Dynamic wave-front generation for the characterization and testing of optical systems

Simultaneous realisation of zonal and modal wavefront sensing using programmable multiplexed grating patterns

In the present work, we propose a programmable multiplexed grating-based wavefront sensor (MGWS) to realise zonal and modal wavefront sensing approaches simultaneously. This is implemented by employing different bit-planes of a color image such that zonal wavefront sensing is performed with enhanced spatial resolution and modal wavefront sensing is performed to measure a large number of aberration modes present in the incident wavefront, simultaneously. We present proof-of-concept simulation results that demonstrate the working of the proposed MGWS and its ability to compensate for the presence of large number of aberration modes significantly, in comparison to either of the sensing approaches when used independently. Further, simulation results are included to quantify the same by considering an optical imaging system to image an array of two-dimensional bead objects. The proposed sensor is flexible in easy switching between either of the sensing approaches and the number of bit-planes can be increased conveniently to further improve the performance of the proposed MGWS.

Optical-component-only adaptive optics

This Letter introduces a technique for performing binary adaptive optics, which is carried out by optical components only, without the help of any electronic or optoelectronic device. In this technique, the interferogram produced by a point diffraction interferometer modulates a light-driven crystal. The modulated light-driven crystal may produce pupil-plane only-phase or only-amplitude binary masks to mitigate phase aberrations. The capability of working unsupported makes it suitable for application in hard-to-reach or hazardous locations such as satellites, underwater, or contaminated places. The Letter includes an experimental validation where the ability of the technique to produce pupil amplitude masking is confirmed.

Quaternary adaptive optics

We present a new Point Diffraction Interferometer (PDI). Binary adaptive optics (BAO) and Quaternary Adaptive Optics (QAO) can be performed with the help of this PDI as a wavefront sensor. The PDI interferogram, once binarized, is used in two consecutive steps to produce a quaternary mask with phase values 0, π/2, π and 3π/2. The addition of the quaternary mask compensates for the aberrated wavefront and allows us to reach a Strehl ratio of about 0.81. We have verified through computer simulations that the use of QAO depends on the number of actuators of the compensating device to achieve effective compensation. The technique was successfully validated through an experiment.

Focusing light in biological tissue through a multimode optical fiber: refractive index matching

Controlling light propagation through a step-index multimode optical fiber (MMF) has several important applications, including biological imaging. However, little consideration has been given to the coupling of fiber and tissue optics. In this Letter, we characterized the effects of tissue-induced light distortions, in particular those arising from a mismatch in the refractive index of the pre-imaging calibration and biological media. By performing the calibration in a medium matching the refractive index of the brain, optimal focusing ability was achieved, as well as a gain in focus uniformity within the field-of-view. These changes in illumination resulted in a 30% improvement in spatial resolution and intensity in fluorescence images of beads and live brain tissue. Beyond refractive index matching, our results demonstrate that sample-induced aberrations can severely deteriorate images from MMF-based systems.

Improvement in error propagation in the Shack-Hartmann-type zonal wavefront sensors

Estimation of the wavefront from measured slope values is an essential step in a Shack-Hartmann-type wavefront sensor. Using an appropriate estimation algorithm, these measured slopes are converted into wavefront phase values. Hence, accuracy in wavefront estimation lies in proper interpretation of these measured slope values using the chosen estimation algorithm. There are two important sources of errors associated with the wavefront estimation process, namely, the slope measurement error and the algorithm discretization error. The former type is due to the noise in the slope measurements or to the detector centroiding error, and the latter is a consequence of solving equations of a basic estimation algorithm adopted onto a discrete geometry. These errors deserve particular attention, because they decide the preference of a specific estimation algorithm for wavefront estimation. In this paper, we investigate these two important sources of errors associated with the wavefront estimation algorithms of Shack-Hartmann-type wavefront sensors. We consider the widely used Southwell algorithm and the recently proposed Pathak-Boruah algorithm [J. Opt.16, 055403 (2014)JOOPDB0150-536X10.1088/2040-8978/16/5/055403] and perform a comparative study between the two. We find that the latter algorithm is inherently superior to the Southwell algorithm in terms of the error propagation performance. We also conduct experiments that further establish the correctness of the comparative study between the said two estimation algorithms.

