Additive-subtractive phase-modulated speckle interferometry: Fringe visibility under partial decorrelation

Additive-subtractive phase modulated speckle interferometry (ASPMSI) is a technique that minimizes the susceptibility of speckle methods to environmental noise while providing fringes of good visibility. The method requires the acquisition of two consecutive video frames of additive-speckle images of the same two deformed states of an object at a rapid enough rate such that ambient noise is not a problem. The additive-speckle images as expected are of very poor visibility due to the presence of the self-interference term. An interframe phase-modulation is introduced and the two additive-speckle images are digitally subtracted to improve the fringe visibility by removing the self-interference term. The ASPM-SI method works with in-plane and out-of-plane deformation sensitive ESPI as well as with displacement-gradient sensitive speckle-shearing interferometry. It is shown that the ASPM-SI scheme has higher visibility than conventional additive-SI and performs consistently better than subtractive-SI schemes in the presence of partial interframe speckle decorrelating optical noise. Furthermore, it is shown that the fringe visibility of the out-of-plane displacement sensitive interferometer which uses a protected reference beam separate from the object beam can be made to be essentially unity even at complete interframe decorrelation.     

光学综合孔径望远镜阵的光束组合器

光束组合器是光学综合孔径望远镜阵重要技术组成部分之一。从光束组合器所产生的光干涉条纹中提取中央条纹（主峰）相位和可见度信息，实现对望远镜状态、延迟线光程补偿与条纹跟踪，光束平行性伺服等进行精细馈控，从而高灵敏度、高效率地得到图像重构的闭合相位等数扭，最后获取高分辨率的目标图像。给出了一个用于光学综合孔径望远镜阵像面光束组合器方案的初步研究结果。     

Geometric phase-shifting for low-coherence interference microscopy

A low-coherence Linnik interference microscope using high numerical aperture optics has been constructed. The system uses a tungsten halogen lamp and Köhler illumination, with separate control over field and aperture stops, so that experiments can be conducted with a range of different operating conditions. The novel feature of the system is the use of an achromatic phase-shifter operating on the principle of the geometric phase, achieved by using a polarising beam splitter, a quarter wave plate and a rotating polariser. Image information is extracted from the visibility of the fringes, the position of the visibility peak along the scanning axis yielding the height of the test surface at the corresponding point.     

Passive ranging and three-dimensional imaging through chiral phase coding

We present a method for single-image passive ranging and three-dimensional (3D) imaging in incoherent light based on chiral phase coding. A chiral linear phase variation across the aperture of an optical system results in a frequency response with a characteristic pattern of fringes such that the spatial period and inclination of the pattern depend on the focusing error. From this dependency, the absolute focusing error and, hence, the distance to the object can be found. In the experiments a resolution of ~1.4 μm is achieved with a 20 mm aperture lens in a 4 mm interval at a distance of 140 mm from the lens. A resolution of ~0.7 mm is obtained at a distance of ~11 m with the range finder employing two 25.4 mm spherical mirrors spaced apart by ~140 mm. We also demonstrate 3D imaging of weakly textured objects.     

Interference-pattern image formation in an optical system with a random phase screen in the space-frequency plane

The process of interference-pattern image formation in an optical system with a random phase screen in the space-frequency plane is analyzed. It is shown that an optical system of this kind can function, under certain conditions, as a shearing interferometer, which determines the dependence of contrast of the average intensity fringes in the interference pattern image on the normalized correlation function of the random phase screen complex transmittance. The dependence of the fringe contrast on the pattern period and aperture of the field of view is established, as well as dependence of the optical transfer function of the system under study on spatial coherence of the light in the pupil of the system with the random phase screen.     

Speckle-pattern interferometry applied to the study of phase objects

If a speckle pattern is photographed through a phase object, the individual speckles are displaced over varying distances depending upon the phase irregularities in the object. A double exposure is made, the object being present during one of the two exposures only. When the processed photographic plate is observed through an aperture stop in the Fourier transform plane, interference fringes representing contours of the optical path gradient are obtained. The sensitivity of the method and the direction along which the gradient is measured can be varied by modifying, respectively, the distance of the Fourier-plane aperture from the optical axis and its azimuth.     

Simultaneous quantitative evaluation of in-plane and out-of-plane deformation by use of a carrier method of large image-shearing shearography

A carrier method for separating out-of-plane displacement from in-plane components based on large imageshearing shearography is presented. A reference surface is fixed on the side of a test object. They are illuminated by two expanded symmetric illuminations respectively. The carrier is introduced by rotating the reference surface to modulate the displacement of an object. By using Fourier transform to demodulate the modulated fringe pattern, two phase maps, which include out-of-plane and in-plane displacements, can be obtained. Then the out-of-plane displacement can be easily separated from in-plane displacement by subtraction and addition of the two unwrapped phase distributions. The principle of the method is presented and proved by a typical three-point-bending experiment. Experimental results show that the method enjoys high visibility of carrier fringes. The system does not need a special beam as a reference light and has simple optical setup.     

