Carrier squeezing interferometry: suppressing phase errors from the inaccurate phase shift

The carrier squeezing interferometry algorithm is proposed to retrieve the phase from interferograms with phase shift errors. A linear carrier is introduced in the interferograms, and the image data is rearranged by the squeezing interferometry technology. In the spectrum of the rearranged image, the error lobe and the phase lobe are separated so the error-free phase can be retrieved by filtering. The simulated interferograms with phase shift errors are computed, and the precisions are better than 8.4×10(-4)λ. Its validation is verified by experiments, where a mean precision of 0.0040λ is obtained.     

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.     

基于选择采样的高效迭代相位提取算法

在光学精密测量中,相移干涉法应用广泛。常用的相移器件容易出现相移误差,采用等步距相位提取算法会产生测量误差。基于最小二乘的迭代相位提取算法可以有效消除该类相位提取误差,提高测量精度,但是其迭代过程运行时间长,效率低。提出了一种基于选择采样的迭代相位提取算法,先对干涉图像进行等间隔抽样,降低计算量;再根据对比度滤除干涉图像中低质量像素点,防止误差增大,进行最小二乘迭代求解相位。仿真实验对算法进行了分析和验证,在抽样间隔为2时的选择采样方法与所有像素点全部代入计算相比,运行时间从6.687 s降为0.725 s,均方根误差仅为0.032 9。实验结果证明:选择采样的迭代相位提取算法运算时间短、误差小,非常适合高速相移干涉测量应用。     

大口径连续相位板面形检测与评价

基于全局最小二乘拼接算法和图像融合算法建立了连续相位板（CPP）子孔径拼接检测算法,并根据全局相关匹配原理提出采用面形残差来评价CPP的加工面形。采用高精度动态干涉仪等设备建立了相应的检测系统,并针对430 mm430 mm口径CPP开展了数值模拟和检测实验。理论计算结果表明:系统计算误差为0.005 nm。实验结果表明,整个检测系统软硬件RMS误差小于5 nm,基本满足CPP面形检测要求。从而验证了CPP检测和评价的正确性和可行性。     

Curvature measurement using phase shifting in-line interferometry,single shot off-axis geometry and Zernike's polynomial fitting

This paper describes the difference between phase shifting in-line interferometry, single shot off-axis geometry and Zernike's polynomial fitting methods for measuring the curvature of a spherical smooth surface by using the Michelson interferometer. In phase shifting in-line interferometry, four interferograms shifted by a piezoelectric actuator (PZT) were captured by a digital detector and corrected by using the flat fielding method. In off-axis geometry, single shot off-axis interferogram was obtained by tilting the reference and the object wave of the off-axis interferogram was reconstructed in the central region of the observation plane by using the digital reference wave concept. The demodulated phase map was obtained and unwrapped to remove the 2π ambiguity. The unwrapped phase map was converted to height and the sagittal length that used for curvature measurement was calculated accurately. The results extracted from phase shifting in-line interferometry and single shot off-axis geometry methods were compared with the results extracted from single shot Zernike's polynomial fitting method and the results were in excellent agreement. A new trial was done to overcome the fringes produced from the object interfaces. Some factors of uncertainty which affected on the measurement were estimated in the order of 6.0 × 10^?5 mm or 0.003 dioptre (▽).     

Instantaneous phase shifting arrangement for microsurface profiling of flat surfaces

Phase shifting interferometry is a well-established technique for non-contact surface profile measurement. Though phase shifting technique has many advantages, it is marred by a few inaccuracies due to the vibration and mechanical movement of the phase shifter itself. Significant amount of work is reported to theoretically compensate these error sources. But for a few works, prominent achievements have not been reported in eliminating these error sources in phase shifting interferometry. In this paper, a novel optical layout, in combination with instantaneous phase shifting interferometry is described. Experiments were carried out with this setup on a super mirror with a λ/20 surface roughness, to demonstrate the validity of the principle.     

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.     

3-D surface profilometry using simultaneous phase-shifting interferometry

Urgent needs for high-speed, non-contact and on-line measurement with high accuracy and repeatability are of great interest for automatic optical inspection (AOI) industries. Therefore, optical phase-shifting interferometry for precision 3-D surface profilometry has become an important metrological method due to its non-contact and high measurement accuracy. Traditional phase-shifting interferometry is very sensitive to vibrations because image acquisition in various phase-shifting sequences could easily introduce measurement errors from environmental influences, such as air disturbance and system structure vibrations. In this paper, we introduce a new simultaneous phase-shifting interferometer for 3-D surface profilometry which employs a single glass plate to generate simultaneous phase-shifted interferograms. Phase reconstruction is performed by using a developed phase-shifting algorithm which uses a three-step phase-shifting method with phase differences of 90°, 180°, and 270° for three interferograms. To verify measurement accuracy and repeatability, the system was employed to measure surface profiles of surface of a flat mirror and set of Mitutoyo gauge blocks. The experiment result shows that the method is proven to be capable of performing one-shot interferometric measurement and minimizing influences from environmental disturbances with measurement repeatability down to 10 nm or less.     

