Common-path phase-shifting interferometer with binary grating

An experimental setup for phase extraction of 2D phase distributions is presented. The system uses a common-path interferometer consisting of two windows in the input plane and a translating grating as spatial filter. In the output, interference of the fields associated with replicated images of the input windows is achieved by a proper choice of the windows spacing with respect to the grating period, the focal length of the transforming lens and the wavelength of the coherent illumination employed. Because in this type of grating interferometer a grating is placed as a spatial filter, the phase changes which are needed for phase-shifting interferometry can be easily performed with translations of the grating driven by a linear actuator. Some experimental results are shown.     

Shifted-phase calibration for a 3-D shape measurement system based on orthogonal composite grating projection

This paper proposes a novel method for reducing measurement error caused by spectrum overlapping in orthogonal-composite-grating-based 3-D measurement method. For 3-D measurement systems based on orthogonal composite grating projection, spectrum overlapping causes phase of each deformed phase-shifting fringe changed differently, which violates the principle that the shifted phases between adjacent deformed fringes must be equivalent to 2π/3, and therefore results in phase measurement error. The proposed shifted-phase calibration method is based on that phase variation of each deformed fringe is independent of height and reflectivity of the measured object. Three composite gratings are projected on the reference plane, and each carrier channel includes three phase-shifting gratings needed in phase measuring profilometry (PMP). Because the adjacent phase-shifting fringes demodulated from the same carrier channel have the phase difference of 2π/3, we can respectively calculate the reference plane's phases of three carrier channels by the phase algorithm of PMP method, and the shifted phases between them are obtained. When an object is measured, the shifted phases between deformed phase-shifting fringes can be calibrated. A new 3-D measurement mathematical model is set to reconstruct object. Our experiments prove that the proposed method can effectively restrain the effect of spectrum overlapping and improve measurement accuracy almost one times.     

Surface profile measurement of moving objects by using an improved π phase-shifting Fourier transform profilometry

The π phase-shifting Fourier transform technique is introduced into the surface profile measurement of moving objects. A digital grating comprising two regions, which have a π phase shifting is projected onto the object. Two line-scan CCD cameras are used to capture two deformed fringe patterns with π phase shifting at the same time. As the object is moving, each point at the object surface can be captured twice. The digital correlation method is used to calibrate the experimental system. The zero-order component can be eliminated by subtracting intensities of the same surface point in two captured images. And then the phase can be extracted by Fourier transform without the disturbance of zero-order component. Experimental results demonstrate that this method is feasible for the moving surface profile detection and the measurable slope of height variation can be extended.     

Sinusoidally phase-modulated interference microscope for high-speed high-resolution topographic imagery

We describe an interference microscope that produces topographic images with a minimum acquisition time of 20 ms. The system is based on phase-shifting interferometry with sinusoidal phase modulation induced by the oscillation of an interferometric objective (Michelson or Mirau). A CCD camera captures four images per oscillation period to produce a phase map in real time. The system is installed on a commercial microscope.     

移相器微位移旋转误差的分析及测试

以压电陶瓷(PZT)微位移器为主要研究对象, 引入一种处理静态干涉图的新方法--虚光栅移相叠栅条纹法,设计实验对一台实际使用的移相器微位移旋转误差进行测试研究,对其引起的波面旋转情况进行了定量的计算分析,并给出测试结果.用虚光栅移相叠栅条纹法处理实验中加有载频的干涉图时,不需要使用任何移相器件,可以进行动态位相的检测,整个移相过程用计算机进行控制,避免了引入额外的移相误差.     

Image encryption based on gyrator transform and two-step phase-shifting interferometry

A novel optical image encryption method is proposed, based on gyrator transform and phase-shifting interferometry. The input two-dimensional image to be encrypted is gyrator transformed two times, and two random phase masks are placed at the input plane and the output plane of the first gyrator transform. Two-step phase-shifting interferometry is used to record the digital holograms of the input image encrypted by use of double-random phase encoding technique in gyrator transform domain. The rotation angles of gyrator transform, the random phase mask in the gyrator plane and the arbitrary phase shift used for recording form the keys for decryption of the input image. Numerical simulations are presented to verify its validity and efficiency.     

