Effects of Noise and Detection Error in a Dynamic Adaptive Optics System

It is well known that noise and detection error can affect the performances of an adaptive optics (AO) system. Effects of noise and detection error on the phase compensation effectiveness in a dynamic AO system are investigated by means of a pure numerical simulation in this paper. A theoretical model for numerically simulating effects of noise and detection error in a static AO system and a corresponding computer program were presented in a previous article. A numerical simulation of effects of noise and detection error is combined with our previous numeral simulation of a dynamic AO system in this paper and a corresponding computer program has been compiled. Effects of detection error, readout noise and photon noise are included and investigated by a numerical simulation for finding the preferred working conditions and the best performances in a practical dynamic AO system. An approximate model is presented as well. Under many practical conditions such approximate model is a good alternative to the more accurate one. A simple algorithm which can be used for reducing the effect of noise is presented as well. When signal to noise ratio is very low, such method can be used to improve the performances of a dynamic AO system.

Performance analysis of bit error rate for free space optical communication with tip-tilt compensation based on gamma-gamma distribution

In this paper, the gamma-gamma probability distribution is used to model turbulent channels. The bit error rate (BER) performance of free space optical (FSO) communication systems employing on-off keying (OOK) or subcarrier binary phase-shift keying (BPSK) modulation format is derived. A tip-tilt adaptive optics system is also incorporated with a FSO system using the above modulation formats. The tip-tilt compensation can alleviate effects of atmospheric turbulence and thereby improve the BER performance. The improvement is different for different turbulence strengths and modulation formats. In addition, the BER performance of communication systems employing subcarrier BPSK modulation is much better than that of compatible systems employing OOK modulation with or without tip-tilt compensation.

Entanglement purification with higher error threshold for imperfection of local operations and bell state measurements

We analyse further the entanglement purification protocol proposed by Feng et al. (Phys. Lett. A 271 (2000) 44) in the case of imperfect local operations and measurements. It is found that this protocol allows of higher error threshold. Compared with the standard entanglement purification proposed by Bennett et al. [Phys. Rev. Lett. 76 (1996) 722], it turns out that this protocol is remarkably robust against the influences of imperfect local operations and measurements.

A new method and instrument for accurately measuring interval between ultrashort pulses

Using second-order autocorrelation conception, a novel method and instrument for accurately measuring interval between two linearly polarized ultrashort pulses with real time were presented. The experiment demonstrated that the measuring method and instrument were simple and accurate (the measurement error <5 fs). During measuring, there was no moving element resulting in dynamic measurement error.

The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces

This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length xi and the roughness exponent alpha, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with alpha = 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.

The gated integration technique for the accurate measurement of the autocorrelation function of speckle intensities scattered from random phase screens

A new approach based on the gated integration technique is proposed for the accurate measurement of the autocorrelation function of speckle intensities scattered from a random phase screen. The Boxcar used for this technique in the acquisition of the speckle intensity data integrates the photoelectric signal during its sampling gate open, and it repeats the sampling by a preset number, in. The average analog of the in samplings output by the Boxcar enhances the signal-to-noise ratio by root m, because the repeated sampling and the average make the useful speckle signals stable, while the randomly varied photoelectric noise is suppressed by 1/ root m. In the experiment, we use an analog-to-digital converter module to synchronize all the actions such as the stepped movement of the phase screen, the repeated sampling, the readout of the averaged output of the Boxcar, etc. The experimental results show that speckle signals are better recovered from contaminated signals, and the autocorrelation function with the secondary maximum is obtained, indicating that the accuracy of the measurement of the autocorrelation function is greatly improved by the gated integration technique. (C) 2006 Elsevier Ltd. All rights reserved.

Design of NRAs having higher aperture opening ratio and autocorrelation compression ratio by means of a global optimization method

When noises considerations are made, nonredundant arrays (NRAs) are endowed with many advantages which other arrays e.g., uniformly redundant arrays (URAs) do not possess in applications of coded aperture imaging. However, lower aperture opening ratio limits the applications of NRA in practice. In this paper, we present a computer searching method based on a global optimization algorithm named DIRECT to design NRAs. Compared with the existing NRAs e.g., Golay's NRAs, which are well known and widely used in various applications, NRAs found by our method have higher aperture opening ratio and auto correlation compression ratio. These advantages make our aperture arrays be very useful for practical applications especially for which of aperture size are limited. Here, we also present some aperture arrays we found. These aperture arrays have an interesting property that they belong to both NRA and URA. (C) 2006 Elsevier GmbH. All rights reserved.

System error removal and structure optimization based on Fizeau interferometer

In the process of interferometric testing, the measurement result is influenced by the system structure, which reduces the measurement accuracy. To obtain an accurate test result, it is necessary to analyze the test system, and build the relationship between the measurement error and the system parameters. In this paper, the influences of the system elements which include the collimated lens and the standard surface on the interferometric testing are analyzed, the expressions of phase distribution and wavefront error on the detector are obtained, the method to remove some element errors is introduced, and the optimization structure relationships are given. (C) 2006 Elsevier GmbH. All rights reserved.

Effect of elliptical manufacture error of an axicon on the diffraction-free beam patterns

Based on the generalized Huygens-Fresnel diffraction integral theory and the stationary-phase method, we analyze the influence on diffraction-free beam patterns of an elliptical manufacture error in an axicon. The numerical simulation is compared with the beam patterns photographed by using a CCD camera. Theoretical simulation and experimental results indicate that the intensity of the central spot decreases with increasing elliptical manufacture defect and propagation distance. Meanwhile, the bright rings around the central spot are gradually split into four or more symmetrical bright spots. The experimental results fit the theoretical simulation very well. (C) 2008 Society of Photo-Optical Instrumentation Engineers.

Modelling and simulation of the second-order Doppler error of a laser dual-frequency interferometer

Only the first- order Doppler frequency shift is considered in current laser dual- frequency interferometers; however; the second- order Doppler frequency shift should be considered when the measurement corner cube ( MCC) moves at high velocity or variable velocity because it can cause considerable error. The influence of the second- order Doppler frequency shift on interferometer error is studied in this paper, and a model of the second- order Doppler error is put forward. Moreover, the model has been simulated with both high velocity and variable velocity motion. The simulated results show that the second- order Doppler error is proportional to the velocity of the MCC when it moves with uniform motion and the measured displacement is certain. When the MCC moves with variable motion, the second- order Doppler error concerns not only velocity but also acceleration. When muzzle velocity is zero the second- order Doppler error caused by an acceleration of 0.6g can be up to 2.5 nm in 0.4 s, which is not negligible in nanometric measurement. Moreover, when the muzzle velocity is nonzero, the accelerated motion may result in a greater error and decelerated motion may result in a smaller error.

Correcting the systematic error of the density functional theory calculation: the alternate combination approach of genetic algorithm and neural network

The alternate combinational approach of genetic algorithm and neural network (AGANN) has been presented to correct the systematic error of the density functional theory (DFT) calculation. It treats the DFT as a black box and models the error through external statistical information. As a demonstration, the AGANN method has been applied in the correction of the lattice energies from the DFT calculation for 72 metal halides and hydrides. Through the AGANN correction, the mean absolute value of the relative errors of the calculated lattice energies to the experimental values decreases from 4.93% to 1.20% in the testing set. For comparison, the neural network approach reduces the mean value to 2.56%. And for the common combinational approach of genetic algorithm and neural network, the value drops to 2.15%. The multiple linear regression method almost has no correction effect here.