Speckle interferometric technique to assess soap films

An speckle interferometric technique to monitor the thinning process of vertical soap film before the film rupture is presented. The interferometric arrangement consists in a double aperture pupil optical system which images an input diffuser. In a first step, a reference specklegram is stored in the computer buffer memory. Afterwards, the soap film is located in front of one pupil aperture, an uniform displacement of the diffuser is produced and a new speckle pattern is stored. The soap film status is characterized in terms of the changes that this dynamic phase object introduces in the correlation fringes obtained by applying a FFT algorithm to the resulting summed specklegram. This procedure is done in real time as far as the soap film evolves in the successive status. It is experimentally demonstrated that the soap film during drawing acts as a variable wedge. The correlation fringes behavior becomes an important tool to establish the wedge shaped soap film angle and the thickness variations.     

Contrast enhanced and phase controlled stroboscopic additive fibre optic TV-holography for whole field out-of-plane vibration analysis

A new technique for real-time contrast enhancement and phase control of fringes in additive Stroboscopic TV-holography applied to out-of-plane vibration analysis and its implementation on a fibre-optic electronic speckle pattern interferometer (FOESPI) are presented. Synchronous Stroboscopic illumination, firing two pulses per object vibration period, is combined with simultaneous inter-pulse (high frequency) and inter-frame (low frequency) phase modulation in the reference arm of the ESPI yielding a sequence of frames (interferograms) that are grabbed and processed in real-time. With this technique both speckle and fringe phases are independently controlled by means of the parameters of modulation enabling speckle contrast inversion, as required to enhance the visibility of fringes by sequential subtraction, as well as dynamic fringe phase shifting to solve peakvalley ambiguities.     

The separation of out-of-plane displacement from in-plane components by fringe carrier method based on large image-shearing ESPI

A fringe carrier method for separating out-of-plane displacement from in-plane components based on large image-shearing electronic speckle pattern interferometry (ESPI) is presented. If the test object is respectively illuminated by two expanded symmetric illuminations in large image-shearing ESPI, two interferometers are formed. Carrier fringe patterns can be introduced by tilting reference surface a small angle. The carrier fringe patterns are demodulated after deformation of the object. Two phase maps, which include out-of-plane and in-plane displacement, can be obtained by using Fourier transform. Then out-of-plane displacement can be easily separated from in-plane displacement by simple operation between two unwrapped phase distributions. The principle of spatial carrier frequency modulation in large image-shearing ESPI is discussed. A typical three-point-bending experiment is completed. Experimental results are offered. The results show that the method offers high visibility of carrier fringes. And the system presented does not need a special beam as a reference light and has simple optical setup.     

Measurement of wedge angle of a transparent parallel plate using quasi-monochromatic light source and phase shifting interferometry

A new technique (to our knowledge), for the measurement of residual wedge angle (RWA) of high optical quality transparent nearly parallel plate (PP), using a quasi-monochromatic light source, is presented. Advantages and drawbacks of the technique and the results obtained for a PP, using a filtered white light source, is discussed. A slightly modified optical setup for accurate determination of RWA, using phase shifting interferometry (PSI), has been described. Results obtained, applying PSI, for a validation experiment and for the determination of RWA of a quasi-PP is presented. The PSI based technique does not suffer from any measurement ambiguities due to limitation in effective beam aperture. Hence the technique is suitable for high accuracy measurement of RWA of PP. In both the optical setups, presented in this paper, the respective interfering beams travel the same optical circuit and are thus subject to same perturbation in optical path, due to external mechanical vibration, which finally cancels out. Thus the measurements are much less affected by external vibrations. Since the respective interfering beams undergo identical reflections and transmissions, the visibility or contrast of the interference fringes is very good.     

基于叠栅技术的二维亚波长周期结构成像设计

用光子学方法研究了叠栅技术中,当试件光栅被拉压和旋转后,叠栅条纹的空间周期和相对于基准光栅的取向,试件光栅被拉压后的节距等相关问题。根据衍射光波的空间周期可能大于试件光栅空间周期的特点,对二维亚波长周期结构衍射成像进行了设计研究。首先,对二维亚波长周期结构衍射物进行编码,以获得包含编码光栅空间信息的均匀波;其次,使编码得到的均匀波通过光学系统,并被放大到CCD相机所能辨识的大小;再次,经解码光栅解码,滤掉编码波,最终获得二维亚波长周期结构物的空间结构信息,达到超分辨的目的。同时,对成像过程进行了较为详尽的分析,对编码器、解码器的位置以及它们相对衍射物的取向进行了设计研究,对滤波器的选择给予了必要的说明,指出了取得超分辨成像的关键。     

Measurement of vibration amplitude by an optical fiber-based moiré interferometer

A projected-fringe fiber-based moiré interferometer is proposed to measure the local amplitude vibration of a diffuse surface. The technique is based on an optical fiber interferometer which projects interference fringes on the object surface. The visibility of these carrier fringes is modulated by a function of local amplitude vibration. Full-field quantitative analysis is performed by analyzing the fringe pattern with a 2-D Fourier transform method. Theoretical details, and experimental results are presented.     

