moment and improved support vector machine (SVM) is proposed.
TL;DR: Wang et al. as discussed by the authors used the nonlinear fitting ability of deep neural networks to establish the mapping relationship between Zernike coefficients and focal degraded image, and showed that the optimal network model after training can quickly and efficiently predict the zernike coefficient directly from a single focal degraded images.
Abstract: Aimed at the slow detection speed and low measurement accuracy of wavefront aberration in current wavefront sensorless adaptive optic technology, different convolution neural networks (CNNs) are established to detect the turbulence wavefront, including an ordinary convolutional neural network, a ResNet network, and an EfficientNet-B0 network. By using the nonlinear fitting ability of deep neural networks, the mapping relationship between Zernike coefficients and focal degraded image can be established. The simulation results show that the optimal network model after training can quickly and efficiently predict the Zernike coefficients directly from a single focal degraded image. The root-mean-square errors of the wavefront detection accuracy of the three networks are 0.075λ, 0.058λ, and 0.013λ, and the time consumed for predicting the wavefront from the single degraded image are 2.3, 4.6, and 3.4 ms, respectively. Among the three networks presented, the EfficientNet-B0 CNN has obvious advantages in wavefront detection accuracy and speed under different turbulence intensities than the ordinary CNN and ResNet networks. Compared with the traditional method, the deep learning method has the advantages of high precision and fast speed, without iteration and the local minimum problem, when solving wavefront aberration.
TL;DR: In this article , an analytical expression of the Ronchigram in this area is derived based on the theory of scalar diffraction and incoherent imaging, and the results show that only the object and image grating with infinite diffraction orders can fully satisfy the Van Cittert-Zernike theorem.
Abstract: Ronchi shearing interferometry is a promising technique for in situ wavefront aberration measurement of the projection lens in advanced photolithography systems. The Van Cittert-Zernike theorem has been used to analyze the interference signal of a Ronchi shearing interferometer in the effective interference area (overlapping area of the ±1st diffraction orders produced by the image grating). However, the applicability of this theorem has not been systematically studied. In this work, the analytical expression of the Ronchigram in this area is derived based on the theory of scalar diffraction and incoherent imaging. The results show that only the object and image grating with infinite diffraction orders can fully satisfy the Van Cittert-Zernike theorem. In the finite diffraction orders case, the theorem can be considered approximately applicable in the overlapping area of the ±3rd diffraction orders produced by the image grating. The applicable area extends to the overlapping area of the ±2nd diffraction orders under a shear ratio of less than 1%, which accounts for 97% of the effective interference area. The theoretical analysis has been verified by simulation and fundamental experiments.
TL;DR: An improved architecture that combines the features derived from the whitening transformed Zernike moments computed for each image and CNNs’ last convolutional layer and the library for support vector machine (LIBSVM) has been used for classification.
TL;DR: In this paper , the authors applied ultrafast laser stress figuring (ULSF) to four thin fused silica mirrors to correct them to 10-20 nm RMS over 28 Zernike terms, without significantly affecting higher-frequency errors.
Abstract: Fabricating freeform mirrors relies on accurate optical figuring processes capable of arbitrarily modifying low-spatial frequency height without creating higher-spatial frequency errors. We present a scalable process to accurately figure thin mirrors using stress generated by a focused ultrafast laser. We applied ultrafast laser stress figuring (ULSF) to four thin fused silica mirrors to correct them to 10-20 nm RMS over 28 Zernike terms, in 2-3 iterations, without significantly affecting higher-frequency errors. We measured the mirrors over a month and found that dielectric-coated mirrors were stable but stability of aluminum-coated mirrors was inconclusive. The accuracy and throughput for ULSF is on par with existing deterministic figuring processes, yet ULSF doesn't significantly affect mid-spatial frequency errors, can be applied after mirror coating, and can scale to higher throughput using mature laser processing technologies. ULSF offers new potential to rapidly and accurately shape freeform mirrors.
TL;DR: In this article , the authors presented an FPGA-based closed-loop adaptive optical system with a bimorph deformable mirror for correction of the phase perturbation caused by artificial turbulence.
