Residual Phase Error Research Articles

Fast Timing Acquisition for Low Signal-to-Noise Ratio High Density Optical Recording

Future optical data storage systems are expected to operate at significantly higher densities and lower signal-to-noise ratios (SNRs) than current systems. Partial response maximum likelihood (PRML) and iterative soft decoding methods are potential candidates for detecting data in such low-SNR, high-density channels. At such low SNRs, conventional timing acquisition methods suffer from not only large residual phase errors but also large frequency errors, leading to large timing jitter and high probability that the timing loop will lose lock during the tracking mode. To achieve rapid timing acquisition, an adaptive gains phase-locked loop (PLL) with a variable threshold timing loop detector is proposed and investigated in this study. Moreover, loss of lock rate (LOLR) is suggested as a measure to characterize the quality of the acquisition.

Partial Fourier imaging in multi-dimensions: a means to save a full factor of two in time.

We present an improvement to the traditional one-dimensional partial Fourier method by extending the method to multi-dimensions. The modified method allowed a full factor of two savings in time with much better coverage of the central k-space information and, because of this, smaller reconstruction artifacts. The residual magnitude error was found to correlate strongly with the residual phase error. Numerical simulation also indicated that with a priori perfect phase information, the original magnitude image could be perfectly reconstructed with half of the k-space data points in the multi-dimensional case. Simulated, phantom, and human data sets were tested with edge differences ranging from 10% (consistent with variable Gibbs ringing) to 25% (consistent with a blurred version of the object). The method was found to be a valuable adjunct to human imaging for short TR, T1-weighted three-dimensional gradient-echo imaging and magnetic resonance (MR) angiographic methods, especially when short echo times were used.

Turbulence-induced Zernike aberrations of optical wavefronts in partial adaptive compensation

Abstract The residual phase error after correction for turbulence-induced phase aberrations by a partially compensating adaptive optics system with a laser guide star (LGS) as reference is computed by using the phase expansion on the Zernike polynomials. To get the most from the compensation, the limitation due to the actuator spacing of a deformable mirror, temporal lag and angular separation between the object and the LGS (anisoplanatism effect) have been analysed in this paper. If Fried's parameter r0 is 10.7 cm, the temporal lag should be less than 2ms for a sodium LGS. Also the higher the aberration radial degree is, the less the actuator spacing is required. To correct for aberration of radial degree higher than 4 (if r0 is 10.7 cm), the actuator spacing should be less than 300mm.

Turbulence-induced zernike aberrations of optical wavefronts in partial adaptive compensation

The residual phase error after correction for turbulence-induced phase aberrations by a partially compensating adaptive optics system with a laser guide star (LGS) as reference is computed by using the phase expansion on the Zernike polynomials. To get the most from the compensation, the limitation due to the actuator spacing of a deformable mirror, temporal lag and angular separation between the object and the LGS (anisoplanatism effect) have been analysed in this paper. If Fried's parameter r0 is 10.7 cm, the temporal lag should be less than 2ms for a sodium LGS. Also the higher the aberration radial degree is, the less the actuator spacing is required. To correct for aberration of radial degree higher than 4 (if r0 is 10.7 cm), the actuator spacing should be less than 300mm.

Measurement of telescope aberrations through atmospheric turbulence by use of phase diversity

We conduct computer simulations of the reconstruction of a wave front at a telescope pupil with the phase-diversity method. An instantaneous wave front is reconstructed from focused and defocused specklegrams of a point star. In the wave-front reconstruction we do not fit the wave front to Zernike polynomials but retrieve the phase with a phase-unwrapping procedure. Averaging over many atmospherically perturbed wave fronts leads to the residual phase error, namely, the aberration of the telescope. The scintillation effect, nonuniformity of amplitude on a telescope pupil, is also discussed.

Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter: pulse compression and shaping

We demonstrate experimentally that an arbitrary phase and amplitude profile can be applied to an ultrashort pulse by use of an acousto-optic programmable dispersive filter (AOPDF). Our filter has a large group-delay range that extends over 3 ps and a 30% diffraction efficiency over 150 THz. Experiments were conducted on a kilohertz chirped-pulse amplification laser chain capable of generating 30-fs pulses without additional pulse shaping. Compensating for gain narrowing and residual phase errors with an AOPDF in place of the stretcher results in 17-fs transform-limited pulses. Arbitrary shaping of these 17-fs pulses is also demonstrated in both the temporal and the spectral domains.

FTS GENERALIZED APPARATUS FUNCTION

A general analytical expression is proposed for the apparatus function of any Fourier transform spectrometer, which takes into account the throughput, a possible slight asymmetry of the line profiles due to a residual phase error, as also a chromatic variation of the radiant energy received by the detectors during the recording of the interferogram. An experimental example is used to exhibit the large errors appearing in the retrieved line intensities and collisional widths when one analyzes the observed line profiles with the classical apparatus function, instead of the generalized expression given in this paper.

