Shack-Hartmann Research Articles

Arbitrary wavefront uncertainty evaluation for the Shack–Hartmann wavefront sensor using physical optics propagation

The Shack–Hartmann wavefront sensor (SHWS) is a common option to characterize optical fields, due to its noninterference, high accuracy, and high-speed advantages. However, the current methods for evaluating measurement accuracy can only work for predefined standard wavefronts and cannot provide the error estimate for an arbitrary wavefront. Here, we propose an SHWS uncertainty evaluation approach for specific wavefronts based on the physical optics propagation. Our approach constructs a comprehensive SHWS model that incorporates twelve error sources. We analyzed the influence of different error sources on the measurement accuracy under the diffraction effect and reported that our model could achieve an accuracy of λ/559 under the ideal condition. In the experiment, we measured three different wavefronts and confined their uncertainty down to λ/65, λ/260, and λ/40, respectively. Our work may offer an effective solution for evaluating measurement errors in the high-accuracy wavefront measurement and provide a reliable, unbiased evaluation criterion.

Deflectometry based calibration of a deformable mirror for aberration correction and remote focusing in microscopy.

Adaptive optics (AO) techniques enhance the capability of optical microscopy through precise control of wavefront modulations to compensate phase aberrations and improves image quality. However, the aberration correction is often limited due to the lack of dynamic range in existing calibration methods, such as interferometry or Shack-Hartmann (SH) wavefront sensors. Here, we use deflectometry (DF) as a calibration method for a deformable mirror (DM) to extend the available range of aberration correction. We characterised the dynamic range and accuracy of the DF-based calibration of DMs depending on the spatial frequency of the test pattern used in DF. We also demonstrated the capability of large magnitude phase control for remote-focusing over a range larger than was possible with SH sensing.

High robustness single-shot wavefront sensing method using a near-field profile image and fully-connected retrieval neural network for a high power laser facility.

This paper proposes a single-shot high robustness wavefront sensing method based on deep-learning for wavefront distortion measurement in high power lasers. This method could achieve fast and robust wavefront retrieval by using a single-shot near-field profile image and trained network. The deep-learning network uses fully-skip cross connections to extract and integrate multi-scale feature maps from various layers and stages, which improves the wavefront retrieval speed and enhances the robustness of the method. The numerical simulation proves that the method could directly predict the wavefront distortion of high power lasers with high accuracy. The experiment demonstrates the residual RMS between the method and a Shack-Hartmann wavefront sensor is less than 0.01 µm. The simulational and experimental results show that the method could accurately predict the incident wavefront distortion in high power lasers, exhibiting high speed and good robustness in wavefront retrieval.

Parafoveal and Perifoveal Accommodation Response to Defocus Changes Induced by a Tunable Lens

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.

Enhanced neuroimaging with a calcium sensor in ex-vivo Drosophila melanogaster brains using closed-loop adaptive optics light-sheet fluorescence microscopy.

Adaptive optics (AO) has been implemented on several microscopy setups and has proven its ability to increase both signal and resolution. However, reported configurations are not suited for fast imaging of live samples or are based on an invasive or complex implementation method. Provide a fast aberration correction method with an easy to implement AO module compatible with light-sheet fluorescence microscopy (LSFM) for enhanced imaging of live samples. Development of an AO add-on module for LSFM based on direct wavefront sensing without requiring a guide star using an extended-scene Shack-Hartmann wavefront sensor. The enhanced setup uses a two-color sample labeling strategy to optimize the photon budget. Fast AO correction of in-depth aberrations in an ex-vivo adult Drosophila brain enables doubling the contrast when imaging with either cell reporters or calcium sensors for functional imaging. We quantify the gain in terms of image quality on different functional domains of sleep neurons in the Drosophila brain at various depths and discuss the optimization of key parameters driving AO. We developed a compact AO module that can be integrated into most of the reported light-sheet microscopy setups, provides significant improvement of image quality and is compatible with fast imaging requirements such as calcium imaging.

Aerosol absorption measurement by a Shack-Hartmann wavefront sensor.