Abstract: This paper presents a FPGA-based closed-loop adaptive optical system with a bimorph deformable mirror for correction of the phase perturbation caused by artificial turbulence. The system’s operating frequency of about 2000 Hz is, in many cases, sufficient to provide the real-time mode. The results of the correction of the wavefront of laser radiation distorted by the airflow formed in the laboratory conditions with the help of a fan heater are presented. For detailed consideration, the expansion of the wavefront by Zernike polynomials is used with further statistical analysis based on the discrete Fourier transform. The result of the work is an estimation of the correction efficiency of the wavefront distorted by the turbulent phase fluctuations. The ability of the bimorph adaptive mirror to correct for certain aberrations is also determined. As a result, it was concluded that the adaptive bimorph mirrors, together with a fast adaptive optical system based on FPGA, can be used to compensate wavefront distortions caused by atmospheric turbulence in the real-time mode.
TL;DR: In this paper , a synthesis method for the design of large planar array antennas with phase-only control is presented, which is based on the use of Zernike polynomials, as global basis function for the phase, to reduce the number of optimization variables with respect to the total number of elements of the array.
Abstract: A synthesis method for the design of large planar array antennas with phase-only control is here presented. The synthesis is based on the use of Zernike polynomials, as global basis function for the phase, to reduce the number of optimization variables with respect to the number of elements of the array. Invasive weed optimization (IWO) is applied to polynomial coefficients’ optimization to circumvent nonlinearity and local trapping issues typical of phase-only problems. The periodicity of the array factor is exploited to reduce the optimization to a Voronoi cell of the grating-lobes’ lattice and nonuniform meshing is introduced to best adapt the control stations to the beam shape requirements. The technique is applied to the design of shaped beams for continental coverage from geostationary satellites.
TL;DR: In this article , a set of 22 Zernike modes have been written upon a DMD micromirror array operating as a binary amplitude spatial light modulator for atmospheric turbulence emulation.
Abstract: Emulated atmospheric turbulence effects constructed from a set of 22 Zernike modes have been written upon a DMD micromirror array operating as a binary amplitude spatial light modulator. Sequences of aberrated frames with controlled amounts of turbulence have been produced and can be operated at controlled rates that can exceed 1 kHz rates which can be seen in strong turbulence. In this case 400 Hz was chosen and the scintillation levels observed for the same turbulence sequence with single, few and multi-mode fibres at a receiver. Resulting scintillation levels are consistent with standard turbulence models. Increased received intensity and reduced scintillation was observed with larger core fibres and related to aberration-induced focal spot size. Correlation between the received intensity variation and the amplitude variations for individual Zernike modes demonstrates specifically the effect of atmospheric induced beam wander when focusing into a receive fibre. The DMD is thus shown to be able to generate both the necessary frequency content and range of scintillation required for atmospheric emulation.
TL;DR: In this paper , the non-local optical response of a guidedmode-resonator metasurface was exploited for phase contrast imaging with a 0.02π phase accuracy.
Abstract: Phase contrast microscopy has played a central role in the development of modern biology, geology, and nanotechnology. It can visualize the structure of translucent objects that remains hidden in regular optical microscopes. The optical layout of a phase contrast microscope is based on a 4 f image processing setup and has essentially remained unchanged since its invention by Zernike in the early 1930s. Here, we propose a conceptually new approach to phase contrast imaging that harnesses the non-local optical response of a guided-mode-resonator metasurface. We highlight its benefits and demonstrate the imaging of various phase objects, including biological cells, polymeric nanostructures, and transparent metasurfaces. Our results showcase that the addition of this non-local metasurface to a conventional microscope enables quantitative phase contrast imaging with a 0.02π phase accuracy. At a high level, this work adds to the growing body of research aimed at the use of metasurfaces for analog optical computing.
TL;DR: Overall, accommodation affected higher order aberration asymmetrically in different peripheral retinal areas as well as central and peripheral retina up to 23° off-axis.
Abstract: Knowledge of the effect of accommodation on image quality of peripheral retina is crucial for better understanding of the visual system, but only a few studies have been carried out in this area. This study was designed to evaluate the effect of accommodation on higher order aberrations from third to sixth Zernike polynomials in central and peripheral retina up to 23° off-axis. We used a Hartmann–Shack aberrometer to measure Zernike coefficients with both accommodated and non-accommodated eyes of 15 healthy subjects. Each Zernike coefficient, total higher order aberrations, spherical aberrations and astigmatism were compared between accommodated and non-accommodated status. Additionally, aberrations in the central retina were compared with the peripheral retina. Accommodation induced significant changes in the Zernike coefficients of vertical pentafoil C5−5 and secondary vertical tetrafoil C6−4 in central retina, secondary vertical astigmatism C4−2 on 23° of temporal retina, secondary vertical tetrafoil C6−4 and tertiary vertical astigmatism C6−2 on 10° of nasal retina, secondary vertical trefoil C5−3 and secondary vertical tetrafoil C6−4 on 23° of nasal retina, and horizontal tetrafoil C44, and secondary horizontal tetrafoil C64 on 23° of inferior retina (p < 0.05). Total higher order aberration was lower in each retinal area examined with accommodation, but it was statistically significant only on 23° temporal retina and 11.5° and 23° of superior retina (p < 0.05). Spherical aberration decreased with accommodation on 23° temporal retina (p = 0.036). Astigmatism was similar in non-accommodated and accommodated eyes. Overall, accommodation affected higher order aberration (HOA) asymmetrically in different peripheral retinal areas.
