Kolmogorov Phase Screens Research Articles

Engineering Super‐Poissonian Photon Statistics of Spatial Light Modes

AbstractThe nature of light sources is defined by the statistical fluctuations of the electromagnetic field. As such, the photon statistics of light sources are typically associated with distinct emitters. Here, the possibility of producing light beams with various photon statistics through the spatial modulation of coherent light is demonstrated. This is achieved by the sequential encoding of controllable Kolmogorov phase screens in a digital micromirror device. Interestingly, the flexibility of this scheme allows for the shaping of spatial light modes with engineered photon statistics at different spatial positions. The performance of this scheme is assessed through the photon‐number‐resolving characterization of different families of spatial light modes with engineered photon statistics. It is believed that the possibility of controlling the photon fluctuations of the light field at arbitrary spatial locations has important implications for quantum spectroscopy, sensing, and imaging.

Phase retrieval of a Kolmogorov phase screen from very sparse data using four binary masks.

We investigate experimentally the phase retrieval of a Kolmogorov phase screen from very sparse data by modulating its amplitude with four binary masks and compare the retrieved phase screen to the ground truth measured with a surface profiler. Previously, we have shown in simulations that this kind of modulation can be successfully used for the phase retrieval of a Kolmogorov phase screen. After subtracting the ground truth from the retrieved phase screen, the root-mean-square error decreased from 0.14 µm to 0.10 µm. We conclude that a Kolmogorov phase screen can be recovered using simple modulation and very sparse data.

WIDEBAND SATCOM MODEL: EVALUATION OF NUMERICAL ACCURACY AND EFFICIENCY

Abstract. The spectral method is typically applied as a simple and efficient method to solve the parabolic wave equation in phase screen scintillation models. The critical factors that can greatly affect the spectral method accuracy is the uniformity and smoothness of the input function. This paper observes these effects on the accuracy of the finite difference and the spectral methods applied to a wideband SATCOM signal propagation model simulated in the ultra-high frequency (UHF) band. The finite difference method uses local pointwise approximations to calculate a derivative. The spectral method uses global trigonometric interpolants that achieve remarkable accuracy for continuously differentiable functions. The differences in accuracy are presented for a Gaussian lens and Kolmogorov phase screen. The results demonstrate loss of accuracy in each method when a phase screen is applied, despite the spectral method's computational efficiency over the finite difference method. These results provide meaningful insights when discretizing an interior domain and solving the parabolic wave equation to obtain amplitude and phase of a signal perturbation.

Asymmetric optical image encryption using Kolmogorov phase screens and equal modulus decomposition

An asymmetric technique for optical image encryption is proposed using Kolmogorov phase screens (KPSs) and equal modulus decomposition (EMD). The KPSs are generated using the power spectral density of Kolmogorov turbulence. The input image is first randomized and then Fresnel propagated with distance d. Further, the output in the Fresnel domain is modulated with a random phase mask, and the gyrator transform (GT) of the modulated image is obtained with an angle α. The EMD is operated on the GT spectrum to get the complex images, Z1 and Z2. Among these, Z2 is reserved as a private key for decryption and Z1 is propagated through a medium consisting of four KPSs, located at specified distances, to get the final encrypted image. The proposed technique provides a large set of security keys and is robust against various potential attacks. Numerical simulation results validate the effectiveness and security of the proposed technique.

Comparative statistical analysis of phase profiles of a pseudo random phase plate with Kolmogorov phase screens

Experimentally retrieved phase profiles of a pseudo random phase plate (PRPP), obtained using coherent laser beam of 633nm wavelength in the Mach–Zehnder interferometric set up with an additional 4f imaging system, are statistically compared with numerically generated Kolmogorov random phase screens. The numerically generated phase screens are obtained using atmospheric structure constants ranging from very weak to very strong turbulence conditions. Our detailed quantitative analysis shows that the unwrapped phase profiles retrieved from the PRPP represent a different class of phase screens which donot match exactly with Kolmogorov phase screens.

