Dynamic range expansion of a Shack-Hartmann sensor by use of a modified unwrapping algorithm

A Method Used to Improve the Dynamic Range of Shack-Hartmann Wavefront Sensor in Presence of Large Aberration

With the successful application of the Shack-Hartmann wavefront sensor in measuring aberrations of the human eye, researchers found that, when the aberration is large, the local wavefront distortion is large, and it causes the spot corresponding to the sub-aperture of the microlens to shift out of the corresponding range of the sub-aperture. However, the traditional wavefront reconstruction algorithm searches for the spot within the corresponding range of the sub-aperture of the microlens and reconstructs the wavefront according to the calculated centroid, which leads to wavefront reconstruction errors. To solve the problem of the small dynamic range of the Shack-Hartmann wavefront sensor, this paper proposes a wavefront reconstruction algorithm based on the autocorrelation method and a neural network. The autocorrelation centroid extraction method was used to calculate the centroid in the entire spot map in order to obtain a centroid map and to reconstruct the wavefront by matching the centroid with the microlens array through the neural network. This method breaks the limitation of the sub-aperture of the microlens. The experimental results show that the algorithm improves the dynamic range of the first 15 terms of the Zernike aberration reconstruction to varying degrees, ranging from 62.86% to 183.87%.

Region-correlation algorithm with improved dynamic range and reconstruction accuracy for extended object wavefront sensing

The correlation Shack-Hartmann wavefront sensor (SHWFS) is widely used in many fields in addition to solar adaptive optics. The requirement for the SHWFS dynamic range increases with the diameter of the telescope, which means a larger detector array is needed. However, the size of the detector would be restricted by the high frame rate needed for the solar observation. To solve this problem, a new, to the best of our knowledge, method called the region-correlation algorithm (RCA) is proposed. In this method, the sub-image array is divided into several regions, and the slopes of sub-apertures are calculated by referring to a selected sub-image in each region. Note that the final slope over a sub-aperture is obtained by combining the relative slopes between the selected sub-image in different regions. The dynamic range in each region is similar to the conventional correlation algorithm, and the final dynamic range of the RCA would be accumulated from those of the regions. The reconstruction accuracy under large aberration would also be improved due to the extended dynamic range. Meanwhile, the RCA does not require any extra device and the increase in calculation time resulting from the RCA is acceptable. The results of numerical simulation and experiment, compared with conventional correlation algorithm, confirm the advantages in the performance of the RCA as well.

Telephoto-lens-based Optical Differentiation Wavefront Sensor for freeform metrology

We report an Optical Differentiation Wavefront Sensor based on a telephoto lens system and binary pixelated filters. It provides a five-fold reduction in the system length compared to a 4f system with identical effective focal length. Measurements of phase plates with this system are compared to measurements performed with a commercial low-coherence interferometer. The telephoto-lens-based system can measure wavefronts with accuracy better than λ/10 Root Mean Squared (RMS) at λ=633 nm. Experimental investigation shows that the system has a high tolerance to components alignment errors.

Extended-aperture Hartmann wavefront sensor with raster scanning

In this paper, we propose an extended-aperture Hartmann wavefront sensor (HWFS) based on raster scanning. Unlike traditional HWFS, where there is a trade-off between the dynamic range and spatial resolution of wavefront measurement, our extended-aperture HWFS breaks the trade-off and thus could achieve a large dynamic range and high spatial resolution simultaneously. By applying a narrow-beam raster-scanning scheme, the detection aperture of our HWFS is extended to 40 × 40 mm2 without using the enlarging 4f relay system. The spatial resolution of our setup depends on the scanning step, the pinhole size, and the wavelength. The sensitivity and dynamic range can be adjusted flexibly by varying the axial distance between the pinhole plane and the imaging sensor plane, because our decoupled large dynamic range could be reasonable traded-off to achieve better sensitivity. Furthermore, compared with tradition HWFS, our method does not need to compute the positions of a two-dimensional spots array where complicated spots tracking algorithms are necessary to achieve high dynamic range, thus remarkably reduces the spots aliasing issue and the computational cost. It should be noted that this scheme is not only applicable for HWFS but also for Shack-Hartmann wavefront sensor (SHWFS) with microlens array to achieve higher accuracy and better power efficiency. Experiments were performed to demonstrate the capability of our method.

