On-orbit self-compensation of satellite optics using a spatial light modulator

Orbital angular momentum (OAM) of vortex beams can extend the capacity and spectral efficiency of free-space optical (FSO) communication for its orthogonality provide an extra dimension. However, atmospheric turbulence (AT) will lead to wave-front distortion, crosstalk between OAM modes and eventually reduce the communication system performance. This paper uses a Phase Diversity (PD)-based adaptive optics (AO) schema to compensate the OAM beam. With the General Regression Neural Network (GRNN), the relationship between the intensity distribution and the wave-front distortion of propagation in AT channel is established, and the wave-front aberration is retrieved. This method is simple in structure without phase sensor and probe beam, and reduces computation compared with the common phase retrieval algorithms. Therefore, it can compensate OAM beam in a second and ensure the similar retrieve effect.

The phase diversity technique is studied as a wave-front sensor to be implemented with widely extended sources. The wave-front phase expanded on the Zernike polynomials is estimated from a pair of images (in focus and out of focus) by use of a maximum-likelihood approach. The propagation of the photon noise in the images on the estimated phase is derived from a theoretical analysis. The covariance matrix of the phase estimator is calculated, and the optimal distance between the observation planes that minimizes the noise propagation is determined. The phase error is inversely proportional to the number of photons in the images. The noise variance on the Zernike polynomials increases with the order of the polynomial. These results are confirmed with both numerical and experimental validations. The influence of the spectral bandwidth on the phase estimator is also studied with simulations.

Phase diversity experimental results: deconvolution of ν Scorpii

Particle surface inspection with fourier-wavelets transform

The well known phase diversity technique has long been used as a premier passive imaging method to mitigate the degrading effects of atmospheric turbulence on incoherent optical imagery. Typically, an iterative, slow method is applied that uses the Zernike basis set and 2-D Fourier transforms in the reconstruction process. In this paper, we demonstrate a direct method for estimating the un-aberrated object brightness from phase or phase difference estimates that 1) does not require the use of the Zernike basis set or the intermediate determination of the generalized pupil function, 2) directly determines the optical transfer function without the requirement for an iterative sequence of 2-D Fourier Transforms, 3) provides a more accurate result than the Zernike-based approaches since there are no Zernike series truncation errors, 4) lends itself to fast and parallel implementation, and 5) can use stochastic search methods to rapidly determine simultaneous phases or phase differences required to determine the correct optical transfer function estimate. As such, this new implementation of phase diversity provides potentially faster, more accurate results than previous approaches yet still retains inherent compatibility with the traditional Zernike-based methods. The theoretical underpinnings of this new method along with demonstrative computer simulation results are presented.

There is high demand for deploying real-time or near real-time implementation of image reconstruction techniques for intelligence, surveillance, and reconnaissance (ISR) systems, as well as biomedical systems, and border applications. While many image restoration techniques have been implemented, their computational complexity makes them unsuitable for real-time systems. This work presents massively parallelized algorithms for two and three-dimensional image reconstruction of objects using deconvolution and bispectrum techniques. Speckle imaging (SI) techniques are more preferred for phase reconstruction because of its high restoration quality at the lower values of signal-to-noise ratio (SNR), especially for smaller targets, and its shift-invariant property which makes it insensitive to random motion of an object. This work proposes, a novel strategy for parallelization of recursive bispectrum algorithm. Furthermore, parallel bispectrum speckle imaging technique is used as an initial step for parallelized multi-frame blind deconvolution (MFBD) image restoration algorithm in order to speed-up the reconstruction process for anisoplanatic, long horizontal path imaging. The parallel hybrid Bispectrum- MFBD (B-MFBD) technique, through massive parallelization, provides significantly large improvement to both bispectrum SI and MFBD parts of the hybrid algorithm. The work also investigates phase diversity (PD) technique as the special case of MFBD algorithm, where the object is observed with a stack of intentionally defocused images. The known defocused information between phases is used to estimate the object and aberration function. The multi-plane PD was implemented for wide field fluorescence microscopy imaging of three-dimensional objects. The PD algorithm was subsequently used to generate 3D point cloud data for the image from its single view.

Wavefront sensorless adaptive optics system for extended objects based on linear phase diversity technique

Exoplanet direct imaging with a ground-based telescope needs a very high performance adaptive optics (AO) system, so-called eXtreme AO (XAO), a coronagraph device, and a smart imaging process. One limitation of AO system in operation remains the Non Common Path Aberrations (NCPA). To achieve the ultimate XAO performance, these aberrations have to be measured with a dedicated wavefront sensor placed in the imaging camera focal plane, and then pre-compensated using the AO closed loop process. In any events, the pre-compensation should minimize the aberrations at the coronagraph focal plane mask. An efficient way for the NCPA measurement is the phase diversity technique. A pixel-wise approach is well-suited to estimate NCPA on large pupils and subsequent projection on the deformable mirror with Cartesian geometry. However it calls for a careful regularization for optimal results. The weight of the regularization is written in close-form for un-supervised tuning. The accuracy of NCPA pre-compensation is below 8 nm for a wide range of conditions. Point-by-point phase estimation improves the accuracy of the Phase Diversity method. The algorithm is validated in simulation and experimentally. It will be implemented in SAXO, the XAO system of the second generation VLT instrument: SPHERE.

