Ultraviolet interferometry with apochromatic reflection optics

To improve the resolution and the sensitivity of optical metrology, we have constructed an interferometer for vacuum-ultraviolet wavelengths. To examine the influence of the wavelength, especially with regard to the period of the object's structure, we chose an apochromatic design. With reflective optics, wavelengths from 157 to 900 nm can be employed for interferometric measurements. The benefits and also the technological problems that accompany the use of vacuum-ultraviolet wavelengths are discussed. The design of this interferometer and measuring results with different wavelengths are presented.     

Adaptive optics performance model for optical interferometry

The optical interferometry community has discussed the possibility of using adaptive optics (AO) on apertures much larger than the atmospheric coherence length in order to increase the sensitivity of an interferometer, although few quantitative models have been investigated. The aim of this paper is to develop an analytic model of an AO-equipped interferometer and to use it to quantify, in relative terms, the gains that may be achieved over an interferometer equipped only with tip-tilt correction. Functional forms are derived for wavefront errors as a function of spatial and temporal coherence scales and flux and applied to the AO and tip-tilt cases. In both cases, the AO and fringe detection systems operate in the same spectral region, with the sharing ratio and subaperture size as adjustable parameters, and with the interferometer beams assumed to be spatially filtered after wavefront correction. It is concluded that the use of AO improves the performance of the interferometer in three ways. First, at the optimal aperture size for a tip-tilt system, the AO system is as much as ~50% more sensitive. Second, the sensitivity of the AO system continues to improve with increasing aperture size. And third, the signal-to-noise ratio of low-visibility fringes in the bright-star limit is significantly improved over the tip-tilt case.     

Phase-locked-loop interferometry applied to aspheric testing with a computer-stored compensator

A recently developed technique for continuous-phase determination of interferograms with a digital phase-locked loop (PLL) is applied to the null testing of aspheres. Although this PLL demodulating scheme is also a synchronous or direct interferometric technique, the separate unwrapping process is not explicitly required. The unwrapping and the phase-detection processes are achieved simultaneously within the PLL. The proposed method uses a computer-generated holographic compensator. The holographic compensator does not need to be printed out by any means; it is calculated and used from the computer. This computer-stored compensator is used as the reference signal to phase demodulate a sample interferogram obtained from the asphere being tested. Consequently the demodulated phase contains information about the wave-front departures from the ideal computer-stored aspheric interferogram. Wave-front differences of ~ 1 λ are handled easily by the proposed PLL scheme. The maximum recorded frequency in the template's interferogram as well as in the sampled interferogram are assumed to be below the Nyquist frequency.     

Opaque optics thickness measurement using a cyclic path optical configuration setup and polarization phase shifting interferometry

Thickness measurement of an opaque optics using a cyclic path optical configuration (CPOC) setup and polarization phase shifting interferometry (PPSI) is presented. The CPOC setup is used to simultaneously focus two orthogonally polarized counterpropagating converging beams at its hypotenuse arm. The opaque optics is placed at the hypotenuse arm of the CPOC setup such that one of its surfaces reflects back one of the counterpropagating focusing beams. Because of the thickness of the opaque optics, the other focusing beam suffers a longitudinal shift in the beam focus. Applying PPSI, the longitudinal shift in the beam focus which is twice the thickness of the opaque optics is determined. The results obtained for a silicon plate of thickness 0.660 mm with a measurement uncertainty of 0.013 mm are presented.     

Extreme-ultraviolet interferometry at 15.5 nm using multilayer optics

The development of multilayer mirror technology capable of operating in the range of 3-30 nm and the construction of thin membranes with excellent uniformity and strength have made it possible to design and implement a Mach-Zehnder interferometer operating at 15.5 nm. We have tested this interferometer by using a soft x-ray laser as a source, and we show its use in probing high-density plasmas.     

