Efficient phase estimation for large-field-of-view adaptive optics

We propose a maximum a posteriori-based estimation of the turbulent phase in a large field of view (FOV) to overcome the anisoplanatism limitation in adaptive optics. We show that, whatever the true atmospheric profile, a small number of equivalent layers (two or three) is required for accurate restoration of the phase in the whole FOV. The implications for multiconjugate adaptive optics are discussed in terms of the number and conjugated heights of the deformable mirrors. The number of guide stars required for wave-front measurements in the field is also discussed: three (or even two) guide stars are sufficient to produce good performance.     

An adaptive greedy technique for inverse boundary determination problem

In this paper, the method of fundamental solutions (MFS) is employed for determining an unknown portion of the boundary from the Cauchy data specified on parts of the boundary. We propose a new numerical method with adaptive placement of source points in the MFS to solve the inverse boundary determination problem. Since the MFS source points placement here is not trivial due to the unknown boundary, we employ an adaptive technique to choose a sub-optimal arrangement of source points on various fictitious boundaries. Afterwards, the standard Tikhonov regularization method is used to solve ill-conditional matrix equation, while the regularization parameter is chosen by the L-curve criterion. The numerical studies of both open and closed fictitious boundaries are considered. It is shown that the proposed method is effective and stable even for data with relatively high noise levels.     

The practicality of adaptive phase estimation

Adaptive phase estimation is the process of estimating the phase of an electromagnetic field via a continually changing measurement. The measurement is varied in an attempt to optimize it at each moment. In this paper, we show that adaptive phase estimation is more accurate than nonadaptive phase estimation for continuous beams of light even when small time delays in the feedback are present.     

A phase unwrapping technique for object relief determination

Phase shifting methods are widely used in photomechanics to analyse fringe patterns obtained from interferometry, moiré, etc. The phase is determined by modulo 2π and an unwrapping process is needed. An algorithm is presented which avoids most of the inconsistency of the phase field. It can be applied to the relief determination of virtually any object shape. In this paper, two applications are performed using the projection of a parallel line grating with a pitch equal to 4 mm. The accuracy is shown to be around 0…1 mm.     

Reference phase shift determination in phase shifting interferometry

The phase shifting technique has recently seen application to many types of interferometers, including holographic, speckle and moiré systems for strain analysis. In these applications, close control of the phase shifts may be impossible due to the effect of mechanical vibrations, and this presents difficulties when extracting the phase information, since the reference phase shifts are generally assumed to be known. In this work, several approaches to the problem of determining the reference phase shifts in a perturbing environment are critically evaluated using computer simulations. The analyses provide a general relationship between precision and reference phase shift errors and demonstrate the performance of each method as certain idealised fringe pattern error parameters are varied. A practical example confirms the predictions of the numerical simulations and demonstrates the feasibility of using reference phase shift estimates to improve data reduction procedures.     

Local fringe density determination by adaptive filtering

We demonstrate a method to easily and quickly determine the local fringe density map of a fringe pattern. The method is based on an isotropic adaptive bandpass filter that is tuned at different frequencies. The modulation map after applying a specific bandpass frequencies filter presents a maximum response in the regions where the bandpass filter and fringe frequencies coincide. We show a set of simulations and experimental results that prove the effectiveness of the proposed method.     

Phase-shifting windowed Fourier ridges for determination of phase derivatives

Determination of the phase or phase derivative from interferometric fringe patterns is an important task in optical interferometry. The use of wavelet ridges was recently shown to be an effective method for phase retrieval from a single fringe pattern. One necessary requirement in this method is the need for carrier frequency. In cases when carrier frequency is not available, the novel phase-shifting windowed Fourier ridges method can be used. Phase derivatives with the proper sign can be directly retrieved even in the presence of noise. An application for curvature determination from speckle shearographic fringes demonstrates the effectiveness of the method.     

A high precision phase reconstruction algorithm for multi-laser guide stars adaptive optics

Adaptive optics(AO) systems are widespread and considered as an essential part of any large aperture telescope for obtaining a high resolution imaging at present.To enlarge the imaging field of view(FOV),multi-laser guide stars(LGSs) are currently being investigated and used for the large aperture optical telescopes.LGS measurement is necessary and pivotal to obtain the cumulative phase distortion along a target in the multi-LGSs AO system.We propose a high precision phase reconstruction algorithm to estimate the phase for a target with an uncertain turbulence profile based on the interpolation.By comparing with the conventional average method,the proposed method reduces the root mean square(RMS) error from 130 nm to 85 nm with a 30% reduction for narrow FOV.We confirm that such phase reconstruction algorithm is validated for both narrow field AO and wide field AO.     

