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In current biomedical and environmental detection, multi-modal optical imaging technology is playing an increasingly important role. By utilizing information from dimensions such as spectra and polarization, it reflects the detailed characteristics and material properties of the targets. However, as detection system performance becomes more complex, issues such as aberrations introduced by multilayered lenses, signal attenuation, decreased polarization sensitivity, and latency can no longer be ignored. These factors directly affect the assessment of image details, influencing subsequent analyses. In this paper, we propose a method for designing and optimizing spectrum-splitting filters that considers the wavefront aberration and transmittance of the multi-modal optical imaging system. The method of optimizing coating phases to minimize scalar phase aberrations while maximizing system transmission leads to substantially improved imaging performance. Simulation and experimental results demonstrate that the method can improve the imaging performance. The proposed approach has potential applications in fields such as biomedical field, multi-spectral, remote sensing and microscopy. [ABSTRACT FROM AUTHOR]

We previously proposed that the optical centroid efficiency (OCE) might be a preferred figure-of-merit to the enclosed energy of a rectangular pixel (EOD) for an instrument subject to unpredictable environmental jitter and alignment conditions. Here we follow the same symbols for the corresponding quantities, particularly the width of the pixel as being equal to 2d. Here we analyze the performance of the OCE vs. the EOD for the three Seidel primary aberrations of an optical component: spherical, coma, and astigmatism, plus defocus. We show that the OCE has an approximate U-shape when graphed against the EOD, for the aberrations ranging from 0 to 1.25λ. We conclude that for pixels larger than 2d = 3λF/#, a small pixel will feature better performance when expecting jitter, misalignment, and other environmental and unpredictable conditions. When evaluating the performance of low-aberration instruments in dynamic and unpredictable environments, the choice of the lager pixel 2d = 7λF/# might be advantageous. Its selection will result in the deterioration of image resolution. [ABSTRACT FROM AUTHOR]

(1) Background: Defining the optimum center for laser refractive corrections is difficult, with many of the available approaches having pros and cons. Decentered ablations result in undesirable side effects like halos, glare, monocular diplopia, and a reduction in visual acuity; (2) Methods: The ideal centration in refractive corrections should fulfil three requirements: covering a scotopic pupil; respecting the visual axis; and minimizing tissue removal. The implications of different centration strategies are discussed and shown graphically; (3) Results: Oversized asymmetric offset ablation faces fewer difficulties in registering static cyclotorsion, features less tissue wastage compared to a symmetric offset, and includes a certain amount of coma (and trefoil) in the profile, benefiting eyes with a pupil offset, which typically present with relevant amounts of coma and trefoil corneal aberrations due to decentered optics; (4) Conclusions: There is a need for a flexible choice of centration in refractive procedures to design customized and non-customized treatments optimally. An ideal optical zone covering the pupil with the widest entrance may be as important as a centration reference. [ABSTRACT FROM AUTHOR]

In this paper, we present a laser triangulation sensor to measure the distance between the sensor and an object without contact using a diffraction slit rather than a traditional lens. We show that by replacing the lens with a slit, we can exploit the resulting diffraction pattern to have finer and yet simpler image analysis, yielding better estimation of the distance to the object. To test our hypothesis, we build a precision position table and a laser triangulation sensor, generate large data sets to test different estimation algorithms on various materials, and compare data acquisition using a traditional lens versus using a slit. We show that position estimation when using a slit is both more precise and more accurate than comparable methods using a lens. [ABSTRACT FROM AUTHOR]

A plane-symmetric optical system with a two-dimensional field light source, such as a soft X-ray and vacuum ultraviolet optical system, is widely used for synchrotron radiation source devices, microscopes and so on. Therefore, this paper studied third-order intrinsic aberration modification with second-order accuracy transfer of pupil coordinates and extrinsic aberration of these kinds of optical systems. First, we discuss the extrinsic aberration calculation method and derive the corresponding aberration expressions; in addition, we apply optical geometric relations and the polynomial fitting method to obtain a second-order accuracy transfer relationship expression of the pupil coordinates between adjacent optical surfaces and derived the modification calculation expressions of the intrinsic aberration caused by the above factor. Finally, the third-order intrinsic aberration modification with second-order accuracy transfer of pupil coordinates and extrinsic aberration expressions derived in this paper are applied to calculate ray spot diagrams of two soft X-ray and vacuum ultraviolet optical systems with meridional and sagittal field angle light sources, and these results are compared with those obtained from the ray-tracing software Shadow; this showed that the calculation accuracy of the aberration expressions is sufficient. [ABSTRACT FROM AUTHOR]

This study presents a numerical simulation-based investigation of a MEMS (micro-electromechanical systems)technology-based deformable mirror employing a piezoelectric film for fundus examination in adaptive optics. Compared to the classical equal-area electrode arrangement model, we optimize the electrode array for higher-order aberrations. The optimized model centralizes electrodes around the mirror center, which realizes low-voltage driving with high-accuracy correction. The optimized models exhibited commendable correction abilities, achieving a unidirectional displacement of 5.74 μm with a driven voltage of 15 V. The voltage–displacement relationship demonstrated high linearity at 0.99. Furthermore, the deformable mirror's influence matrix was computed, aligning with the Zernike standard surface shape of the order 1–3. To quantify aberration correction capabilities, fitting residuals for both models were calculated. The results indicate an average removal of 96.8% of aberrations to the human eye. This underscores that the optimized model outperforms the classical model in correcting high-order aberrations. [ABSTRACT FROM AUTHOR]

Fourier ptychographic microscopy, as a computational imaging method, can reconstruct high-resolution images but suffers optical aberration, which affects its imaging quality. For this reason, this paper proposes a network model for simulating the forward imaging process in the Tensorflow framework using samples and coherent transfer functions as the input. The proposed model improves the introduced Wirtinger flow algorithm, retains the central idea, simplifies the calculation process, and optimizes the update through back propagation. In addition, Zernike polynomials are used to accurately estimate aberration. The simulation and experimental results show that this method can effectively improve the accuracy of aberration correction, maintain good correction performance under complex scenes, and reduce the influence of optical aberration on imaging quality. [ABSTRACT FROM AUTHOR]

