Holography-based wavefront sensing

We describe a modal wavefront sensing technique of using multiplexed holographic optical elements (HOEs). The phase pattern of a set of aberrations is angle multiplexed in a HOE, and the correlated information is obtained with a position sensing detector. The recorded aberration pattern is based on an orthogonal basis set, the Zernike polynomials, and a spherical reference wave. We show that only two recorded holographic patterns for any particular aberration type are sufficient to allow interpolated readout of aberrations to lambda/50. In this paper, we demonstrate the capability of detecting errors between +/-2lambda PV for each orthogonal set at rates limited only by the speeds of the detection electronics, which could be up to 1 MHz. We show how we take advantage of the unavoidable intermodal and intramodal cross talks in determining the type, amplitude, and orientation of the wavefront aberrations.     

High-diffractive-efficiency defocus grating for wavefront curvature sensing

The optimum phase defocus grating for wavefront curvature sensing is proposed. It features an equidistantly quantized, binary-phase-step defocus grating with a phase-step height of pi. The diffractive efficiency of the phase defocus grating is theoretically computed. The optical transfer function is obtained. The optimum phase defocus grating is fabricated. The high diffractive efficiencies of the +/-1 diffraction orders are verified experimentally, the average values of which are 38.08% and 40.36%, respectively.     

Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing

Adaptive optics provides a real-time compensation for atmospheric turbulence that severely limits the resolution of ground-based observation systems. The correction quality relies on a key component, that is, the wavefront sensor (WFS). When observing extended sources, WFS precision is limited by anisoplanatism effects. Anisoplanatism induces a variation of the turbulent phase and of the collected flux in the field of view. We study the effect of this phase and scintillation anisoplanatism on wavefront analysis. An analytical expression of the error induced is given in the Rytov regime. The formalism is applied to a solar and an endoatmospheric observation. Scintillation effects are generally disregarded, especially in astronomical conditions. We shall prove that this approximation is not valid with extended objects.     

Optimization of scanning strategy of digital Shack-Hartmann wavefront sensing

In the traditional Shack-Hartmann wavefront sensing (SHWS) system, a lenslet array with a bigger configuration is desired to achieve a higher lateral resolution. However, practical implementation limits the configuration and this parameter is contradicted with the measurement range. We have proposed a digital scanning technique by making use of the high flexibility of a spatial light modulator to sample the reflected wavefront [X. Li, L. P. Zhao, Z. P. Fang, and C. S. Tan, "Improve lateral resolution in wavefront sensing with digital scanning technique," in Asia-Pacific Conference of Transducers and Micro-Nano Technology (2006)]. The lenslet array pattern is programmed to laterally scan the whole aperture. In this paper, the methodology to optimize the scanning step for the purpose of form measurement is proposed. The correctness and effectiveness are demonstrated in numerical simulation and experimental investigation.     

Performance analysis of multiplexed phase computer-generated hologram for modal wavefront sensing

We investigate the performance and capability of a holographic modal wavefront sensor (HMWS) that is based on a multiplexed phase computer-generated hologram (MPCGH). The theoretical treatments of the HMWS are presented with scalar diffraction approximations and Fourier analysis. Several MPCGHs have been designed with different linear carrier frequencies, by using of the multiplexed coding scheme we have proposed, and by coding some common Zernike modes. The numerical simulation is carried out to investigate the performance of the HMWS to detect particular aberration mode(s), by considering the effect of different carrier frequency selections and the capability of coding a large number of modes. The results exhibit the expected characteristics of a corresponding symmetric spot pair, and indicate that the wavefront distorted by a particular Zernike mode(s) can be retrieved immediately through solving the amplitude of each mode coded in MPCGHs through the response curves of the HMWS.     

Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions

Maximum-likelihood (ML) estimation in wavefront sensing requires careful attention to all noise sources and all factors that influence the sensor data. We present detailed probability density functions for the output of the image detector in a wavefront sensor, conditional not only on wavefront parameters but also on various nuisance parameters. Practical ways of dealing with nuisance parameters are described, and final expressions for likelihoods and Fisher information matrices are derived. The theory is illustrated by discussing Shack-Hartmann sensors, and computational requirements are discussed. Simulation results show that ML estimation can significantly increase the dynamic range of a Shack-Hartmann sensor with four detectors and that it can reduce the residual wavefront error when compared with traditional methods.     

Intrinsic limitations of Shack-Hartmann wavefront sensing on an extended laser guide source

In this paper we investigate the behavior of various centroiding methods (weighted center of gravity, matched filtering, and correlation) classically used in Shack-Hartmann wavefront sensing when dealing with an elongated asymmetric spot. We study the impact of model errors on these centroiding methods at high signal-to-noise ratios, and, using a one-dimensional formalism, we show that the associated estimates all suffer from a bias uncorrelated with the actual spot displacement if its shape is not known precisely. Additionally, we show that the correlation method provides an estimate with a unitary gain whatever the parameters used, while the other two methods introduce a non-unitary gain in the estimation process. Finally, we show that the sampling of the spot structures after filtering by some convolution kernels is crucial to get an unbiased estimate of the spot displacement.     

