A simple phase unwrapping approach based on filtering by windowed Fourier transform

Phase unwrapping is an interesting yet challenging problem in optical interferometry. In this paper, we limit our interest to unwrapping noisy phase maps as it is a common but difficult task. Our aim is to propose a simple solution to phase unwrapping. We first remove the noise by a novel windowed Fourier transform approach and then use sequential line scanning method for phase unwrapping. This simple approach is verified to be very effective.     

An effective method in calibrating nonlinear errors for phase-shifting interferometry

In phase measurement or digital holography for phase-shifting interferometry, the key role is the variation of reference light wave and recover algorithm based on interferograms and reference phase, so the calculation result is directly affected by phase-shift accuracy. However, because of the errors of nonlinear and other random factors, it is difficult to control the actual phase-shifting amount accurately. In this paper, we aim to propose an efficient method for phase-shifting interferometry which does not require accurate initial estimation of phase-shift amounts, only a few pixels with several randomly shifted interferograms are sufficient for accurate extraction of phase information. This method has reduced the dependence of reference phase, and can obtain phase-shifting amount directly without using complex revised algorithm for correcting phase-shifting nonlinear errors.     

Two-step phase-shifting interferometry and its application in image encryption

Conventional phase-shifting interferometry (PSI) needs at least three interferograms. A novel algorithm of two-step PSI, with an arbitrary known phase step, by which a complex object field can be reconstructed with only two interferograms is proposed. This algorithm is then applied to an information security system based on double random-phase encoding in the Fresnel domain. The feasibility of this method and its robustness against occlusion and additional noise attacks are verified by computer simulations. This approach can considerably improve the efficiency of data transmission and is very suitable for Internet use.     

Nanoscale deformation measurement by using the hybrid method of gray-level and holographic interferometry

This study extends the use of holographic interferometry to measure the nanoscale out-of-plane displacement with high surface resolution. It is noted that if the deformation is less than half of the optical wavelength, it is hard to find an obvious fringe pattern. Under such a situation, in general, the phase shift method is used. However, it needs to take more than 3 images for phase shifting and phase reconstruction In this paper, a more simple hybrid method of gray-level and holographic interferometry is used to extract fringe skeletons, in which it just needs to take one or two images for the normal deformation measurement directly, even if there exists no obvious fringe pattern. The displacement field with high surface resolution can also be obtained. The proposed method yielded a theoretical precision of 0.15 nm for out-of-plane displacement with a monochromatic CCD camera of 10-bit gray scale (1024 gray scales) sensitivity and microscale surface resolution for millimeter scale object with 640×480 pixels image resolution by an He–Ne LASER (632.8 nm wavelength) light source. The gray-level method is proposed to calculate the non-obvious interferometry fringe by traditional holographic interferometry hologram, and the result showed that this method works for this purpose.     

A refractive index interferometry method based on the X-ray crystallography

The absorption contrast image is very low for those weakly absorbing materials or weak phase object, such as the soft biological tissues, however, the phase item value of refractive index is a thousand larger than the absorption item, therefore the refractive index interferometry method is expected to be a new imaging tool for them. An interferometry method based on the X-ray crystallography is explored to the measurement of refractive index in this paper. The theoretical foundation, the optical design, the crystal transistor performance are the key parts to this interferometry method based on the X-ray crystallography. We give out a special refractive index detection scheme, using a laboratory hard X-ray source, and four single Si crystals. With this instrument, refractive index profile of those weak phase object can be unfolded accurately using this method. This refractive index interferometry method based on the X-ray crystallography will provide a new research tool for those special material properties or biological tissues study.     

Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry

White-light interferometric techniques have been widely used in three-dimensional (3D) profiling. This paper presents a new method based on vertical scanning interferometry (VSI) for the 3D profile measurement of a micro-component that contains sharp steps. The use of a white-light source in the system overcomes the phase ambiguity problem often encountered in monochromatic interferometry and also reduces speckle noises. A new algorithm based on the continuous wavelet transform (CWT) is used to retrieve the phase of an interferogram. The algorithm accurately determines local fringe peak and improves the vertical resolution of the measurement. The proposed method is highly resistant to noise and is able to achieve high accuracy. A micro-component (lamellar grating) fabricated by sacrificial etching technique is used as a test specimen to verify the proposed method. The measurement uncertainty of the experimental results is discussed.     