Characterization of Pseudo-Random-Phase-Plate as a Kolmogorov/non-Kolmogorov turbulence simulator using statistical parameters and the phase structure function

A He-Ne laser lasing at 633 nm is used as source in Mach-Zehnder and Michelson’s interferometric geometries separately, for characterizing a Pseudo-Random-Phase-Plate (PRPP), which presents atmospheric turbulence like conditions to a light beam passing through it. Two methods are employed for the same. The first method involves a comparison of the retrieved phase profiles of sections of PRPP (used as object in one of the arms of Mach-Zehnder Interferometer) with those of numerically generated Kolmogorov phase screens, using statistical parameters commonly used for characterizing optically rough surfaces. The second method uses the phase profiles obtained in Mach-Zehnder (single passage through the object, PRPP) and Michelson’s (double passage through the object, PRPP) interferometric geometries separately for calculating phase structure function, D φ (r). Through both the methods, we try to determine whether the PRPP presents a Kolmogorov or non-Kolmogorov turbulence regime at 633 nm wavelength. A comparison of the two methods shows that the phase structure function analysis provides a better method for such a characterization.

Laboratory demonstrations on a pyramid wavefront sensor without modulation for closed-loop adaptive optics system

The feasibility and performance of the pyramid wavefront sensor without modulation used in closed-loop adaptive optics system is investigated in this paper. The theory concepts and some simulation results are given to describe the detection trend and the linearity range of such a sensor with the aim to better understand its properties, and then a laboratory setup of the adaptive optics system based on this sensor and the liquid-crystal spatial light modulator is built. The correction results for the individual Zernike aberrations and the Kolmogorov phase screens are presented to demonstrate that the pyramid wavefront sensor without modulation can work as expected for closed-loop adaptive optics system.

Karhunen–Loève basis of Kolmogorov phase screens covering a rectangular stripe

Karhunen–Loève functions are statistically independent base functions to be multiplied with randomized coefficients to generate instances of the underlying statistics with specific covariances. In the context of numerical simulation of atmospheric turbulence, they are tools to generate phase distributions in the input pupil of telescope optics. Within the Taylor frozen screen approximation, the favorable geometry of phase screens is a stripe as wide as the telescope diameter, but much longer. A phase screen movie is generated by dragging the stripe across the telescope pupil. The aim is to avoid the wasteful alternative of cutting through a virtual circular phase screen with a diameter equal to the stripe's length. We calculate Karhunen–Loève functions over rectangular stripes by solving the well-known integral equation for isotropic variance of the phase distribution. They are expanded in products of Legendre functions along the two Cartesian coordinates, represented by spherical Bessel functions in Fourier space. The rectangular shape of the integral's domain breaks the symmetry of the structure function. Yet, the matrix elements of the eigenvalue equation can be calculated by separating the primitive Cartesian basis via a Neumann series of radial and azimuthal terms.

Orthogonal Basis Functions over the Binocular Pupil

AbstractSets of orthogonal basis functions over circular areas - pupils in optical applications - are known in the literature for the full circle (Zernike or Jacobi polynomials) and the annulus. Here, an orthogonal set is proposed if the area is two non-overlapping circles of equal size. The geometric master parameter is the ratio of the pupil radii over the distance between both circles. Increasingly higher order aberrations - as defined for a virtual larger pupil in which both pupils are embedded - are fed into a Gram-Schmidt orthogonalization to distill one unique set of basis functions. The key effort is to work out the overlap integrals between a full set of primitive basis functions of hyperspherical type centered at the mid-point between both pupils. Constructed from the same primitive basis, the orthogonal Karhunen-Loève modes of spatially filtered Kolmogorov phase screens are computed for this shape of mask. Matrix elements of the covariance matrix - an established intra-circle and a special inter-circle category - are worked out in wavenumber space.

