Wavefront Aberration Measurement Research Articles

Convolutional neural network for improved event-based Shack-Hartmann wavefront reconstruction

Shack-Hartmann wavefront sensing is a technique for measuring wavefront aberrations, whose use in adaptive optics relies on fast position tracking of an array of spots. These sensors conventionally use frame-based cameras operating at a fixed sampling rate to report pixel intensities, even though only a fraction of the pixels have signal. Prior in-lab experiments have shown feasibility of event-based cameras for Shack-Hartmann wavefront sensing (SHWFS), asynchronously reporting the spot locations as log intensity changes at a microsecond time scale. In our work, we propose a convolutional neural network (CNN) called event-based wavefront network (EBWFNet) that achieves highly accurate estimation of the spot centroid position in real time. We developed a custom Shack-Hartmann wavefront sensing hardware with a common aperture for the synchronized frame- and event-based cameras so that spot centroid locations computed from the frame-based camera may be used to train/test the event-CNN-based centroid position estimation method in an unsupervised manner. Field testing with this hardware allows us to conclude that the proposed EBWFNet achieves sub-pixel accuracy in real-world scenarios with substantial improvement over the state-of-the-art event-based SHWFS. An ablation study reveals the impact of data processing, CNN components, and training cost function; and an unoptimized MATLAB implementation is shown to run faster than 800 Hz on a single GPU.

An Iterative High-Precision Algorithm for Multi-Beam Array Stitching Method Based on Scanning Hartmann

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.

A Model-Based Approach for Measuring Wavefront Aberrations Using Random Ball Residual Compensation

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.

Efficacy of estimations of Hartmann-Shack sensors in small pupil sizes.

The purpose of this study was to evaluate the in vivo efficacy of the estimations of wavefront analyzers using Hartmann-Shack technology to measure optical aberrations when the pupil size is smaller than the evaluated pupil area. Patients implanted with the monofocal ZCB00 intraocular lens (Johnson and Johnson) were examined with the KR-1W Wavefront Analyzer (Topcon) without pharmacological mydriasis and with it afterward. Optical aberrations were analyzed considering a 4-mm pupil and a 6-mm pupil for both examinations. Sixty-six eyes of 33 patients with a mean axial length of 23.35 ± 0.91 mm were assessed. The mean pupil diameter at the baseline examination was 5.05 ± 0.88 mm and under pharmacological mydriasis, it was 6.29 ± 0.84 mm. Outcomes were similar with and without dilation in the 4-mm comparison. However, there was a great disparity in the 6-mm comparison. Most of the values obtained under mydriasis were statistically lower than at baseline (P < 0.05). The iris interferes with measurements of wavefront aberrations, and therefore, real pupil size should always be checked before evaluating optical aberrations with Hartman-Shack sensors. When pupil size is smaller than the analyzed diameter, ocular, and internal, and sometimes, corneal aberrations are estimated far more positive than real values.

Rigorous simulation model of double-Ronchi shearing interferometry on lithographic tools.

Double-Ronchi shearing interferometry is widely used in wavefront aberration measurements for advanced lithography projection lens systems. A rigorous simulation model of double-Ronchi shearing interferometry on lithographic tools is the precondition for phase-shifting retrieval algorithm design and error analysis. This paper presents a rigorous simulation model of double-Ronchi shearing interferometry considering the vector nature of light. The model is accurate and can be used in the study of double-Ronchi shearing interferometry.

Effects and elimination of image grating defocusing on a double-Ronchi shearing interference field.

Double-Ronchi shearing interferometry is a promising wavefront aberration measurement system for advanced lithography projection lens systems. The image grating defocusing is a key systematic error of the interferometer. However, the effects and elimination of this error have not been systematically researched. In this work, the interference field effects caused by the image grating defocusing are analyzed based on the theories of scalar diffraction, and a method to eliminate the effects is proposed. The theoretical analysis has been verified by a simulation and experiments. The results show that the error of image grating defocusing is mainly expressed as the Zernike Z4 term and Z9 term in the reconstructed wavefront, and the coefficients of Z4, and Z9, respectively, are related to NA2, NA4, and the defocus distance z. When the numerical aperture (NA) of the under-test projection lens is 0.6, 99.8384% of the errors caused by the image grating defocusing can be removed. When the NA is reduced to 0.3, 99.9854% of the errors can be removed. Additionally, when the NA is less than 0.1, almost all the errors can be eliminated.

