Wavefront Error Research Articles

Potential vision tester using adaptive optics, Maxwellian view, and small pupil.

We demonstrate a free-space, trolley-mounted potential vision tester (PVT), designed to study and improve the accuracy of visual acuity (VA) measurements in the aging eye. Key features include a high-resolution visual display presented in Maxwellian view, a 3 mm pupil to limit wavefront (WF) aberrations, and a moderate cost deformable mirror to induce or correct higher order optical aberrations. The visual display supported accurate measurement of visual acuities down to 20/5. The moderate cost, piezo deformable mirror induced seven nominal aberrations, calibrated as 0, -0.32, -0.23, + 0.27, and +0.39 microns spherical aberration; + 0.49 microns Y coma; and -0.51 microns X coma. A custom Hartmann Shack (HS) calibration (HSc) system demonstrated that induced aberrations were repeatable and stable. A Badal optometer provided the coarse focus. WF aberrations were measured for five normal subjects with a commercially available HS device (HSP) (OCULUS Pentacam AXL Wave), providing estimates of WF errors for 3 mm and other pupil sizes. VA was measured using four alternative forced-choice for a single black on white E stimulus in each trial. Using the method of constant stimuli yielded robust standard deviation measurements. The 50% fit for VA plotted against induced aberration resulted in linear functions for each subject for the range of our positive and negative spherical aberration data. Subjects differed, but higher order terms were unnecessary to describe data across spherical aberrations.

Adaptive Optics Microscopy with Wavefront Sensing Based onNeighbor Correlation.

Complex structures in living cells and tissues induce wavefront errors when light waves pass through them, and images observed with optical microscopes are undesirably blurred. This problem is especially serious for living plant cells because images are strikingly degraded even within a single cell. Adaptive optics (AO) is expected to be a solution to this problem by correcting such wavefront errors, thus enabling high-resolution imaging. In particular, scene-based AO involves wavefront sensing based on the image correlation between subapertures in a Shack-Hartmann wavefront sensor and thus does not require an intense point light source. However, the complex 3D structures of living cells often cause low correlation between subimages, leading to loss of accuracy in wavefront sensing. This paper proposes a novel method for scene-based sensing using only image correlations between adjacent subapertures. The method can minimize changes between subimages to be correlated and thus prevent inaccuracy in phase estimation. Using an artificial test target mimicking the optical properties of a layer of living plant cells, an imaging performance with a Strehl ratio of approximately 0.5 was confirmed. Upon observation of chloroplast autofluorescence inside living leaf cells of the moss Physcomitrium patens, recovered resolution images were successfully obtained even with complex biological structures. Under bright-field illumination, the proposed method outperformed the conventional method, demonstrating the future potential of this method for label- and damage-free AO microscopy. Several points for improvement in terms of the effect of AO correction are discussed.

Nonlinear Wave Front Reconstruction from a Pyramid Sensor using Neural Networks

The pyramid wave front sensor (PyWFS) has become increasingly popular to use in adaptive optics (AO) systems due to its high sensitivity. The main drawback of the PyWFS is that it is inherently nonlinear, which means that classic linear wave front reconstruction techniques face a significant reduction in performance at high wave front errors, particularly when the pyramid is unmodulated. In this paper, we consider the potential use of neural networks (NNs) to replace the widely used matrix vector multiplication (MVM) control. We aim to test the hypothesis that the NN's ability to model nonlinearities will give it a distinct advantage over MVM control. We compare the performance of a MVM linear reconstructor against a dense NN, using daytime data acquired on the Subaru Coronagraphic Extreme Adaptive Optics system (SCExAO) instrument. In a first set of experiments, we produce wavefronts generated from 14 Zernike modes and the PyWFS responses at different modulation radii (25, 50, 75, and 100 mas). We find that the NN allows for a far more precise wave front reconstruction at all modulations, with differences in performance increasing in the regime where the PyWFS nonlinearity becomes significant. In a second set of experiments, we generate a data set of atmosphere-like wavefronts, and confirm that the NN outperforms the linear reconstructor. The SCExAO real-time computer software is used as baseline for the latter. These results suggest that NNs are well positioned to improve upon linear reconstructors and stand to bring about a leap forward in AO performance in the near future.