15 Aug 2022
TL;DR: In this article , a triple-stage AO (TSAO) system for GMT/GMagAO-X was proposed. But the triple-stage AO architecture is not suitable for large-scale telescopes.
Abstract: The Extremely Large Telescopes will require hundreds of actuators across the pupil for high Strehl in the visible. We envision a triple-stage AO (TSAO) system for GMT/GMagAO-X to achieve this. The first stage is a 4K DM controlled by an IR pyramid wavefront sensor that provides the first order correction. The second stage contains the high-order parallel DM of GMagAO-X that has 21000 actuators and contains an interferometric delay line for phasing of each mirror segment. This stage uses a Zernike wavefront sensor for high-order modes and a Holographic Dispersed Fringe Sensor for segment piston control. Finally, the third stage uses a dedicated 3K dm for non-common path aberration control and the coronagraphic wavefront control by using focal plane wavefront sensing and control. The triple stage architecture has been chosen to create simpler decoupled control loops. This work describes the performance of the proposed triple-stage AO architecture for ExAO with GMagAO-X.
TL;DR: In this paper , a noise robust phase unwrapping algorithm based on the combination of global Zernike polynomials fitting and the wrapped Kalman filter (WKF) is proposed.
TL;DR: In this paper , the first on-sky results of an adaptive optics fed ZWFS on a segmented aperture telescope, W.M. Keck Observatory's Keck II, were presented.
Abstract: The next generation of large ground- and space-based optical telescopes will have segmented primary mirrors. Co-phasing the segments requires a sensitive wavefront sensor capable of measuring phase discontinuities. The Zernike wavefront sensor (ZWFS) is a passive wavefront sensor that has been demonstrated to sense segmented-mirror piston, tip, and tilt with picometer precision in laboratory settings. We present the first on-sky results of an adaptive optics fed ZWFS on a segmented aperture telescope, W.M. Keck Observatory's Keck II. Within the Keck Planet Imager and Characterizer light path, the ZWFS mask operates in the H band using an InGaAs detector (CRED2). We piston segments of the primary mirror by a known amount and measure the mirror's shape using both the ZWFS and a phase retrieval method on data acquired with the facility infrared imager, NIRC2. In the latter case, we employ slightly defocused NIRC2 images and a modified Gerchberg–Saxton phase retrieval algorithm to estimate the applied wavefront error. We find good agreement when comparing the phase retrieval and ZWFS reconstructions, with average measurements of 408 ± 23 and 394 ± 46 nm, respectively, for three segments pistoned by 400 nm of optical path difference (OPD). Applying various OPDs, we find that we are limited to ∼100 nm OPD of applied piston, due to insufficient averaging of the adaptive optics residuals of our observations. We also present simulations of the ZWFS that help to explain the systematic offset observed in the ZWFS reconstructed data.
TL;DR: In this paper , an adaptive method for determining the type and magnitude of aberration in a wide range is proposed on the basis of an optical processing of the analyzed wavefront using a multichannel filter matched to the adjustable Zernike phase functions.
Abstract: An adaptive method for determining the type and magnitude of aberration in a wide range is proposed on the basis of an optical processing of the analyzed wavefront using a multichannel filter matched to the adjustable Zernike phase functions. The approach is based on an adaptive (or step-by-step) compensation of wavefront aberrations based on a dynamically tunable multichannel filter implemented on a spatial light modulator. For adaptive filter adjustment, a set of criteria is proposed that takes into account not only the magnitude of the correlation peak, but also the maximum intensity, compactness, and orientation of the distribution in each diffraction order. The experimental results have shown the efficiency of the proposed approach for detecting wavefront aberrations in a wide range (from 0.1λ to λ).
TL;DR: In this paper , a class of "dark" traps created from the superposition of two out-of-phase Gaussian modes with different waist diameters is introduced, which can trap dark-seeking particles rigidly in three dimensions.