Researchers at the U.S. Army Space and Missile Defense Command have developed a method for quantifying high energy near-infrared (NIR) laser heating of air resulting from laser absorption of suspended dry aerosols in a controlled environmental chamber. The measurements were accomplished using an ISO standard test dust and NIR high energy laser using a Shack-Hartmann wavefront sensor. This paper presents the methodology of the measurement as well as the quantitative reconstruction of the air temperature profile, absorption efficiency, and imaginary refractive index of the aerosol. The resulting measurement of the aerosol imaginary index of refraction was significantly lower than values typically found in the literature from measurements using low power techniques. These findings are in general agreement with other recently published works that have found that previously published values of mineral dust aerosols could be significantly overestimated.

Wavefront Characteristics of a Digital Holographic Optical Element.

In this study, a 50 × 50 mm holographic optical element (HOE) with the property of a spherical mirror was recorded digitally on a silver halide photoplate using a wavefront printing method. It consisted of 51 × 96 hologram spots with each spot measuring 0.98 × 0.52 mm. The wavefronts and optical performance of the HOE were compared with those of reconstructed images from a point hologram displayed on DMDs of different pixel structures. The same comparison was also performed with an analog-type HOE for a heads-up display and with a spherical mirror. A Shack-Hartmann wavefront sensor was used to measure the wavefronts of the diffracted beams from the digital HOE and the holograms as well as the reflected beam from the analog HOE and the mirror when a collimated beam was incident on them. These comparisons revealed that the digital HOE could perform as a spherical mirror, but they also revealed astigmatism-as in the reconstructed images from the holograms on DMDs-and that its focusability was worse than that of the analog HOE and the spherical mirror. A phase map, i.e., the polar coordinate-type presentation of the wavefront, could visualize the wavefront distortions more clearly than the reconstructed wavefronts obtained using Zernike polynomials. The phase map revealed that the wavefront of the digital HOE was more distorted than those of the analog HOE and the spherical mirror.

Measuring spatio-temporal couplings using modal spatio-spectral wavefront retrieval.

Knowledge of spatio-temporal couplings such as pulse-front tilt or curvature is important to determine the focused intensity of high-power lasers. Common techniques to diagnose these couplings are either qualitative or require hundreds of measurements. Here we present both a new algorithm for retrieving spatio-temporal couplings, as well as novel experimental implementations. Our method is based on the expression of the spatio-spectral phase in terms of a Zernike-Taylor basis, allowing us to directly quantify the coefficients for common spatio-temporal couplings. We take advantage of this method to perform quantitative measurements using a simple experimental setup, consisting of different bandpass filters in front of a Shack-Hartmann wavefront sensor. This fast acquisition of laser couplings using narrowband filters, abbreviated FALCON, is easy and cheap to implement in existing facilities. To this end, we present a measurement of spatio-temporal couplings at the ATLAS-3000 petawatt laser using our technique.

Branch-point identification using second-moment Shack-Hartmann wavefront sensor statistics.

In this paper, an approach for detecting branch points using a Shack-Hartmann wavefront sensor (SHWFS) is introduced. Simulated data are created using Monte Carlo wave-optics simulations of varying turbulence strengths. It is assumed that the presence of a branch point in the SHWFS subaperture lenslet pupils causes appreciable beam spreading in the image plane. Therefore, second-moment statistics are used to quantify beam spread for each subaperture image-plane irradiance pattern. Thresholding is then employed to dictate what degree of beam spreading is sufficient to determine the presence of a branch point. Three different thresholds are imposed: liberal, moderate, and conservative. Furthermore, the collected SHWFS signal is treated as analog, digitized, and digitized with three levels of additive noise: low, moderate, and high. Monte Carlo simulations are conducted for 20 different spherical-wave Rytov numbers (R S W ) ranging from 0.1 to 2.0. It was found that when conservative thresholds were employed, for the analog signal, digitized signal with no noise, and digitized signal with low noise, the percent of detections mostly comprised actual branch points, and false-positive detections were largely minimized. For the liberal thresholding cases, many false-positives were detected for all SHWFS signal types; however, significantly more branch points were also detected. The results presented in this paper are encouraging, and such results will inform efforts to develop branch-point tolerant least-squares reconstructors or use a SHWFS for optical-turbulence characterization in high-R S W environments.

System for Objective Assessment of the Accommodation Response During Subjective Refraction.