Optimization of Virtual Shack-Hartmann Wavefront Sensing

Virtual Shack–Hartmann wavefront sensing (vSHWS) can flexibly adjust parameters to meet different requirements without changing the system, and it is a promising means for aberration measurement. However, how to optimize its parameters to achieve the best performance is rarely discussed. In this work, the data processing procedure and methods of vSHWS were demonstrated by using a set of normal human ocular aberrations as an example. The shapes (round and square) of a virtual lenslet, the zero-padding of the sub-aperture electric field, sub-aperture number, as well as the sequences (before and after diffraction calculation), algorithms, and interval of data interpolation, were analyzed to find the optimal configuration. The effect of the above optimizations on its anti-noise performance was also studied. The Zernike coefficient errors and the root mean square of the wavefront error between the reconstructed and preset wavefronts were used for performance evaluation. The performance of the optimized vSHWS could be significantly improved compared to that of a non-optimized one, which was also verified with 20 sets of clinical human ocular aberrations. This work makes the vSHWS’s implementation clearer, and the optimization methods and the obtained results are of great significance for its applications.

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.

High-performance optical differentiation wavefront sensing towards freeform metrology

We report the demonstration of freeform optics metrology with an optical differentiation wavefront sensor that relies on spatially dithered distributions of binary pixels to synthesize a far-field amplitude filter. Analysis of experimental results and comparison with a commercial low-coherence-length interferometer shows that freeform phase plates with different magnitude of wavefront slopes can be accurately characterized. RMS accuracy of ∼ λ/10 and precision of ∼ λ/70 at 633 nm were achieved with pixelated filters having 2.5-µm pixels. Simulations that describe the characterization of a freeform optical component in the presence of photodetection noise and filter nonlinearity demonstrate the robustness of this wavefront-sensing approach for freeform optics characterization.

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.

Customised aberration-controlling corrections for keratoconic patients using contact lenses

Technological advancements in the design of soft and scleral contact lenses have led to the development of customised, aberration-controlling corrections for patients with keratoconus. As the number of contact lens manufacturers producing wavefront-guided corrections continues to expand, clinical interest in this customisable technology is also increasing among both patients and practitioners. This review outlines key issues surrounding the measurement of ocular aberrations for patients with keratoconus, with a particular focus on the possible factors affecting the repeatability of Hartmann-Shack aberrometry measurements. This review also discusses and compares the relative successes of studies investigating the design and fitting of soft and scleral customised contact lenses for patients with keratoconus. A series of key limitations that should be considered before designing customised contact lens corrections is also described. Despite the challenges of producing and fitting customised lenses, improvements in visual performance and comfortable wearing times, as provided by these lenses, could help to reduce the rate of keratoplasty in keratoconic patients, thereby significantly reducing clinical issues related to corneal graft surgery. Furthermore, enhancements in optical correction, provided by customised lenses, could lead to increased independence, particularly among young adult keratoconic patients, therefore leading to improvements in quality of life.

Large dynamic range autorefraction with a low-cost diffuser wavefront sensor

Wavefront sensing with a thin diffuser has emerged as a potential low-cost alternative to a lenslet array for aberrometry. Here we show that displacement of caustic patterns can be tracked for estimating wavefront gradient in a diffuser wavefront sensor (DWFS), enabling large dynamic-range wavefront measurements with sufficient accuracy for eyeglass prescription measurements. We compare the dynamic range, repeatability, precision, and number of resolvable prescriptions of a DWFS to a Shack-Hartmann wavefront sensor (SHWFS) for autorefraction measurement. We induce spherical and cylindrical errors in a model eye and use a multi-level Demon's non-rigid registration algorithm to estimate caustic displacements relative to an emmetropic model eye. When compared to spherical error measurements with the SHWFS using a laser diode with a laser speckle reducer, the DWFS demonstrates a ∼5-fold improvement in dynamic range (-4.0 to +4.5 D vs. -22.0 to +19.5 D) with less than half the reduction in resolution (0.072 vs. 0.116 D), enabling a ∼3-fold increase in the number of resolvable prescriptions (118 vs. 358). In addition to being lower-cost, the unique, non-periodic nature of the caustic pattern formed by a diffuser enables a larger dynamic range of aberration measurements compared to a lenslet array.

