High-precision analysis of a lateral shearing interferogram by use of the integration method and polynomials

Interferograms obtained with ordinary interferometers, such as the Fizeau interferometer or the Twyman-Green interferometer, show the contour maps of a wave front under test. On the other hand, lateral shearing interferograms show the difference between a wave front under test and a sheared wave front, that is, the inclination of the wave front. Therefore the shape of the wave front under test is reconstructed by means of analyzing the difference. To reconstruct the wave front, many methods have been proposed. An integration method is usually used to reconstruct the wave front under test rapidly. However, this method has two disadvantages: The analysis accuracy of the method is low, and part of the wave front cannot be measured. To overcome these two problems, a new, to our knowledge, integration method, improved by use of polynomials, is proposed. The validity of the proposed method is evaluated by computer simulations. In the simulations the analysis accuracy achieved by the proposed method is compared with the analysis accuracy of the ordinary integration method and that of the method proposed by Rimmer and Wyant. The results of the simulations show that the analysis accuracy of the newly proposed method is better than that of the integration method and that of the Rimmer-Wyant method.     

Sub-Nyquist null aspheric testing using a computer-stored compensator

A novel method to demodulate undersampled interferograms using a computer-stored undersampled compensator is presented. First, the sine and cosine of the computer-stored wave front is correlated with the interferogram that emerges from the asphere under test. Afterward, these two correlation images are used to find the phase map. The detected phase of the correlation fringes is the estimated phase difference between the software compensator and the frame-grabbed interferogram. The prior information required for this method is a good knowledge of the wave front being tested to a few wavelengths of error. Complying with this prior knowledge, the undersampled interferogram under analysis may be easily demodulated. Given that the proposed method is based on the correlation of the frame-grabbed interferogram and the computer-stored one, the method also withstands noise.     

Solution to the shearing problem

Lateral shearing interferometry is a promising reference-free measurement technique for optical wave-front reconstruction. The wave front under study is coherently superposed by a laterally sheared copy of itself, and from the interferogram difference measurements of the wave front are obtained. From these difference measurements the wave front is then reconstructed. Recently, several new and efficient algorithms for evaluating lateral shearing interferograms have been suggested. So far, however, all evaluation methods are somewhat restricted, e.g., assume a priori knowledge of the wave front under study, or assume small shears, and so on. Here a new, to our knowledge, approach for the evaluation of lateral shearing interferograms is presented, which is based on an extension of the difference measurements. This so-called natural extension allows for reconstruction of that part of the underlying wave front whose information is contained in the given difference measurements. The method is not restricted to small shears and allows for high lateral resolution to be achieved. Since the method uses discrete Fourier analysis, the reconstructions can be efficiently calculated. Furthermore, it is shown that, by application of the method to the analysis of two shearing interferograms with suitably chosen shears, exact reconstruction of the underlying wave front at all evaluation points is obtained up to an arbitrary constant. The influence of noise on the results obtained by this reconstruction procedure is investigated in detail, and its stability is shown. Finally, applications to simulated measurements are presented. The results demonstrate high-quality reconstructions for single shearing interferograms and exact reconstructions for two shearing interferograms.     

Interferometric testing for off-axis aspherical mirrors with computer-generated holograms

The interferometers with computer generated holograms (CGHs) have been used to measure off-axis aspherical mirrors. However, the conventional CGH interferometer could not produce a high lateral resolution because of the blur and the distortion of the interferogram of the test mirror caused by the nonzero order diffraction of the CGH. We further develop the application of CGHs concerning interferometers in order to improve the lateral resolution of the interferogram. In particular, we change the application of the CGH in such a way that the returned test beam passes through the CGH with zeroth order diffraction and demonstrates the performance of the CGH interferometer when used for the measurement of the primary mirror of the Okayama Astrophysical Observatory 3.8 m telescope project. As a result, our CGH interferometer produces a good interferogram with high resolution of 2.8 mm for the off-axis aspherical mirror with a size of 1.2 m. With improved usage of the CGH, we successfully demonstrated a high lateral resolution interferometer.     

Phase-difference amplification in near-real-time phase-stepping interferometers

We present results from two interferometer systems incorporating phase amplification and phase stepping that operate in near real time. Each system contains two interferometers. The first interferometer projects an interferogram of the test object onto the write side of an optically addressed phase-only liquid-crystal spatial light modulator (LCSLM). The read side of the LCSLM is illuminated by two beams from the second interferometer that are adjusted so that their +n- and -n-order beams are diffracted back along the optic axis. These produce an output interferogram that is phase amplified by a factor 2n. This phase distribution is retrieved by phase stepping.     