Single-shot and lensless complex-amplitude imaging with incoherent light based on machine learning

We present a single-shot incoherent light imaging method for simultaneously observing both amplitude and phase without any imaging optics, based on machine learning. In the proposed method, an object with a complex-amplitude field is illuminated with incoherent light and is captured by an image sensor with or without a coded aperture. The complex-amplitude field of the object is reconstructed from a single captured image using a state-of-the-art deep convolutional neural network, which is trained with a large number of input and output pairs. In experimental demonstrations, the proposed method was verified with a handwritten character database, and the effect of a coded aperture printed on an overhead projector film in the reconstruction was examined. Our method has advantages over conventional wavefront sensing techniques using incoherent light, namely simplification of the optical hardware and improved measurement speed. This study shows the importance and practical impact of machine learning techniques in various fields of optical sensing.     

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.     

Fourier fringe processing using a regressive Fourier-transform technique

Since the introduction of a fourier fringe algorithm by Takeda, it has been possible to determine the phase of a particular light source impinging on an object from one sole image. This has led to applications in many whole field optical measurement techniques such as ESPI, holography, profilometry and so on. However, the basic processing technique, in case of the 2D-Fourier transform, is subject to a major drawback. Because this technique supposes periodicity in a fringe image, the so-called leakage effects occur. This gives rise to non-negligible errors, which can be resolved by using a regressive Fourier transformation technique. In the method introduced in this article, the fringe signal is represented by a model using sines and cosines where the frequency is not fixed (which is the case for classical FFT-techniques). The coefficients of those sines and cosines together with the frequency components are then estimated locally by means of a frequency domain system identification technique. This allows the fringe pattern to be unwrapped without any distortion. This method will be applied in particular to Fourier-transform profilometry (determines object geometry using shifts of projected fringes) although it can be used in any of the techniques mentioned above. Moreover, it will be shown that the proposed method can deal with other distortions that occur in practice such as over-modulation and varying fringe visibility. The proposed technique will be validated on both simulations and on a profile measurement of a pipe section.     

条纹法实现高分辨率成像

 研究了一种高分辨率成像的方法，该方法利用余弦条纹照射目标以获取目标更宽的频谱。条纹对目标的照射起到了对目标频谱的搬移作用，使光学系统截止频率外的一部分高频分量通过系统。利用多幅条纹照射目标并分别成像，各条纹空间频率相同而相位按照一定规律变化，综合处理照射条纹后获得的图像将叠加在一起的频谱分量分离开并恢复到相应的位置，经过反变换获得高分辨率的图像。通过计算机仿真验证了这种方法的可行性。     

Interferometrie a double plage par photographie “speckle”

The image of a partial diffusor is recorded on a holographic plate. After development, the hologram is repositioned to observe “live fringes”. Half of the aperture of the optical system has been masked during the exposure, but the full aperture is used for the reconstruction. Two separate reconstructed images of the half aperture show two different interferograms. This set up can be used to measure displacements of objects, or defocusing.     

Full field deformation measurement of centimeter sized objects using optical phase retrieval

Most papers in the field of optical phase retrieval either consider only the intensity (or amplitude) profile of the object under inspection (or scatterer location in the X-ray version), or a uniform tilt/rotation of the object beam. However, phase retrieval is able to recover the phase profile of the object (beam) as well, which theoretically makes the observable interference of phase retrieved object waves possible. In this paper we demonstrate this principle experimentally on centimeter sized deformable reflective objects (as large as 40 mm by 40 mm) and corresponding simulations are also presented. When the CCD camera is moved along the optical axis in the Fresnel region, the interference fringes of the displacement field have low contrast. On the other hand, when an imaging setup is built, and the camera moves near the image plane, high fringe contrast can be obtained. These fringes however suffer from some phase error. In our work the iterative modulus projection algorithm was used as a simply implementable phase retrieval method.     

光学综合孔径成像中的傅里叶相位研究

傅里叶相位是光学综合孔径成像的重要信息,观测目标的傅里叶相位包含于干涉条纹中。从像平面干涉条纹形成原理出发,推导出大气扰动、星光方向与基线方向不垂直和望远镜系统机械误差等因素是影响干涉条纹初始相位的主要因素。利用条纹原点值和峰值位移从条纹中提取初始相位,采用闭合相位法从条纹初始相位中去除其它因素的影响,从而最终获取目标傅里叶相位：结合计算机模拟对噪声给条纹峰值位置的影响进行分析,模拟结果表明在频域中对条纹能量谱进行阈值处理有较好的去噪效果。最后结合目标重构迭代法阐述了闭合相位在像重构中的作用。