A freeform off-axis three-mirror anastigmat (TMA) optical system with a large field of view (FOV) can obtain target image information with a larger spatial range and more spatial details, which is a development trend within the realm of space optics. The optical aberration increases exponentially with the FOV, resulting in a significant increase in error sensitivity for large-FOV optical systems. To address this issue, a method for designing optical systems with a large FOV and low error sensitivity is proposed. The FOV is gradually expanded from a small initial value in equal-length increments until it reaches the full FOV. At each step, the error sensitivity is recalculated and controlled to a lesser extent than in the previous step. In this design process, the freeform surface is used to correct the aberration and obtain low error sensitivity. An optical system with a focal length of 1000 mm and an F-number of 10 is used as an example, and the FOV is enlarged from 5° × 1° to 20° × 4°. The design results show that the modulation transfer function (MTF) of the optical system can reach 0.45@50 lp/mm, and the average wavefront aberration is 0.029λ. After four rounds of FOV expansion and error sensitivity optimization, the error sensitivity is reduced by 37.27% compared to the initial system, which verifies the correctness and practicality of the method. [ABSTRACT FROM AUTHOR]

This study proposes a parabolic off-axis reflective optical system design method to reduce the wave aberration of the optical system of a large aperture single star simulator and improve the optical system's imaging quality. Firstly, we determined the design indexes of the optical system of the large aperture single star simulator by analyzing the technical indexes of the star sensitizer and the development status of the single star simulator; secondly, the initial structural parameters of the optical system were calculated based on the theory of primary aberration; then, we carried out the design optimization of the optical system, the image quality evaluation, and the tolerance analysis using Zemax software; finally, the study tested the wave aberration of the optical system by using the four-dimensional interferometer and the standard mirror together. The simulation results of the optical system are as follows: in the entire field of view, the aberration of the optical system is far less than 0.002%, the modulation transfer function (MTF) reaches the diffraction limit, and the maximum wave aberration is 0.0324 λ. The experimental results are as follows: the maximum wave aberration of the optical system is 0.0337 λ, which is less than 1/25 λ, and it meets the requirements of the index. The simulation and experimental results show that the optical system of the large aperture single star simulator designed by this method has good imaging quality and a simple system structure. [ABSTRACT FROM AUTHOR]

This study aimed to evaluate the spherical aberration (SA) in different corneal areas before and after femtosecond laser-assisted in situ keratomileusis (fLASIK) and transepithelial photorefractive keratectomy (tPRK), with the goal of identifying the limitations of and potential improvements in using SA within a 6 mm area. The study included 62 patients who underwent fLASIK and tPRK. Complete eye examinations including keratometry, corneal epithelial thickness, central corneal thickness, and topography were performed preoperatively and postoperatively. Anterior, posterior, and total corneal aberrations were measured preoperatively and three months postoperatively, with pupil diameters ranging from 2 to 8 mm. In the fLASIK group, compared to the preoperative SA, the anterior and total SA increased postoperatively in the 6 and 7 mm areas. In the tPRK group, meanwhile, the anterior and total SA of the 5 mm or larger areas increased postoperatively. An area of 6 mm or larger showed an increase in correlation with the changes in Q value and refractive correction. As the corneal SA and asphericity in the 6 mm zone cannot specifically demonstrate the status of areas smaller than 6 mm or changes in the optical zone after laser refractive surgery, comparison with normal values in various areas of the cornea is necessary. [ABSTRACT FROM AUTHOR]

Aiming at the problem that traditional design methods make it difficult to control the polarization aberration distribution of optical systems quickly and accurately, this study proposes an automatic optimization design method for polarization optical systems based on deep learning. The unsupervised training model based on ray tracing and polarized ray tracing was constructed by learning the reference lens structural feature data from the optical lens library, and the generalization ability of the deep neural network model was improved to achieve the automatic optimization design of the polarized optical system. The design results show that the optical system structure optimized by the network model is close to the reference lens in the full field of view and the full spectrum and that the optical system structure can be designed for different focal length requirements. The success rate of 1 million groups of initial structures designed is better than 96.403%, and the polarization effect of the optical system is effectively controlled. The proposed deep learning approach to optical design provides a new solution for future complex optical systems and also provides an effective way to improve the design accuracy of special optical systems such as polarization optical systems. [ABSTRACT FROM AUTHOR]

The optical quality of an image depends on both the optical properties of the imaging system and the physical properties of the medium the light passes while travelling from the object to the image plane. The computation of the point spread function (PSF) associated to the optical system is often used to assess the image quality. In a non-ideal optical system, the PSF is affected by aberrations that distort the final image. Moreover, in the presence of turbid media, the scattering phenomena spread the light at wide angular distributions that contribute to reduce contrast and sharpness. If the mathematical degradation operator affecting the recorded image is known, the image can be restored through deconvolution methods. In some scenarios, no (or partial) information on the PSF is available. In those cases, blind deconvolution approaches arise as useful solutions for image restoration. In this work, a new blind deconvolution method is proposed to restore images using spherical aberration (SA) and scatter-based kernel filters. The procedure was evaluated in different microscopy images. The results show the capability of the algorithm to detect both degradation coefficients (i.e., SA and scattering) and to restore images without information on the real PSF. [ABSTRACT FROM AUTHOR]