孔径径向扫描白光散斑干涉法的研究

提出了一种用于动态研究的新方法-孔径径向扫描白光散斑干涉法,介绍了两孔和直三孔径向扫描器.该方法是一种非接触式的用于动态测量的白光散斑法.分析了孔径径向扫描白光散斑干涉法的基本原理,给出了白光散斑全场滤波分析的平均光强解析式和实验结果.该方法的优点是利用散斑的调频技术能在一张白光散斑图上记录物体的连续动态变形的信息,在全场滤波分时,能将物体动态变形的信息方便地提取出来,得到清晰的全场白光散斑条纹图.直三孔径向扫描法能得到物体在x方向、y方向和45°方向上的变形信息.在实时全场滤波分析观察时,将滤波孔连续地沿径向扫描,可观察到物体连续动态变形的全过程,从而为物体的动态研究提供了一种新方法.     

Synthetic aperture focusing technique signal processing

The synthetic aperture focusing technique (SAFT) is briefly reviewed and addressed as a heuristic digital ultrasonic imaging scheme which exploits the idea of back-propagating a set of measured and digitally stored A-scans. It is shown that for a far-field experimental set-up, ie for small, isolated defects remote to the transducer, SAFT reduces to the filtered back-projection imaging scheme which is well known within the framework of conventional X-ray computer tomography. Therefore, alternative data processing via Fourier transforms only, similar to the Fourier slice theorem of tomography, is possible, which sheds considerable light upon the heuristic SAFT pixel-space envelope-detection scheme. The resulting imaging identity has been termed POFFIS (physical optics far-field inverse scattering). The far-field assumption is then omitted yielding a Fourier-transform-SAFT algorithm (FT-SAFT) whose results are identical to back-propagation imaging with the definite advantage of fast processing capabilities based upon standard hardware and allowing immediate implementation of high resolution procedures as well as inclusion of mode-conversion effects; the theoretical background is pulse-echo diffraction tomography. The above results are supported and illustrated by application of all three algorithms — SAFT, POFFIS, FT-SAFT — to experimental data obtained from scanning a line aperture for several test specimens.     

Chromium-doped forsterite: dispersion measurement with white-light interferometry

Using a Michelson white-light interferometer, we measure the group-delay dispersion and third-order dispersion coefficients, d2(phi)/d(omega)2 and d3(phi)/d(omega)3, of chromium-doped forsterite (Cr:Mg2SiO4) over wavelengths of 1050-1600 nm for light polarized along both the c and b crystal axes. In this interval, the second-order dispersion for the c axis ranges from 35 fs2/mm to -14 fs2/mm, and the third-order dispersion ranges from 36 fs3/mm to 142 fs3/mm. For the b axis the second-order dispersion ranges from 35 fs2/mm to -15 fs2/mm and the third-order from 73 fs3/mm to 185 fs3/mm. Our data are relevant for the development of optimized dispersion compensation tools for Cr:Mg2SiO4 femtosecond lasers. These measurements help to clarify previously published results and show some significant discrepancies that existed, especially in the third-order dispersion. Our results should furthermore be useful to build up an analytic expression for the index of refraction of chromium forsterite.     

Synthetic aperture imaging for small scale systems

Multi-element synthetic aperture imaging methods suitable for applications with severe cost and size limitations are explored. Array apertures are synthesized using an active multi-element receive subaperture and a multi-element transmit subaperture defocused to emulate a single-element spatial response with high acoustic power. Echo signals are recorded independently by individual elements of the receive subaperture. Each method uses different spatial frequencies and acquisition strategies for imaging, and therefore different sets of active transmit/receive element combinations. Following acquisition, image points are reconstructed using the complete data set with full dynamic focus on both transmit and receive. Various factors affecting image quality have been evaluated and compared to conventional imagers through measurements with a 3.5 MHz, 128-element transducer array on different gel phantoms. Multielement synthetic aperture methods achieve higher electronic signal to noise ratio and better contrast resolution than conventional synthetic aperture techniques, approaching conventional phased array performance     