Zonal wavefront sensing with enhanced spatial resolution

In this Letter, we introduce a scheme to enhance the spatial resolution of a zonal wavefront sensor. The zonal wavefront sensor comprises an array of binary gratings implemented by a ferroelectric spatial light modulator (FLCSLM) followed by a lens, in lieu of the array of lenses in the Shack-Hartmann wavefront sensor. We show that the fast response of the FLCSLM device facilitates quick display of several laterally shifted binary grating patterns, and the programmability of the device enables simultaneous capturing of each focal spot array. This eventually leads to a wavefront estimation with an enhanced spatial resolution without much sacrifice on the sensor frame rate, thus making the scheme suitable for high spatial resolution measurement of transient wavefronts. We present experimental and numerical simulation results to demonstrate the importance of the proposed wavefront sensing scheme.

Experimental observation of the aberration effects on a radially polarized beam

In the last couple of decades the radially polarized beam has been gaining a lot of importance in diverse areas owing to its unique properties, especially near the focus of a lens. For instance, when focused tightly, the radially polarized beam produces a strong axially polarized field on the optical axis near the focus. Some of the areas where the radially polarized beam is found to be useful are optical trapping, laser machining, optical data storage, optical superresolution, and so on. Considering the fact that there is not any optical system that can be treated as perfectly aberration free, the applications of the radially polarized beam can, in practice, more or less be affected by the presence of aberrations. Indeed, there have been studies to understand the properties of the radially polarized beam in the presence of various aberrations. However, most such studies have been purely theoretical without being complimented by experimental results. In this paper, we present a comprehensive experimental investigation on the effect of aberrations on a focused radially polarized beam. The accuracy of our experimental results is confirmed by comparing them with the equivalent numerical simulation results.

Programmable simulator for beam propagation in turbulent atmosphere

The study of light propagation though the atmosphere is crucial in different areas such as astronomy, free-space communications, remote sensing, etc. Since outdoors experiments are expensive and difficult to reproduce it is important to develop realistic numerical and experimental simulations. It has been demonstrated that spatial light modulators (SLMs) are well-suited for simulating different turbulent conditions in the laboratory. Here, we present a programmable experimental setup based on liquid crystal SLMs for simulation and analysis of the beam propagation through weak turbulent atmosphere. The simulator allows changing the propagation distances and atmospheric conditions without the need of moving optical elements. Its performance is tested for Gaussian and vortex beams.

Non-iterative phase hologram computation for low speckle holographic image projection

Phase-only spatial light modulators (SLMs) are widely used in holographic display applications, including holographic image projection (HIP). Most phase computer generated hologram (CGH) calculation algorithms have an iterative structure with a high computational load, and also are prone to speckle noise, as a result of the random phase terms applied on the desired images to mitigate the encoding noise. In this paper, we present a non-iterative algorithm, where simple Discrete Fourier Transform (DFT) relations are exploited to compute phase CGHs that exactly control half of the desired image samples (those on even - or odd - indexed rows - or columns) via a single Fast Fourier Transform (FFT) and trivial arithmetic operations. The encoding noise appearing on the uncontrolled half of the image samples is reduced by the application of structured, non-random initial phase terms so that speckle noise is also kept low. High quality reconstructions are obtained under temporal averaging of several SLM frames. Interlaced video within half of the addressable image area is readily deliverable without frame rate division. Our algorithm provides about 6X and 20X reduction in computational cost compared to IFTA and FIDOC algorithms, respectively. Simulations and experiments verify that the algorithm constitutes a promising option for real-time computation of phase CGHs.

Zonal wavefront sensing using a grating array printed on a polyester film

In this paper, we describe the development of a zonal wavefront sensor that comprises an array of binary diffraction gratings realized on a transparent sheet (i.e., polyester film) followed by a focusing lens and a camera. The sensor works in a manner similar to that of a Shack-Hartmann wavefront sensor. The fabrication of the array of gratings is immune to certain issues associated with the fabrication of the lenslet array which is commonly used in zonal wavefront sensing. Besides the sensing method offers several important advantages such as flexible dynamic range, easy configurability, and option to enhance the sensing frame rate. Here, we have demonstrated the working of the proposed sensor using a proof-of-principle experimental arrangement.