Adaptive Shack-Hartmann wavefront sensor accommodating large wavefront variations

Shack-Hartmann wavefront sensors (SHWFSs) usually have fixed subaperture areas on the detector, in order to fix the minimum and maximum amounts of wavefront departure, or the dynamic range of measurement. We introduce an active approach, named Adaptive Shack Hartmann Wavefront Sensor (A-SHWFS). A-SHWFS is used to reconfigure detection subaperture areas by either blocking or unblocking desired lenslets by using an electronically modulated mask. This mask either increases or decreases the measurable aberration magnitude by placing a liquid crystal display (LCD) panel in front of the lenslet array. Depending on which control signal that is sent to the LCD, the variable, application-dependent blocking pattern (horizontal, vertical, diagonal, uneven) makes this an adaptive and efficient sensor with a variable dynamic range of measurement. This scheme is also useful for regional blocking, which occurs when the wavefront is severely aberrated in a limited region.

Modeling near-null testing method of a freeform surface with a deformable mirror compensator

We present and analyze a new measurement method of freeform surfaces with a deformable mirror (DM), which functions as a wavefront compensator. We discuss the maximum slope compensation of a DM in the first-order approximation and derive how to calculate the ideal DM form. A constrained optimization procedure is conducted to ensure the actual DM form fits the ideal DM form as closely as possible. To demonstrate the feasibility and understand the measurable range of our method, we evaluate freeform surfaces with a single Zernike term, the first 36 random Zernike terms, and 230 random Zernike terms. A tolerance analysis of the DM position is carried out to show the effect of the tilt and the decenter of the DM on the measurement accuracy. Our studies show that the proposed system is very flexible for freeform surface metrology.

Comparison of the plenoptic sensor and the Shack-Hartmann sensor

Adaptive optics has been successfully used for decades in the field of astronomy to correct for atmospheric turbulence. A well-developed example involves sensing the slightly distorted wavefronts with a Shack-Hartmann sensor and then correcting them with a phase conjugate device. While the Shack-Hartmann sensor has proven effective for astronomical purposes, it has been less successful for use in deep turbulence conditions often found in ground-to-ground-based optical systems. We have studied an alternative way to sense and correct distorted wavefronts using a plenoptic sensor. We review the design of the plenoptic sensor and directly compare it with the well-known Shack-Hartmann sensor. An experimental comparison of the plenoptic sensor and the Shack-Hartmann sensor is performed to highlight their differences in real-world atmospheric turbulence conditions.

Design, fabrication, and testing of a Shack-Hartmann sensor with an automatic registration feature

In this research, design, construction, and testing of an innovative Shack-Hartmann sensor are described. As the most critical component, a polymer microlens array is injection molded and mounted on a board-level CMOS camera such that the focal plane of the microlens array is on the camera's image plane. To allow for automatic registration of the spots of the measured area, a diffusing surface was created at the center of the lens array in the same diamond machining process in an uninterrupted operation. This unique diffusing surface does not generate an image spot. The no-spot feature functions as the reference in the measurement on the camera's image plane. Using this unique feature, large global tip-tilt error can be detected and eliminated. In this research, both experiments and simulation have shown that the Shack-Hartmann sensor built using low cost components is capable of precision wavefront detection. This research also demonstrated that automatic registration based on the diffusing surface is simple and reliable.

Shack-Hartmann wavefront sensor with large dynamic range by adaptive spot search method

A Shack-Hartmann wavefront sensor (SHWFS) that consists of a microlens array and an image sensor has been used to measure the wavefront aberrations of human eyes. However, a conventional SHWFS has finite dynamic range depending on the diameter of the each microlens. The dynamic range cannot be easily expanded without a decrease of the spatial resolution. In this study, an adaptive spot search method to expand the dynamic range of an SHWFS is proposed. In the proposed method, spots are searched with the help of their approximate displacements measured with low spatial resolution and large dynamic range. By the proposed method, a wavefront can be correctly measured even if the spot is beyond the detection area. The adaptive spot search method is realized by using the special microlens array that generates both spots and discriminable patterns. The proposed method enables expanding the dynamic range of an SHWFS with a single shot and short processing time. The performance of the proposed method is compared with that of a conventional SHWFS by optical experiments. Furthermore, the dynamic range of the proposed method is quantitatively evaluated by numerical simulations.

Simple and robust algorithm to extend the dynamic range of tip-tilt for a Shack-Hartmann sensor

We propose an algorithm to extend the dynamic range of tip-tilt (TT) for a Shack-Hartmann wave-front sensor. With this method, the dynamic range of TT is determined by the size of the whole CCD pixel array rather than the size of the sub-aperture. Thus the separate TT sensor in adaptive optics (AO) systems for optical telescope can be saved, which will simplify the systems and enhance the light energy efficiency. The proposed algorithm is computationally effective and appropriate for the real-time TT computation of AO systems. The simulated and experimental results show that the algorithm is robust to realistic scintillation and photon noise and can work well under poor observing conditions. For the given condition with r₀ of 5 cm at 550 nm and average flux of 100 photons per sub-aperture, the ultimate measurement accuracy of TT is about 5% pixels (peak-to-valley value).