Fast measurement of wavefront aberration in double-grating Ronchi lateral shearing interferometry

The accuracy of the shear-phase retrieval method is critical for accurate wavefront aberration measurements in double-grating Ronchi lateral shearing interferometry. Currently, the suppression of the interferences of unwanted diffractions generated by the Ronchi grating at the image plane is eliminated by adding more phase shifts, which increases the measurement time. Here, a stepped phase-shifting algorithm is proposed to suppress the unwanted diffractions and retrieve the shear phase between ±1st orders accurately with fewer phase shifts, and the measurement efficiency can be increased by 25% at least. The minimum number of phase shifts, which depends on the high diffraction orders existing in the interferograms, is analyzed. The proposed method was verified via numerical simulations and experiments. The wavefront measurement was validated via a comparison with the results of point-diffracted interferometry, and the root-mean-square difference was within 2.0 nm.

Wavefront measurement of a large aperture high image quality off-axis Fresnel lens.

Large aperture off-axis Fresnel lens will play an important role in the future 10 m scale aperture transmission space telescope system. Improving diffraction efficiency and wavefront image quality is always the goal of engineering applications. A 4-level off-axis fresnel lens with Ф350 mm effective aperture was fabricated through overlay etching technique by laser direct writing system. The wavefront aberration characteristics of the off-axis Fresnel lens at 632.8 nm wavelength are analyzed and discussed in detail, and the large aperture off-axis Fresnel lenses wavefront aberration measurement scheme, including a high-precision plane reflector, measured LAOFL, CGH, interferometer and laser tracker to compensate for certain low-order aberrations caused by LAOFL imperfect imaging, is proposed. Wavefront aberration of 0.020 λ(1/50 λ) RMS was achieved. This work presented the best results to our knowledge among the same field with similar aperture in open publications and provided a strong foundation for the future 10 m scale aperture transmission space telescope system.

Wavefront Aberration Measurement Technique Based on Principal Component Analysis of Aerial Image for Lithographic Projection Lens

Wavefront Aberration Measurement Technique Based on Principal Component Analysis of Aerial Image for Lithographic Projection Lens

Comparison of Ocular Wavefront Aberration Measurements Obtained Using Two Hartmann-Shack Wavefront Aberrometers.

To assess agreement between measurements of ocular wavefront aberrations obtained using the Pentacam AXL Wave (Oculus Optikgeräte GmbH) (Aberrometer A) and KR-1W (Topcon Corp) (Aberrometer B), both of which are based on the Hartmann-Shack principle. In this prospective case-control study, ocular wavefront aberrations measurements were obtained using both aberrometers in patients with keratoconus (KC) and control participants. Ocular wavefront aberrations were measured through the natural pupil without dilation using both devices in a dark room. For both aberrometers, accommodation was inhibited by automatically adding fogging. The individual Zernike coefficients from the second to fourth order were compared between the two aberrometers for a 4-mm pupil diameter. Twenty-six KC and 29 control eyes were assessed. Statistically significant correlations ( P <0.05) were observed for all Zernike coefficients, except for Z 4-2 in the control group. Bland-Altman analysis indicated good agreement between aberrometers and no statistically significant differences in the control group. However, in the KC group, patterns of proportional error were observed in vertical coma Z 3-1 (r=0.338, P =0.008), trefoil Z 4-4 (r=0.701, P =0.003), secondary astigmatism Z 4-2 (r=0.348, P =0.025), and spherical aberrations Z 40 (r=0.407, P =0.012). The Zernike coefficient values measured by the two aberrometers were well correlated in the control and KC groups. However, in eyes with KC, Aberrometer B tended to present greater values in several Zernike coefficients than Aberrometer A, suggesting that wavefront measurements obtained using the two aberrometers are not interchangeable in patients with KC.

Effects of illumination non-uniformity on the double-Ronchi lateral shearing interference field.

Double-Ronchi shearing interferometry is a promising technique for insitu wavefront aberration measurement of the projection lens in photolithography systems. In practice, the non-uniformity of illumination is an important issue affecting the interference field, which has not been systematically researched. In this work, the interference field errors caused by non-uniform illumination distributions are analyzed utilizing the theories of scalar diffraction. The theoretical analysis has been verified by simulation and fundamental experiments. Results show that the uniformity requirements for the abrupt annular, Gaussian, and uniform random illumination distribution (RD) are 0.9434, 0.8439, and 0.2751, respectively, with a shear ratio of 5% and a relative wavefront reconstruction error of 1%. The uniformity of the three distributions is reduced to 0.6513, 0.5864, and 0.1234, respectively, with the shear ratio shrunk to 3%. When the shear ratio is less than 1%, there is no specific requirement for illumination uniformity.

