Modified double-wedge-plate shearing interferometer for collimation testing

A modified configuration of the double-wedge-plate shearing interferometer for collimation testing is described. Results of the measurements to determine the setting sensitivity with this configuration are presented.     

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.     

Simple phase-shifting method in a wedge-plate lateral-shearing interferometer

A simple phase-shifting method in a wedge-plate lateral shearing interferometer is described. Simply moving the wedge plate in an in-plane parallel direction gives the amount of phase shift required for phase-shifting interferometry because the thickness of a wedge plate is not constant and varies along the wedge direction. This method requires only one additional linear translator to move the wedge plate. The required moving distance for a phase shift of the wave front with this method is of the order of a millimeter, whereas the typical moving distance for another method that uses a piezoelectric transducer is of the order of a wavelength. This method yields better precision in controlling the moving distance than do the other methods.     

Improved collimation testing technique

Laser collimation is an essential part of many experimental setups including optical coherent processors, image transformers, Fourier transform generators, and 4f-based optical systems. A device is required to test the collimation of lasers in such experiments. We are proposing a modification in the existing two-lens-system (TLS)-based collimation testing technique in which a combination of a convex and a concave lens is placed in space between the collimating lens and the first grating of the conventional setup. In the proposed method, we change the position of the second TLS component, placing it between the two gratings. The proposed idea not only reduces the size of the system but also gives improved results. Theoretical modeling and simulated and experimental results are presented to support our idea.     

A phase-conjugate Twyman-Green interferometer with increased sensitivity for laser beam collimation

Abstract

A Twyman-Green interferometer having a phase-conjugate mirror in one arm and double mirror in another arm is described to measure divergence and to check the collimation of a laser beam. It uses an internally self-pumped phase conjugation in BaTiO₃ crystal as phase-conjugate mirror. The use of double mirror gives a dual interference field which results in improved sensitivity in collimation testing. The dual-field interferogram is also useful in easily distinguishing between the divergent and convergent nature of the test beam. Measurement results are presented.     

A modified approach for collimation testing using Lau interferometry

A modified approach for the collimation testing of an incoherent optical beam using the Lau effect coupled with moiré readout is proposed. In the experimental set-up a white-light incoherent source illuminates a coarse grating G_1. The collimating lens is mounted on a translation stage, so that the grating G₁ can be adjusted to be at the ‘in-focus’, ‘at-focus’ or ‘out-of-focus’ position. Grating G₂ and grating G₃ are mounted on a precision rotational stage and are so positioned that the lines of the gratings make a small but equal and opposite angle with the vertical. The inclination angle of the resulting moiré fringe demonstrates the quality of collimation of optical beam. The proposed technique can also be conveniently used for measurement of the focal length of a collimating lens, at a very low cost.     

用于检测激光棒的变倾角马赫-曾德尔干涉仪

为实现激光棒透射波前的测量,改善一般泰曼型或斐索型干涉仪测量小口径激光棒透射波前时的边缘衍射效应,研究了一种变倾角移相马赫-曾德尔干涉仪。通过调整移相反射镜的倾斜姿态,改变入射到马赫-曾德尔干涉光路的光束倾角,参考光束与测试光束的光程差随之变化,从而在相干光之间引入相移,实现了相移干涉测量。利用该干涉仪测量一根口径为Ф6 mm、长度为60 mm激光棒(Nd:YAG)的透射波前,测量结果的峰谷值(PV)为0.391λ,均方根值(RMS)为0.056λ;使用ZYGO激光干涉仪测量同一根激光棒,其透射波前的峰谷值(PV)为0.370λ,均方根值(RMS)为0.064λ。对比结果表明该干涉仪能实现光学元件透射波前的高精度检测,测试结果的一致性验证了该方案的可行性。该变倾角移相方法具有较高的移相精度和较大的移相范围,且该变倾角干涉系统中光束仅一次透过待测激光棒,可有效抑制多光束干涉现象,改善小口径激光棒的边缘衍射效应。     

Wave-front analysis method of circular aperture sampling for collimation testing

A new type of wave-front analysis method for the collimation testing of laser beams is proposed. A concept of wave-front height is defined, and, on this basis, the wave-front analysis method of circular aperture sampling is introduced. The wave-front height of the tested noncollimated wave can be estimated from the distance between two identical fiducial diffraction planes of the sampled wave, and then the divergence is determined. The design is detailed, and the experiment is demonstrated. The principle and experiment results of the method are presented. Owing to the simplicity of the method and its low cost, it is a promising method for checking the collimation of a laser beam with a large divergence.     