Optimal modal wave-front compensation for anisoplanatism in adaptive optics

We examine how modal aberration measurements degraded by turbulence-induced anisoplanatism may be used to optimally conjugate atmospheric phase aberrations. By examining the form of the aperture-averaged mean square residual phase error, we show that atmospheric compensation is suboptimal when the measured coefficients from off-axis or finite-altitude guide stars are applied directly. The optimal compensation is obtained only when conjugate phase coefficients are estimated, given the guide-star measurements and knowledge of the spatial correlation of the on-axis and measured phase coefficients, by use of a minimum-mean-square-error (MMSE) estimator. The form of this estimator is outlined, thus motivating the need to quantify the spatial cross correlation of the Zernike coefficients of the phase aberrations. With a knowledge of the modal cross correlation, we show that wave-front compensation performance can be enhanced by use of the MMSE estimator over use of the beacon measurements directly for all orders of correction. For high-order off-axis natural-guide-star correction, equivalent imaging performance is obtained at a beacon offset 10% larger than when beacon measurements are used directly. For high-order laser-guide-star correction, equivalent imaging performance is obtained at laser-guide-star altitudes 20% lower when the MMSE estimator is employed.

Variance of the Strehl ratio of an adaptive optics system

The variance σS2 of the Strehl ratio of a reasonably well-corrected adaptive optics system is derived as a power series in the log-amplitude variance σl2 and the residual phase error variance σδϕ2. It is shown that, to leading order, the variance of the Strehl ratio is dependent on the first power of the log-amplitude variance, (σl2)1, of the incident optical field but only on the second power of the residual phase variance, (σδϕ2)2, of that field after adaptive optics correction, and on the first power of the product of the log-amplitude variance times the phase variance, (σl2σδϕ2)1. As long as the adaptive optics correction is good enough to ensure that the variance of the residual phase, σδϕ2, is significantly less than unity, then even for fairly small values of the log-amplitude variance σl2, the value of the variance of the Strehl ratio, σS2, will be dominated by the value of the log-amplitude variance.

Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts: comment

In the framework of phase-shifting interferometry, the characteristic polynomial theory is extended to deal with nonlinear and nonuniform phase-shift miscalibration. A general procedure for designing algorithms that are insensitive to those errors is presented. It is also shown how analytical expressions for the residual phase errors can be obtained. Finally, it is demonstrated that the coefficients of any algorithm can be given a Hermitian symmetry.

Adaptive compensation of phase and magnitude aberrations

A new method for aberration correction is presented. Using multiple receive beams reconstructed at each transmit direction, image artifacts due to imperfect beam forming can be identified and greatly reduced. Previous studies have demonstrated the efficacy of such a compensation algorithm for blocked elements. In this study, the algorithm is extended for magnitude and phase aberrations. Experimental results show that substantial improvements are possible for small amplitude and phase errors. The compensation method is less effective for large errors, however. Based on this, a two-step procedure is proposed for general aberration correction. First, cross-correlation processing is used to reduce significant phase errors. Then, the adaptive compensation method is applied to remove remaining artifacts due to blocked elements, amplitude aberrations, and residual phase errors. This two-step procedure is shown to be effective in significantly reducing image artifacts due to amplitude and phase errors.

Global wave-front reconstruction using Shack–Hartmann sensors

A method is proposed for deriving the form of a turbulence-distorted wave front from Shack–Hartmann data by modeling the polychromatic imaging process in detail. In this way a higher order of reconstruction is possible than by methods that use only the barycenters (centers of gravity) of the individual spots. Simulations are presented showing the possible gains for a range of conditions of turbulence and photon flux. When photon noise is negligible the residual phase errors are approximately three times smaller than what is achievable by use of only the barycenters. The choice of functions for representing wave-front distortions is also considered with regard to the quality of the reconstruction obtained and to numerical efficiency.

Increased flexibility in GRASE imaging by k space-banded phase encoding.

GRASE (GRadient and spin Echo) is an echo train imaging technique that combines gradient and RF refocusing. Although overall signal decay is with T2 and field inhomogeneity phase errors do not accumulate, the small residual phase errors are periodic with echo number. The echo order described previously eliminates the phase error periodicity in k space but instead creates periodicity in the T2 modulation function that can also cause artifacts. In addition, with this order, the effective TE must be half the echo train time, and asymmetric Fourier sampling is difficult to implement. A new method is described that greatly reduces artifacts due to T2 decay, permits greater control of T2 contrast, and lends itself to asymmetric Fourier sampling. Different time segments of the echo train are encoded with different bands of spatial frequency in k space (hence "k banding"). Both computer simulations and experimental results demonstrate improvements in GRASE images acquired by this method.

