Correction of non-uniform angular velocity and sub-pixel jitter in optical scanning.

Optical scanners are widely used in high-resolution scientific, medical, and industrial devices. The accuracy and precision of these instruments are often limited by angular speed fluctuations due to rotational inertia and by poor synchronization between scanning and light detection, respectively. Here we demonstrate that both problems can be mitigated by recording scanner orientation in synchrony with light detection, followed by data resampling. This approach is illustrated with synthetic and experimental data from a point-scanning microscope with a resonant scanner and a non-resonant scanner. Fitting of the resonant scanner orientation data to a cosine model was used to correct image warping and sampling jitter, as well as to precisely interleave image lines collected during the clockwise and counterclockwise resonant scanner portions of the rotation cycle. Vertical scanner orientation data interpolation was used to correct image distortion due to angular speed fluctuations following abrupt control signal changes.

Shack-Hartmann wavefront sensor optical dynamic range.

The widely used lenslet-bound definition of the Shack-Hartmann wavefront sensor (SHWS) dynamic range is based on the permanent association between groups of pixels and individual lenslets. Here, we formalize an alternative definition that we term optical dynamic range, based on avoiding the overlap of lenslet images. The comparison of both definitions for Zernike polynomials up to the third order plus spherical aberration shows that the optical dynamic range is larger by a factor proportional to the number of lenslets across the SHWS pupil. Finally, a pre-centroiding algorithm to facilitate lenslet image location in the presence of defocus and astigmatism is proposed. This approach, based on the SHWS image periodicity, is demonstrated using optometric lenses that translate lenslet images outside the projected lenslet boundaries.

Multi-layer Shack-Hartmann wavefront sensing in the point source regime.

The Shack-Hartmann wavefront sensor (SHWS) is often operated under the assumption that the sensed light can be described by a single wavefront. In biological tissues and other multi-layered samples, secondary wavefronts from axially and/or transversely displaced regions can lead to artifactual aberrations. Here, we evaluate these artifactual aberrations in a simulated ophthalmic SHWS by modeling the beacons that would be generated by a two-layer retina in human and mouse eyes. Then, we propose formulae for calculating a minimum SHWS centroid integration area to mitigate these aberrations by an order of magnitude, potentially benefiting SHWS-based metrology and adaptive optics systems such as those used for retinal imaging and microscopy.

Dynamic wavefront distortion in resonant scanners.

Dynamic mirror deformation can substantially degrade the performance of optical instruments using resonant scanners. Here, we evaluate two scanners with resonant frequencies >12kHz with low dynamic distortion. First, we tested an existing galvanometric motor with a novel, to the best of our knowledge, mirror substrate material, silicon carbide, which resonates at 13.8 kHz. This material is stiffer than conventional optical glasses and has lower manufacturing toxicity than beryllium, the stiffest material currently used for this application. Then, we tested a biaxial microelectromechanical (MEMS) scanner with the resonant axis operating at 29.4 kHz. Dynamic deformation measurements show that wavefront aberrations in the galvanometric scanner are dominated by linear oblique astigmatism (90%), while wavefront aberrations in the MEMS scanner are dominated by horizontal coma (30%) and oblique trefoil (27%). In both scanners, distortion amplitude increases linearly with deflection angle, yielding diffraction-limited performance over half of the maximum possible deflection for wavelengths longer than 450 nm and over the full deflection range for wavelengths above 850 nm. Diffraction-limited performance for shorter wavelengths or over larger fractions of the deflection range can be achieved by reducing the beam diameter at the mirror surface. The small dynamic distortion of the MEMS scanner offers a promising alternative to galvanometric resonant scanners with desirable but currently unattainably high resonant frequencies.

Optical and Visual Quality With Physical and Visually Simulated Presbyopic Multifocal Contact Lenses.