Traceable interferometry using binary reconfigurable holograms

We describe the characterization of a ferroelectric-liquid-crystal-on-silicon (FLCOS) spatial light modulator (SLM) in the production of holograms for use in interferometric metrology. It has already been shown that such a device can be used in producing small-amplitude arbitrary reference surfaces with small but appreciable errors due to the contaminating effect of higher-order structures being propagated through the spatial filter. Here we further quantify the size of these residuals for increasingly large aberrations up to nine waves rms Zernike astigmatism, showing a Zernike-corrected rms wavefront error of roughly 0.06 waves with high vibrational stability. We also present measurements of a vacuum window element using the FLCOS device to drastically reduce interferometric fringe density, showing a residual wavefront error of 0.046 waves rms with dominant components originating from test piece structure rather than holographic errors.

Note: laser beam scanning using a ferroelectric liquid crystal spatial light modulator

In this work we describe laser beam scanning using a ferroelectric liquid crystal spatial light modulator. Commercially available ferroelectric liquid crystal spatial light modulators are capable of displaying 85 colored images in 1 s using a time dithering technique. Each colored image, in fact, comprises 24 single bit (black and white) images displayed sequentially. We have used each single bit image to write a binary phase hologram. For a collimated laser beam incident on the hologram, one of the diffracted beams can be made to travel along a user defined direction. We have constructed a beam scanner employing the above arrangement and demonstrated its use to scan a single laser beam in a laser scanning optical sectioning microscope setup.

Zonal wavefront sensor with reduced number of rows in the detector array

In this paper, we describe a zonal wavefront sensor in which the photodetector array can have a smaller number of rows. The test wavefront is incident on a two-dimensional array of diffraction gratings followed by a single focusing lens. The periodicity and the orientation of the grating rulings of each grating can be chosen such that the +1 order beam from the gratings forms an array of focal spots in the detector plane. We show that by using a square array of zones, it is possible to generate an array of +1 order focal spots having a smaller number of rows, thus reducing the height of the required detector array. The phase profile of the test wavefront can be estimated by measuring the displacements of the +1 order focal spots for the test wavefront relative to the +1 order focal spots for a plane reference wavefront. The narrower width of the photodetector array can offer several advantages, such as a faster frame rate of the wavefront sensor, a reduced amount of cross talk between the nearby detector zones, and a decrease in the maximum thermal noise. We also present experimental results of a proof-of-concept experimental arrangement using the proposed wavefront sensing scheme.

Interferometry using binary holograms without high order diffraction effects

We describe a technique for a phase-stepping interferometer based on programmable binary phase holograms, particularly useful for optical testing of aspheric or free-form surfaces. It is well-known that binary holograms can be used to generate reference surfaces for interferometry, but a major problem is that cross talk from higher diffraction orders and aliasing can reduce the fidelity of the system. Here, we propose a new encoding technique which improves the accuracy of the technique and demonstrate its implementation using a binary liquid crystal spatial light modulator.

Adaptive phase compensation for ultracompact laser scanning endomicroscopy

We present an approach to laser scanning endomicroscopy that requires no moving parts and can be implemented with no distal scanners or optics, permitting extremely compact endoscopic probes to be developed. Our approach utilizes a spatial light modulator to correct for phase variations across a fiber imaging bundle and to encode for arbitrary wavefronts at the distal end of the fiber bundle. Thus, it is possible to realize both focusing and beam scanning at the output of the fiber bundle with no distal components. We present proof of principle results to illustrate three-dimensional scanning of the focal spot and exemplar images of a United States Air Force resolution test chart.