A High Precison Phase Extraction Algorithm from a Single Shot Interferogram

Abstract. Phase shifting interferometry is an optical metrology with a high precision, but it usually requires the expensive high precision phase shifter. Therefore, low cost methods of extracting phase from a single shot interferogram were very valuable, but available algorithms are usually effective only in a limited conditions. To solve these problems, a novel method is presented in this work. Based on this method, the interference fringe is retrieved to a wrapped phase and divided into different regions and the index of the pixel is calculated. The pixels in the same region have the same parity and the PSF’s gravity center of part wavefront so as to solve the sign ambiguity. The theoretical simulation results indicate that the PV of wavefront error is 0.00054λ and the rms is 0.000125λ,which is much better than the results from the Fast Fourier Transformation method. The experimentally measured interferogram is also used to validate the method. It has the advantages of simplicity, high precision and effective for both open and closed interferometer fringes.

Active Adjustment of the Subreflector Shape for the Large Dual-Reflector Antenna.

A shape adjustment method for subreflectors based on minimizing the residual wavefront error of the large dual-reflector antenna is presented. This method is used to compensate for the antenna structural deformation caused by environment loading. The shape of the subreflector is adjusted using actuators fixed under the panels. The shape adjustment response function for the subreflector shape and the actuators' adjustment amount is established, which is based on the inverse distance weighting function, and then the control function of the subreflector shape is obtained. The actuators' adjustment amount can be calculated using the least squares matrix transformation with the minimum residual wavefront error. Analysis of the experiment's results shows the residual wavefront error and primary aberration are greatly reduced under different elevation angles, and the effectiveness of the proposed method is verified.

Numerical modelling for retrieval of the coating thickness variations from wavefront errors measurements.

Multilayers coating are needed for large optical components performances, but the thickness non-uniformities over the useful aperture can generate spatial and chromatic variations of the reflectance, the transmittance and the wavefront errors. Although these dependences can be measured, they are difficult to anticipate if the underlying thickness variations are unknown. We present a model to retrieve these variations from wavefront error measurements that enables the computation of any optical properties over the useful aperture at any wavelength, angle of incidence or polarization.

Design and Analysis of Target Simulator Using All Spherical System with High Matching Rate

To achieve low wavefront error and high throughput with vignetting-free target simulators, a concave-convex-concaveoff-axis spherical system is designed in this paper, which effectively eliminates astigmatism and coma of the system by fields of view (FOVs) and aperture offset and provides theoretical basis for the realization of 100% matching between the exit pupil of the field lens and entrance pupil of the three-mirror anastigmat (TMA) system. Only spherical mirror element is used in this target simulator, which not only reduces the difficulty of manufacturing and cost but also greatly reduces the difficulty of assembling and adjusting. It provides an effective scheme for the design of target simulator and has strong engineering application value.

Multidisciplinary integrated optimal design process for optomechanical structures.

This paper presents an integrated design process for optomechanical structures based on multidisciplinary optimization. The proposed integrated optimal design process comprises a finite element analysis by ANSYS Workbench, the MATLAB optomechanical transfer program, an optical analysis by ZEMAX, and the multidisciplinary optimization solver by Isight. In ANSYS Workbench, the deformation of optical surfaces, structures, and responses according to the design requirements is calculated in one project. Then, Zernike polynomial coefficients are calculated from surface deformation data of optical surfaces through a MATLAB optomechanical transfer program. In ZEMAX, the Zernike polynomial coefficients are imported into optical surface models of an optical system; then, optical performance parameters, such as the wavefront error, optical aberration, MTF, and OPD, are calculated. In the Isight environment, automatic iterative computations are performed between these three programs and, as a result, the design dimensions of optomechanical structures are determined, satisfying the design requirements and improving the performance of an optical system. By using this integrated optimal design process, the optimal design and analysis for a complete optomechanical structure, as well as individual structure parts, can be performed successfully. In this paper, the optimal design problem for three parts of a Cassegrain telescope, which consists of a primary mirror with an outer diameter of 156mm and a secondary mirror with an outer diameter of 46mm, was taken as an example. By using optimal parts, the image wavefront error of the Cassegrain telescope was decreased from 29.9 to 16.1nm.