The multi-beam array stitching test system (MASTS) based on the Hartmann principle is employed to measure the aberrations in large-aperture optical systems. As each small-aperture and ideal parallel beam traverses the optical system, it is converged into a spot at the focal plane of the optical system. The centroid position of the spot contains the information about the wavefront slope of the sub-aperture at that specific location in the optical system. Scanning the optical system with this small-aperture beam across the entire aperture of the optical system, we can yield the aberration information to be tested. To mitigate pointing errors induced by scanning motion and accurately obtain the aberration signals of the optical system, nine beams are integrated into a 3 × 3 multi-beam array system, and their directions are aligned to be identical. However, achieving complete alignment in the same direction for all nine beams is a challenging task, resulting in errors due to their pointing differences within the array. This paper introduces an iterative algorithm designed to obtain high-precision multi-beam pointing errors and to reconstruct the wavefront of the optical system under test. This enables a more accurate measurement of wavefront aberrations in the optical system to be tested. Firstly, simulation models were implemented to validate the algorithm's feasibility. Additionally, a scanning optical measurement system with a multi-beam array was developed in our lab, and the iterative algorithm was applied to process our experimental data. The results were then compared with interferometer data, demonstrating that our algorithm is feasible for MASTS to measure aberrations in large-aperture optical systems with high accuracy. [ABSTRACT FROM AUTHOR]

The aspheric surface is a commonly used method to improve the imaging quality of the fisheye lens, but it is difficult to determine the position and initial value. Based on the wave aberration theory of the plane-symmetric optical system, a method of using an aspheric surface to design a fisheye lens is proposed, which can quickly determine the appropriate aspheric surface to improve the imaging performance. First, the wave aberration of each optical surface of the fisheye lens is calculated and its aberration characteristics are analyzed. Then, a numerical evaluation function is reported based on the aberration distribution of the fisheye lens on the image plane. According to the functional relationship between the evaluation function and the aspheric coefficient, the position of the aspheric surface and the initial value of the aspheric coefficient can be calculated. Finally, the adaptive and normalized real-coded genetic algorithm is used as the evaluation function to optimize the fisheye lens using an aspheric surface. The proposed method can provide an effective solution for designing a fisheye lens using an aspheric surface. [ABSTRACT FROM AUTHOR]

Digital holographic microscopy (DHM) is a valuable technique for investigating the optical properties of samples through the measurement of intensity and phase of diffracted beams. However, DHMs are constrained by Lagrange invariance, compromising the spatial bandwidth product (SBP) which relates resolution and field of view. Synthetic aperture DHM (SA-DHM) was introduced to overcome this limitation, but it faces significant challenges such as aberrations in synthesizing the optical information corresponding to the steering angle of incident wave. This paper proposes a novel approach utilizing deep neural networks (DNNs) for compensating aberrations in SA-DHM, extending the compensation scope beyond the numerical aperture (NA) of the objective lens. The method involves training a DNN from diffraction patterns and Zernike coefficients through a circular aperture, enabling effective aberration compensation in the illumination beam. This method makes it possible to estimate aberration coefficients from the only part of the diffracted beam cutoff by the circular aperture mask. With the proposed technique, the simulation results present improved resolution and quality of sample images. The integration of deep neural networks with SA-DHM holds promise for advancing microscopy capabilities and overcoming existing limitations. [ABSTRACT FROM AUTHOR]

A theoretical approach for reducing multiple monochromatic aberrations using a flat metalens doublet is proposed and verified through ray tracing simulations. The theoretical relation between the Abbe sine condition and the generalized Snell's law is revealed in the doublet system. Starting from the Abbe aplanat design, minimization conditions of astigmatism and field curvature are derived. Based on the theory, a metalens doublet is semi-analytically optimized as a compact, practical-level meta-microscope objective lens working for a target wavelength. The proposed approach also reveals how to reduce lateral chromatism for an additional wavelength. The design degree of freedom and fundamental limits of the system are both rigorously analyzed in theory and verified through ray tracing simulations. It is expected that the proposed method will provide unprecedented practical opportunities for the design of advanced compact microscopic imaging or sensing systems. [ABSTRACT FROM AUTHOR]

To address the problem of slit limitation in traditional slit imaging spectrometers, which hampers fast the identification, efficient tracking, and precise avoidance of faint targets in lunar orbit, this article proposes a lenslet-array integral field spectrometer structure that is free of slits, static, and that is fast and efficient for the visible-to-near-infrared wavelength band. Firstly, the field of view segmentation model is analyzed, and the requirement of the telecentric degree of the pre-imaging system is obtained. Secondly, the influence of aberrations, such as spherical aberration and coma distortion on the micro-pupil dispersion model is analyzed. Based on this, the pre-imaging system is designed to meet the requirements of aberration correction and the telecentricity of the system. Finally, the structure of the spectral system is designed, and the integrated system is optimized. The smile of the lenslet-array integral field spectrometer is ±1 nm, and the MTF is greater than 0.7 at 60 lp/mm and close to the diffraction limit. [ABSTRACT FROM AUTHOR]

The projection objective lens holds a pivotal role in lithography, directly influencing imaging system quality and, consequently, the lithography machine's feature dimensions. Optical inspection methods for this lens require advancements in calibrating systematic error and enhancing alignment precision of auxiliary devices, given their impact on calibration accuracy. In the random averaging method, random ball can give rise to additional wavefront aberrations due to misalignment and numerical aperture mismatch. To mitigate these aberrations and enhance the accuracy of systematic error calibration, this paper introduces a random ball residual compensation (RBRC) model. Additionally, when combined with the random averaging technique, it elevates the calibration accuracy of the measured lens's wavefront aberrations. The experimental results underscore the method's effectiveness, accurately determining optical component eccentricities and numerical aperture errors. After eliminating these errors, more accurate values of lens wavefront aberrations are achieved. This research significantly contributes to enhancing error calibration of lithography objective lens systems. [ABSTRACT FROM AUTHOR]

For traditional imaging systems, high imaging quality and system miniaturization are often contradictory. In order to meet the requirements of high imaging quality and system miniaturization, this paper proposes a method to correct the aberration of coherent imaging optical systems. The method is based on the idea of phase recovery and the imaging principle of a coherent imaging system to recover the aberrations at the exit pupil of the system. According to the recovered aberrations, conjugate filters are constructed to correct the image quality in the frequency domain. The imaging quality of the system is improved without changing the original optical path, and the simplicity of the system is guaranteed. To solve the pupil frequency domain aberration more accurately, this paper adopts the dual competition and parallel recombination strategy based on the genetic algorithm and introduces the disaster model. The improved genetic algorithm can effectively restrain the appearance of the "precocity" phenomenon. Finally, the paraxial imaging optical path is simulated and verified by experiments. The results show that, after aberration correction, the image sharpness is improved and the edge information is richer, which verifies the feasibility of the coherent imaging system image quality enhancement method proposed in this paper. [ABSTRACT FROM AUTHOR]