Optical sectioning microscope with a binary hologram based beam scanning

We describe the development of a beam scanning microscope that can perform optical sectioning based on the principle of confocal microscopy. The scanning is performed by a laser beam diffracted from a dynamic binary hologram implemented using a liquid crystal spatial light modulator. Using the proposed scanning mechanism, unlike the conventional confocal microscopes, scanning over a two-dimensional area of the sample can be obtained without the use of a pair of galvo mirror scanners. The proposed microscope has a number of advantages, such as superior frame to frame repeatability, simpler optical arrangement, increased pixel dwell time relative to the time between two pixels, illumination of only the sample points without pulsing the laser, and absolute control over the amplitude and phase of the illumination beam on a pixel to pixel basis. The proposed microscope can be particularly useful for applications requiring very long exposure time or very large working distance objective lenses. In this paper we present experimental implementation of the setup using a nematic liquid crystal spatial light modulator and proof-of-concept experimental results.

Novel spectral range expansion method for liquid crystal adaptive optics

Energy loss is a main problem of liquid crystal adaptive optics systems (LC AOSs). It is caused by the polarization dependence and narrow spectral range. The polarization dependence has been avoided by Love and Mu et al. [Appl. Opt. 32, 2222 (1993); Appl. Opt. 47, 4297 (2008)]. In this paper, a novel method was proposed to extend the spectral range of LC AOSs using multiple liquid crystal wavefront correctors (LCWFCs) to improve the energy utilization. Firstly, the chromatism of an LCWFC was measured and analyzed. The calculated results indicate that one LCWFC is only suitable to perform adaptive correction for a narrow waveband; therefore, multiple LCWFCs must be used to achieve a broadband correction. Secondly, based on open-loop control, a novel optical layout consisting of three LCWFCs was proposed to extend the spectral range of LC AOSs and thus achieve correction in the whole waveband of 520-810 nm. Thirdly, a broadband correction experiment was conducted and near diffraction-limited resolution was achieved in the waveband of 520-690 nm. Finally, a 500 m horizontal turbulence correction experiment was performed in the waveband of 520-690 nm. With adaptive correction, the resolution of the optical system was improved significantly and the image of the single fiber was clearly resolved. Furthermore, compared with a sub-waveband system, the system energy was improved. The energy of the whole waveband is equal to the sum of all the sub-wavebands. The experiment results validated our method and indicate that the chromatism in a broad waveband of LC AOSs can be eliminated. And then, the system energy can be improved greatly using the novel method.

Experimental detection of optical vortices with a Shack-Hartmann wavefront sensor

Laboratory experiments are carried out to detect optical vortices in conditions typical of those experienced when a laser beam is propagated through the atmosphere. A Spatial Light Modulator (SLM) is used to mimic atmospheric turbulence and a Shack-Hartmann wavefront sensor is utilised to measure the slopes of the wavefront surface. A matched filter algorithm determines the positions of the Shack-Hartmann spot centroids more robustly than a centroiding algorithm. The slope discrepancy is then obtained by taking the slopes measured by the wavefront sensor away from the slopes calculated from a least squares reconstruction of the phase. The slope discrepancy field is used as an input to the branch point potential method to find if a vortex is present, and if so to give its position and sign. The use of the slope discrepancy technique greatly improves the detection rate of the branch point potential method. This work shows the first time the branch point potential method has been used to detect optical vortices in an experimental setup.

Zonal wavefront sensing using an array of gratings

We describe a zonal-wavefront-sensing technique using an array of plane diffraction gratings. A spatially coherent beam, whose wavefront is to be measured, is incident on the array of gratings. The direction of a diffracted beam of a certain diffraction order is a function of the orientation and periodicity of the corresponding grating. Thus, by choosing the orientation and periodicity of each grating appropriately and by having a lens immediately behind the grating array, it is possible to get an array of focal spots. The profile of the incident wavefront can be estimated from the displacements of these focal spots relative to those due to an unaberrated beam. The arrangement makes it possible to increase the separation between two adjacent focal spots corresponding to two nearby gratings without effecting the areas of the gratings. Consequently, a relatively large dynamic range in wavefront measurement can be achieved without compromising the accuracy. With the arrangement it is also possible to use a photodetector array whose outline is independent of the grating array outline. The proposed wavefront-sensing technique is implemented experimentally using a liquid-crystal spatial-light modulator in conjunction with a CCD camera, and the obtained results are presented.