Purpose: As multifocal contact lenses (MCLs) expand as a solution for presbyopia correction, a better understanding of their optical and visual performance becomes essential. Also, providing subjects with the experience of multifocal vision before contact lens fitting becomes critical, both to systematically test different multifocal designs and to optimize selection in the clinic. In this study, we evaluated the ability of a simultaneous vision visual simulator (SimVis) to represent MCLs. Methods: Through focus (TF) optical and visual quality with a center-near aspheric MCL (low, medium and high near adds) were measured using a multichannel polychromatic Adaptive Optics visual simulator equipped with double-pass, SimVis (temporal multiplexing), and psychophysical channels to allow measurements on-bench and in vivo. On bench TF optical quality of SimVis-simulated MCLs was obtained from double-pass (DP) images and images of an E-stimulus using artificial eyes. Ten presbyopic subjects were fitted with the MCL. Visual acuity (VA) and DP retinal images were measured TF in a 4.00 D range with the MCL on eye, and through SimVis simulations of the same MCLs on the same subjects. Results: TF optical (on bench and in vivo) and visual (in vivo) quality measurements captured the expected broadening of the curves with increasing add. Root mean square difference between real and SimVis-simulated lens was 0.031/0.025 (low add), 0.025/0.015 (medium add), 0.019/0.011 (high add), for TF DP and TF LogMAR VA, respectively. A shape similarity metric shows high statistical values (lag κ = 0), rho = 0.811/0.895 (low add), 0.792/0.944 (medium add), and 0.861/0.915 (high add) for TF DP/LogMAR VA, respectively. Conclusions: MCLs theoretically and effectively expand the depth of focus. A novel simulator, SimVis, captured the through-focus optical and visual performance of the MCL in most of the subjects. Visual simulators allow subjects to experience vision with multifocal lenses prior to testing them on-eye. Translational Relevance: Simultaneous visual simulators allow subjects to experience multifocal vision non-invasively. We demonstrated equivalency between real multifocal contact lenses and SimVis-simulated lenses. The results suggest that SimVis is a suitable technique to aid selection of presbyopic corrections in the contactology practice.

Average gradient of Zernike polynomials over polygons.

Wavefront estimation from slope sensor data is often achieved by fitting measured slopes with Zernike polynomial derivatives averaged over the sampling subapertures. Here we discuss how the calculation of these average derivatives can be reduced to one-dimensional integrals of the Zernike polynomials, rather than their derivatives, along the perimeter of each subaperture. We then use this result to derive closed-form expressions for the average Zernike polynomial derivatives over polygonal areas, only requiring evaluation of polynomials at the polygon vertices. Finally, these expressions are applied to simulated Shack-Hartmann wavefront sensors with 7 and 23 fully illuminated lenslets across a circular pupil, with their accuracy and calculation time compared against commonly used integration methods.

Dynamic distortion in resonant galvanometric optical scanners.

High-speed optical systems are revolutionizing biomedical imaging in microscopy, DNA sequencing, and flow cytometry, as well as numerous other applications, including data storage, display technologies, printing, and autonomous vehicles. These systems often achieve the necessary imaging or sensing speed through the use of resonant galvanometric optical scanners. Here, we show that the optical performance of these devices suffers due to the dynamic mirror distortion that arises from the variation in torque with angular displacement. In one of two scanners tested, these distortions result in a variation of signal-to-noise (Strehl) ratio by an order of magnitude across the field of view, degrading transverse resolution by more than a factor of 2. This mirror distortion could be mitigated through the use of stiffer materials, such as beryllium or silicon carbide, at the expense of surface roughness, as these cannot be polished to the same degree of smoothness as common optical glasses. The repeatability of the dynamic distortion indicates that computational and optical corrective methods are also possible.

Accounting for focal shift in the Shack-Hartmann wavefront sensor.

The Shack-Hartmann wavefront sensor samples a beam of light using an array of lenslets, each of which creates an image onto a pixelated sensor. These images translate from their nominal position by a distance proportional to the average wavefront slope over the corresponding lenslet. This principle fails in partially and/or non-uniformly illuminated lenslets when the lenslet array is focused to maximize peak intensity, leading to image centroid bias. Here, we show that this bias is due to the low Fresnel number of the lenslets, which shifts the diffraction focus away from the geometrical focus. We then demonstrate how the geometrical focus can be empirically found by minimizing the bias in partially illuminated lenslets.

Centroid error due to non-uniform lenslet illumination in the Shack-Hartmann wavefront sensor.