Contrast limits of coherence-gated imaging in scattering media

The fundamental difference between time-resolved and coherence-gated imaging modalities in scattering media is analyzed in terms of their optical transfer functions. The effectiveness of coherence gating for multiple-scattering rejection is shown by imaging a 100-mum-thick razor blade hidden in the scattering phantoms (i.e., Intralipid suspensions) with different scattering coefficients. We found that the imaging contrast is limited by multiple scattering and speckle effects in high-scattering media, and the measured effective penetration depth of optical coherence tomography is approximately equal to six mean free paths under the experimental conditions of a numerical aperture of less than 0.1 and a scattering anisotropy of approximately 0.8.     

Optimization of star-oriented and layer-oriented wavefront sensing concepts for ground layer adaptive optics

Multiconjugate adaptive optics is one of the major challenges in adaptive optics. It requires the measurement of the volumic distribution of the turbulence. Two wavefront sensing (WFS) concepts have been proposed to perform the wavefront analysis for such systems: the star-oriented and layer-oriented approaches. We give a performance analysis and a comparison of these two concepts in the framework of the simplest of the multi-guide-star adaptive optics systems, that is, ground layer adaptive optics. A phase-related criterion is proposed to assess analytically the performance of both concepts. This study highlights the main advantages and drawbacks of each WFS concept and shows how it is possible to optimize the concepts with respect to the signal to noise ratio on the phase measurement. A comparison of their optimized versions is provided and shows that one can expect very similar performance with the two optimized concepts.     

Laser guide star wavefront sensing for ground-layer adaptive optics on extremely large telescopes

We propose ground-layer adaptive optics (GLAO) to improve the seeing on the 42?m European Extremely Large Telescope. Shack-Hartmann wavefront sensors (WFSs) with laser guide stars (LGSs) will experience significant spot elongation due to off-axis observation. This spot elongation influences the design of the laser launch location, laser power, WFS detector, and centroiding algorithm for LGS GLAO on an extremely large telescope. We show, using end-to-end numerical simulations, that with a noise-weighted matrix-vector-multiply reconstructor, the performance in terms of 50% ensquared energy (EE) of the side and central launch of the lasers is equivalent, the matched filter and weighted center of gravity centroiding algorithms are the most promising, and approximately 10×10 undersampled pixels are optimal. Significant improvement in the 50% EE can be observed with a few tens of photons/subaperture/frame, and no significant gain is seen by adding more than 200 photons/subaperture/frame. The LGS GLAO is not particularly sensitive to the sodium profile present in the mesosphere nor to a short-timescale (less than 100?s) evolution of the sodium profile. The performance of LGS GLAO is, however, sensitive to the atmospheric turbulence profile.     

Shack-Hartmann wavefront sensing with elongated sodium laser beacons: centroiding versus matched filtering

We describe modeling and simulation results for the Thirty Meter Telescope on the degradation of sodium laser guide star Shack-Hartmann wavefront sensor measurement accuracy that will occur due to the spatial structure and temporal variations of the mesospheric sodium layer. By using a contiguous set of lidar measurements of the sodium profile, the performance of a standard centroid and of a more refined noise-optimal matched filter spot position estimation algorithm is analyzed and compared for a nominal mean signal level equal to 1000 photodetected electrons per subaperture per integration time, as a function of subaperture to laser launch telescope distance and CCD pixel readout noise. Both algorithms are compared in terms of their rms spot position estimation error due to noise, their associated wavefront error when implemented on the Thirty Meter Telescope facility adaptive optics system, their linear dynamic range, and their bias when detuned from the current sodium profile.     

Random phase plate for wavefront sensing via phase retrieval and a volume speckle field

A random phase plate is prepared by illuminating a photoresist plate with a fully developed speckle field and using the developed phase plate (DPP) as a diffuser. Wavefront sensing is implemented using phase retrieval based on the recording of speckle intensity patterns at various distances from the DPP and the wave propagation equation. The effects of the roughness height of the DPP on the phase retrieval are investigated. From simulations a roughness height of lambda/10 results in a speckle field that yields good phase reconstruction for the spherical test wavefront incident on the DPP. From the experiments different portions of the DPP that received varying exposures are examined. A section of the phase plate with a characteristic roughness height facilitated the generation of a speckle field that is optimum for the phase retrieval algorithm. Thus a random phase plate with varying roughness height allows optimized measurements of wavefronts with different curvatures. Analytical expressions describing the second-order intensity statistics (fourth-order field statistics) for a field traversing a specific diffuser are presented. This DPP will not give rise to a fully developed speckle field, but knowing the statistics of the depth of the DPP will facilitate a rigorous treatment of the problem.     