Talbot interferometry with an adaptive light intensity compensator

Talbot interferometry with a larger applicable scope has been investigated based on the intensity amplification method to weak moiré fringes by using photorefractive crystal as a light amplifier. It not only has function of conventional Talbot interferometry, but also is suitable for situations such as weak incident beam and detected object with strong absorption. The investigation indicates that the method or technique is feasible and the results of theoretical analysis are verified by experiments. Based on this investigation, Talbot interferometry with an adaptive light intensity compensator is proposed and some merits and demerits of the technique have briefly been discussed.     

State of the art of color interferometry at ONERA

At ONERA-Lille center a lot of studies have been conducted to characterize complex flows using an optical method based on differential interferometry with Wollaston prism and white polarized light source. Several applications are presented in two-dimensional and axisymmetric flows and in a gaseous mixture where the two gases interface is submitted to acceleration. Then, real-time color holographic interferometry (RCHI) has been developed to obtain the refractive index itself in two dimensional wake flow. The last improvements concern the extension of this method for analyzing three dimensional flows. The authors present a specific setup defined in a single sight direction, the aim being to reproduce the same optical setup along several sight directions, each shifted by a given angle. This optical technique uses reflection holograms where the diffraction efficiency of plates is strongly influenced by the variations in the gelatin thickness produced during the holograms treatment. Problems are discussed and solutions are proposed to control the gelatin shrinkage for two different types of used holograms. The results obtained in a one sight direction make it possible to build in the future an optical setup allowing several simultaneous line-of-sight optical measurements.     

Rapid and accurate chromatic dispersion measurement of fiber using asymmetric Sagnac interferometer

We propose and experimentally demonstrate an advanced method for chromatic dispersion measurement of fiber. This technique is based on spectral interferometry by using an asymmetric Sagnac loop and broadband optical source. The chromatic dispersion can be directly obtained from the spectral interferogram seen from an optical spectral analyzer. This method is rapid (<1?s), accurate, simple, low cost, and can provide a large dispersion measurement range.     

Correction of quadratic phase error in two-wavelength digital holographic interferometry using laser diodes

We present the correction of a quadratic phase error in two-wavelength digital holographic interferometry using laser diodes. This phase error arises from numerical reconstructions of wavefronts from digital holograms based on the Fresnel diffraction integral. To correct the quadratic phase error, it is numerically produced by computer on the basis of the theoretical prediction and is subtracted from the phase difference map in two-wavelength digital holographic interferometry. Experimental results show that the method of correction in this paper is useful for two-wavelength digital holographic interferometry using laser diodes.     

Fast localized wavefront correction using area-mapped phase-shift interferometry

We propose an innovative method for localized wavefront correction based on area-mapped phase-shift (AMPS) interferometry. In this Letter, we present the theory and then experimentally compare it with a previously demonstrated method based on spot-optimized phase-stepping (SOPS) interferometry. We found that AMPS outperforms SOPS interferometry in terms of speed by threefold, although in noisy environments the improvements may be larger. AMPS yielded similar point-spread functions (PSF) as SOPS for moderate system-induced aberrations, but yielded a slightly less ideal PSF for larger aberrations. The method described in this Letter may prove crucial for applications where the phase-stepping solution does not have sufficient speed.     

Analysis of the form of ultrashort pulses by spectral nonlinear interferometry

A new method for recording the phase structure of ultrashort optical pulses is proposed that makes no use of a reference pulse. Using three-wave interactions in a nonlinear optical medium, a wave of spectral decomposition of an ultrashort pulse is transformed into a monochromatic wave. The spatial phase structure of this wave contains information on the phase structure of the pulse spectrum and on the pulse form. This structure is analyzed by shearing interferometry.

     

Time-domain interferometry for direct electric-field reconstruction by use of an acousto-optic programmable filter and a two-photon detector

We introduce a new approach to the characterization of femtosecond optical pulses based on a remarkably simple setup combining a two-photon detector and a pulse shaper consisting of a longitudinal acousto-optic programmable filter. The operation of this setup is demonstrated through the use of a new version of spectral phase interferometry for direct electric-field reconstruction based on time-domain instead of on frequency-domain interferometry.     

