Analysis of Lau interferometric fringe for measurement of focal length by using wavelet filtering techniques

New filtering scheme is investigated and implemented on Lau interferometric fringes to enhance the signal-to-noise ratio (SNR) in the Lau interferograms. Towards this, the applicability of Haar, Daubechies and Symlet wavelet based filtering schemes have been tested. Of these schemes, the Symlet based filtering scheme gives the best results in terms of improved signal to noise ratio and speckle index. This scheme is then used to analyse Lau interferograms recorded in the experimental arrangement for focal length measurement. The processed interferograms yield improved accuracy and precision of measurement.     

Application of wavelet filtering techniques to Lau interferometric fringe analysis for measurement of small tilt angles

This communication presents the results of investigation undertaken towards testing the viability of wavelet filtering techniques in analyzing the Lau interferometric fringes. Towards this, the applicability of Haar, Daubechies and Symlet wavelet based filtering schemes have been tested. Of these schemes, the Symlet based filtering scheme gives the best results in terms of improved signal to noise ratio. This scheme is then used to analyze Lau interferograms recorded in the experimental arrangement for tilt angle measurement. The processed interferograms yield improved accuracy and precision of measurement.     

通过相移条纹图差分测定相移量的方法

提出一种通过两幅相移条纹图相减来确定它们之间相移量的方法,进行了理论分析和实验验证。两幅相移条纹图相减并归一化后,得到的相移差分函数是振幅只与相移量有关的正弦函数,可以通过确定该函数最大极值的方法得到振幅,进而计算出相移量。介绍了极值直接查找法和平均法两种实现最大极值测量的方法。由于不使用傅里叶变换,减少了运算时间,既可以用于高空间频率条纹,也可以用于稀疏平行条纹,以及任意花样的条纹。在衬比度因子确定后,用这种方法就能够直接在空域内确定两幅条纹图之间的相移量,通过大量采样点进行统计计算,使结果达到很高的精度。将所得到的结果与用傅里叶变换方法得到的结果进行了比较,表明两种方法得到的结果具有完全相同的精度。     

Experimental validation of closed-loop adaptive optics based on a self-referencing interferometer wavefront sensor and a liquid-crystal spatial light modulator

A closed-loop adaptive optics system based on a self-referencing interferometer wavefront sensor (SRI WFS) using phase-shifting point-diffraction technique and an electrically addressed phase-only liquid-crystal spatial light modulator (LC SLM) is built and validated experimentally. The wavefront aberration of incoming beam is directly measured by analyzing four frames phase-shifted interferograms captured by a single CCD camera in two camera shots, and then by loading the conjugate function onto the SLM the wavefront aberration is corrected. The proposed scheme does not rely on any complicated control algorithm or wavefront-reconstruction algorithm and can achieve high-resolution and high-accuracy correction. Closed-loop correction results of single order Zernike aberrations and a Kolmogorov turbulence phase screen show that considerable improvements in the Strehl ratio (of greater than 0.94) is achieved.     

Measurement of non-monotonous phase changes in temporal speckle pattern interferometry using a correlation method without a temporal carrier

Recently, a phase evaluation method was proposed to measure nanometric displacements by means of digital speckle pattern interferometry when the phase change introduced by the deformation is in the range [0,π) rad. This method is based on the evaluation of a correlation coefficient between two speckle interferograms generated by both deformation states of the object. In this paper, we present a novel technique to measure non-monotonous displacements in temporal speckle pattern interferometry using a correlation method without a temporal carrier. In this approach, the sign ambiguity is resolved automatically due to the introduction of a function that determines the correct sign of the displacement between two consecutive speckle interferograms. The rms phase errors introduced by the proposed method are determined using computer-simulated speckle interferograms. An application of the phase retrieval method to process experimental data is also presented.     

Two-dimensional cell parameters measurement of nematic liquid crystal using optical interferometry and Fourier transform fringe analysis technique

We report a method for the measurement of nematic liquid crystal (NLC) cell parameters i.e., switching voltage, birefringence, retardation, dielectric anisotropy, average tilt angle and change in refractive index with applied DC voltage to LC material. The proposed method is based on optical interferometry and Fourier transform fringe analysis technique, in which we obtain 2-dimensional (2D) phase map of the interferograms as a function of applied voltage. Mach-Zehnder interferometer (MZI) was used for the study of cell parameters and interferograms were recorded at different applied DC voltages to NLC cell using CCD camera. From the phase map, 2D-refractive index distribution of the LC cell with applied voltage was reconstructed. Analytical equations are derived based on optical interferometry and then solved to obtain cell parameters. The present method is fast and can give 2D-cell parameters from only two quick interferograms.     