Pupil aberrations correction of the afocal telescope for the TianQin project

TianQin is a planned Chinese space-based gravitational wave (GW) observatory with a frequency band of 10−4–1 Hz. Optical telescopes are essential for the delivery of the measurement beam to support a precise distance measurement between pairs of proof masses. As the design is driven by the interferometric displacement sensitivity requirements, the stability control of optical path length (OPL) is extremely important beyond the traditional requirement of diffraction-limited imaging quality. The recurring tilt-to-length (TTL) coupling noise arises from the OPL variation due to the wavefront deformation and angular misalignment. Reducing the residual chief ray aberration in the optical design helps suppress TTL coupling noise. To correct the pupil aberrations, we derive primary pupil aberrations in a series expansion form, and then refine the formulation of merit function by combining the pupil aberration theory and traditional image aberration theory. The automatic correction of pupil aberrations is carried out by using the macro programming in the commercial optical software Zemax, leading to a high performance telescope design. The design results show that on one side the pupil aberrations have been corrected, and on the other side, its optical performance meets the requirements for TianQin project. The RMS wavefront error over the science field of view (FOV) is less than λ/200 and the maximum TTL coupling noise over the entire ±300 μrad FOV is 0.0152 nm µrad−1 . We believe that our design approach can be a good guide for the space telescope design in any other space-based GW detection project, as well as other similar optical systems.

Adaptive Petal Reflector: In-Lab Software Configurable Optical Testing System Metrology and Modal Wavefront Reconstruction.

This paper addresses two aspects of the metrology of spherical, petal polymer reflectors which are part of an effort by the European Space Agency (ESA) to develop actively controlled foldable reflectors, enabling larger apertures on CubeSats and small satellites. The first problem is that of measuring the surface figure error of the spherical reflector alone during the development phase, and to assess the quality before assembling the telescope (large stroke, low accuracy). The SCOTS (Software Configurable Optical Testing System) appears to provide a fast and satisfactory solution to this problem. The second problem is the wavefront error reconstruction when the petal reflector is mounted on the telescope, because parts of the petals are obscured by the secondary mirror, in such a way that the petals appear completely disconnected, making the gradient-based metrology impossible. Using the fact that the petals have common mechanical boundary conditions at the central support ring, the problem is solved by using a set of orthogonal modes satisfying the same boundary conditions. The vibration modes are used for this purpose; the modal amplitudes are reconstructed from slope data outside the obstruction, allowing for wavefront error reconstruction over the entire surface.

Effects of aberrations on isoSTED microscopy

Aberrations are inevitable in optical microscopes and affect the image quality. In STED microscopy, the optical resolution is especially dominated by the performance of depletion pattern. To quench fluorescence only in the periphery of the excitation focus, the depletion focus ideally has a zero-intensity point that is surrounded by a high-intensity crest. Otherwise, distortion of the depletion beam causes unwanted fluorescence inhibition. The influence of aberrations on isoSTED microscopy differs from that on STED microscopy because isoSTED microscopy generates a more complicated shape of the depletion focal spot with two opposing objectives which have different focusing properties. We present analysis that elucidates the effects on the shape, the central minimum intensity, and the peak intensity of the isoSTED pattern regarding primary aberrations such as astigmatism, coma, and spherical aberration when those aberrations are added in the shared beam path and each beam path in the 4Pi-cavity. The simulation results demonstrate significant resolution degradation (>160%; defined as the focal volume) for the aberrations with root mean square wavefront errors of 0.5 rad.

Comparative study of small incision refractive lenticule extraction with 5 mm versus 6.5 mm optic zone for myopia.

To compare residual stromal thickness (RST) in eyes undergoing small incision refractive lenticule extraction (SMILE) using a lenticular diameter of 6.5 mm versus those with a diameter of 5 mm. comparative case series. patients who underwent SMILE between 2016 and 2021 with at least 6 months of follow-up were included. Preoperative best-corrected distance visual acuity (BCDVA), refractive error, contrast sensitivity, central corneal thickness, keratometry, higher order aberrations, and scotopic pupil size were recorded using a Placido disk topography with Sheimpflug tomography-based system. Patients underwent SMILE with a lenticular diameter of 6.5 mm until 2018 (n = 372 eyes). Thereafter, the lenticular diameter was reduced to 5 mm (n = 318). The RST, postoperative refraction, aberrations, subjective glare, and halos were compared across groups at 1 and 6 months. The mean age of participants was 26.8 ± 5.8 years with a mean preoperative spherical equivalent of -4.48 D ± 2.16 D (range: -0.75 to -12.25 D) and mean scotopic pupil of 3.7 ± 0.75 mm. Eyes in the 5 mm group had 30.6 m (95% confidence interval [CI] = 28 to 33 m, P < 0.001) greater RST compared to the 6.5 mm group after adjusting for spherical equivalent and preoperative pachymetry. There were no differences in vision, contrast sensitivity, aberrations (wavefront error of 0.19 ± 0.2 vs. 0.25 ± 0.2, P = 0.19) or glare between the two groups. SMILE performed with a lenticular diameter of 5 mm leads to greater RST across the myopic range, but without inducing significant higher-order aberrations.