Images formed by individual Shack-Hartmann wavefront sensor lenslets are displaced proportionally to the average wavefront slope over their aperture. This principle fails when the lenslet illumination is non-uniform. Here we demonstrate that the resulting error is proportional to the linear component of the illumination intensity, the quadratic wavefront component, and the lenslet size. For illustrative purposes, we compare the error due to centered Gaussian illumination decaying by 30% at the pupil edge against the error due to assuming the wavefront at the lenslet center being equal to the wavefront average across each lenslet. When testing up to ninth-order Zernike polynomial wavefronts and simulating nine lenslets across the pupil, the maximum centroid errors due to non-uniform illumination and sampling are 1.4% and 21%, respectively, and 0.5% and 6.7% when considering 25 lenslets across the pupil in the absence of other sources of error.

Visual simulators replicate vision with multifocal lenses.

Adaptive optics (AO) visual simulators based on deformable mirrors, spatial light modulators or optotunable lenses are increasingly used to simulate vision through different multifocal lens designs. However, the correspondence of this simulation with that obtained through real intraocular lenses (IOLs) tested on the same eyes has not been, to our knowledge, demonstrated. We compare through-focus (TF) optical and visual quality produced by real multifocal IOLs (M-IOLs) -bifocal refractive and trifocal diffractive- projected on the subiect's eye with those same designs simulated with a spatial light modulator (SLM) or an optotunable lens working in temporal multiplexing mode (SimVis technology). Measurements were performed on 7 cyclopleged subjects using a custom-made multichannel 3-active-optical-elements polychromatic AO Visual Simulator in monochromatic light. The same system was used to demonstrate performance of the real IOLs, SLM and SimVis technology simulations on bench using double-pass imaging on an artificial eye. Results show a general good correspondence between the TF performance with the real and simulated M-IOLs, both optically (on bench) and visually (measured visual acuity in patients). We demonstrate that visual simulations in an AO environment capture to a large extent the individual optical and visual performance obtained with real M-IOLs, both in absolute values and in the shape of through-focus curves.

Tunable lenses: dynamic characterization and fine-tuned control for high-speed applications.

Tunable lenses are becoming ubiquitous, in applications including microscopy, optical coherence tomography, computer vision, quality control, and presbyopic corrections. Many applications require an accurate control of the optical power of the lens in response to a time-dependent input waveform. We present a fast focimeter (3.8 KHz) to characterize the dynamic response of tunable lenses, which was demonstrated on different lens models. We found that the temporal response is repetitive and linear, which allowed the development of a robust compensation strategy based on the optimization of the input wave, using a linear time-invariant model. To our knowledge, this work presents the first procedure for a direct characterization of the transient response of tunable lenses and for compensation of their temporal distortions, and broadens the potential of tunable lenses also in high-speed applications.

Experimental validations of a tunable-lens-based visual demonstrator of multifocal corrections.

The Simultaneous Vision simulator (SimVis) is a visual demonstrator of multifocal lens designs for prospective intraocular lens replacement surgery patients and contact lens wearers. This programmable device employs a fast tunable lens and works on the principle of temporal multiplexing. The SimVis input signal is tailored to mimic the optical quality of the multifocal lens using the theoretical SimVis temporal profile, which is evaluated from the through-focus Visual Strehl ratio metric of the multifocal lens. In this paper, for the first time, focimeter-verified on-bench validations of multifocal simulations using SimVis are presented. Two steps are identified as being critical to accurate SimVis simulations. Firstly, a new iterative approach is presented that improves the accuracy of the theoretical SimVis temporal profile for three different multifocal intraocular lens designs - diffractive trifocal, refractive segmented bifocal, and refractive extended depth of focus, while retaining a low sampling. Secondly, a fast focimeter is used to measure the step response of the tunable lens, and the input signal is corrected to include the effects of the transient behavior of the tunable lens. It was found that the root-mean-square of the difference between the estimated through-focus Visual Strehl ratio of the multifocal lens and SimVis is not greater than 0.02 for all the tested multifocal designs.

In Vivo Measurement of Longitudinal Chromatic Aberration in Patients Implanted With Trifocal Diffractive Intraocular Lenses.