Signal averaging of photoacoustic FTIR data: I. Computation of spectra from double-sided low resolution interferograms

Five different strategies for calculating average photoacoustic infrared spectra were applied to a series of 10 double-sided low resolution interferograms recorded for fusinite (a separated coal maceral). Both multiplicative phase correction and computation of modulus (power) spectra were considered. It was found that the sequence chosen for averaging and Fourier transformation of the interferograms makes only slight differences in the average spectra. When calculating average modulus spectra, the position of the interferogram centreburst must be constant in order to produce accurate results, a criterion that always applies to averaging interferograms. In multiplicative phase correction, it was found that the number of interferogram points used to calculate the phase function can vary over a significant range without producing any observable change in the computed spectrum.     

Slightly dispersive white-light spectral interferometry to measure distances and displacements

A new spectral-domain interferometric technique of measuring distances and displacements is realized when the effect of low dispersion in a Michelson interferometer, which comprises two coated plates of a beam splitter and a compensator, is known and the spectral interference fringes are resolved over a wide wavelength range. First, processing the recorded spectral interferograms by an adequate method, the unmodulated spectrum, the spectral fringe visibility function and the unwrapped phase function are obtained. Then, knowing the dispersion relation for the fused-silica plates, the ambiguity of the unwrapped phase function is removed and the thickness of fused silica and the nonlinear phase function due to the effect of the coatings are determined by using a new procedure. It is based on the linear dependence of the overall optical path difference between interferometer beams on the refractive index of fused silica. Once the thickness and the nonlinear phase function are known, the positions of the interferometer mirror are determined precisely by a least-squares fitting of the theoretical spectral interferograms to the recorded ones.     

High-precision molecular wave-packet interferometry with HgAr dimers

Molecular wave-packet (WP) interferometry has been demonstrated in the A electronic state of the HgAr van der Waals complex with two time-delayed UV fs pulses at 254 nm. The interferograms of three vibrational levels in the WP's display almost 100% fringe contrast as a function of the interpulse delay tau, which is tuned with sub-10 as stability and resolution. It is clearly observed that the three interferograms show their dephasing and rephasing within a single vibrational period, allowing us to prepare arbitrary relative populations of the three levels by adjusting a single parameter tau.     

用实时全息术研究低速变化过程的一种简易系统

研制了一种用于研究物体低速过程的简易系统，它由带有液门原位化学处理的实时全息干涉装置和具有连拍功能的相机以及一台氦氮激光器组成，是一种简易实用的“低速、实时全息干涉摄影系统”。用它记录了火箭推进剂样品在室温，常压下的燃烧过程，１００瓦普通只灯逐级加压的点燃过程，对实时全息图的记录和处理采用了一种可获得高反衬度的新技术，拍摄的成功率高，干涉条纹的反衬度好，它为研究物体的低速变化过程提供了一种有力的手     

Fast f-to-2f interferometer for a direct measurement of the carrier-envelope phase drift of ultrashort amplified laser pulses

We propose a novel method to directly extract the phase from spectral interferograms, without the need for digital signal processing. This method is demonstrated with single-shot measurement and stabilization of the carrier-envelope phase of a 3 kHz amplifier system. Our scheme allows for real-time monitoring of the carrier-envelope drift and an increased loop width for stabilization. We find that in our amplifier laser system fast carrier-envelope phase jitter is mainly inherited from the oscillator stabilization loop but we also find previously unreported indications for a rapid pulse-to-pulse jitter from the amplifier pump laser.     

Measurement of transverse vibrations/visualization of mode shapes in square plate by using digital speckle pattern interferometry and wavelet transform

New filtering scheme is investigated and implemented on digital speckle pattern interferometric fringes to enhance the signal-to-noise ratio (SNR) in the speckle interferograms. To establish the potential of new filtering scheme the experiment was conducted on the vibrating cantilever beam. Experimental results revealed that the new filtering scheme is more powerful than other known filtering schemes (Kumar et al. Opt Laser Eng 2004;41:81–93. Kumar et al. Opt Laser Technol 2001;33:567–571. Shakher et al. Opt Eng 2002;41:176–180. Shakher et al. Proceedings ICICS, Singapore, 9–12 September 1997, p. 953–956. Bowler et al. Proceedings of IEE second international conference on image processing, London, 1986, p. 24–26. Lim. Opt Eng 1981;20:670–678. Devila et al. J Mod Opt 1995;42:1795–1804; Kaufmann et al. Opt Eng 1996;35:9–14). The new scheme reduced the speckle noise and improved SNR in speckle interferograms. Further, the new investigated filtering scheme is implemented to study the mode shapes of square plates under two different boundary conditions. In the first condition all the edges of the square plate were fixed while in the second condition two adjacent edges were fixed and the remaining two edges were free. From the experimental results it is clear that the mode shapes are more distinctly visible with the implementation of the new filtering scheme as compared to other known schemes. Under both the boundary conditions the recorded resonance frequencies were compared with the calculated values of resonance frequencies based on classical theory. The results obtained form DSPI show good agreement with classical theory.     