To build a representative 3D finite element model (FEM) for intracorneal ring segment (ICRS) implantation and to investigate localized optical changes induced by different ICRS geometries, a hyperelastic shell FEM was developed to compare the effect of symmetric and progressive asymmetric ICRS designs in a generic healthy and asymmetric keratoconic (KC) cornea. The resulting deformed geometry was assessed in terms of average curvature via a biconic fit, sagittal curvature (K), and optical aberrations via Zernike polynomials. The sagittal curvature map showed a locally restricted flattening interior to the ring (Kmax −11 to −25 dpt) and, in the KC cornea, an additional local steepening on the opposite half of the cornea (Kmax up to +1.9 dpt). Considering the optical aberrations present in the model of the KC cornea, the progressive ICRS corrected vertical coma (−3.42 vs. −3.13 µm); horizontal coma (−0.67 vs. 0.36 µm); and defocus (2.90 vs. 2.75 µm), oblique trefoil (−0.54 vs. −0.08 µm), and oblique secondary astigmatism (0.48 vs. −0.09 µm) aberrations stronger than the symmetric ICRS. Customized ICRS designs inspired by the underlying KC phenotype have the potential to achieve more tailored refractive corrections, particularly in asymmetric keratoconus patterns. [ABSTRACT FROM AUTHOR]

The accommodative response of the human eye is predominantly driven by foveal vision, but reacts also to off-foveal stimuli. Here, we report on monocular accommodation measurements using parafoveal and perifoveal annular stimuli centered around the fovea and extending up to 8° radial eccentricity for young emmetropic and myopic subjects. The stimuli were presented through a sequence of random defocus step changes induced by a pupil-conjugated tunable lens. A Hartmann–Shack wavefront sensor with an infrared beacon was used to measure real-time changes in ocular aberrations up to and including the fourth radial order across a 3 mm pupil at 20 Hz. Our findings show a significant reduction in accommodative response with increased radial eccentricity. [ABSTRACT FROM AUTHOR]

Background: Corneal refractive surgery induces high-order aberrations, specifically spherical aberration (SA). These aberrations can have implications when patients later develop cataracts and require the implantation of multifocal intraocular lenses (MIOLs). MIOLs with asymmetric designs pose challenges in predicting outcomes, particularly in these cases. The aim of this study was to evaluate how different values of SA, resulting from various types of refractive surgeries, affect the optical performance of the FEMTIS Comfort intraocular lens. Methods: The through-focus modulation transfer function (TF-MTF) curve and high-contrast images of tumbling E were used as parameters to assess the optical performance of the MIOL. These parameters were measured using an adaptive optics visual simulator. Results: Increasingly negative values of SA make the MIOL more bifocal, moderating its extended-depth-of-focus characteristic. Conversely, higher positive SA values cause the TF-MTF curve to shift towards positive vergences, leading to worsened distance vision in the +1.00 to +2.00 D range, but improved vision in the +0.50 D to +1.00 D range. Conclusions: Assessing SA in patients prior to implanting MIOLs with asymmetric designs is necessary for predicting outcomes and making informed decisions based on the visual requirements of patients. [ABSTRACT FROM AUTHOR]

A capillary discharge extreme ultraviolet laser is focused and wavefront split at 46.9 nm by a tubular optical element. The reflectivity at 46.9 nm is both simulated and measured to be higher than 90% with a slight optical aberration. The operating principle of the tubular element for focusing and wavefront splitting is discussed. Dense and intense grating-like fringes with a period of ~150 nm are achieved. The method used in this work allows nano-scale processing with extreme ultraviolet laser at single-shot exposure mode. [ABSTRACT FROM AUTHOR]

The impact of intraocular scatter and higher order aberrations (HOAs) on ocular optical quality was investigated. An optical eye model was constructed using the measured ocular aberrations, corneal surfaces, axial length, and scatter fraction, and the impact of HOAs and scatter on modulation transfer functions (MTFs) was studied based on the newly established optical eye model. For uniform intraocular scatter, the monochromatic and polychromatic MTF decreased as the HOAs or scatter fractions increased independently at each spatial frequency, which implied that both were essential for visual quality. In addition, the scatter effect on MTF was more significant for the eye with less HOA. The combined deterioration effect of these two factors on the MTF was less than their summation, suggesting a potential compensatory mechanism between HOAs and scatter. [ABSTRACT FROM AUTHOR]

Ellipticity performance of space telescopes is important for exploration of dark matter. However, traditional on-orbit active optical alignment of space telescopes often takes "minimum wavefront error across the field of view" as the correction goal, and the ellipticity performance after correcting the wave aberration is not optimal. This paper proposes an active optical alignment strategy to achieve optimal ellipticity performance. Based on the framework of nodal aberration theory (NAT), the aberration field distribution corresponding to the optimal full field-of-view ellipticity is determined using global optimization. The degrees of freedom (DOFs) of the secondary mirror and the folded flat mirror are taken as the compensation DOFs to achieve the optimal ellipticity performance. Some valuable insights into aberration field characteristics corresponding to optimal ellipticity performance are presented. This work lays a basis for the correction of ellipticity for complicated optical systems. [ABSTRACT FROM AUTHOR]