Single-shot chirped-pulse spectral interferometry used to measure the femtosecond ionization dynamics of air

A novel interferometry technique is presented by which, in one shot, one can measure phase changes with a resolution of tens of femtoseconds while extending the measurement over picoseconds or even longer. The method is based on spectral (frequency-domain) interferometry with a pair of linearly chirped pules as probes. With this technique we obtained single-shot measurements of the rapid phase changes induced by optical field ionization of air. This allowed us to calculate the time profile of the electron density created by an intense short laser pulse.     

Cross-talk free image encryption and watermarking by digital holography and random composition

In previous image watermarking methods an encoded host image and a watermark image are usually directly added, consequently the two images have cross-talk in the decryption step. To eliminate this effect, we propose a novel method based on digital holography, in which all the image pixels of the two sets of holograms resulted from two hidden images are rearranged and integrated into one set of composite holograms with a random scattering matrix (RSM). In decryption the use of this matrix can ensure the exact retrieval of each hologram, and then the perfect reconstruction of each image without cross-talk noise can be achieved. The feasibility of this method and its robustness against occlusion and additional noise are verified by computer simulations with phase-shifting interferometry and double random-phase encoding technique. This approach is suitable for both two- and three-dimensional images, and the additional RSM as a key provides a much higher level of security.     

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.     

基于调制方向提取载波散斑条纹中心线的方法

条纹中心线法是一种重要的电子散斑干涉条纹解调方法,其前提条件是获得高准确度的条纹中心线.本文在分析载波电子散斑干涉条纹自身特征的基础上,提出了一种基于载波条纹调制方向提取条纹中心线的方法.该方法首先通过同态滤波有效滤除高频乘性散斑噪音,提取出载波条纹;然后应用基于调制方向提取中心线算法确定载波条纹灰度极值点并做二值化处理;再采用基于中心线拟合或者基于条纹间距的边沿中心线补偿法,获得完整的条纹中心线图.实验结果表明:该方法简单、可靠,能快速、准确地提取出连续的中心线.     

Highly accurate film thickness measurement based on automatic fringe analysis

This paper describes an automated multiple-beam interferometry for measuring a calibrated step height of (27.00 ± 3.00) nm nominally. The fringes captured from the multiple-beam Fizeau–Tolansky interferometer were thinned by using a written program to obtain accurate measurement. We claim that multiple-beam interferometry based on automatic fringe thinning process can provide a real time solution for calibrating step heights precisely and with high accuracy. The uncertainty budget of the multiple-beam interferometry method due to incomplete parallelism of the incident beam and the inhomogeneity of the reflecting layers was calculated automatically with a written ray tracing program. The uncertainty budget in multiple-beam interferometry was estimated to be of the order of 3.00 nm.     

Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes

The 1D empirical mode decomposition method is applied to reduce speckle noise in the correlation fringes produced in digital speckle pattern interferometry. This method is based on the decomposition of a signal in a sum of well-behaved fast and slow oscillation modes through a sifting process, which generates a fully data-driven technique. Consequently, this is an adaptive approach and the use of basis functions in the analysis process is not required. The denoised signal is given by the residue obtained after the fast oscillation modes are removed. The performance and limitations of the denoising technique are analyzed using computer simulated fringes and these results are compared with those obtained using a wavelet sub-band removal approach. An application of the EMD method to denoise experimental correlation fringes is also presented.     

基于调制方向提取载波散斑条纹中心线的方法

条纹中心线法是一种重要的电子散斑干涉条纹解调方法,其前提条件是获得高准确度的条纹中心线.本文在分析载波电子散斑干涉条纹自身特征的基础上,提出了一种基于载波条纹调制方向提取条纹中心线的方法.该方法首先通过同态滤波有效滤除高频乘性散斑噪音,提取出载波条纹;然后应用基于调制方向提取中心线算法确定载波条纹灰度极值点并做二值化处理;再采用基于中心线拟合或者基于条纹间距的边沿中心线补偿法,获得完整的条纹中心线图.实验结果表明:该方法简单、可靠,能快速、准确地提取出连续的中心线.