Wavefront error of PHI/HRT on Solar Orbiter at various heliocentric distances

Aims.We use wavefront sensing to characterise the image quality of the High Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager (SO/PHI) data products during the second remote sensing window of the Solar Orbiter (SO) nominal mission phase. Our ultimate aims are to reconstruct the HRT data by deconvolving with the HRT point spread function (PSF) and to correct for the effects of optical aberrations on the data.Methods.We use a pair of focused–defocused images to compute the wavefront error and derive the PSF of HRT by means of a phase diversity (PD) analysis.Results.The wavefront error of HRT depends on the orbital distance of SO to the Sun. At distances &gt; 0.5 au, the wavefront error is small, and stems dominantly from the inherent optical properties of HRT. At distances &lt; 0.5 au, the thermo-optical effect of the Heat Rejection Entrance Window (HREW) becomes noticeable. We develop an interpolation scheme for the wavefront error that depends on the thermal variation of the HREW with the distance of SO to the Sun. We also introduce a new level of image reconstruction, termed ‘aberration correction’, which is designed to reduce the noise caused by image deconvolution while removing the aberrations caused by the HREW.Conclusions.The computed PSF via phase diversity significantly reduces the degradation caused by the HREW in the near-perihelion HRT data. In addition, the aberration correction increases the noise by a factor of only 1.45 compared to the factor of 3 increase that results from the usual PD reconstructions.

Image plane wavefront sensing and Kalman filtering for automated alignment of off-axis aspherics.

Automated alignment can significantly increase optical system precision and flexibility, and reduce time and labor costs in system setup and maintenance. We present an automated alignment technique on a double off-axis parabolic mirror system, which poses challenging alignment problems due to the mirrors' high sensitivity to aberrations, rotational asymmetry, and non-orthogonality in stage adjustments. In our methodology, we use focal plane wavefront sensing to eliminate the non-common path error, increase optical throughput, and reduce cost and system complexity. We incorporate model-based optimal estimation and control to better handle the nonlinearity, model uncertainty, and noise. Using either an iterated extended Kalman filter or a square-root unscented Kalman filter as the optimal nonlinear misalignment state estimator, we are able to consistently reduce the linear misalignment from around 1mm to <5µm and the angular misalignment from around 500 to <6a r c s e c in simulation, achieving a final wavefront error of <5∗10-5 waves in the field of view when tested at wavelength 635nm. We discover a multi-state coupling effect, which implies that different misalignment states have compensating effects on system measurements, thus interfering with the estimator's observation of misalignment state changes. We further investigate the coupling's effects on alignment quality through observability analysis.

Comparison of optical myopia control interventions: effect on peripheral image quality and vision.

This study compares the effects on peripheral vision and image quality of four myopia control interventions: a) Perifocal spectacles/ArtOptica, b) Stellest spectacles/Essilor), c) MiyoSmart spectacles/Hoya and d) MiSight contact lenses/CooperVision. Five subjects participated with habitual or no correction as reference. Three techniques were used: 1) Hartmann-Shack sensors for wavefront errors, 2) double-pass imaging system for point-spread-functions (PSF), and 3) peripheral acuity evaluation. The results show that multiple evaluation methods are needed to fully quantify the optical effects of these myopia control interventions. Perifocal was found to make the relative peripheral refraction (RPR) more myopic in all subjects and to interact with the natural optical errors of the eye, hence showing larger variations in the effect on peripheral vision. MiSight had a smaller effect on RPR, but large effect on peripheral vision. Stellest and MiyoSmart also showed small effects on RPR but had broader double-pass PSFs for all participants, indicating reduced retinal contrast. Reduction in peripheral retinal contrast might thereby play a role in slowing myopia progression even when the peripheral refraction does not turn more myopic.

Method to construct the initial structure of optical systems based on full-field aberration correction.