PURPOSE: To measure the longitudinal chromatic aberration (LCA) by both psychophysical methods and in vivo double-pass retinal imaging in patients bilaterally implanted with trifocal diffractive intraocular lenses (IOLs). METHODS: Measurements were performed with a polychromatic adaptive optics system provided with a supercontinuum laser, a Hartmann-Shack wavefront sensor, a deformable mirror, a motorized Badal system, a pupil monitoring system, a double-pass retinal imaging channel, and a psychophysical channel with monochromatically illuminated stimuli. Ten patients (20 eyes) bilaterally implanted with hydrophilic trifocal diffractive IOLs (POD F [FINeVision]; PhysIOL, Liege, Belgium) participated in the study. Measurements were performed in both eyes at three different viewing distances (0.00, +1.75, and +3.50 diopters [D]). Subjective best focus of monochromatic stimuli at five wavelengths (480 to 700 nm) was obtained using the Badal system. Best focused images of through-focus double-pass image series were obtained at three wavelengths (480 to 700 nm). LCA was computed from chromatic difference of focus curves (objective and subjective) as the difference between 480 and 700 nm at near, intermediate, and far. RESULTS: The average subjective LCA was 0.82 ± 0.05 D for far, 0.27 ± 0.15 D for intermediate, and 0.15 ± 0.15 D for near. The average objective LCA was 0.72 ± 0.10 D for far, 0.19 ± 0.15 D for intermediate, and 0.07 ± 0.17 D for near. CONCLUSIONS: Objective LCA was lower than subjective LCA, which was in agreement with previous studies on patients with phakic and monofocal IOLs. In vivo measurements of LCA enable understanding of the relative contribution of refractive and diffractive LCA and will eventually optimize IOL designs to improve polychromatic image quality. [J Refract Surg. 2017;33(11):736-742.].

Temporal multiplexing to simulate multifocal intraocular lenses: theoretical considerations.

Fast tunable lenses allow an effective design of a portable simultaneous vision simulator (SimVis) of multifocal corrections. A novel method of evaluating the temporal profile of a tunable lens in simulating different multifocal intraocular lenses (M-IOLs) is presented. The proposed method involves the characteristic fitting of the through-focus (TF) optical quality of the multifocal component of a given M-IOL to a linear combination of TF optical quality of monofocal lenses viable with a tunable lens. Three different types of M-IOL designs are tested, namely: segmented refractive, diffractive and refractive extended depth of focus. The metric used for the optical evaluation of the temporal profile is the visual Strehl (VS) ratio. It is shown that the time profiles generated with the VS ratio as a metric in SimVis resulted in TF VS ratio and TF simulated images that closely matched the TF VS ratio and TF simulated images predicted with the M-IOL. The effects of temporal sampling, varying pupil size, monochromatic aberrations, longitudinal chromatic aberrations and temporal dynamics on SimVis are discussed.

Evaluation of the True Wavefront Aberrations in Eyes Implanted With a Rotationally Asymmetric Multifocal Intraocular Lens.

PURPOSE: Standard evaluation of aberrations from wavefront slope measurements in patients implanted with a rotationally asymmetric multifocal intraocular lens (IOL), the Lentis Mplus (Oculentis GmbH, Berlin, Germany), results in large magnitude primary vertical coma, which is attributed to the intrinsic IOL design. The new proposed method analyzes aberrometry data, allowing disentangling the IOL power pupillary distribution from the true higher order aberrations of the eye. METHODS: The new method of wavefront reconstruction uses retinal spots obtained at both the near and far foci. The method was tested using ray tracing optical simulations in a computer eye model virtually implanted with the Lentis Mplus IOL, with a generic cornea or with anterior segment geometry obtained from custom quantitative spectral-domain optical coherence tomography in a real patient. The method was applied to laser ray tracing aberrometry data at near and far fixation obtained in a patient implanted with the Lentis Mplus IOL. RESULTS: Higher order aberrations evaluated from simulated and real retinal spot diagrams following the new reconstruction approach matched the nominal aberrations (approximately 98%). Previously reported primary vertical coma in patients implanted with this IOL lost significance with the application of the proposed reconstruction. CONCLUSIONS: Custom analysis of ray tracing-based retinal spot diagrams allowed decoupling of the true higher order aberrations of the patient's eye from the power pupillary distribution of a rotationally asymmetric multifocal IOL, therefore providing the appropriate phase map to accurately evaluate through-focus optical quality. [J Refract Surg. 2017;33(4):257-265.].

Virtual pyramid wavefront sensor for phase unwrapping.