Performance comparison between Shack-Hartmann and astigmatic hybrid wavefront sensors

Simulations on Kolmogorov phase screens are employed to compare the relative performance of an astigmatic hybrid wavefront sensor (AHS) to that of a Shack-Hartmann sensor (SHS). The AHS is shown to improve phase reconstruction accuracy when the subaperture phase contains significant energy in curvature modes and a moderate to high number of photons are collected. Dual use of the AHS and SHS may extend enhanced reconstruction to low signal levels. The AHS is also shown to have a small benefit for tilt-only reconstruction when the beam has sufficient power.

Special issue on reconfigurable architecture for real-time image processing

The performance requirements of image processing applications have led to increase in the computing power of implementation platforms, in particular when real-time constraints are to be met. Image processing applications may consist of different standards, or different algorithms used at different stages of the processing chain. The computing paradigm of reconfigurable architectures promises a trade-off between flexibility and performance. Reconfigurable architectures can exploit fine-grain (more suitable for low-level and medium-level operations in the image processing chain) and coarse-grain parallelism (more suitable for high-level operations in the image processing chain). Many reconfigurable architectures have been constructed specifically for image processing using different processors and dedicated circuits such as ASICs and FPGAs. This special issue on Reconfigurable Architecture for Real-Time Image Processing presents articles addressing reconfigurable computing for real-time image processing, programming frameworks with FPGA-style mapping as well as real-time and embedded image processing applications and implementations. This special issue includes nine papers that are briefly outlined below: The first paper, by Denoulet and Merigot, presents a massively parallel SIMD architecture based on reconfigurability and asynchronism called Associative Mesh. The introduced virtualized associative mesh achieves real-time execution for split and merge segmentation, watershed segmentation and motion detection. The second paper, by Kessal, Karabernou and Demigny, focuses on the Ardoise project. The goal of this project is to realize a dynamically reconfigurable platform. This paper proposes a methodology that can be easily adapted to common SoC architecture. The third paper, by Sen, Hemaraj, Plishker, Shekhar and Bhattacharya, presents a novel architecture that enables dynamically-reconfigurable image registration. It also addresses some data-flow-motivated parallel architectures for image registration. The fourth paper, by Meng, Freeman, Pears and Bailey, details the implementation of a human action recognition system on a reconfigurable, FPGA based video processing architecture. The fifth paper, by Jiang, Crookes and Bouridane, describes a parallel-matching processor architecture to perform high-speed biometric fingerprint database retrieval. The processor was implemented on Xilinx Virtex-E and runs up to 65 MHz. The sixth paper, by Chandrasekaran, Amira, Minghua and Bermak, covers the presentation of an architecture for the Finite Ridgelet Transform. It presents a parallel architecture as well as FPGA and ASIC implementations. The seventh paper, by Srinam and Eng, presents various implementations of the Kolmogorov phase screen generator. The FPGA hardware implementation provides a speedup of more than 60 times of the original algorithm. The eight paper, by Saponara, Casula and Fanucci proposes to combine the application specific instruction-set processor (ASIP) paradigm with the reconfigurable hardware one. The ninth paper, by Seetharaman, Venkataramani and Lakshminarayanan, describes how to get the benefits of M. Akil (&) Department of Computer Science, Institut Gaspar-Monge, Unite mixte de recherche CNRS-UMLVPE-ESIEE (UMR 8049), ESIEE, Cite Descartes, BP 99, 93162 Noisy-le-Grand Cedex, France e-mail: akilm@esiee.fr

Simulation of the interstellar scintillation and the extreme scattering events of pulsars