To evaluate a system based on a Hartmann-Shack wavefront sensor attached to a phoropter that allows the user to obtain real-time information about the refractive state of the eye and the accommodation response (AR). The objective refractions (ME) and ARs of 73 subjects (50 women, 23 men; ages, 19-69 years) were assessed with the system developed while placing in the phoropter the subjective refraction (MS) plus a set of trial lenses with differences in spherical equivalent power (ΔM) between ±2 diopters (D). The objective estimations (ME) showed a good correlation with the subjective values (MS) (r = 0.989; P < 0.001). The means of the ARs presented a region where the accommodation remained stable (ΔM from +2 D to about 0 D), followed by another in which the response increased progressively (ΔM from about 0 to -2 D) with the magnitude of the accommodation stimulus. The analysis of variance within subjects applied to ARs introducing age and MS as covariates showed an increasing effect size of age from medium to large between ΔM of -0.5 and -2 D. In contrast, MS had a medium effect size (between ΔM of +2 and 0 D). The implemented system permitted an objective estimation of the refraction of the eye and its AR. Because it is coupled to a phoropter, the system can be used to retrieve the AR during subjective refraction procedures. The developed system can be used as a supporting tool during subjective refraction to provide certainty about the true state of accommodation.

Compensation of wavefront aberration introduced by DMDs’ operation principle

The wavefront aberration introduced by both rhomb and square pixel Digital Micromirror Devices (DMDs) to the reconstructed images from the holograms displayed on them is visualized with a color phase map obtained from a Shack-Hartmann wavefront sensor. The aberration causes blurring and distortions in the reconstructed images. The map informs that the aberration is induced by the virtual shrinkage of pixels introduced by their rotation because 1) the aberration is appearing along the DMDs' pixel rotation directions and 2) the DMD with a bigger size pixel introduces more aberration than that with a smaller size pixel. It is also shown that the aberration can be minimized with use of a white beam. The white beam is a reflected beam from the no image loaded On-state DMDs’ surfaces when a collimated illumination beam is normally incident to them. Nevertheless, when the phase maps are compensated by the white beam, the reconstructed images become more distinguished and identified for both DMDs.

Central and peripheral refraction measured by a novel double-pass instrument.

A novel double-pass instrument and its data analysis method for the measurement of central and peripheral refraction is presented and validated in a group of healthy subjects. The instrument acquires in-vivo, non-cycloplegic, double-pass, through-focus images of the eye's central and peripheral point-spread function (PSF) using an infrared laser source, a tunable lens and a CMOS camera. The through-focus images were analyzed to determine defocus and astigmatism at 0° and 30° visual field. These values were compared to those obtained with a lab-based Hartmann-Shack wavefront sensor. The two instruments provided data showing good correlation at both eccentricities, particularly in the estimation of defocus.

Higher order aberrations and retinal image quality during short-term accommodation in myopic and non-myopic children.

Despite the known associations between near work and myopia, and retinal image quality and eye growth, accommodation-induced changes in higher order aberrations (HOA's) and retinal image quality in children with different refractive errors are poorly understood. Ocular HOA's were measured using a Hartmann-Shack wavefront sensor (COAS-HD, Wavefront Sciences) in 18 myopic and 18 age- and sex-matched non-myopic children during short-term accommodation tasks (four demands of 0, 3, 6 and 9 D) presented using a Badal optometer. Eighth order Zernike polynomials were fitted across a 2.3 mm pupil diameter to determine refractive power vectors (M, J180 and J45 ) and the accommodation error, and a 4 mm pupil was used for HOA analyses. Retinal image quality was examined using the visual Strehl ratio based on the optical transfer function (VSOTF) for third to eighth radial orders only. Most refractive error group differences were observed for the 6 and 9 D demands. Myopic children underwent greater changes in with-the-rule astigmatism (J180 ), higher order and third order RMS values, primary vertical ( ) and horizontal coma ( ), and several other individual Zernike coefficients compared with non-myopic children (all refractive error group by demand interaction p-values of ≤0.02). Non-myopic children exhibited a greater negative shift in primary ( ) and positive shift in secondary spherical aberration ( ) (both refractive error group by demand interaction p-values of ≤0.002). The VSOTF degraded for the 6 and 9 D demands in both groups, but the myopic children underwent a greater mean (SE) reduction from 0 D of -0.274 (0.048) for the 9 D demand, compared with -0.131 (0.052) for the non-myopic children (p = 0.001). These results may have implications for the association between near work, accommodation and myopia development, particularly related to the use of short working distances during near tasks.