Shape identification using phase shifting interferometry and liquid-crystal phase modulator

A phase shifting technique using a Michelson interferometry system is presented and applied to surface contour measurement. Hyperbolic fringes are produced by the interference of two spherical wavefronts expanded from a beam expander. The fringe pattern is projected on an object surface and the deformed grating image is captured by a CCD camera for subsequent analysis by a PC. Phase variation is achieved by a liquid-crystal device incorporated in the Michelson interferometry system. Results obtained using the proposed method for objects of various shapes and sizes compared well with those from a conventional profilometer.     

基于模拟退火的傅里叶变换成像光谱仪干涉图相位修正

相位修正是傅里叶变换成像光谱仪光谱复原的关键技术之一,针对现有算法对带有噪声的干涉图相位修正不足的问题,文章提出了一种基于模拟退火算法求解相位误差的修正方法.该方法通过控制相位下降函数,利用相位区间内产生的随机相位值修正干涉图数据得到同标函数值,依据Metropolis准则判断目标函数增最以确定相位最优解.该算法仿真结...     

Realization of high sensitivity displacement field from moiré interferometer with rough phase shifting mechanism and pattern matching technique

In this study, phase shifting method is used to modify moiré system into micro moiré interferometer which can measure displacement field with highly improved sensitivity. Apart from existing micro moiré technique, a low cost and less precise translation stage with rough resolution (10 μm resolution) is adapted for the phase shifter. Least square algorithm is applied to estimate the arbitrary phase shifted amount and to minimize the errors induced by lowering the cost. Moreover, specimen grating is phase shifted instead of reference grating which enables simple construction from given moiré system. To compensate for rigid body in-plane translation of specimen that may occur during phase shifting, pattern matching algorithm is put into practice to ensure pixel correspondence for each phase shifted images. To verify the newly constructed micro moiré technique, local displacement fields of Fine pitch Ball Grid Array package and Wafer Level Chip Size Package with elevated sensitivity up to 26 nm per fringe was acquired.     

干涉显微镜中相移误差分析

相移误差是影响干涉显微镜测量表面形貌精度的主要因素之一。介绍了四帧算法、五帧算法、四帧免疫算法、五帧免疫算法的原理和计算公式 ,并对其特点进行了分析比较。利用自行研制的带旋转检偏器的干涉显微测量系统 ,分别用四种算法对Ra=0 35μm和Ra=0 .0 9μm粗糙度样块进行了实测。结果表明 ,五帧算法的重复测量精度优于0 5nm ,五帧免疫算法的重复测量精度优于 0 3nm。同时对在普通干涉显微镜上进一步提高其测量精度做了初步探讨     

相位差法波前传感系统自身误差的分析及消除方法

 针对附加像差为离焦的情况,对焦面位置误差、离焦量误差、图像对准误差以及图像噪声等因素带来的波前传感误差进行了数值模拟,并给出了确定焦面位置、对准焦面图像和离焦面图像、精确计算分光比、确定离焦量以及处理图像噪声的方法。使得传感结果的均方根误差分别由0.088 8λ,0.059 0λ,0.128 4λ,4.170 6λ,0.152 6λ降为0.002 1λ,0.002 1λ,0.002 1λ,0.002 1λ,0.029 2λ。结果表明:这些方法可以有效地减小传感误差,大大提高了传感精度,为相位差法的实际应用提供了重要的技术支持。     

两步相移数字全息物光重建误差分析与校正

系统研究了两步相移数字全息干涉术中相移误差引起的波前再现误差的计算和校正方法. 基于衍射物光相位分布的随机性和振幅相位的相互独立性原理,介绍了相移数字全息中物光波前再现误差的表达形式,推导出步长为π/2的两步算法中物光重建误差的表达式. 通过进一步分析这一重建误差的结构和特点,结合物光表达式,给出了自动校正相移误差引起的波前重建误差的校正方法. 该方法无需增加测量,在未知相移误差大小的情况下,只对标准两步相移算法恢复的物光复振幅进行处理就可以实现对物光振幅和相位的同时校正. 计算机模拟结果表明,校正后可将 关键词： 相移干涉术 数字全息 物光重建 误差校正     