Shack–Hartmann wavefront sensor based on Kalman filter

The Shack–Hartmann wavefront sensor (SHWFS) traditionally employs the center of gravity (CoG), windowing, and thresholding CoG (TCoG) algorithms to measure wavefront aberrations. Nevertheless, these algorithms yield low accuracy in a low signal-to-noise ratio (SNR) environment, and therefore, we propose a measurement algorithm based on the Kalman filter to correct the three algorithms’ centroid position of the Shack–Hartmann spot. When the Euclidean distance between the reference centroid in a sub-aperture and the measurement centroid exceeds a certain threshold, the sub-apertures centroid position is untrusted and must be corrected. Several simulation experiments are conducted in three environments: no noise, Poisson noise, and Gaussian noise; they demonstrate that the proposed algorithm effectively improves the centroid’s accuracy by more than 10% and ensures real-time performance for the adaptive optics system. In addition, experimental results on wavefront reconstruction tasks reveal that our algorithm produces wavefronts close to the original.

Wavefront aberrometry repeatability and agreement-A comparison between Pentacam AXL Wave, iTrace and OPD-Scan III.

To compare intrasession agreement and repeatability of wavefront aberration measurements from three different aberrometers obtained using Hartmann-Shack, ray tracing and automated retinoscopy methods, as well as their interdevice agreement. Three consecutive measurements were obtained using the Pentacam AXL Wave, the iTrace and the OPD-Scan III in 47 eyes of 47 patients. Wavefront refractions, root mean square of total aberrations (RMS total), RMS of higher-order aberrations (HOA) and second-, third- and fourth-order HOAs were exported for 4-mm pupils. Wavefront refractions were converted into vector components: M, J0 and J45 . Intrasession agreement and repeatability were evaluated using intraclass correlation coefficients (ICCs) and repeatability coefficients (RCs); interdevice agreement was assessed using the Bland-Altman method. The intrasession agreement and repeatability of RMS HOA were comparable between the three devices; both the Pentacam AXL Wave and the OPD-Scan III had better intrasession agreement and repeatability for the RMS total than the iTrace (p ≤ 0.02). Intrasession repeatability for the majority of second- and third-order aberrations was better on the Pentacam AXL Wave than on the iTrace (p ≤ 0.01) and OPD-Scan III (p ≤ 0.04), although their agreement and repeatability in spherical aberration were comparable (p ≥ 0.24). Significant systematic differences and proportional bias were detected for almost all refraction power vectors and Zernike coefficients among the three devices. In this study, all three devices provided good-to-excellent agreement for aberration measurements. Most of the individual Zernike's components were not exchangeable between different aberrometers. Their relative intrasession performance in agreement and repeatability varied significantly across different ocular aberration parameters.

Comparison of wavefront aberrations in the object and image spaces using wide-field individual eye models.

Wavefront aberrations in the image space are critical for visual perception, though the clinical available instruments usually give the wavefront aberrations in the object space. This study aims to compare the aberrations in the object and image spaces. With the measured wavefront aberrations over the horizontal and vertical ±15° visual fields, the in-going and out-going wide-field individual myopic eye models were constructed to obtain the wavefront aberrations in the object and image spaces of the same eye over ±45° horizontal and vertical visual fields. The average differences in the mean sphere and astigmatism were below 0.25 D between the object and image spaces over the horizontal and vertical ±45° visual fields under 3 mm and 6 mm pupil diameter. The wavefront aberrations in the object space are a proper representation of the aberrations in the image space at least for horizontal visual fields ranging from -35°to +35° and vertical visual fields ranging from -15°to +15°.

Wavefront Aberration Measurement Deflectometry for Imaging Lens Tests

Lenses play an important role in imaging systems. Having an effective way to test the aberrations of imaging lenses is important. However, the existing methods cannot satisfy the requirements in some conditions. To overcome these difficulties, wavefront aberration measurement deflectometry (WAMD) is proposed in this paper, which can reconstruct the wavefront aberrations of imaging lenses by measuring the angular aberrations. The principle of WAMD is analyzed in detail, and the correctness and feasibility of the proposed method are verified by both a simulation and an experiment. A telephoto lens and a single imaging lens were tested in an experiment, and the RMS errors were 166.8 nm (5.71%) and 58.9 nm (4.74%), respectively, as compared with the interferometer’s results. This method is widely applicable with relatively reasonable accuracy. It has potential to be applied in the lens manufacturing and alignment process.