Characterization of thick and contact lenses using an adaptive Shack–Hartmann wavefront sensor: Limitations and solutions

Lens characterization is a key challenge for reliable optical and imaging techniques. Shack–Hartmann wavefront sensor (SHWFS) is frequently used as an efficient tool for characterizing optical elements. However, the aberrations arising from the incident wavefront, utilized for the characterization process, cause imprecision in the spherical power measurement. Accordingly, the aim of the present study is to construct an experimental configuration that consists of SHWFS incorporated with a deformable mirror (DM) to provide a correction for the incident wavefront aberrations which yields an ideal plane wave. Different types of thick lenses with a wide range of focal lengths and three single-vision contact lenses were tested before and after aberrations compensation and compared to the reference-based method. The comparison was based on measuring the spherical powers for the tested lenses. The results indicate that the accuracy of measurements is influenced by the incident wavefront aberrations, which has been improved by the proposed compensation system. Finally, the limitations are investigated and it was concluded that the system in its current configuration failed to accurately measure some thick lenses. This issue was solved by suggesting a compound lens correction methodology that extended the measurement range of spherical powers beyond the designated measurable range of the system.

Understanding the limits of remote focusing.

It has previously been demonstrated in both simulation and experiment that well aligned remote focusing microscopes exhibit residual spherical aberration outside the focal plane. In this work, compensation of the residual spherical aberration is provided by the correction collar on the primary objective, controlled by a high precision stepper motor. A Shack-Hartmann wave front sensor is used to demonstrate the magnitude of the spherical aberration generated by the correction collar matches that predicted by an optical model of the objective lens. The limited impact of spherical aberration compensation on the diffraction limited range of the remote focusing system is described through a consideration of both on-axis and off-axis comatic and astigmatic aberrations, which are an inherent feature of remote focusing microscopes.

Two-dimensional peripheral refraction in adults.

Peripheral refraction has been studied for decades; however, its detection and description are somehow simplistic and limited. Therefore, their role in visual function and refractive correction, as well as myopia control, is not completely understood. This study aims to establish a database of two-dimensional (2D) peripheral refraction profiles in adults and explore the features for different central refraction values. A group of 479 adult subjects were recruited. Using an open-view Hartmann-Shack scanning wavefront sensor, their right naked eyes were measured. The overall features of the relative peripheral refraction maps showed myopic defocus, slight myopic defocus, and hyperopic defocus in the hyperopic and emmetropic groups, in the mild myopic group, and in other myopic groups, respectively. Defocus deviations with central refraction vary in different regions. The defocus asymmetry between the upper and lower retinas within 16° increased with the increase of central myopia. By characterizing the variation of peripheral defocus with central myopia, these results provide rich information for possible individual corrections and lens design.

Performance of the adaptive optics system for Laser Communications Relay Demonstration's Ground Station 1.

The Laser Communications Relay Demonstration is NASA's multi-year demonstration of laser communication from the Earth to a geosynchronous satellite. The mission currently has two optical ground stations (OGSs), with one in California (OGS1) and one in Hawaii (OGS2). Each ground terminal optical system consists of a high-order adaptive optics (AO) system, a laser transmit system, and a camera for target acquisition. The OGS1 AO system is responsible for compensating for the downlink beam for atmospheric turbulence and coupling it into the modem's single mode fiber. The mission requires a coupling efficiency of 50%, which necessitates a high-order AO system. To achieve this performance, the AO system uses two deformable mirrors with one mirror correcting for low-spatial-frequency aberrations with large amplitude and a second deformable mirror correcting for high-spatial-frequency aberrations with small amplitude. Turbulence is sensed with a Shack-Hartmann wavefront sensor. To meet its performance requirements in the most stressing conditions, the system can operate at frame rates of 20kHz. This high frame rate is enabled by the design of the real-time control system. We present an overview of both the hardware and software design of the system, and describe the control system and methods of reducing non-common path aberrations. Finally, we show measured system performance.