Abstract: The intensity distribution of a holographically-projected optical trap can be tailored to the physical properties of the particles it is intended to trap. Dynamic optimization is especially desirable for manipulating dark-seeking particles that are repelled by conventional optical tweezers, and even more so when dark-seeking particles coexist in the same system as light-seeking particles. We address the need for dexterous manipulation of dark-seeking particles by introducing a class of "dark" traps created from the superposition of two out-of-phase Gaussian modes with different waist diameters. Interference in the difference-of-Gaussians (DoG) trap creates a dark central core that is completely surrounded by light and therefore can trap dark-seeking particles rigidly in three dimensions. DoG traps can be combined with conventional optical tweezers and other types of traps for use in heterogeneous samples. The ideal hologram for a DoG trap being purely real-valued, we introduce a general method based on the Zernike phase-contrast principle to project real-valued holograms with the phase-only diffractive optical elements used in standard holographic optical trapping systems. We demonstrate the capabilities of DoG traps (and Zernike holograms) through experimental studies on high-index, low-index and absorbing colloidal particles dispersed in fluid media.
TL;DR: In this paper , the authors carried out a series of numerical experiments with artificial solar images to investigate the performance of phase diversity for different choices of the relative defocus among the two images, and found a correlation between the amount of defocus needed for optimal restorations and the number of Zernike polynomials employed in the optimization.
Abstract: Phase diversity techniques are widely employed in solar astronomy to evaluate and correct the aberrations stemming from atmospheric turbulences, the telescope, and its instruments. The method uses information provided by a pair of images. One of them is usually focused while the other one is defocused. The amount of defocus to be induced is somehow arbitrary, though. In this work we carry out a series of numerical experiments with artificial solar images to investigate the performance of phase diversity for different choices of the relative defocus among the two images. The experiments allow us to determine the amount of defocus that produces the best wave front restoration when changing: (1) the number of Zernike polynomials of the retrieved and/or incident wave fronts; (2) the signal-to-noise ratio of the images; (3) the amplitude of the incident aberrations; and (4) the observed scene. We find a correlation between the amount of defocus needed for optimal restorations and the number of Zernike polynomials employed in the optimization. Values larger than the typically accepted choice of 1λ (peak to peak) are obtained in most cases.
TL;DR: In this paper , a general auto-shift minimal-step phase-shifting algorithm (AMPA) for arbitrary cavity lengths is presented. And the performance of the developed algorithm is studied under various factors, and its superiority over traditional algorithms is verified.
TL;DR: In this article, the authors proposed a new hybrid framework for improved estimation by combining both the appearance and geometric-based conventional methods to extract local and global features for head pose and gaze estimation.
Abstract: A real-time head pose and gaze estimation (HPGE) algorithm has excellent potential for technological advancements either in human–machine or human–robot interactions. For example, in high-accuracy advent applications such as Driver’s Assistance System (DAS), HPGE plays a crucial role in omitting accidents and road hazards. In this paper, the authors propose a new hybrid framework for improved estimation by combining both the appearance and geometric-based conventional methods to extract local and global features. Therefore, the Zernike moments algorithm has been prominent in extracting rotation, scale, and illumination invariant features. Later, conventional discriminant algorithms were used to classify the head poses and gaze direction. Furthermore, the experiments were performed on standard datasets and real-time images to analyze the accuracy of the proposed algorithm. As a result, the proposed framework has immediately estimated the range of direction changes under different illumination conditions. We obtained an accuracy of ~85%; the average response time was 21.52 and 7.483 ms for estimating head poses and gaze, respectively, independent of illumination, background, and occlusion. The proposed method is promising for future developments of a robust system that is invariant even to blurring conditions and thus reaching much more significant performance enhancement.
TL;DR: In this article , the authors explore the validity of extremely fast best fit polynomial expansion based noise recreation tools that provide a clear picture for which transmit beam perturbations couple most strongly with spacecraft angular jitter into LISA noise.
Abstract: The laser interferometer space antenna (LISA) will open the signal-rich 100 μHz to 1 Hz gravitational wave window. LISA is expected to be limited by acceleration noise in the low frequency range and noise associated with the optical measurement system above a few mHz. Of the latter, apparent length changes due to spacecraft (SC) angular jitter are among the most critical contributors. One of the coupling mechanisms is via wavefront error in the transmitted beam. Utilizing a Zernike polynomial decomposition of such wavefront error, we introduce and explore the validity of extremely fast best fit polynomial expansion based noise recreation tools that provide a clear picture for which transmit beam perturbations couple most strongly with SC jitter into LISA noise.