Repeatability of i.Profiler for measuring wavefront aberrations in healthy eyes.

To evaluate the repeatability of wavefront aberration measurements and the correlation between corneal aberration and pupil size in normal eyes using a wavefront-based autorefractor (i.ProfilerPlus; Carl Zeiss Vision, Germany). A prospective cross-sectional study. Wavefront aberrations, including spherical aberration (SA) (Z40), coma (Z3-1, Z31), trefoil (Z3-3, Z33) and total higher-order aberrations (tHOA), were measured at different pupil diameters. The repeatability was evaluated using one-way ANOVA method, and statistical indicators including within-subject standard deviation (Sw), test-retest repeatability (TRT), and intra-class correlation coefficient (ICC). The correlations between corneal aberrations and pupil sizes were evaluated by Pearson correlation analysis. A total of 96 healthy young volunteers were enrolled. Corneal and ocular higher-order aberrations (HOA) measured by i.Profiler showed Sw < 0.01μm, TRT < 0.10μm, ICC > 0.90. There was a linear positive correlation between the corneal HOA and pupil size. The correlation coefficient between SA and tHOA was the largest (r = 0.996, P < 0.001). The measurements of wavefront aberrations by i.Profiler are highly repeatable. Corneal HOA was significantly dependent on pupil size. SA was the most influential aberration for visual quality in this study.

Applicability of the Van Cittert-Zernike theorem in a Ronchi shearing interferometer.

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.

Polychromatic through-focus image quality in a wavefront-shaping presbyopia correcting intraocular lens

ABSTRACT Objectives To compute the polychromatic through-focus image quality in eyes implanted with a new extended depth of focus (EDOF) intraocular lens (IOL). Methods Eight eyes of four patients who underwent implantation with the AcrySof IQ Vivity EDOF IOL were analyzed. Wavefront aberrations were measured. The optical metric for the polychromatic through-focus image quality used was the Visual Strehl ratio computed in the spatial domain (VSX). Eight eyes implanted with a monofocal IOL were also examined. Results The normalized VSX values change with vergence for both group of IOLs. However, the depth-of-focus (DoF) for the Vivity IOL was about 0.75, 1.00, and 1.25 D larger than the monofocal IOL, for 0.1, 0.2, and 0.3 logMAR visual acuities. The DoF computed from the polychromatic through-focus image quality for the Vivity IOL was about 2.50D, being this value 1.25D wider than the monofocal one. The DoF obtained from the defocus curve was about 2.25 D for eyes implanted with the Vivity IOL. Conclusions Polychromatic through-focus image quality analysis agrees with the clinical outcomes indicating that this methodology may be useful to estimate the DoF and the expected quality of vision in patients implanted with lenses from wavefront aberration measurement. This approach shows the increased DoF of the EDOF lens compared to a monofocal.

Measurement of Wavefront Aberration of Lens Based on Phase Measuring Deflectometry

Measurement of Wavefront Aberration of Lens Based on Phase Measuring Deflectometry

High NA objective lens wavefront aberration measurement using a cat-eye retroreflector and Zernike polynomial.

Wavefront aberration is one important parameter for objective lenses. When the NA (Numerical Aperture) of the objective lens becomes larger than 0.8, wavefront aberration measurement with high accuracy and low cost is difficult to realize because of the lack of a reference sphere. In this paper, a new method is proposed to measure the wavefront aberration of a high NA objective lens. A cat-eye retroreflector with a plane mirror is used to reflect the wavefront. The plane mirror is tilted in at least three different directions by certain tilt angles to collect sufficient information of the wavefront aberration under test. Specific grid-combined Zernike polynomial is built for each set of tilt angles and directions to fit the corresponding returned wavefronts. The wavefront aberration can be reconstructed from the fitting results of the returned wavefronts. The measurement accuracy is influenced by the tilt angle, tilt angle error, NA, defocus amount of the plane mirror, detector's resolution, and other random noise. The tilt angle error is the main source of the measurement error. The relative measurement error is within 5% and 1% when the relative tilt angle error is below 0.5% and 0.1% respectively. The feasibility of the proposed method is verified experimentally by measuring the wavefront aberrations of 0.14 NA, 0.65 NA, and 0.9 NA objective lenses. Wavefront aberration measurement for a high NA objective lens with high accuracy and low cost is achievable through this method.