Fast-acting adaptive mirrors and their efficiency at compensating for random phase perturbations

Research in adaptive optics represents a new stage in the development of optical systems. Adaptive optics can be used for compensating for phase fluctuations of a light field propagated through the atmosphere and through optical media. The idea of dynamic compensation of phase fluctuations originated in the 1950s [1] as an effort to improve the resolutions of telescopes designed for observing stars through the turbulent atmosphere. However, the technological level required for applying this technique to detection and transmission systems has only recently been achieved with the successful development of fast-acting optical elements — adaptive mirrors [2].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 106–117, November, 1985.     

The deformable mirror method of adaptive phase correction

In this paper, a simple method of phase correction by using a micromachined deformable mirror (MMDM)is demonstrated. With correction of high-order phases due to propagating through medium, we obtaineda clean pulse shape, flattened spectral phase and decreased the femtosecond laser pulse duration. It isshown by our experiment that the deformable mirror is an effective and easy method for adaptive phasecorrection.     

Sequence of phase correction in multiconjugate adaptive optics

The way in which the sequence of phase correction impinges on performance in multiconjugate adaptive optics systems is described. When multiple phase modulators with different conjugate ranges are used, the conjugate images of the phase modulators in the atmosphere must be reimaged in the reverse order post focus, and adaptive phase correction applied in this sequence for perfect amplitude and phase cancellation. Performing the correction without relay optics results in residual amplitude and phase aberrations. It is shown, by Monte Carlo simulations of Fresnel propagation, that the effects of wave optical propagation become nonnegligible at visible wavelengths and for large air masses.     

Methods for determination of weight vector of adaptive arrays with short samples

Methods are proposed for determination of the weight vector in adaptive antenna arrays (AA) in the case of a short input-process sample, when the number of sampled vectors is smaller than the number of AA elements and an inverted correlation matrix of the interference in the AA receiving channels does not exist.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 4, pp. 493–509, April, 1994.     

An adaptive quarter-wave tube that uses the sliding-Goertzel algorithm for estimation of phase

This paper describes an adaptive quarter wave tube used to attenuate a tone from the exhaust noise of a large diesel engine. A sliding-Goertzel algorithm was used to calculate the phase angle of the transfer function between a microphone in the adaptive quarter wave tube and in the main exhaust duct. The control system adjusted the length of the adaptive quarter wave tube until the phase angle was −90° and caused the sound pressure level at the cylinder firing frequency in the exhaust duct to be minimized. The system was able to adapt to changes in engine speed, exhaust gas temperature, and load applied to the engine. The results demonstrate that the sliding-Goertzel algorithm can be used effectively to estimate the phase angle in an adaptive–passive acoustic control system.     

Combining GPS carrier phase and Doppler observations for precise velocity determination

The truncation error and propagation error are analyzed for velocity determination through differential GPS carrier phase observations,and an approach for the choice of the best number of points for the central difference method is developed.In order to overcome the disadvantages of existing GPS velocity determination methods,a new velocity determination algorithm is presented,based on combining carrier phase and Doppler observations.The basic idea is that two types of observation are combined by adding the...     

Enhanced x-ray phase determination by three-beam diffraction

For decades, solving the phase problem of x-ray scattering has been a goal that, in principle, could be achieved by means of n-beam diffraction (n-BD). However, the phases extracted by the actual n-BD phasing techniques are not very precise, mainly due to systematic errors that are difficult to estimate. We present an innovative theoretical approach and experimental procedure that, combined, eliminate two major sources of error. It is a high precision phasing technique that provides the triplet-phase angle with an error of about 2 degrees.     

Path and phase determination for an interfering photon with orbital angular momentum

A polarized photon with well-defined orbital angular momentum that emerges from a Mach-Zehnder interferometer (MZI) is shown to seemingly circumvent wave-particle duality constraints. For certain phase differences between the MZI arms, this pattern yields both reliable which-path information and high phase sensitivity.     

Design and optimization of phase plates for shaping partially coherent beams by adaptive genetic algorithms

The adaptive genetic algorithms (AGAs) are applied to the design and optimization of phase plates for shaping partially coherent beams. The simulation procedure based on the AGAs is described. Numerical examples for shaping partially coherent Cosh-Gaussian (ChG) and Hermite-Gaussian (HG) beams demonstrate the advantage of the AGAs in applications to the partially coherent beam transformation and shaping.