Shack-Hartmann spot dislocation map determination using an optical flow method

We present a robust, dense, and accurate Shack-Hartmann spot dislocation map determination method based on a regularized optical flow algorithm that does not require obtaining the spot centroids. The method is capable to measure in presence of strong noise, background illumination and spot modulating signals, which are typical limiting factors of traditional centroid detection algorithms. Moreover, the proposed approach is able to face cases where some of the reference beam spots have not a corresponding one in the distorted Hartmann diagram, and it can expand the dynamic range of the Shack-Hartmann sensor unwrapping the obtained dense dislocation maps. We have tested the algorithm with both simulations and experimental data obtaining satisfactory results. A complete MATLAB package that can reproduce all the results can be downloaded from [http://goo.gl/XbZVOr].

50 years of optics research [Invited]

The 50-year life span of Applied Optics covers also approximately the time I have been engaged in optics. I started in 1962 [1] with the Institute for Optics and Spectroscopy, which was one of several Academy Institutes (mission statement: "theoria cum praxi," G. Leibniz) located in Berlin-Adlershof on the area of the first airfield in Berlin dating back to the beginning of the 20th century.

Adaptive optics technology for high-resolution retinal imaging

Adaptive optics (AO) is a technology used to improve the performance of optical systems by reducing the effects of optical aberrations. The direct visualization of the photoreceptor cells, capillaries and nerve fiber bundles represents the major benefit of adding AO to retinal imaging. Adaptive optics is opening a new frontier for clinical research in ophthalmology, providing new information on the early pathological changes of the retinal microstructures in various retinal diseases. We have reviewed AO technology for retinal imaging, providing information on the core components of an AO retinal camera. The most commonly used wavefront sensing and correcting elements are discussed. Furthermore, we discuss current applications of AO imaging to a population of healthy adults and to the most frequent causes of blindness, including diabetic retinopathy, age-related macular degeneration and glaucoma. We conclude our work with a discussion on future clinical prospects for AO retinal imaging.

Wave-front analysis of personal eye protection

Shack-Hartmann wave-front sensing has been successfully applied to many fields of optical testing including the human eye itself. We propose wave-front measurement for testing protective eye wear for production control and investigation of aberrations. Refractive power data is derived from the wave-front data and compared to a subjective measurement technique based on a focimeter. Additional image quality classification was performed with a multivariate model using objective parameters to resample a subjectively determined visual quality. Wave-front measurement advances optical testing of protective eye wear and may be used for objective quality control.

Comparison of sorting algorithms to increase the range of Hartmann-Shack aberrometry

Recently many software-based approaches have been suggested for improving the range and accuracy of Hartmann-Shack aberrometry. We compare the performance of four representative algorithms, with a focus on aberrometry for the human eye. Algorithms vary in complexity from the simplistic traditional approach to iterative spline extrapolation based on prior spot measurements. Range is assessed for a variety of aberration types in isolation using computer modeling, and also for complex wavefront shapes using a real adaptive optics system. The effects of common sources of error for ocular wavefront sensing are explored. The results show that the simplest possible iterative algorithm produces comparable range and robustness compared to the more complicated algorithms, while keeping processing time minimal to afford real-time analysis.

Multi-pass Shack-Hartmann planeness test: monitoring thermal stress

The multi-pass solution for surface measurements with the help of a Shack-Hartmann sensor (SHS) on the basis of a Fizeau cavity enables fast access to surface deviation data due to the high speed of the SHS and easy referencing of the measured data through difference measurements. The multi-pass solution described in a previous publication [J. Schwider, Opt. Express 16, 362 (2008)], provides highly sensitive measurements of small displacements caused by thermal non-equilibrium states of the test set up. Here, we want to demonstrate how a pulsed thermal load changes the surface geometry. In addition the temporal response for different plate materials is monitored through a fast wave front measurement with very high sensitivity. The thermal load close to a delta-function in time will be applied from the back-side of a plane plate by heating a small Peltier element with a heat impulse of known order of magnitude. The development of the surface deviation on the time axis can be monitored by storing a set of successive deviation pictures.