Age-related macular degeneration (AMD) causes severe vision impairments, including blindness. An option to improve vision in AMD patients is through intraocular lenses and optics. Among others, implantable miniaturized telescopes, which direct light to healthy lateral regions of the retina, can be highly effective in improving vision in AMD patients. Yet, the quality of the restored vision might be sensitive to the optical transmission and aberrations of the telescope. To shed light on these points, we studied the in vitro optical performance of an implantable miniaturized telescope, namely, the SING IMT™ (Samsara Vision Ltd., Far Hills, NJ, USA) designed to improve vision in patients affected by late-stage AMD. Specifically, we measured the optical transmission in the spectral range 350–750 nm of the implantable telescope with a fiber-optic spectrometer. Wavefront aberrations were studied by measuring the wavefront of a laser beam after passing through the telescope and expanding the measured wavefront into a Zernike polynomial basis. Wavefront concavity indicated that the SING IMT™ behaves as a diverging lens with a focal length of −111 mm. The device exhibited even optical transmission in the whole visible spectrum and effective curvature suitable for retinal images magnification with negligible geometrical aberrations. Optical spectrometry and in vitro wavefront analysis provide evidence supporting the feasibility of miniaturized telescopes as high-quality optical elements and a favorable option for AMD visual impairment treatments. [ABSTRACT FROM AUTHOR]

A prime-focus optical system is a common type of large aperture survey telescope with a small obscuration ratio, high transmittance, and simple structure. As the detection capabilities and search efficiency of the telescope are improved, the aperture of the primary mirror becomes larger. The primary mirror aperture of a high-performance survey telescope has a four-meter scale, and the aperture of the corrector lenses of a corresponding prime-focus optical system can reach a one-meter scale. In this study, optical surface shape changes due to gravity were studied via an integrated optomechanical analysis. The Zernike polynomial was used to characterize the changed optical surface. The influence of optical surface variations on the wavefront and imaging quality of the optical system was analyzed by calculating the optical path differences. From the perspective of optical aberration, the optical properties of meter-level corrector lenses were quantitatively analyzed. The effect of the meter-level corrector lenses on imaging was explained in principle, and the feasibility of this optical scheme was verified. [ABSTRACT FROM AUTHOR]

Due to the relatively low optical power of a liquid lens, it is usually difficult to achieve a large zoom ratio and a high-resolution image simultaneously in an optofluidic zoom imaging system. We propose an electronically controlled optofluidic zoom imaging system combined with deep learning, which achieves a large continuous zoom change and a high-resolution image. The zoom system consists of an optofluidic zoom objective and an image-processing module. The proposed zoom system can achieve a large tunable focal length range from 4.0 mm to 31.3 mm. In the focal length range of 9.4 mm to 18.8 mm, the system can dynamically correct the aberrations by six electrowetting liquid lenses to ensure the image quality. In the focal length range of 4.0–9.4 mm and 18.8–31.3 mm, the optical power of a liquid lens is mainly used to enlarge the zoom ratio, and deep learning enables the proposed zoom system with improved image quality. The zoom ratio of the system reaches 7.8×, and the maximum field of view of the system can reach ~29°. The proposed zoom system has potential applications in camera, telescope and so on. [ABSTRACT FROM AUTHOR]

AOTF calibration is a complex topic that has various aspects. As far as geometric calibration is concerned, it includes not only processing errors and fixing errors in the optical system, but also the error of geometric parameters of crystal (GPC). GPC is the preset input in the optical design and optimization of Zemax, which determines the key parameters, including the spatial resolution, the field of view, and aberration. In particular, the compensation of aberration during the optical design requires accurate values of GPC. However, it is currently considered ideal. Therefore, two calibration methods based on the principle of parallel tangent are proposed: (1) the minimum-central wavelength method; (2) the minimum-frequency method. The deviation of the parallel tangent incident angle calibrated by the two methods is 0.03°. As a result, the tuning curve calculated in theory with the calibrated geometric parameters of AOTF is consistent with the tuning curve measured in practice. [ABSTRACT FROM AUTHOR]

Active optics and aberration correction techniques for sparse aperture segmented mirrors are studied. A finite element model of the sparse aperture segmented mirror was established, and a multi-aperture aberration polynomial was derived. According to the hard spot theorem, a co-phase maintenance method based on the change of the edge sensor position in the conventional mode is derived. And a co-phase maintenance method based on the change of the aberration of the segmented mirror surface without the participation of the edge sensor is proposed. The method can correct aberrations of the segmented mirror surface, which are caused by the rigid body displacement along the horizontal direction of the segments. This method can reduce the RMS of the segmented mirror surface to 2.2 nm. The correction principle of the Warping Harness (WH) technique is derived. For the problems of tedious steps and a small number of target aberrations, the correction method is proposed to directly target the aberrations of the segmented mirrors, which is simple and has a wider range of target aberrations. Using this method, the amplitude of each aberration of the stitched mirror is corrected to below 10 − 4 nm . It is also verified that combining the generalized ridge estimation method and the differential evolution algorithm can effectively solve the correction quantity. Finally, it is verified that the SiC material can effectively improve the adaptability of the segmented mirror to gravity load by reducing the mirror's weight. [ABSTRACT FROM AUTHOR]

In the process of image reconstruction of compressed sensing algorithms, building a measurement matrix related to the parameters of the imaging system is necessary to improve its imaging quality. Additionally, building a compressed ultrafast imaging system based on a streak camera, which includes aberrations in the imaging system, is necessary. However, the aberration coefficient of the streak tube can be obtained only by numerical calculation based on the known internal structure of the streak tube, and it does not apply to a tube with an unknown structure. Based on the Lagrange–Helmholtz relation, which is widely established in electronic optical imaging systems, this study proposes a method to obtain the Petzval image plane of a streak tube by measuring only a single image without considering the internal structure of the streak tube. This method provides a reference for the construction of the measurement matrix in the application of the compressed sensing algorithm; additionally, it provides a test scheme for the performance index of the streak tube after assembly in commercial production to further optimize the assembly process and improve the yield of production. [ABSTRACT FROM AUTHOR]