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 (▽).     

Phase profile analysis of transparent objects through the use of a two windows interferometer based on a one beam splitter configuration

In this research we implemented a two windows interferometer based on polarization phase shifting and grating interferometry techniques in order to retrieve the phase data profile of the object in a single capture. The optical configuration has two optical beams with circular polarization in opposite directions, and it is coupled with a 4-f system. An amplitude grid is used as a filter which is placed at the Fourier plane to obtain replicas of each beam which can properly interfere, depending on the separation between beams. The interferometer presents the capability of changing the beam separation in order to make different orders interfere properly. The interference patterns produced can be separately modulated through the operation of linear polarizer's placed on each interference replica. In order to present the capabilities of the system we will select four interferograms result of contiguous orders interference.     

Parallel two-step phase-shifting microscopic interferometry based on a cube beamsplitter

Parallel two-step phase-shifting interferometry for microscopy is presented, and the recording condition for generalized two-step phase-shifting interferometry is discussed. A 45° tilted cube beamsplitter enables to replicate the orthogonally linear polarized object and reference waves into two parallel beams, respectively. As a consequence, two interferograms with quadrature phase shift are obtained along the two beams, and phase reconstructed with an improved algorithm. To reconstruct the phase distribution from the two-step phase-shifting interferograms, a certain recording condition should be satisfied. However, the recording condition has not ever been discussed before. In this paper, the recording condition for the two-step phase-shifting interferometry is derived and that is: the intensity of reference wave should be no less than two times object wave intensity.     

Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry

The phase error and its periodic behavior caused by the partial intensity saturation of fringe patterns in the digital projection grating phase-shifting profilometry are studied. A saturation coefficient K is defined to describe the saturation degree of the fringe patterns projected on a measured object. The distribution of the phase error is analyzed through a simulation method. Moreover, a novel phase-recovering algorithm is studied to resolve the phase error issue introduced by the partial saturated fringe patterns. The real phase can be recovered by the unsaturated intensity values. A series of results corresponding to different degrees of saturation defined by K are given to prove the validity of the proposed algorithm.     

Wavelength modulation in a two-window common path interferometer for phase-shifting

A novel and simple method for phase-shifting under the scheme of a two-window 4f common path interferometer configuration with a binary grating at the Fourier plane is proposed. The proposal is based on periodicity variations of the grating grooves in the frequency space, which is emulated in an experimental implementation by changing the wavelength of a tunable laser diode used as the light source. Because of the common path configuration, it is expected to diminish errors due to undesired vibrations and optical aberrations. The viability of the proposal will be sustained with simulated and experimental, which include phase-shifted interferograms and reconstructed wavefronts. Due to the characteristics of the proposed experimental setup, it can be easily replicated and automated.     

基于二维光栅分光的同步移相干涉测量技术

为了干涉测量的抗振目的,提出了一种新的同步移相干涉测量方案并搭建了实验装置。整个测量系统在迈克耳孙偏振移相干涉仪的基础上,利用一个正交的二维光栅产生对称分光,选取对于理想光栅衍射效率一致的(±1,±1)级衍射光作为测量分光路,使之分别通过偏振方向依次相差45°的一个偏振片组,从而分别形成0°、90°、180°和270°相移的四幅移相干涉图,按照传统的四步移相算法,对被测波面进行了复原。分析了光强畸变和移相误差对系统的测量误差的影响。利用该系统测量一球面系统,结果与在ZYGO干涉仪上相比较,球面系统的均方根误差相差0.012λ,峰谷值相差0.051λ。     

单周期条纹双四步相移投影仪的标定方法

针对投影仪标定方法中存在畸变及倾斜投影引起条纹周期、条纹级数变化的问题,提出一种单周期条纹双四步相移投影仪的标定方法.设计生成横向和纵向各两组单周期条纹图像,经投影仪投影到带有圆形标识的标定板上,相机同步采集标定板图像,叠加由双四步相移获得的两幅相位主值图,对叠加相位主值图相位展开,利用展开的绝对相位值计算投影仪像素坐标值,最终将投影仪标定转换为成熟的相机标定.实验结果表明:仿真投影仪标定实验准确度的最大重投影误差约为0.4pixel,均方根误差为0.132 96pixel;实际投影仪标定实验准确度的最大反投影误差约为0.46pixel,均方根误差为0.143 12pixel;实验结果与仿真结果的最大反投影误差相差15%,均方根误差相差7.6%.与现有的采用三频相位展开进行投影仪标定的方法相比,投影光栅图像数可减少8幅.该方法改善了现有投影仪标定方法的不足,标定准确度和标定效率均得到提高.     