A simple and robust method to extend the dynamic range of an aberrometer

We present an algorithm to extend significantly the dynamic range of a Shack-Hartmann wavefront sensor. With this method, the recorded Shack-Hartmann spots are not constrained to stay in the field of view of their lenslet. The proposed algorithm is computationally effective, robust to a high level of noise on the measured centroid positions and also to missing centroid values. The principle is closely related to the description of wavefronts using Zernike polynomials, which makes optimization for a given sensor and application achievable thanks to numerical simulation. These features make it useful for the measurements of highly aberrated eyes.

Asymmetrical optical lenslet array realized by spatial light modulator for measuring toroidal surfaces

The Shack-Hartmann wavefront sensor (SHWS) recently has been extensively researched for optical surface metrology due to its extendable dynamic range compared with interferometry technique. In this paper, we proposed to use a digital SHWS to measure toroidal surfaces, which are widely used in many optical systems due to their different symmetries and curvatures in the X and Y directions. For what is believed to be the first time, an asymmetrical optical lenslet array implemented by a spatial light modulator was presented to tackle the measurement challenge. This unconventional design approach has a great advantage to provide different optical powers in the X and Y directions so that focusing spots can be formed and captured on the detector plane for accurate centroid finding and precise wavefront evaluation for 3D shape reconstruction of the toroidal surface. A digital SHWS system with this extraordinary microlens array was built to verify the design concept, and the experimental results were presented and analyzed.

Generalized method for sorting Shack-Hartmann spot patterns using local similarity

The sensitivity and dynamic range of a Shack-Hartmann wavefront sensor is enhanced when the spots produced by the lenslet array are allowed to shift more than one lenslet radius from their on-axis positions. However, this presents the problem of accurately and robustly associating the spots with their respective subapertures. This paper describes a method for sorting spots that takes advantage of the local spot position distortions to unwrap the spot pattern. The described algorithm is both simple and robust and also applicable to any lenslet array geometry that can be described as a two-dimensional lattice, including hexagonal arrays, which are shown here to be more efficient than square arrays.

Characterizing the wave aberration in eyes with keratoconus or penetrating keratoplasty using a high-dynamic range wavefront sensor

PURPOSE

The purpose of this study was to characterize aberrations in 2 populations of eyes, namely those with keratoconus (KC) and those having undergone penetrating keratoplasty (PK), using a large-dynamic range Shack-Hartmann wavefront sensor.

DESIGN

Prospective comparative case series.

PARTICIPANTS

Twenty-one people with ocular pathologic features (either KC or PK) were recruited for this study. A previously compiled population of 190 people with no pathologic features other than refractive error was used as a means for comparison.

METHODS

Thirty-three abnormal eyes (19 with KC and 14 PK) were measured using a high-dynamic range wavefront sensor, and Zernike coefficients were computed over a 6-mm pupil. The data then were used to characterize the populations by themselves, as well as to compare them with the population of normal eyes.

MAIN OUTCOME MEASURES

Root mean square (RMS) higher-order aberration (HOA), percent of higher-order or total aberration variance, and magnitude of individual Zernike modes (in micrometers). Visual benefit of correcting higher-order aberrations was used when comparing pathologic and normal populations.

RESULTS

The keratoconic eyes exhibited 2.24 microm of HOA RMS on average. Vertical coma accounted for 53+/-32% (mean+/-standard deviation [SD]) of the HOA variance and was the most dominant higher-order aberration. The PK subjects had an average higher-order RMS of 2.25 microm, and trefoil dominated in this population with an average HOA variance contribution of 38+/-23% (mean+/-SD). The KC and PK higher-order aberrations represented 16+/-20% and 16+/-13% (mean+/-SD) of the total aberration variance, whereas the ratio was only 1+/-1% in the normal population. A visual benefit calculation on 15 KC eyes and 14 PK eyes yielded a result of 4.4+/-2.0 and 6.0+/-1.5 (mean+/-SD), respectively, whereas the normal population had a visual benefit of only 2.1+/-0.4.

CONCLUSIONS

Eyes with KC and PK have higher-order aberrations that are approximately 5.5 times more than what is typical in normal eyes. Vertical coma is the dominant higher-order aberration in people with KC, whereas PK eyes are dominated by trefoil, spherical aberration, and coma. Correcting these aberrations may provide substantial improvements in vision beyond what is possible with conventional correction methods.