An integrated optomechanical analysis (IOA) can predict the response of an optomechanical system to temperature, gravity, vibrations, and other local loadings; thus, the normal operation of instruments under special conditions is guaranteed. Zernike polynomials are the most popular for fitting the IOA-derived mechanical deformation data. By solving the Zernike coefficients of all deformed optical surfaces, the relationship between aberrations and deformations can be further revealed. The process of IOA is summarized in this article. The principles of four primary Zernike coefficient-solving algorithms (CSAs) were expounded, and the corresponding applications are reviewed in detail, including the least squares method, the Gram–Schmidt orthogonalized method, the Householder transformation, and singular value decomposition (SVD). Artificial neural networks (ANNs) trained for solving a similar overdetermined set of equations are also discussed; an innovative Zernike CSA based on a one-dimensional convolutional neural network (1D-CNN) was proposed, emphasizing its potential for Zernike CSA. The feasibility of the neural network method was verified by conducting experiments on the primary mirror of the front reflection system of a space camera. This review can provide references for the precise optimization of IOA. [ABSTRACT FROM AUTHOR]

Instead of acquiring the previous aberrations of an optical wavefront with a sensor, wavefront sensor-less (WFSless) adaptive optics (AO) systems compensate for wavefront distortion by optimizing the performance metric directly. The stochastic parallel gradient descent (SPGD) algorithm is pervasively adopted to achieve performance metric optimization. In this work, we incorporate CoolMomentum, a method for stochastic optimization by Langevin dynamics with simulated annealing, into SPGD. Numerical simulations reveal that, compared with the state-of-the-art SPGD variant, the proposed CoolMomentum-SPGD algorithm achieves better convergence speed under various atmospheric turbulence conditions while requiring only two tunable parameters. [ABSTRACT FROM AUTHOR]

Macro vivo fluorescence imaging is becoming more and more important in the medical field. It is also necessary to design the optical design system for the visible light of the NIR-II detector. This paper discusses the design method of the wide spectrum achromatic optical system from visible light to NIR-II. Based on ZEMAX, a wide spectrum zoom system is designed to freely observe experimental targets in the fields of view of 3.1–18.6°. The four components layout was adopted by the wide spectrum zoom system, which is suitable for 8.2 mm (1/2 inch) CCD, with an f-number of 5.0~6.0, zoom range of 25 mm~150 mm, working spectral band of 400 nm~1700 nm, full field MTF ≥ 0.3 at the spatial frequency of 100 lp/mm, and the maximum distortion of ≤±3%. All optical elements adopt the standard spherical, which can correct all kinds of aberrations well and meet each part's basic processing requirements. [ABSTRACT FROM AUTHOR]

In this paper, we present a hybrid refractive-diffractive lens that, when paired with a deep neural network-based image reconstruction, produces high-quality, real-world images with minimal artifacts, reaching a PSNR of 28 dB on the test set. Our diffractive element compensates for the off-axis aberrations of a single refractive element and has reduced chromatic aberrations across the visible light spectrum. We also describe our training set augmentation and novel quality criteria called "false edge level" (FEL), which validates that the neural network produces visually appealing images without artifacts under a wide range of ISO and exposure settings. Our quality criteria (FEL) enabled us to include real scene images without a corresponding ground truth in the training process. [ABSTRACT FROM AUTHOR]

Space-based gravitational wave detection programs, such as the Laser Interferometer Space Antenna (LISA) or Taiji program, obtain gravitational wave signals by measuring the change in the distance between three satellites by laser. The telescope is an important part of the measurement system, and its function is to transmit and receive laser signals. Due to changes in the space environment, the telescope will inevitably introduce additional dynamic aberrations, which will bring optical path errors to the inversion of gravitational wave signals. Taking LISA as an example, to achieve pm-level measurement accuracy at the detection frequency of 0.1 mHz–1 Hz, the stability requirements of the telescope are less than 1 pm/Hz1/2. This paper theoretically deduces the aberration types that affect the telescope's stability and conducts simulation analysis according to the actual phase demodulation method, which verifies the theory's correctness. In addition, using this theory, it can be concluded that under the condition that the total size of the telescope aberration is determined to be stable, reducing the ratio of rotationally symmetric aberrations such as "spherical aberration" and "defocusing" among common aberrations can significantly improve the stability of the telescope. The conclusion guides the optical system design of LISA or Taiji. [ABSTRACT FROM AUTHOR]

This paper proposes a method with an off-axis interferometer and an ensemble deep learning (I-EDL) hologram-classifier to interpret noisy digital holograms captured from the tissues of flawed biological specimens. The holograms are captured by an interferometer, which serves as a digital holographic scanner to scan the tissue with 3D information. The method achieves a high success rate of 99.60% in identifying the specimens through the tissue holograms. It is found that the ensemble deep learning hologram-classifier can effectively adapt to optical aberration coming from dust on mirrors and optical lens aberrations such as the Airy-plaque-like rings out-turn from the lenses in the interferometer. The deep learning network effectively adapts to these irregularities during the training stage and performs well in the later recognition stage without prior optical background compensations. The method does not require an intact sample with a full outline shape of the specimens or the organs to understand the objects' identities. It demonstrates a new paradigm in object identification by ensemble deep learning through a direct wavefront recognition technique. [ABSTRACT FROM AUTHOR]

Adaptive optics (AO) is employed for the continuous measurement and correction of ocular aberrations. Human eye refractive errors (lower-order aberrations such as myopia and astigmatism) are corrected with contact lenses and excimer laser surgery. Under twilight vision conditions, when the pupil of the human eye dilates to 5–7 mm in diameter, higher-order aberrations affect the visual acuity. The combined use of wavefront (WF) technology and AO systems allows the pre-operative evaluation of refractive surgical procedures to compensate for the higher-order optical aberrations of the human eye, guiding the surgeon in choosing the procedure parameters. Here, we report a brief history of AO, starting from the description of the Shack–Hartmann method, which allowed the first in vivo measurement of the eye's wave aberration, the wavefront sensing technologies (WSTs), and their principles. Then, the limitations of the ocular wavefront ascribed to the IOL polymeric materials and design, as well as future perspectives on improving patient vision quality and meeting clinical requests, are described. [ABSTRACT FROM AUTHOR]