一种同步移相干涉测量系统的误差研究

根据偏振光的琼斯矩阵理论,分析了一种基于二维光栅分光的同步移相干涉测量系统的工作原理。从干涉系统、分光系统以及移相系统三个部分详细研究了该系统的误差产生原因和作用机理,并针对各种误差源提出了相应的解决办法,为同步移相干涉测量系统中光学元件的选择、光路的调整及其误差的补偿提供了理论依据。结果表明,干涉部分的误差影响较小,可以通过光路的设计降低分光部分的误差;移相系统的误差最大,必须要对移相误差进行标定。     

Digital phase-shifting interferometer with an electrically addressed liquid-crystal spatial light modulator

A digital phase-shifting interferometer with a liquid-crystal-display coupled, parallel aligned, nematic liquid-crystal spatial light modulator is developed. The optical phase shift in the Michelson-type polarization interferometer is achieved by a digital phase shift of a grating displayed on the spatial light modulator. Accurate experimental results of using the heterodyne system for pi/2 phase steps were demonstrated. A phase-shifting interferometer with no moving parts and no requirement for calibration of the value of the phase shift was achieved.     

Phase-shifting in-line digital holography on a digital micro-mirror device

A digital phase-shifting in-line holographic system based on the single coherence beam is developed. A series of phase-shifting fringes are generated by computer and outputted by a digital micro-mirror device (DMD). These fringes modulate the coherence beam because of the intensity modulation ability of DMD. In this work, the reconstructed conjugate image would not appear because of applying the phase-shifting algorithm. And calibration for the value of the optical phase shift is not necessary. An experiment based on a lens-less digital in-line micro-holographic setup with a phase grating specimen is conducted to demonstrate the validity of the present method.     

Uncertainty analysis of temporal phase-stepping algorithms for interferometry

We have addressed the problem of the uncertainty evaluation of phase values rendered by two popular algorithms: the N-bucket and the (N + 1)-bucket, both used to exploit temporal phase-stepping techniques. These algorithms, are mainly affected by errors in the calibration of the piezoelectric transducers used to achieve the phase shift, external vibration and optical noise. We have characterized and compared the influences of these errors on the phase uncertainty. We applied a Monte Carlo-based technique of uncertainty propagation that allowed us to consider in the uncertainty evaluation the simultaneous contributions of different error sources. The uncertainty evaluation was performed for phase values in the range (0, 2π), with different values of N and assuming that the phase was calculated from fringe patterns generated by using either Moiré interferometry or electronic speckle-pattern interferometry. We found that the uncertainties associated with the phases rendered by both algorithms are similar and they can be significantly affected by the optical noise and the value of N.     

Common-path interferometer with a tri-window

A common-path interferometer is proposed with a tri-window. It is built using a 4f optical system with Ronchi ruling as a spatial filter. The input rectangular aperture is formed by three windows; the central window supports a phase object, and the other two are used for reference beams. Using an appropriate grating period relative to input aperture size, an interferogram containing three patterns can be obtained in the output plane. The object phase can then be reconstructed from the three patterns using just one interferogram. The experiments are carried out to demonstrate the feasibility and reliability of the proposed scheme.     

Phase shifting grating-slit test utilizing a liquid crystal display

A quantified focal plane testing method, termed phase-shifting grating-slit test, is demonstrated by utilizing a micro liquid crystal display. In contrast to the setup in the Ronchi Test, an incoherent illuminating grating is used and an optical slit is located at the image plane of the tested lens to modulate the aberrated wavefront. With the micro liquid crystal display generating and phase shifting the incoherent illuminating grating with variable frequency, a higher measurement dynamic range can be achieved on demand.