To meet full-field image quality requirements for extremely low aberration optical systems, an initial structure construction method for reflective optical systems based on full-field aberration correction is proposed. The aberration of the full field is used as the main evaluation criterion in this method. A multi-field evaluation function is established using the aberration values of multiple characteristic field points to represent the full-field imaging quality, and spatial ray tracing is introduced to constrain the optical system structure. Multi-objective optimization of the evaluation function is performed using a combinatorial nondominated sorting and metaheuristics algorithm; an initial optical system with a reasonable structure and corrected third-order aberrations over the full field is subsequently obtained. After optimization, an extreme ultraviolet lithography objective with a numerical aperture of 0.33 and root-mean-square wavefront error of 0.128 nm ($1/105\lambda, \lambda = 13.5\;{\rm nm}$) is obtained.

Fault Traveling Wave Detection Method based on ICEEMDAN-MCKD

To address the challenge of calibrating the traveling wave-front for fault location in high noise environments, we propose an improved method that combines the ICEEMDAN and maximum correlation kurtosis deconvolution (MCKD). Our approach first decomposes the fault traveling wave signal into modal components using the ICEEMDAN algorithm. Next, the MCKD algorithm enhances the energy amplitude of the decomposed signal, suppresses strong background noise interference, and accurately calibrates the fault traveling wave-front. Simulation results demonstrate that ICEEMDAN-MCKD achieves precise calibration of the wave-front, exhibits strong denoising ability, and performs better than existing methods in terms of detecting traveling waves and minimizing wave-front determination time errors in noisy environments.

Experimental Verification of a One-dimensional Diffraction-limit Coronagraph

We performed an experimental verification of a coronagraph. As a result, we confirmed that, at the focal region where the planetary point spread function exists, the coronagraph system mitigates the raw contrast of a star-planet system by at least 1 × 10−5 even for the 1-λ/D star-planet separation. In addition, the verified coronagraph keeps the shapes of the off-axis point spread functions when the setup has the source angular separation of 1λ/D. The low-order wave front error and the non-zero extinction ratio of the linear polarizer may affect the currently confirmed contrast. The sharpness of the off-axis point spread function generated by the sub-λ/D separated sources is promising for the fiber-based observation of exoplanets. The coupling efficiency with a single mode fiber exceeds 50% when the angular separation is greater than 3–4×10−1 λ/D. For sub-λ/D separated sources, the peak positions (obtained with Gaussian fitting) of the output point spread functions are different from the angular positions of sources; the peak position moved from about 0.8λ/D to 1.0λ/D as the angular separation of the light source varies from 0.1λ/D to 1.0λ/D. The off-axis throughput including the fiber-coupling efficiency (with respect to no focal plane mask) is about 40% for 1-λ/D separated sources and 10% for 0.5-λ/D separated ones (excluding the factor of the ratio of pupil aperture width and Lyot stop width), where we assumed a linear-polarized-light injection. In addition, because this coronagraph can remove point sources on a line in the sky, it has another promising application for high-contrast imaging of exoplanets in binary systems.

Active Alignment of Large-Aperture Space Telescopes for Optimal Ellipticity Performance

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.

Study of transient behaviors of wavefront error caused by natural convection for improving mirror seeing.

Astronomical seeing parameters calculated based on the Kolmogorov turbulence model cannot fully evaluate the effect of the natural convection (NC) above a solar telescope mirror on the image quality, as the convective air motions and temperature variations of the NC are significantly different from the Kolmogorov turbulence. In this work, a new method based on the transient behaviors and frequency characteristics of NC-related wavefront error (WFE) are investigated in detail and used to evaluate the image quality degradation caused by a heated telescope mirror, aiming to make up for the deficiency of astronomical seeing parameters with the conventional method in evaluating the image quality degradation. Transient computational fluid dynamics (CFD) simulations and WFE calculations based on discrete sampling and ray segmentation are performed to quantitatively evaluate the transient behaviors of the NC-related WFE. It clearly exhibits apparent oscillatory characteristics, which are coupled by main oscillation with low frequencies and minor oscillation with high frequencies. Moreover, the generation mechanisms of two types of oscillations are studied. The conspicuous oscillation frequencies of the main oscillation caused by heated telescope mirrors with varying dimensions are primarily lower than 1 Hz, suggesting that active optics may be adopted to correct the main oscillation of NC-related WFE while the adaptive optics may correct the minor oscillation. Furthermore, a mathematical relationship between WFE, temperature rise, and mirror diameter is derived, revealing a significant correlation between WFE and mirror diameter. Our work suggests the transient NC-related WFE should be considered as one of the critical supplements to the mirror seeing evaluation.