Deformable mirrors enable the control of wave fronts for the compensation of aberrations in optical systems and/or for beam scanning. Manufacturers of deformable mirrors typically provide calibration data that encode for the fabrication tolerances among the actuators and mirror segments to support open-loop control with high wave front fidelity and accuracy. We report a calibration method that enables users of the deformable mirrors to measure the response of the mirror itself to validate and improve the calibration data. For this purpose, an imaging off-axis Michelson interferometer was built that allowed measuring the mirror topography with high accuracy and sufficient spatial resolution. By calibrating each actuator over its entire range, the open-loop performance for our deformable mirror was improved. [ABSTRACT FROM AUTHOR]

Studying how to use the coupling characteristics of net aberration fields induced by different perturbation parameters to realize the wave aberration compensation correction of perturbed telescopes is of great significance for the development of active optics. Based on nodal aberration theory, this paper studies the wave aberration compensation correction method of an unobscured off-axis three-mirror telescope. Specifically, first of all, it theoretically analyzes the coupling effects and compensation relationships of net aberration fields induced by different perturbation parameters of the telescope. Furthermore, it establishes wave aberration correction models with the secondary mirror as the compensator and the third mirror as the compensator for the telescope, respectively. In the end, it verifies the two compensation correction models by simulations. The results show that the tolerance of the secondary mirror compensation correction mode (SMCM) to the perturbation parameter threshold is significantly better than that of the third mirror compensation correction model (TMCM). When the introduced perturbation parameter threshold is small, the correction accuracy of the two models for the wave aberrations is equivalent, and both reach the order of 10 − 3 λ (RMS, λ = 632.8 nm). When the perturbation parameter threshold is increased, the correction accuracy of SMCM can still be maintained at the order of 10 − 3 λ but the correction accuracy of TMCM would decrease by an order of magnitude. [ABSTRACT FROM AUTHOR]

It is known that the astigmatic transformation can be used to analyze the topological charge of a vortex beam, which can be implemented by using various optical methods. In this case, in order to form an astigmatic beam pattern suitable for the clear detection of a topological charge, an optical adjustment is often required (changing the lens tilt and/or the detection distance). In this article, we propose to use multi-channel diffractive optical elements (DOEs) for the simultaneous implementation of the astigmatic transformations of various types and levels. Such multi-channel DOEs make it possible to insert several types of astigmatic aberrations of different levels into the analyzed vortex beam simultaneously, and to form a set of aberration-transformed beam patterns in different diffraction orders in one detection plane. The proposed approach greatly simplifies the analysis of the characteristics of a vortex beam based on measurements in the single plane without additional adjustments. In this article, a detailed study of the effect of various types of astigmatic aberrations based on a numerical simulation and experiments was carried out, which confirmed the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Ultra-short laser filamentation has been intensively studied due to its unique optical properties for applications in the field of remote sensing and detection. Although significant progress has been made, the quality of the laser beam still suffers from various optical aberrations during long-range transmission. Astigmatism is a typical off-axis aberration that is often encountered in the off-axis optical systems. An effective method needs to be proposed to suppress the astigmatism of the beam during filamentation. Herein, we numerically investigated the impact of the nonlinear effects on the focusing properties of the astigmatic Gaussian beams in air and obtained similar results in the experiment. As the single pulse energy increases, the maximum on-axis intensity gradually shifted from the sagittal focus to the tangential focus and the foci moved forward simultaneously. Moreover, the astigmatism could be suppressed effectively with the enhancement of the nonlinear effects, that is, the astigmatic difference and the degree of beam distortion were both reduced. Through this approach, the acoustic intensity of the filament (located at the tangential focal point) increased by a factor of 22.8. Our work paves a solid step toward the practical applications of the astigmatism beam as the nonlinear lidar. [ABSTRACT FROM AUTHOR]

Achieving aberration correction can improve the imaging quality of an optical system, and reducing the error sensitivity of system can improve the realizability of the system. In order to obtain an off-axis three-mirror optical system with high image quality and low error sensitivity, a design method is proposed which obtains the initial structure of the three-mirror anastigmatic (TMA) optical system with low error sensitivity through a nondominated sorting genetic algorithm II (NSGA-II). Combining the comprehensive evaluation function of image quality and error sensitivity, this method iteratively selects multiple freeform surface types to determine the combination with the lowest error sensitivity and obtains the freeform TMA optical system with optimal overall performance. A freeform TMA optical system is designed by the method proposed in this paper, and the error sensitivity of the optical system is analyzed. The results show that the image quality of the freeform optical system is effectively improved and the error sensitivity is effectively reduced with the same error applied, which verifies the correctness and practicality of the method. [ABSTRACT FROM AUTHOR]

The special dispersion and temperature characteristics of diffractive optical element (DOE) make them widely used in optical systems that require both athermalization and achromatic aberrations designs. The multi-layer DOE (MLDOE) can improve the diffraction efficiency of the overall broad waveband, but its diffraction efficiency decreases with changes in ambient temperature. When the ambient temperature changes, the micro-structure heights of MLDOE and the refractive index of the substrate materials change, ultimately affecting its diffraction efficiency, and, further, the optical transform function (OTF). In this paper, the influence of ambient temperature on the diffraction efficiency of MLDOE in a dual-infrared waveband is proposed and discussed, the diffraction efficiency of MLDOE caused by ambient temperature is derived, and a computational imaging method that combines optical design and image restoration is proposed. Finally, a dual-infrared waveband infrared optical system with athermalization and achromatic aberrations corrected based on computational imaging method is designed. Results show that this method can effectively reduce the diffraction efficiency of MLDOE by ambient temperature and improve the imaging quality of hybrid optical systems. [ABSTRACT FROM AUTHOR]

When performing in vivo imaging of live samples, it is a big challenge to penetrate thick tissues while still maintaining high resolution and a large field of view because of the sample-induced aberrations. These requirements can be met by combining the benefits of two-photon excitation, beam modulation and adaptive optics in an illumination path. However, the relationship between aberrations and the performance of such a microscopy system has never been systematically and comprehensively assessed. Here, two-photon Gaussian and Bessel beams are modulated as illumination beams, and how aberrations affect the thickness of the illumination beams is evaluated. It is found that the thickness variation is highly related to the azimuthal order of Zernike modes. The thickness of the two-photon Gaussian beam is more sensitive to Zernike modes with lower azimuthal order, while the thickness of the two-photon Bessel beam is more sensitive to the higher-azimuthal-order Zernike modes. So, it is necessary to design a new strategy to correct aberrations according to the effects of different Zernike modes in order to maximize the correction capability of correctors and reduce the correction errors for those insensitive Zernike modes. These results may provide important guidance for the design and evaluation of adaptive optical systems in a two-photon excitation microscope. [ABSTRACT FROM AUTHOR]