Influence of missing array elements on phase aberration correction for medical ultrasound

The influence of missing array elements on aberration correction based on time delay estimation using radio frequency signals of neighboring elements is experimentally investigated. Normalized cross correlation and sum of absolute differences are employed as the cost functions in aberration estimation. Their performance is tested through various measurements using radio frequency data acquired with a 3.3 MHz, 64-element phased array. Variation of cost functions and phase estimation error are obtained for different combinations of number of missing elements, amount of aberration, and noise level. For a particular combination of these parameters, a set of B-scan images is reconstructed and presented to examine the effects of residual phase errors on image quality. >

WAVEFRONT RECONSTRUCTION ERRORS OF SHACK-HARTMANN WAVEFRONT SENSORS

ABSTRACT We have evaluated the wavefront reconstruction error for Shack-Hartmann wavefront sensors based on a series of simulations for various numbers of subapertures at various levels of measurement error in determining the Hartmann spot centroids. The optimum number of subapertures is derived for a given magnitude reference star in the cases of photon-noise limited and detector-noise limited sensors. When centroid measuring error is absent, the maximum number of Zernike terms that can be corrected by mans of modal adaptive compensation is about 1/5 of the number of subapertures. The residual phase error in wavefront reconstruction is shown to be sensitive to the measuring erorr of the spot centroids. It is essential to reduce the centroid measuring erorr in wavefront sensors for high level adaptive optics systems with a large number of degrees of freedom.

Patch diameter limitation due to high chirp rates in focused SAR images

Polar-format processed synthetic aperture radar (SAR) images have a limited focused patch diameter that results from unmitigated phase errors. Very high chirp rates, encountered with fine-resolution short-pulse radars, exasperate the problem via a residual video phase error term. This letter modifies the traditional maximum patch diameter expression to include effects of very high chirp rates.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analysis of multiconjugate adaptive optics

We investigate a method for widening the compensated field of view of an adaptive-optical telescope with multiple deformable mirrors and an array of artificial guide stars. An ensemble of wavefront sensor measurements, made with the individual guide stars in the array, is used to estimate the contribution of a region of the atmosphere to the cumulative phase distortion. Our analysis includes the effects of measurement noise, wavefront-sensor sampling, and reconstruction of the wave front from slope measurements. We performed numerical computations for an atmosphere consisting of two turbulent layers: one at 1% of the guide-star altitude with 90% of the total turbulence strength and one at 10% of the guide-star altitude with the remaining 10% of the total turbulence strength. If we assume that r0 = 0.15 m and that a photon-limited wave-front sensor detecting 50 photons/r0-sized subaperture is used, the results indicate that a 0.9-m-square telescope with a diagonal field of view of ~92 μrad ≈ 19 arcsec can use two deformable mirrors, four laser guide stars, and a natural tilt reference star to achieve an rms residual phase error that is <λ/7 over its entire field of view.

Comparative analysis of low-pass filters for the demodulation of projected gratings in 3-D adaptive profilometry

In 3-D adaptive profilometry based on structured light projection, the choice of the low-pass filter to he used in the deformed pattern demodulation is crucial. In this paper, we have studied the performance of a typical finite impulse response (FIR) and of an infinite impulse response (IIR) Butterworth low-pass filter. Adaptiveness of the filters to both coarse and small variations of the grating frequency has been investigated. The ability of the filters to adapt to coarse changes of the grating frequency has been quantified in terms of their speed of synthesis, while the ability of the filters to tolerate small variations of the grating frequency has been quantified by measuring the residual phase errors. The analysis shows that the IIR Butterworth filter performs better than the FIR filter both in the coarse and in the fine grating frequency variation cases.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Image reconstruction by means of wave-front sensor measurements in closed-loop adaptive-optics systems

Theoretical and experimental investigations of the imaging technique referred to as speckle holography have shown that wave-front information can be used in the postprocessing of astronomical data to improve the quality of images. In a closed-loop adaptive-optics system the wave-front sensor is continuously measuring the residual wave-front error. Thus wave-front information is continuously available for use in image reconstruction. We show here that wave-front information in a closed-loop adaptive-optics system, used in a postprocessing scheme, can improve the phase of the compensated optical-transfer function in systems with finite delays between wave-front sensing and phase correction. This technique is closely related to speckle holography and is referred to here as compensated speckle holography. This method requires good spatial sampling of the residual phase error and degrades gracefully as the wave-front sensor signal-to-noise ratio decreases. Also, the technique can be used to reduce the required closed-loop bandwidth of an imaging system, permitting longer integration times in the wave-front sensor, and thus allowing dimmer objects to be imaged without the use of an artificial guide star.

Wide-span optical frequency comb generator for accurate optical frequency difference measurement

An optical frequency comb (OFC) generator was realized for accurate optical frequency difference measurement of 1.5 mu m wavelength semiconductor lasers by using a high frequency LiNbO/sub 3/ electrooptic phase modulator which was installed in a Fabry-Perot cavity. It was confirmed that the span of the OFC was wider than 4 THz. By using semiconductor lasers whose spectrum linewidths were narrowed to 1 kHz and a sensitive optical balanced-mixer-receiver for measuring beat signal between the sideband of the comb and the laser, we demonstrated a frequency difference measurement up to 0.5 THz with a signal-to-noise ratio higher than 61 dB, and a heterodyne optical phase locking with a heterodyne frequency of 0.5 THz in which the residual phase error variance was less than 0.01 rad/sup 2/. The maximum measurable frequency difference, which was defined as the sideband frequency with the signal-to-noise ratio of 0 dB, was estimated to be 4 THz.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>