Noise affects wavefront reconstruction from wrapped phase data. A novel method of phase unwrapping is proposed with the help of a virtual pyramid wavefront sensor. The method was tested on noisy wrapped phase images obtained experimentally with a digital phase-shifting point diffraction interferometer. The virtuality of the pyramid wavefront sensor allows easy tuning of the pyramid apex angle and modulation amplitude. It is shown that an optimal modulation amplitude obtained by monitoring the Strehl ratio helps in achieving better accuracy. Through simulation studies and iterative estimation, it is shown that the virtual pyramid wavefront sensor is robust to random noise.

Phase unwrapping with a virtual Hartmann-Shack wavefront sensor.

The use of a spatial light modulator for implementing a digital phase-shifting (PS) point diffraction interferometer (PDI) allows tunability in fringe spacing and in achieving PS without the need for mechanically moving parts. However, a small amount of detector or scatter noise could affect the accuracy of wavefront sensing. Here, a novel method of wavefront reconstruction incorporating a virtual Hartmann-Shack (HS) wavefront sensor is proposed that allows easy tuning of several wavefront sensor parameters. The proposed method was tested and compared with a Fourier unwrapping method implemented on a digital PS PDI. The rewrapping of the Fourier reconstructed wavefronts resulted in phase maps that matched well the original wrapped phase and the performance was found to be more stable and accurate than conventional methods. Through simulation studies, the superiority of the proposed virtual HS phase unwrapping method is shown in comparison with the Fourier unwrapping method in the presence of noise. Further, combining the two methods could improve accuracy when the signal-to-noise ratio is sufficiently high.

Closed-loop adaptive optics using a spatial light modulator for sensing and compensating of optical aberrations in ophthalmic applications.

Sensing and compensating of optical aberrations in closed-loop mode using a single spatial light modulator (SLM) for ophthalmic applications is demonstrated. Notwithstanding the disadvantages of the SLM, in certain cases, this multitasking capability of the device makes it advantageous over existing deformable mirrors (DMs), which are expensive and in general used for aberration compensation alone. A closed-loop adaptive optics (AO) system based on a single SLM was built. Beam resizing optics were used to utilize the large active area of the device and hence make it feasible to generate 137 active subapertures for wavefront sensing. While correcting Zernike aberrations up to fourth order introduced with the help of a DM (for testing purposes), diffraction-limited resolution was achieved. It is shown that matched filter and intensity-weighted centroiding techniques stand out among others. Closed-loop wavefront correction of aberrations in backscattered light from the eyes of three healthy human subjects was demonstrated after satisfactory results were obtained using an artificial eye, which was simulated with a short focal length lens and a sheet of white paper as diffuser. It is shown that the closed-loop AO system based on a single SLM is capable of diffraction-limited correction for ophthalmic applications.

Digital phase-shifting point diffraction interferometer.

A digital phase-shifting (PS) point diffraction interferometer is demonstrated with a transmitting liquid crystal spatial light modulator. This novel wavefront sensor allows tunability in the choice of pinhole size and eliminates the need for mechanically moving parts to achieve PS. It is shown that this wavefront sensor is capable of sensing Zernike aberrations introduced with a deformable mirror. The results obtained are compared with those of a commercial Hartmann-Shack wavefront sensor.

Digital pyramid wavefront sensor with tunable modulation.

The pyramid wavefront sensor is known for its high sensitivity and dynamic range that can be tuned by mechanically altering its modulation amplitude. Here, a novel modulating digital scheme employing a reflecting phase only spatial light modulator is demonstrated. The use of the modulator allows an easy reconfigurable pyramid with digital control of the apex angle and modulation geometry without the need of any mechanically moving parts. Aberrations introduced by a 140-actuator deformable mirror were simultaneously sensed with the help of a commercial Hartmann-Shack wavefront sensor. The wavefronts reconstructed using the digital pyramid wavefront sensor matched very closely with those sensed by the Hartmann-Shack. It is noted that a tunable modulation is necessary to operate the wavefront sensor in the linear regime and to accurately sense aberrations. Through simulations, it is shown that the wavefront sensor can be extended to astronomical applications as well. This novel digital pyramid wavefront sensor has the potential to become an attractive option in both open and closed loop adaptive optics systems.