Hybrid wavefront sensor for the fast detection of wavefront disturbances

Strongly aberrated wavefronts lead to inaccuracies and nonlinearities in holography-based modal wavefront sensing (HMWS). In this contribution, a low-resolution Shack-Hartmann sensor (LRSHS) is incorporated into HMWS via a compact holographic design to extend the dynamic range of HMWS. A static binary-phase computer-generated hologram is employed to generate the desired patterns for Shack-Hartmann sensing and HMWS. The low-order aberration modes dominating the wavefront error are first sensed with the LRSHS and corrected by the wavefront modulator. The system then switches to HMWS to obtain better sensor sensitivity and accuracy. Simulated as well as experimental results are shown for validating the proposed method.     

Tomographic wavefront error using multi-LGS constellation sensed with Shack-Hartmann wavefront sensors

Noise effects induced by laser guide star (LGS) elongation have to be considered globally in a multi-LGS tomographic reconstruction analysis. This allows a fine estimation of performance and the comparison of different launching options. We present a modal analysis of the wavefront error with Shack-Hartmann wavefront sensors based on quasi-analytical matrix formalism. Including spot elongation and the Rayleigh fratricide effect, edge launching produces similar performance to central launching and avoids the risk of possible underestimation of fratricide scatter. Performance improves slightly with an optimized centroid estimator and is not affected by a slight field-of-view truncation of the subapertures. Finally we discuss detector characteristics for a LGS Shack-Hartmann wavefront sensor.     

Properties and sensing characteristics of surface-plasmon resonance in infrared light

Conditions of surface-plasmon resonance (SPR) production with use of IR pumping light (800-2300 nm) in the Kretschmann-Raether prism arrangement were investigated. Both calculations and experimental data showed that SPR characteristics in the IR are strongly influenced by the properties of the coupling prism material. Indeed, quite different regularities of plasmon excitation, polarity of sensing response, and sensitivity are observed for two different glasses and silicon. The observed differences in SPR properties are related to essentially different behavior of dispersion characteristics of materials near the SPR coupling point. Methods for improving sensor performance and miniaturizing the SPR technique using novel coupling materials (silicon) are discussed.     

Optimal modal fourier-transform wavefront control

Optimal modal Fourier-transform wavefront control combines the speed of Fourier-transform reconstruction (FTR) with real-time optimization of modal gains to form a fast, adaptive wavefront control scheme. Our modal basis is the real Fourier basis, which allows direct control of specific regions of the point-spread function. We formulate FTR as modal control and show how to measure custom filters. Because the Fourier basis is a tight frame, we can use it on a circular aperture for modal control even though it is not an orthonormal basis. The modal coefficients are available during reconstruction, greatly reducing computational overhead for gain optimization. Simulation results show significant improvements in performance in low-signal-to-noise-ratio situations compared with nonadaptive control. This scheme is computationally efficient enough to be implemented with off-the-shelf technology for a 2.5 kHz, 64 x 64 adaptive optics system.     

Modeling and correction of incoherent wavefront distortion

There are two types of wavefront distortion inside the female breast: incoherent scattering and coherent interference. Adaptive wavefront compensation algorithms developed so far are useful for correction of incoherent distortion caused by scattering. The performances of these algorithms differ according to the extent of wavefront amplitude distortion. It is shown analytically and experimentally in this article that the matched filtering approach, while optimal for detection, is not so for imaging when the wavefront amplitude is distorted in addition to phasefront distortion. Matched filtering algorithms increase wavefront amplitude variance and therefore decrease image contrast. The inverse filtering approach, while ideal for fidelity, is not stable when the signal-to-noise ratio is low. An approach toward inverse filtering, amplitude compression operation in addition to phase deaberration, is introduced in this article. Analysis and experiments show that its performance is superior to matched filtering algorithms and to time-delay type correction algorithms without introducing stability problems. © 1996 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 322–335, 1997     

Interocular high-order corneal wavefront aberration symmetry

The interocular symmetry of the high-order corneal wavefront aberration (WA) in a population of myopic eyes was analyzed before and after photorefractive keratectomy (PRK). The preoperative and one-year postoperative corneal aberration data (from third to seventh Zernike orders) for 4- and 7-mm pupils from right and left eyes were averaged after correcting for the effects of enantiomorphism to test for mirror symmetry. Also, the mean corneal point-spread function (PSF) for right and left eyes was calculated. Preoperatively, a moderate and high degree of correlation in the high-order corneal WA between eyes was found for 4- and 7-mm pupils, respectively. Myopic PRK did not significantly change the interocular symmetry of corneal high-order aberrations. No discernible differences in the orientation PSF between eyes were observed one year after surgery in comparison with the preoperative state over the two analyzed pupils.     

Response analysis of holography-based modal wavefront sensor

The crosstalk problem of holography-based modal wavefront sensing (HMWS) becomes more severe with increasing aberration. In this paper, crosstalk effects on the sensor response are analyzed statistically for typical aberrations due to atmospheric turbulence. For specific turbulence strength, we optimized the sensor by adjusting the detector radius and the encoded phase bias for each Zernike mode. Calibrated response curves of low-order Zernike modes were further utilized to improve the sensor accuracy. The simulation results validated our strategy. The number of iterations for obtaining a residual RMS wavefront error of 0.1λ is reduced from 18 to 3.