Wave-aberration control with a liquid crystal on silicon (LCOS) spatial phase modulator

Liquid crystal on Silicon (LCOS) spatial phase modulators offer enhanced possibilities for adaptive optics applications in terms of response velocity and fidelity. Unlike deformable mirrors, they present a capability for reproducing discontinuous phase profiles. This ability also allows an increase in the effective stroke of the device by means of phase wrapping. The latter is only limited by the diffraction related effects that become noticeable as the number of phase cycles increase. In this work we estimated the ranges of generation of the Zernike polynomials as a means for characterizing the performance of the device. Sets of images systematically degraded with the different Zernike polynomials generated using a LCOS phase modulator have been recorded and compared with their theoretical digital counterparts. For each Zernike mode, we have found that image degradation reaches a limit for a certain coefficient value; further increase in the aberration amount has no additional effect in image quality. This behavior is attributed to the intensification of the 0-order diffraction. These results have allowed determining the usable limits of the phase modulator virtually free from diffraction artifacts. The results are particularly important for visual simulation and ophthalmic testing applications, although they are equally interesting for any adaptive optics application with liquid crystal based devices.

Correction of horizontal turbulence with nematic liquid crystal wavefront corrector

To correct horizontal turbulences, a nematic liquid crystal wavefront corrector (NLC WFC) with a fast response is used. It can linearly modulate 2pi radian at a wavelength of 633 nm. The closed-loop frequency of the adaptive optics system was originally only 12 Hz. Hence, a control system using the NLC WFC was developed, graphic processing units (GPUs) were used to compute the compensated wavefront, and the driving software for the NLC WFC was optimized. With these improvements, the closed loop frequency increased up to 60 Hz. Finally, the correction of a 500-m horizontal turbulence was performed with this fast adaptive system. After the correction, the averaged peak-to-valley (PV) and root-mean-square (RMS) values of the wavefront were reduced to 0.2 lambda and 0.06 lambda, respectively. The core of a fiber bundle is also resolved with a field angle of 0.68". As the limit of the angular resolution of the telescope is 0.65", the quasi-diffraction limited image is acquired with the closed-loop correction. It is shown that the NLC WFC has the ability to correct weak turbulences.

Wavefront sensorless adaptive optics for large aberrations

In some adaptive optics systems the aberration is determined not by using a wavefront sensor but by sequential optimization of the adaptive correction element. Efficient schemes for the control of such systems are essential if they are to be effective. A scheme is introduced that permits the efficient measurement of large amplitude wavefront aberrations that are represented by an appropriate series of modes. This scheme uses an optimization metric based on the root-mean-square spot radius (or focal spot second moment) and an aberration expansion using polynomials suited to the representation of lateral aberrations. Experimental correction of N aberration modes is demonstrated with a minimum of N+1 photodetector measurements. The geometrical optics basis means that the scheme can be extended to arbitrarily large aberrations.

Susceptibility to and correction of azimuthal aberrations in singular light beams

We show how the effects of azimuthal optical aberrations on singular light beams can result in an intensity modulation in the beam waist or focal point spread function (PSF) that is directly proportional to the amplitude of the applied phase aberration. The resulting distortions are enough to significantly degrade the utility of the singular beams even in well corrected optical systems. However we show that pattern of these intensity modulations is related to the azimuthal order of the applied aberration and we suggest how this can be used to measure those aberrations. We demonstrate a closed loop system using a liquid crystal spatial light modulator as a programmable diffractive optical element to both generate the beam and correct for the sensed aberrations based on feed back from a CCD detected intensity image of the focal point spread function.

Methods for the characterization of deformable membrane mirrors

We demonstrate two methods for the characterization of deformable membrane mirrors and the training of adaptive optics systems that employ these mirrors. Neither method employs a wave-front sensor. In one case, aberrations produced by a wave-front generator are corrected by the deformable mirror by use of a rapidly converging iterative algorithm based on orthogonal deformation modes of the mirror. In the other case, a simple interferometer is used with fringe analysis and phase-unwrapping algorithms. We discuss how the choice of singular values can be used to control the pseudoinversion of the control matrix.