Combined Twyman-Green and Mach-Zehnder interferometer for microlens testing

A new interferometer design for microlens testing is presented. The phase-shifting system combines the advantages of a Twyman-Green and a Mach-Zehnder interferometer and permits full characterization of the aberrations of microlenses as well as radius of curvature and focal length measurements. The Twyman-Green system is applied to surface testing in reflection (single reflection), whereas the Mach-Zehnder system is used for lens testing in transmission (single pass). Both measurements are performed without removal of the test part, allowing for combination of the results without confusion of the actual lens and without an azimuthal orientation error. The interferometer setup is explained, the test procedure is described, and experimental results are given.     

Nonnull interferometer simulation for aspheric testing based on ray tracing

The nonnull interferometric method that employs a partial compensation system to compensate for the longitude aberration of the aspheric under test and a reverse optimization procedure to correct retrace errors is a useful technique for general aspheric testing. However, accurate system modeling and simulation are required to correct retrace errors and reconstruct fabrication error of the aspheric. Here, we propose a ray-tracing-based method to simulate the nonnull interferometer, which calculates the optical path difference by tracing rays through the reference path and the test path. To model a nonrotationally symmetric fabrication error, we mathematically represent it with a set of Zernike polynomials (i.e., Zernike deformation) and derive ray-tracing formulas for the deformed surface, which can also deal with misalignment situations (i.e., a surface with tilts and/or decenters) and thus facilitates system modeling extremely. Simulation results of systems with (relatively) large and small Zernike deformations and their comparisons with the lens design program Zemax have demonstrated the correctness and effectiveness of the method.     

Multitaper scan-free spectrum estimation using a rotational shear interferometer

Multitaper methods for a scan-free spectrum estimation that uses a rotational shear interferometer are investigated. Before source spectra can be estimated the sources must be detected. A source detection algorithm based upon the multitaper F-test is proposed. The algorithm is simulated, with additive, white Gaussian detector noise. A source with a signal-to-noise ratio (SNR) of 0.71 is detected 2.9 degrees from a source with a SNR of 70.1, with a significance level of 10(-4), approximately 4 orders of magnitude more significant than the source detection obtained with a standard detection algorithm. Interpolation and the use of prewhitening filters are investigated in the context of rotational shear interferometer (RSI) source spectra estimation. Finally, a multitaper spectrum estimator is proposed, simulated, and compared with untapered estimates. The multitaper estimate is found via simulation to distinguish a spectral feature with a SNR of 1.6 near a large spectral feature. The SNR of 1.6 spectral feature is not distinguished by the untapered spectrum estimate. The findings are consistent with the strong capability of the multitaper estimate to reduce out-of-band spectral leakage.     

无线激光通信中的多光束发射技术研究

在大气激光通信中,大气湍流所引起的光强闪烁会严重影响通信系统的性能,导致系统误码率的增加,多光束发射是克服这种影响的有效方法。本文分析了用不同数目光束发射时的光强概率分布;以及多束光发射时接收端用不同直径的接收透镜进行接收时的光强概率分布,结果表明随着发射光束的增加、孔径直径的增大,光强概率分布更加趋于正态分布,光强概率的均值增大。文中还分析了多光束发射的归一化相关系数和光强方差的关系以及多光束发射在不同湍流环境下的误码率性能,分析结果表明多光束发射系统可以很好地改善接收面的光强起伏,降低系统的误码率。     

Generalized data reduction approach for aspheric testing in a non-null interferometer

Data reduction in non-null tests is difficult due to the presence of retrace error. We propose a simple yet effective data reduction approach for aspheric testing in a non-null interferometer. The new approach gives figure error of the aspheric by just subtracting the theoretical wavefront and first-order errors from the real wavefront obtained in the non-null interferometer. Precise prediction of the theoretical wavefront can be achieved by accurate calibration of the partial compensation system. The approach can be considered a generalization of the traditional data processing method in null tests, and errors that may affect its accuracy are discussed. A set of experiments have been carried out to demonstrate its validity and feasibility.     

Point diffraction interferometer with adjustable fringe contrast for testing spherical surfaces

A point diffraction interferometer (PDI) with adjustable fringe contrast is presented for the high-precision testing of spherical surfaces. The polarizing components are employed in the PDI to transform the polarization states of the test and reference beams, and a good fringe contrast can be realized by adjusting the relative intensities of interfering waves. The proposed system is compact and simple in structure, and it provides a feasible way for high-precision testing of spherical surfaces with low reflectivity. The theory of the interferometer is introduced in detail, along with the properties of optical components employed in the system, numerical analysis of systematic error, and the corresponding calibration procedure. Compared with the testing results of the ZYGO interferometer, a high accuracy with RMS value about 0.0025λ is achieved with the proposed interferometer. Finally, the error consideration in the experiment is discussed.