The rare and conspicuous flux density variations of some radio sources (extragalactic and pulsars) for periods of weeks to months have been denoted Extreme Scattering Events (ESE's) by Fiedler et al. (1987). Presently, there is no astrophysical mechanism that satisfactorily produces this phenomenon. In this paper, we conjecture that inhomogeneities of the electronic density in the turbulent interstellar medium might be the origin of this phenomenon. We have tested this conjecture by a simulation of the scintillation of the pulsar B1937+21 at 1.4 GHz and 1.7 GHz for a period of six months. To this end, we have constructed a large square Kolmogorov phase screen made of 131k x 131k pixels with electron inhomogeneity scales ranging from 6 x $10^6$ m to $10^{12}$ m and used the Kirchhoff-Fresnel integral to simulate dynamic spectra of a pulsar within the framework of Physical Optics. The simulated light curves exhibit a 10 day long variation simultaneously at 1.41 and 1.7 GHz that is alike the ``ESE'' observed with the Nancay radiotelescope toward the pulsar B1937+21 in October 1989. Consequently, we conclude that ``ESE'' toward pulsars can be caused naturally by the turbulence in the ionized interstellar medium instead of invoking the crossing of discrete over pressured ionized clouds on the line of sight as in the model of Fiedler et al. (1987). We suggest that longer events could occur in a simulation of scintillation, if larger electron inhomogeneities > $10^{12}$ m were included in the construction of the Kolmogorov phase screen. This next step requires a supercomputer.

Breadboard testing of a phase-conjugate engine with an interferometric wave-front sensor and a microelectromechanical systems-based spatial light modulator

Laboratory breadboard results of a high-speed adaptive-optics system are presented. The wave-front sensor for the adaptive-optics system is based on a quadrature interferometer, which directly measures the turbulence-induced phase aberrations. The spatial light modulator used in the phase-conjugate engine was a microelectromechanical systems-based piston-only correction device with 1024 actuators. Laboratory experiments were conducted with this system utilizing Kolmogorov phase screens to simulate atmospheric phase distortions. The adaptive-optics system achieved correction speeds in excess of 800 Hz and Strehl ratios greater than 0.5 with the Kolmogorov phase screens.

Open- and closed-loop aberration correction by use of a quadrature interferometric wave-front sensor.

Experimental results are presented for an adaptive optics system based on a quadrature Twyman-Green interferometric wave-front sensor. The system uses a circularly polarized reference beam to form two interferograms with a pi/2 phase shift. The experiments conducted used Kolmogorov phase screens to simulate atmospheric phase distortions. Strehl ratio improvements by a factor of 8, to an absolute value of 0.45, are demonstrated.

Adaptive detector arrays for optical communications receivers

An optimal adaptive array receiver for use in groundbased optical communications is investigated. Kolmogorov phase screen simulations are used to generate realistic focal-plane distributions of the received optical fields in the presence of turbulence. The array detection concept reduces interference from background radiation by effectively assigning higher confidence levels at each instant of time to those detector elements that contain significant signal energy and suppressing those that do not. A simpler suboptimum structure that replaces the continuous weighting of the optimal receiver by a hard decision over each detector element is also described. It is shown that, for photon counting receivers observing Poisson distributed signals, performance improvements of up to 5 dB can be obtained over conventional single-detector photon counting receivers when observing turbulent optical fields in high background environments.

Fast simulation of a kolmogorov phase screen

A previously presented method for modeling Kolmogorov phase fluctuations over a finite aperture is both formalized and improved on. The method relies on forming an initial low-resolution Kolmogorov phase screen from direct factorization of a covariance. The resolution of the screen is then increased by a randomized interpolation to produce a Kolmogorov phase screen of the desired size. The computational requirement is asymptotically proportional to the number of points in the phase screen.

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

We describe a simple method for generating known optical aberrations dynamically, using a ferroelectric liquid-crystal spatial light modulator. Aberrations inherent in the optical system are measured and corrected, and as an example Kolmogorov turbulence is simulated for aperture sizes D/r(0) from 0 to 30, varying at frame rates up to 2.5 kHz. A measure of wave-front generation efficiency is introduced and is shown to be better than 86% for Kolmogorov phase screens with D/r(0) in the range from 0 to 30.