Surrogate-based multiobjective optimization to rapidly size low impact development practices for outflow capture

Walsh functions have been modified and utilized as binary-aberration-mode basis which are especially suitable for representing discrete wavefronts. However, when wavefront sensing techniques based on binary-aberration-mode detection trying to reconstruct common wavefronts with continuous forms, the Modified Walsh functions are incompetent. The limited space resolution of Modified Walsh functions will leave substantial residual wavefronts. In order to sidestep the space-resolution problem of binary-aberration modes, it’s necessary to transform the Modified-Walsh-function expansion coefficients of wavefront to Zernike-polynomial coefficients and use Zernike polynomials to represent the wavefront to be reconstructed. For this reason, a transformation method for wavefront expansion coefficients of the two aberration modes is proposed. The principle of the transformation is the linear of wavefront expansion and the method of least squares. The numerical simulation demonstrates that the coefficient transformation with the transformation matrix is reliable and accurate.

The most widespread verification method for optical elements is interferometry but, in the case of freeform surfaces, a strong deviation of the slope along the surface can create areas in which the fringe density is too high for the interferometer to resolve them. The most desirable solution is to create a null or near null interferogram introducing compensating elements like a spatial light modulator (SLM) that provides the flexibility to accommodate the measurement of a wide range of free-form surfaces. This paper shows the process for a convex freeform mirror metrology. The method consists of inserting the SLM in the optical path to compensate the freeform component of the surface to be verified and to generate a null of aberrations in the interferometer. The system is previously modelled in an optical design software to calculate the required phase to be introduced in the SLM to generate the null. The arrangement of the SLM makes possible to keep its position fixed and use the same setup to measure a wide range of freeform surfaces, limited by the dynamic range of the SLM. For each specific surface, it is necessary to introduce suitable elements to compensate the base surface, reserving the SLM for the freeform component compensation. The method is illustrated with the verification of a convex freeform mirror whose freeform component is described by the astigmatism Zernike polynomial Z5.

We validate by simulations an extension of the phase diversity technique that uses long exposure adaptive optics corrected images for sensing quasi-static aberrations during the scientific observation, in particul ar for high-contrast imaging. The principle of the method is th at, for a su ciently long exposure time, the residual turbulence is averaged into a convolutive component of the image and that phase diversity estimates the sole static aberrations of interest. The advantages of such a pro cedure, compared to the processing of short- exposure image pairs, are that the separation between static aberrat ions and turbulence-induced ones is performed by the long-exposure itself and not numerically, that only one image pair must be processed, that the estimation benefits from the high SNR of long-exposure images, and that only the static aberrations of interest are to be estimated. Long-exposure phase diversity can also be used as a phasing sensor for a segmented aperture telescope. Thus, it may be particularly useful for future planet finder projects such as EPICS on the European ELT.

Having full control of light propagation in free space represents the ultimate goal for an imaging system. Spatial Light Modulators (SLMs), featuring the ability to actively control the spatial distribution of light components, are usually limited either to performing small and continuous adjustments to imaging aberrations or to rapidly shifting discrete segments of the wavefront with severe diffraction artifacts. Here a photothermally modulated optical structure is introduced as a highly responsive SLM capable of producing arbitrarily shaped wavefront patterns with smooth as well as step‐like features. The phase‐shift inducing temperature profile within the plasmonic metamaterial at the core of the SLM structure replicates closely the pattern of illuminating light intensity avoiding the common speed and spatial gradient limitations. As a result, the SLM concept is insensitive to polarization, free of diffraction artifacts, and offers sub‐millisecond response time and high transmittance >80%. The dynamic generation of a set of common optical functions is demonstrated, including low‐order Zernike polynomials patterns, phase grating, or vortex, which build an essential phase modulation toolbox across different imaging applications.

Shack-Hartmann wavefront sensor (SHWFS) is considered as an efficient and complementary tool in the field of optics metrology. It is widely used for evaluating and characterizing rigid glass and soft eye contact lenses. However, the presence of any type of aberrations will cause measurement errors decreasing the precision of the sensor. Therefore, in the current study an experimental configuration based on an active adaptive SHWFS was presented for optical testing of circular optical elements such as thin and soft eye contact lenses. As an adaptive element, deformable mirror (DM), was integrated to the SHWFS setup to dynamically compensate for the wavefront aberrations of the illumination laser beam to provide an ideal plane. The concept was firstly verified by measuring standard thin lenses then applied to measure soft eye contact lenses. For the quantitative evaluation, Zernike polynomials was used to accurately define the dominant modes of wavefront aberrations and thus to calculate the wavefront to be written on the DM. Based on the standard deviation (1σ) between the given and the measured focal lengths of the tested thin glass lenses, the measurements show an improvement of the measurement error from 15.18% difference of the uncompensated wavefront and 3.90% of the referencebased method to only 2.11% after aberration compensation of the illumination beam. While for the contact lenses, the measurement error was 22.93% for uncompensated aberrations, 51% for the reference-based method, and 1.75% after aberrations compensation. The results reveal that the aberrations of the illumination laser beam and the wet cell induced aberrations affect the accuracy of the measurements which can be drastically improved by compensating the existing aberrations utilizing the active adaptive SHWFS setup. In conclusion, adaptive-SHWFS can be considered as an in-production, accurate and complementary tool for testing of optical components.

Wavefront aberrations can be represented accurately by a number of Zernike polynomials. We develop a method to retrieve small-phase aberrations from a single far-field image with a Zernike modal-based approach. The difference between a single measured image with aberration and a calibrated image with inherent aberration is used in the calculation process. In this paper, the principle of linear phase retrieval is introduced in a vector-matrix format, which is a kind of linear calculation and is suitable for real-time calculation. The results of numerical simulations on atmosphere-disturbed phase aberrations show that the proposed Zernike modal-based linear phase retrieval method works well when the rms of phase error is less than 1 rad, and it is valid in a noise condition when the signal-to-noise ratio (SNR) >3.