Phase retrieval for high-numerical-aperture optical systems

We describe a phase retrieval approach for intensity point-spread functions of high-numerical-aperture optical systems such as light microscopes. The method calculates a generalized pupil function defined on a spherical shell, using measured images at several defocus levels. The resultant pupil functionsreproduce measured point-source images significantly better than does an ideal imaging model. Availability of pupil function information will facilitate new approaches to aberration correction in such systems.

Method for the generation of arbitrary complex vector wave fronts

We describe an extremely versatile method that permits the accurate generation of arbitrary complex vector wave fields. We implement the scheme using a reconfigurable binary optical element that also permits additional fine tuning, such as aberration correction, to be performed. As examples we demonstrate the generation of both azimuthally and radially polarized beams.

Retinal imaging with a low-cost micromachined membrane deformable mirror

PURPOSE

To study the retina in normal subjects with a high-resolution imaging system using adaptive optics for wave front aberration correction.

METHODS

We used a low-cost 37-element micromachined membrane deformable mirror (MMDM) with a continuous membrane as the reflective surface. A Hartmann-Shack wave front sensor with cooled charge coupled device camera was used to measure the wave front aberration. Zernike polynomials were used to describe the wave front shape. We developed a mirror control system to compensate for wave aberrations. We tested this instrument in normal subjects.

RESULTS

We were able to image the retina in monochromatic laser light and document the increase in resolution. While it is hard to estimate the exact size of the smallest structures in the image, we were able to subjectively grade the image quality. The system is able to compensate for higher order aberrations present in the human eye.

CONCLUSION

The capabilities of correcting ocular aberrations are limited by the number of adjustable elements in the mirror and the deflection range of the surface. The advantage of the MMDM system is its low cost when compared with other adaptive optics solutions such as piezodriven mirrors and spatial light modulators. This technique may allow for improved resolution for clinical fundus photography.

Active aberration correction for the writing of three-dimensional optical memory devices

We describe an active optical system that both measures and corrects the aberrations introduced when writing three-dimensional bit-oriented optical memory by a two-photon absorption process. The system uses a ferroelectric liquid-crystal spatial light modulator (FLCSLM) configured as an arbitrary wave-front generator that is reconfigurable at speeds as great as 2.5 kHz. A method of aberration measurement by the FLCSLM wave-front generator is described. The same device is also used to correct the induced aberrations by preshaping the wave fronts with the conjugate phase aberration as well as to scan the focal spot in three dimensions. Experimental results show the correction of both on- and off-axis aberrations, allowing the writing of data at depths as great as 1 mm inside a LiNbO3 crystal.

A dual path programmable array microscope (PAM): simultaneous acquisition of conjugate and non-conjugate images

A programmable array microscope (PAM) incorporates a spatial light modulator (SLM) placed in the primary image plane of a widefield microscope, where it is used to define patterns of illumination and/or detection. We describe the characteristics of a special type of PAM collecting two images simultaneously. The conjugate image (Ic) is formed by light originating from the object plane and returning along the optical path of the illumination light. The non-conjugate image (Inc) receives light from only those regions of the SLM that are not used for illuminating the sample. The dual-signal PAM provides much more time-efficient excitation than the confocal laser scanning microscope (CLSM) and greater utilization of the available emission light. It has superior noise characteristics in comparison to single-sided instruments. The axial responses of the system under a variety of conditions were measured and the behaviour of the novel Inc image characterized. As in systems in which only Ic images are collected (Nipkow-disc microscopes, and previously characterized PAMs), the axial response to thin fluorescent films showed a sharpening of the axial response as the unit cell of the repetitive patterns decreased in size. The dual-signal PAM can be adapted to a wide range of data analysis and collection strategies. We investigated systematically the effects of patterns and unit cell dimensions on the axial response. Sufficiently sparse patterns lead to an Ic image formed by the superposition of the many parallel beams, each of which is equivalent to the single scanning spot of a CLSM. The sectioning capabilities of the system, as given by its axial responses, were similar for a given scan pattern and for processed pseudorandom sequence (PRS) scans with the same size of the unit cell. For the PRS scans, optical sectioning was achieved by a subtraction of an Inc image or, alternatively, a scaled widefield image from the Ic image. Based on the comparative noise levels of the two methods, the non-conjugate subtraction was significantly superior. A point spread function for Ic and Inc was simulated and properties of the optical transfer functions (OTFs) were compared. Simulations of the OTF in non-conjugate imaging did not suffer from the missing cone problem, enabling a high quality deconvolution of the non-conjugate side alone. We also investigated the properties of images obtained by subjecting the Ic and Inc data to a combined maximum likelihood deconvolution.