Changes in visual function and optical and tear film quality in computer users

To assess changes in visual function and optical and tear film quality in computer users. Forty computer workers and 40 controls were evaluated at the beginning and end of a working day. Symptoms were assessed using the Quality of Vision questionnaire (QoV), 5-item Dry Eye Questionnaire (DEQ-5) and Symptom Assessment in Dry Eye version II (SANDE II). Tear film quality was evaluated using the Medmont E300 dynamic corneal topography tool to measure the tear film surface quality (TFSQ), TFSQ area and auto tear break-up time (TBUT). Optical quality was assessed by measuring high, low and total ocular aberrations with a Hartmann-Shack wavefront sensor. Visual performance was assessed by measuring photopic and mesopic visual acuity, photopic and mesopic contrast sensitivity and light disturbance. Poorer DEQ-5, QoV and SANDE II scores were obtained in computer workers at the end of the working day compared with controls (p ≤ 0.02). Computer workers exhibited a higher (worse) TFSQ and TFSQ area at visit 2 compared with visit 1 (p ≤ 0.04), while no significant differences in TBUT (p = 0.19) or ocular aberrations were observed (p ≥ 0.09). Additionally, both light disturbance (p ≤ 0.04) and mesopic and photopic contrast sensitivity worsened at several spatial frequencies (p ≤ 0.04) throughout the working day in computer workers, while visual acuity remained unchanged (p ≥ 0.07). In contrast, control subjects exhibited no decrease in any variable during the day. While visual acuity remained unchanged, several aspects of visual function and quality of vision decreased over a day of computer use. These changes were accompanied by greater dry eye symptoms and tear film changes, which are likely to have played a fundamental role. The present study provides insight into new metrics to assess digital eye strain.

Spherical Aberration and Accommodative Insufficiency: Is There a Link?

Given the relationship between spherical aberrations and accommodation, the study of these aberrations can be helpful to understand accommodative response in subjects with accommodative dysfunctions. The purpose of this study was to evaluate on-axis and off-axis changes of primary and secondary spherical aberrations, Z(4,0) and Z(6,0), with accommodation in subjects with accommodative insufficiency (AI). Ten subjects with AI and eleven without any accommodative dysfunction (control) participated in this study. On-axis defocus Z(2,0), Z(4,0), and Z(6,0) were obtained in both groups with a Hartmann–Shack aberrometer for the unaccommodated state and with 1.00 D, 2.44 D, 3.83 D, and 4.73 D of accommodative stimuli. Z(4,0) and Z(6,0) were also measured on 11.5° and 23° temporal, nasal, superior, and inferior retinal areas for unaccommodated state and for 2.44 D of accommodative stimulus. In the control group, Z(4,0) became more negative with accommodation and Z(6,0) became more positive, as was expected according to previous studies. This tendency was not observed in the group of subjects with AI group for Z(4,0) or for Z(6,0). No differences on off-axis Z(4,0) and Z(6,0) were observed between the groups. The changes of spherical aberrations with accommodation seem different in subjects with AI compared to those without any accommodative dysfunction. Those with AI do not present a decrease in Z(4,0) and an increase in Z(6,0) with accommodation as occurs in eyes without this type of dysfunction. Understanding how the optics of the eye changes with accommodation can be helpful to understand the origin of accommodative dysfunctions.

One-Dimensional High-Resolution Wavefront Sensor Enabled by Subwavelength Compound Gratings

Angle sensors are widely used for wavefront measurements, which is attributed to their integration and robustness. Currently, commercial sensors are available with pixel sizes in the order of wavelengths. However, the spatial resolution of angle sensors still lags far behind. Here, we report a one-dimensional, high-resolution wavefront sensor. It was produced by introducing subwavelength compound gratings above the pixels. The gratings involved could be replaced by the sensor’s intrinsic readout circuitry without additional operation. The experimental results showed that it had a spatial resolution of 1.4 µm, two orders of magnitude higher than that of the Shack–Hartmann wavefront sensor. The significant increase in spatial resolution enables angle sensors to reconstruct complex wavefronts accurately.