The optical system that combines imaging and image motion compensation is conducive to the miniaturization of aerial mapping cameras, but the movement of optical element for image motion compensation will cause a decrease in image quality. To solve this problem, reducing the sensitivity of moving optical element is one of the effective ways to ensure the imaging quality of aerial mapping cameras. Therefore, this paper proposes an optimization method for the low tilt sensitivity of the secondary mirror based on the Nodal aberration theory. In this method, the analytical expressions of the tilt sensitivity of the secondary mirror in different tilt directions are given in the form of zernike polynomial coefficients, and the influence of the field of view on the sensitivity is expressed in the mathematical model. The desensitization optimization function and desensitization optimization method are proposed. The catadioptric optical system with a focal length of 350 mm is used for desensitization optimization. The results show that the desensitization function proposed in this paper is linearly related to the decrease of sensitivity within a certain range, and the standard deviation of the system after desensitization is 0.020, which is 59% of the system without desensitization. Compared with the traditional method, the method in this paper widens the range of angle reduction sensitivity and has a better desensitization effect. The research results show that the optimization method for low tilt sensitivity of the secondary mirror based on the Nodal aberration theory proposed in this paper reduces the tilt sensitivity of the secondary mirror, revealing that the reduction of the sensitivity depends on the reduction of the aberration coefficient related to the misalignment in the field of view, which is critical for the development of an optical system for aerial mapping cameras that combines imaging and image motion compensation. [ABSTRACT FROM AUTHOR]

A laser scanning confocal microscope (LSCM) is an effective scientific instrument for studying sub-micron structures, and it has been widely used in the field of biological detection. However, the illumination depth of LSCMs is limited due to the optical aberrations introduced by living biological tissue, which acts as an optical medium with a non-uniform refractive index, resulting in a significant dispersion of the focus of LSCM illumination light and, hence, a loss in the resolution of the image. In this study, to minimize the effect of optical aberrations, an image-based adaptive optics technology using an optimized stochastic parallel gradient descent (SPGD) algorithm with an adaptive coefficient is applied to the optical path of an LSCM system. The effectiveness of the proposed aberration correction approach is experimentally evaluated in the LSCM system. The results illustrate that the proposed adaptive optics system with an adaptive coefficient SPGD algorithm can effectively reduce the interference caused by aberrations during depth imaging. [ABSTRACT FROM AUTHOR]

The eye, the photoreceptive organ used to perceive the external environment, is of great importance to humans. It has been proven that some diseases in humans are accompanied by fundus changes; therefore, the health status of people may be interpreted from retinal images. However, the human eye is not a perfect refractive system for the existence of ocular aberrations. These aberrations not only affect the ability of human visual discrimination and recognition, but restrict the observation of the fine structures of human eye and reduce the possibility of exploring the mechanisms of eye disease. Adaptive optics (AO) is a technique that corrects optical wavefront aberrations. Once integrated into ophthalmoscopes, AO enables retinal imaging at the cellular level. This paper illustrates the principle of AO in correcting wavefront aberrations in human eyes, and then reviews the applications and advances of AO in ophthalmology, including the adaptive optics fundus camera (AO-FC), the adaptive optics scanning laser ophthalmoscope (AO-SLO), the adaptive optics optical coherence tomography (AO-OCT), and their combined multimodal imaging technologies. The future development trend of AO in ophthalmology is also prospected. [ABSTRACT FROM AUTHOR]

This paper presents an intentional investigation of the effect of the object tilt angle on the tracking local minimum method (TL method), which is the one for detecting the measurement target position of the object optical axis, in a chromatic confocal probe employing a differential dual-fiber-detector optical system with a mode-locked femtosecond laser as the light source. The effect of the object tilt angle on dual-detector confocal probes, and even chromatic confocal probes, has not been investigated in detail so far, although the effect of object tilt angle on scanning confocal probes has been studied. At first, to examine the influence of the object tilt angle on the TL method, a theoretical model is established, and numerical simulations are performed based on the established theoretical equation. Then, the effect of aberrations in confocal optics on the confocal response curve is investigated in experiments. Finally, investigations on the effect of the object tilt angle on the TL method are demonstrated in experiments. [ABSTRACT FROM AUTHOR]

The paper proposes a new set of normalization techniques for precoding/beamforming matrices applicable to broadband multiuser multiple-input multiple-output (MIMO) satellite systems. The proposed techniques adapt known normalization methods to account for the signal attenuation experienced by users due to the degradation of antenna gain and free space losses towards the edge of the coverage. We use, as an example, an array-fed reflector (AFR) antenna onboard a satellite in geosynchronous orbit (GEO), which provides a favorable trade-off between high-directivity, reconfigurability, and the requirement for digital processing, but suffers from high scan losses away from broadside due to optical aberrations when considered for global coverage applications. Three different precoding/beamforming techniques are employed, namely zero forcing (ZF), minimum mean squared error (MMSE), and matched filtering (MF). Low-complexity power normalization techniques digitally applied after the beamformer are introduced that, in the absence of any atmospheric effects, lead to iso-flux-like characteristics whilst satisfying the power constraint per feed. In comparison with other methods reported in the literature, mainly based on iterative algorithms, the proposed techniques consist in closed-form expressions to provide uniform signal-to-noise ratio (SNR) and signal-to-noise plus interference ratio (SNIR) across the users without significant impact on the payload sum rate. Numerical results are presented to comparatively demonstrate the achieved performance in terms of total capacity and distribution of SNR and SNIR at various noise and interference scenarios. [ABSTRACT FROM AUTHOR]