基于主元分析的随机相移算法

将统计理论中的主元分析应用到干涉条纹分析中,提出一种基于主元分析的随机相移算法。该算法先将多帧条纹数据分解成不相关的主元成分,然后从主元成分中提取2维相位信息。数值模拟结果表明:该算法不需要迭代运算就能从4帧完全随机相移干涉图中有效提取相位信息,运算时间少,精度高。实验结果表明主元分析相移算法比现有迭代相移算法更适合于随机相移干涉图分析。     

Femtosecond time-resolved interferometric microscopy

We describe optical interferometry with 100 fs time resolution and a spatial resolution of approximately one micrometer. Using a pump-probe scheme and a 2D-Fourier transformation algorithm, we are able to retrieve from the interferograms very small changes in the phase and the amplitude of the reflected probe pulses. The performance of the technique is illustrated by measurements of transient and permanent surface modifications of crystalline GaAs after exposure to intense femtosecond laser pulses with fluences near the ablation threshold. PACS 78.47.+p; 42.65.Re; 42.15.Eq; 68.35.Ja     

长干涉腔波长移相计算的自适应相位筛选法

波长移相干涉仪可用于大口径光学元件的测试。其移相量需经过标定方可采用定步长移相算法计算相位分布。在长腔长测试条件下,由于激光器的波长调谐驱动源的精度有限,采用定步长移相算法求解相位分布的精度不高。在分析干涉腔长和波面计算误差的基础上,提出了一种自适应相位筛选计算方法。根据电压-相位标定曲线采集多组周期干涉图,对干涉图中的光强值进行均匀分布抽样后,对其进行随机移相计算,求取每帧干涉图精确的步进移相量,从中筛选出移相量为π/2的四帧干涉图,利用四步移相计算公式求得精确的相位分布。实验结果表明,在波长移相干涉仪中运用该方法,可以很好地解决长腔长测试条件下的相位计算问题,与未进行筛选的计算结果比较,其测试精度得到了显著提高。     

Michelson interferometer with multichannel interferogram recording

A schematic diagram of a Michelson interferometer with a diffraction grating for which the length of one arm is a function of the transverse coordinate of the light beam is proposed. The possibility of recording the interferograms without mechanical displacement of optical elements of the interferometer is demonstrated.     

Collective phase measurement of an array of fiber lasers by quadriwave lateral shearing interferometry for coherent beam combining

We present a new configuration of quadriwave lateral shearing interferometer dedicated to phase detection for beam-combining purposes. Assuming that the fibers are disposed in a matrix arrangement, our scheme gives direct access to the phase step between adjacent fibers in two dimensions. Experimentally recorded interferograms are made only of two-wave interference fringes that scroll as the phase evolves in the fibers. This simplicity allows fast treatment by the spatial demodulation process, and the phase map from the fibers can be estimated in real time. No external reference is required, and the technique is fully compatible with a high number of fibers.     

Extreme ultraviolet Fourier-transform spectroscopy with high order harmonics

We demonstrate a new scheme for extreme ultraviolet (xuv) Fourier-transform spectroscopy based on the generation of two phase-locked high-harmonic beams. It allows us to measure for the first time interferograms at wavelengths as short as 90 nm, and open the perspective of performing high-resolution Fourier-transform absorption spectroscopy in the xuv. Our measurements also demonstrate that a precise control of the relative phase of harmonic pulses can be obtained with an accuracy on an attosecond time scale, of importance for future xuv pump-xuv probe attosecond spectroscopy.     

Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency-domain optical coherence tomography

Standard Fourier-domain optical coherence tomography (FDOCT) suffers from the presence of autocorrelation terms that obscure the object information and degrade the sensitivity and signal-to-noise ratio. By exploiting the phase information of the recorded interferograms, it is possible to remove those autocorrelation terms and to double the measurement range. However, standard phase-retrieval algorithms need three to five interferograms. We present a novel technique that shows all the features of complex FDOCT with only two recorded interferograms.     

Phase Measurement Algorithm without Phase unwrapping Problem for Phase stepping interferometry

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