Microelectromechanical system programmable aberration generator for adaptive optics

Adaptive optics systems and control algorithms can be tested in the laboratory with controlled disturbances. We have a micromachined deformable mirror that we use as a programmable aberration generator. We present a method of programming the actuator amplitudes so that the wave front reflecting from the surface will simulate atmospheric turbulence. We present experimental results that show that we can simulate the Kolmogorov spatial spectrum within the constraints of the useful region of the deformable mirror.

Phase-diversity wave-front sensing with a distorted diffraction grating

We describe a novel wave-front sensor comprising a distorted diffraction grating, simple optics, and a single camera. A noniterative phase-diversity algorithm is used for wave-front reconstruction. The sensor concept and practical implementation are described in detail, and performance is validated against different Zernike modes and a representative atmospheric phase map.

Closed-loop aberration correction by use of a modal Zernike wave-front sensor

We describe the practical implementation of a closed-loop adaptive-optics system incorporating a novel modal wave-front sensor. The sensor consists of a static binary-phase computer-generated holographic element, which generates a pattern of spots in a detector plane. Intensity differences between symmetric pairs of these spots give a direct measure of the Zernike mode amplitudes that are present in the input wave front. We use a ferroelectric liquid-crystal spatial light modulator in conjunction with a 4-f system and a spatial filter as a wave-front correction element. We present results showing a rapid increase in Strehl ratio and focal spot quality as the system corrects for deliberately introduced aberrations.

New modal wave-front sensor: a theoretical analysis

We present a new design of a modal wave-front sensor capable of measuring directly the Zernike components of an aberrated wave front. The sensor shows good linearity for small aberration amplitudes and is particularly suitable for integration in a closed-loop adaptive system. We introduce a sensitivity matrix and show that it is sparse, and we derive conditions specifying which elements are necessarily zero. The sensor may be temporally or spatially multiplexed, the former using a reconfigurable optical element, the latter using a numerically optimized binary optical element. Different optimization schemes are discussed, and their performance is compared.

A low cost adaptive optics system using a membrane mirror

A low cost adaptive optics system constructed almost entirely of commercially available components is presented. The system uses a 37 actuator membrane mirror and operates at frame rates up to 800Hz using a single processor. Numerical modelling of the membrane mirror is used to optimize parameters of the system. The dynamic performance of the system is investigated in detail using a diffractive wavefront generator based on a ferroelectric spatial light modulator. This is used to produce wavefronts with time-varying aberrations. The ability of the system to correct for Kolmogorov turbulence with different strengths and effective wind speeds is measured experimentally using the wavefront generator.

Optimized pupil-plane filters for confocal microscope point-spread function engineering

We present a new method of superresolving pupil-plane filter design in confocal microscopy in which we specify the properties of the desired point-spread function and use an optimization procedure to determine a suitable pupil-plane filter. A new, flexible method of filter implementation using reconfigurable binary optical elements is described, and experimental results are presented.

Wave-front generation of Zernike polynomial modes with a micromachined membrane deformable mirror

We investigate the characteristics of a 37-channel micromachined membrane deformable mirror for wave-front generation. We demonstrate wave-front generation of the first 20 Zernike polynomial modes, using an iterative algorithm to adjust driving voltages. The results show that lower-order-mode wave fronts can be generated with good accuracy and large dynamic range, whereas the generation of higher-order modes is limited by the number of the actuator channels and the working range of the deformable mirror. The speed of wave-front generation can be as fast as several hundred hertz. Our results indicate that, in addition to generation of wave fronts with known aberrations, the characteristics of the micromachined membrane deformable mirror device can be useful in adaptive optics systems for compensating the first five orders of aberration.