Analysis of phase encoding for optical encryption

A phase encoded image is encrypted using the double random phase encoding technique, (DRPE). The effects of using a variable dynamic range of phase distribution during phase encoding (pre-encryption) are examined. We begin by phase encoding the input image using the full phase range, from −π to π. We perform numerically perfect encryption and we then introduce errors into the decrypting phase-keys in the form of a pseudo-random distribution (position and phase) of incorrect pixels values. By quantifying the resulting error in the attempted decryptions, for increasing amounts of error in the decrypting phase-keys, we examine the effects of reducing the phase range to, +/− (π − Δ). In this way we attempt to improve the phase encoding procedure for use with the DRPE technique. When the pixel values calculated, during an attempted decryption, fall outside the phase range used to phase encode the assigned input image, we examine different methods of redistributing the value of that pixel to an assigned value within the allowed phase range. The effects of the phase quantisation used in the keys are also examined.     

Third-order nonlinearity of Er3+-doped lead phosphate glass

In a laser coherent combination, the phase detection and control is the most critical. Using the beat frequency method, consistence of the phase in output beams can be ensured through real-time detection and correction for the phase change. Phase noises are controlled by a liquid crystal phase modulator. At the same time, the liquid crystal polarization controller is used to make the polarization state stable, which is good for the improvement of the combining efficiency. The wave length of the main oscillation laser is 532 nm. The output power of laser can be adjusted continuously from 0 to 6 W. The shifted frequency of the system is 40 MHz. The accuracy for phase control is superior to λ/70 RMS. In the process of closed-loop control, using the liquid crystal phase and polarization controller, a better signal phase correction of optical path has been achieved for the coherent combination of high power laser arrays.     

Comparison of phase recovery methods in spiral speckle pattern interferometry correlation fringes

Spiral interferometry can be used as a solution to the problem of sign ambiguity presented in the conventional speckle pattern interferometric technique when the optical phase needs to be reconstructed from a single closed fringe system. Depressions and elevations of the topography corresponding to the object deformation are distinguished by the direction of rotation of the local spiral fringe pattern. In this work, we implement and compare several methods for optical phase reconstruction by analyzing a single image composed of spiral speckle pattern interferometry correlation fringes. The implemented methods are based on contour line demodulation, center line demodulation, Spiral Phase Quadrature Transform and the 2D Riesz transform with multivector structure. Contour line and center line demodulation approaches are exclusively dedicated to images containing a fringe system with spiral structure. The others are based on the 2D Riesz transform, these being well known approaches in conventional interferometry. We examine simulated experiments and analyze some of the emerging drawbacks for solving the phase reconstruction problem by using different mean values of speckle size and background noise levels. We also discuss several numerical procedures that may well improve the efficiency and robustness of the presented numerical implementations. The performance of the implemented demodulation methods is evaluated by using a universal image quality index and therefore a quantitative comparison is also presented.     

Decoupling error for the atmospheric correction in ocean color remote sensing algorithms

This paper studies the decoupling error associated with the atmospheric correction procedures in the ocean color remote sensing algorithms. The decoupling error is caused by the lack of proper consideration of multiple scattering between the atmospheric and ocean components. In other words, the atmosphere and ocean are not coupled properly. A vector radiative transfer model for the coupled atmosphere and ocean (CAO) system based on the successive order of scattering (SOS) method is used to study the error. The inherent optical properties (IOPs) of the ocean are provided by the most updated bio-optical models. Two wavelengths are used in the study, 412 and 555 nm. For a detector located just above the ocean interface, the decoupling errors range from 0.3% to 7% at 412 nm; and from 0.3% to 3 % at 555 nm for zenith viewing angles smaller than 70°. The decoupling errors are significantly larger for larger zenith viewing angles for this detector. For a detector at the top of the atmosphere (TOA), it is hard to separate the decoupling error from the error introduced by the diffuse transmittance. If we assume the upwelling radiance is uniform just below the ocean surface when estimating the diffuse transmittance, the decoupling errors are from ?4% to 8% for zenith viewing angles smaller than 70°; and negative decoupling errors show up at mainly large zenith viewing angles.     

Sur la restitution du signe de la phase en interferometrie

Phase variations are transformed into intensity variations by means of interferometry. It is then possible to form a visible image of a pure phase object. But then information on the sign of the phase or the direction of surface relief is lost. Principles of a method for extracting only the imaginary part of the complex amplitude of the object, which is an odd function of the phase, are studied. From this it is possible to obtain the sign of the phase.     

几种任意步距步进相移算法的误差分析与对比

介绍了到目前为止的几种任意步距步进相移算法,并针对相移干涉仪的两种主要误差———移相误差和探测器非线性误差进行了计算仿真,进而比较分析了它们对这这些误差的抑制能力,其结果可为实际应用合理地选择算法提供理论依据。