Accurate and precise optical testing with a differential Hartmann wavefront sensor

A novel differential Hartmann sensor is described. It can be used to determine the characteristics of an optic accurately, precisely, and simply without detailed knowledge of the wavefront used to illuminate the optical system or of the geometry of the measurement system. We demonstrate the application of this sensor to both zonal and modal optical testing of lenses. We also describe a dual-camera implementation of the sensor that would enable high-speed optical testing.

Sorting method to extend the dynamic range of the Shack-Hartmann wave-front sensor

We propose a simple and powerful algorithm to extend the dynamic range of a Shack-Hartmann wave-front sensor. In a conventional Shack-Hartmann wave-front sensor the dynamic range is limited by the f-number of a lenslet, because the focal spot is required to remain in the area confined by the single lenslet. The sorting method proposed here eliminates such a limitation and extends the dynamic range by tagging each spot in a special sequence. Since the sorting method is a simple algorithm that does not change the measurement configuration, there is no requirement for extra hardware, multiple measurements, or complicated algorithms. We not only present the theory and a calculation example of the sorting method but also actually implement measurement of a highly aberrated wave front from nonrotational symmetric optics.

Unwrapping Hartmann-Shack Images from Highly Aberrated Eyes Using an Iterative B-spline Based Extrapolation Method

PURPOSE

When the wavefront aberrations of the eye are measured with a Hartmann-Shack (HS) sensor, the resulting spot pattern must be unwrapped, that is, for each lenslet the corresponding spot must be identified. This puts a limitation on the measurable amount of aberrations. To extend the range of an HS sensor, a powerful unwrapping algorithm has been developed.

METHODS

The unwrapping algorithm starts by connecting the central HS spots to the central lenslets. It then fits a B-spline function through a least squares estimate to the deviations of the central HS spots. This function is then extrapolated to find the expected locations of HS spots for the unconnected lenslets. The extrapolation is performed gradually in an iterative manner; the closest unconnected lenslets are extrapolated and connected, and then the B-spline function is least squares fitted to all connected HS spots and extrapolated again.

RESULTS

Wavefront aberrations from eyes with high aberrations can be successfully unwrapped with the developed algorithm. The dynamic range of a typical HS sensor increases 3.5 to 13 times compared with a simple unwrapping algorithm.

CONCLUSIONS

The implemented algorithm is an efficient unwrapping tool and allows the use of lenslets with a low numerical aperture and thus gives a relatively higher accuracy of measurements of the ocular aberrations.

Comparative study with double-exposure digital holographic interferometry and a shack-hartmann sensor to characterize transparent materials

We compare wave-front measurements using double-exposure digital holography and a Shack-Hartmann sensor. A voltage-driven liquid-crystal wedge modulates the optical wave front and provides a refractive-index gradient typical of interesting transparent materials. Measurement accuracy and reliability are similar for both methods. In our opinion, digital holographic interferometry has several advantages for both laboratory and field environments. When compared with Shack-Hartmann methods, these advantages include hardware simplicity and robustness, relative insensitivity to sample dynamic range, and less computational demanding and more straightforward data evaluation algorithms. We believe that digital holography provides the methodology of choice for field studies of transparent materials such as microgravity protein crystal growth experiments.

Nonnull testing of rotationally symmetric aspheres: a systematic error assessment

An optical setup for the testing of rotationally symmetric aspheres without a null optic is proposed. The optical setup is able to transfer the strongly curved wave fronts that stem from the reflection of a spherical testing wave front at a rotationally symmetric asphere. By simulation it is proved that the algorithms of the Shack-Hartmann sensor that is used can cope with the steep wave-front slopes (approximately 110lambda/mm) in the detection plane. The systematic errors of the testing configuration are analyzed and separated. For all types of error, functionals are derived whose significance is proved by simulation. The maximum residual errors in the simulations are fewer than lambda/500 (peak to valley).

Wave-front reconstruction with a shack-hartmann sensor with an iterative spline fitting method

One limitation of the conventional Shack-Hartmann sensor is that the spots of each microlens have to remain in their respective subapertures. We present an algorithm that assigns the spots to their reference points unequivocally even if they are situated far outside their subaperture. For this assignment a spline function is extrapolated in successive steps of the iterative algorithm. The proposed method works in a single-shot technique and does not need any aid from mechanical devices. The reconstruction of a simulated steep aspherical wave front (approximately 100 lambda/mm slope) is described as well as experimental results of the measurement of a spherical wave front with a huge peak-to-valley value (approximately 400 lambda). The performance of the method is compared with the unwrapping method, which has been published before.