Observation of Magnetic Fine Structures by Electron Differential Microscopy

New techniques for electron differential interferometry and microscopy that are free from the effect of distorted reference waves have been developed using an electron trapezoidal prism. This new prism, which replaces an electron biprism, makes a hologram with the object wave inclined and the reference wave perpendicular to the image plane. A differential interferogram can be produced from one double-exposed hologram. A differential phase image from two independently recorded holograms can also be easily achieved. These two techniques retain the advantages of conventional off-axis electron holography, that is, resolution and sensitivity. Their performance is evaluated by reconstructing the electrostatic potential around a charged polystyrene latex particle and by the observation of magnetic fine structures in a permalloy thin film. A two-dimensional vector map of the magnetic flux density enables an interpretation of the contrast of the Lorenz micrograph of the same specimen area.     

Two-wavelength interferometry that uses a fourier-transform method

Two-wavelength interferometry that is based on a Fourier-transform method has been investigated. A phase profile at a synthetic wavelength has been measured from a two-wavelength interferogram with two spatial carrier frequencies. A phase error caused by the difference between modulation intensities at two wavelengths has been theoretically and numerically analyzed. A phase map without the error can be obtained from a power-spectrum adjustment in the two-wavelength interferogram.     

Dynamic range of Ronchi test with a phase-shifted sinusoidal grating

The dynamic range of a Ronchi test with a phase-shifted sinusoidal grating was investigated theoretically and experimentally. As the number of fringes in a Ronchi interferogram increases, the fringe visibility decreases, which results in a decrease of phase-measurement resolution. It is shown that in order to optimize the dynamic range the effective wavelength of the interferogram should be tuned to the characteristic wavelength of the object wave front. The maximum dynamic range achievable is estimated to be 16 times larger than that of a Fizeau interferometer. Suppressing higher-order diffraction components has achieved sheared interferograms with a signal-to-noise ratio in excess of 60:1. The effects of nonsinusoidal transmittance of the grating and the phase-shift errors were minimized by a seven-sample phase-shifting algorithm, and a phase measurement uncertainty of less than 1/700 has been achieved.     

Analysis of interferograms with a spatial radial carrier or closed fringes and its holographic analogy

It is well known that an interferogram can be demodulated to find the wave-front shape if a linear carrier is introduced. We show that it can also be demodulated if it has many closed fringes or a circular carrier appears. A basic assumption is that the carrier fringes are of a bandwidth adequate to contain the wave-front distortion. This phase determination, called here demodulation, is made in the space domain, as opposed to demodulation in Fourier space, but the low-pass filter characteristics must be properly chosen. For academic purposes a holographic analogy of this demodulation process is also presented, which shows that the common technique of multiplying by a sine function and a cosine function is equivalent to holographically reconstructing with a tilted-flat wave front. Alternatively, a defocused (spherical) wave front can be used as a reference to perform the reconstruction or demodulation of some closed-fringe interferograms.     

液晶空间光调制器相位调制特性研究

研究了美国BNS公司生产的Modal P256反射型电寻址液晶空间光调制器的相位调制特性和时间响应特性.采用He-Ne激光作光源,建立迈克尔孙干涉光路观察波前相位变化,给出器件的相位调制特性曲线.分析测量了器件的相位响应不一致性和像素间的相位交连.通过测量液晶器件对方波和正弦控制信号的相位响应延迟,分析了液晶空间光调制器(LC-SLM)的时间响应特性.理论分析与实验结果说明:在特定的入射偏振条件下,LC-SLM实现纯相位调制,可用作高分辨力波前校正器件,然而极慢的响应速度和极低的时间带宽限制了它在动态变化波前相差校正中的应用.     

Synthetic aperture interferometry: in-process measurement of aspheric optics

A scanning probe consisting of a source and receive fiber pair is used to measure the phase difference between wave fronts scattered from the front and rear surfaces of an aspheric optic. This system can be thought of as a classical interferometer with an aperture synthesized from the data collected along the path of the probe. If the form of either surface is known, the other can be deduced. In contrast with classical interferometers, the method does not need test or null plates and has the potential to be integrated into the manufacturing process.     

Compensation of wavelength dependent image shifts in imaging optical interferometry

In modern interferometers for absolute length measurements, when applying phase stepping interferometry, several different wavelengths are used as light sources, and the interferogram is projected to a CCD-camera array. Such interferometers are equipped with wedged optical components as windows and beam splitters, to prevent additional interferences. The wedged optics causes the position of a test piece within the interferogram related to the camera pixel coordinates to be dependent on the wavelength used. This effect depends on the wedge angles and the thicknesses of optical components as well as on their distances within the interferometer's optical pathway. We give a quantitative analysis and suggest a compensation of this dispersion effect by an additional wedge plate outside the interferometer.     

Multiple-beam lateral shear interferometry for optical testing

Lateral shear interferometry is used to obtain the lateral aberrations of a lens. The zeroth-order fringe in an interferogram obtained from a wedge-plate lateral shear interferometer, however, directly displays the lateral aberration curve of a test lens. Nevertheless, the intensity distribution, is cosinusoidal. Multiple-beam interferometry results in sharpened fringes; hence the multiple-beam wedge-plate shear interferometer displays the lateral aberration curve of a lens sharply, provided the shear is small. For large shear, some new artifacts appear in the interferogram, which are also explained.     

Wave-front-dividing array interferometers without moving parts for real-time spectroscopy from the IR to the UV

Interferometers of the Michelson or Mach-Zehnder type are designed as array interferometers. The number of array channels is equal to the number of points needed for an interferogram for Fourier transformation. Similarly one may use an array of step gratings with each grating having a different step height and producing one point of the interferogram. These interferometers, which do not have moving parts, use all the incident light, and the interferogram is instantly produced for real-time spectroscopy.     

Wave-front sensing by use of a Green's function solution to the intensity transport equation

A method for reconstructing an unknown wave front from measurements of its intensity distribution on two planes along the direction of propagation is described. The method solves the intensity transport equation by use of Neumann boundary conditions, leading to a solution that requires only matrix multiplication. The method provides real-time wave-front reconstruction with high accuracy and is easily reposed to permit reconstruction of the wave front in any orthonormal basis set.     

Interferometric phase reconstruction by nonuniform shifting of the reference beam

A method for phase measurement in common-path interferometers, believed to be novel, is presented. We use the property of phase reconstruction algorithms, such as the Carré and Hariharan algorithms, that do not require uniform phase across the reference beam. Only the ratio of the phase steps must be the same at each pixel. We show phase measurement and reconstruction in a common-path interferometer by shifting either the tilt or the focus of the reference wave front. We present a theoretical explanation of phase measurement using this property. We also present results from a proof-of-principle experiment using a scatterplate interferometer, in conjunction with the tilt phase-shifting technique, to measure the reflected phase of a test optical element. Furthermore, we present a computer simulation to demonstrate the mathematical validity of this measurement technique using defocus shifting, rather than tilt shifting, in the reference wave front.     

Hologram Interferometry: Identification of the Sign of Surface Displacements

It is difficult to test aspheric surfaces with a Twyman-Green interferometer because the interferogram frequently contains too many fringes. A simple way of overcoming this problem is to use a lateral-shearing interferometer, in which case the number of fringes in the interferogram can be controlled by varying the shear. However, this has the drawback that two interferograms with orthogonal directions of shear are required; in addition, the accuracy with which the shape of the surface can be evaluated from measurements on photographs of the fringes is limited. In this paper it is shown how these difficulties can be overcome by using a microcomputer-controlled digital radial-shear interferometer. The values of the phase difference in the interferogram at a matrix of points covering the pupil are processed directly in the same microcomputer to give the actual shape of the surface. Typical results obtained with an off-axis paraboloid are presented.     

一种改进的遥感图像融合方法

针对传统的IHS变换和Mallat算法在融合多光谱图像和高空间分辨力图像时存在的不足,提出了一种将IHS变换和平稳小波变换相结合的遥感图像融合方法;另外,对多光谱图像和高空间分辨力图像因空间分辨力的不同而带来的融合图像中所存在的虚假轮廓问题,提出在融合过程中先定位虚假轮廓出现的位置,然后加以处理的方法.仿真结果表明,本文算法在光谱失真上小于IHS变换法,克服了Mallat算法存在的方块效应,同时较好的抑制了虚假轮廓.     

高精度FTIR数据处理方法研究

为了实现对红外光谱的准确测量,对切趾、相位校正、波数校正等方法进行研究,建立了高精度的傅里叶红外光谱仪数据处理系统.在比较各种窗函数的优缺点的情况下选用四阶布莱克曼窗函数对干涉图进行切趾,根据红外光干涉图相位误差特点采用卷积法对单边干涉图进行相位校正,深入研究波数校正方法,采用能量重心法进行波数校正.实验结果表明,傅里...     

Depth fingerprint map of active range-gated imaging for real-time three-dimensional measurement of foreground objects

We present a depth fingerprint map to obtain three-dimensional (3D) spatial information from objects in a large deterministic background by active range-gated imaging, for night remote surveillance. This method first gives the depth fingerprint map of the region of interest in the background by gate viewing in the form of contour bands in range. The map is then embedded in the range-gated laser surveillance system. Finally, 3D spatial information such as target scale and location can be estimated by segmenting the target from the background and matching them with the depth fingerprint map. The measurement is performed by computer background processing. Therefore, the method has no influence on the frame rate of surveillance systems and can realize real-time surveillance. In this paper, the approach to acquisition of the depth fingerprint map is also demonstrated without an echo-broadening effect.