Synthetic aperture superresolution with multiple off-axis holograms

An optical setup to achieve superresolution in microscopy using holographic recording is presented. The technique is based on off-axis illumination of the object and a simple optical image processing stage after the imaging system for the interferometric recording process. The superresolution effect can be obtained either in one step by combining a spatial multiplexing process and an incoherent addition of different holograms or it can be implemented sequentially. Each hologram holds the information of each different frequency bandpass of the object spectrum. We have optically implemented the approach for a low-numerical-aperture commercial microscope objective. The system is simple and robust because the holographic interferometric recording setup is done after the imaging lens.     

光学元件残余应力无损检测技术概述

残余应力是光学元件的一个重要性能参数,对光学元件的制造和使用意义重大。光学元件残余应力的无损检测方法可粗略概括为两大类：一类是基于应变的测量方法,包括X射线衍射法、Stoney曲率法和显微拉曼光谱法,这些方法基于晶体和弹性力学分析方法,发展成熟、应用广泛;另一类是基于应力双折射效应的测量方法,包括数字光弹法、光弹调制器法和偏振光腔衰荡法,都是对残余应力导致的双折射相位差的测量,具有更直接的光学关联性、测量精度高的特点。本文归纳了光学元件残余应力测量的几种常见方法的测量原理、测量精度和应用场景,对比了它们的性能并分析了它们之间的关联性,以期建立起光学元件残余应力无损检测的宏观印象。

     

用于大口径非球面的波前功率谱密度检测

光学元件加工质量的检测和评价工作是保证整个光学系统安全、正常运行的关键。在总结非球面常用检验指标优、缺点的基础上,讨论了测量大口径非球面的波前功率谱密度时的系统组成、工作原理和软件设计的总体思路。为了减少系统误差的影响,求解波前功率谱密度时,通过引入系统传递函数校正测量值来实现。使用大口径相位干涉仪作为波前检测仪器,证实波前功率谱密度能定量给出波前畸变的空间频率分布,并用于作为大口径光学元件质量的评价标准。给出一个测试口径为64mm×64mm光学元件测试结果,有效频率为0.03mm-1～3.87mm-1,rms为0.0064λ。     

Encryption of digital hologram based on phase-shifting interferometry and virtual optics

A new information encryption system is presented, based on phase-shifting interferometry and virtual optics. Three-step phase-shifting interferometry is used to record a digital hologram of the input data and a virtual optical system based on the scaled optical fractional Fourier transform is used for encryption of the recorded digital hologram. In the virtual optical system, the digital hologram to be encrypted is fractional Fourier transformed two times, and a random phase mask is placed at the output plane of the first fractional Fourier transform. Both the encryption and decryption processes are performed digitally. The encrypted data and the keys for decryption can be stored and transmitted in a conventional communication channel. Numerical simulations are presented to verify validity and efficiency.     

Mathematical formulation for estimation of baseline in synthetic aperture radar interferometry

Terrain height estimation through spaceborne interferometric synthetic aperture radar (INSAR) requires accurate knowledge of the orbital shift between repeat passes. Mathematical models are available for the estimation of horizontal orbital shift. However, in reality, the orbital shift between repeat passes is modelled as two-dimensional for the same azimuth scanline. In this paper, a new mathematical formulation has been developed for the estimation of the two-dimensional orbital shift of INSAR based on the fringe line pattern in the interferogram of flat earth.     

Synthetic aperture techniques with a virtual source element

A new imaging technique has been proposed that combines conventional B-mode and synthetic aperture imaging techniques to overcome the limited depth of field for a highly focused transducer. The new technique improves lateral resolution beyond the focus of the transducer by considering the focus a virtual element and applying synthetic aperture focusing techniques. In this paper, the use of the focus as a virtual element is examined, considering the issues that are of concern when imaging with an array of actual elements: the tradeoff between lateral resolution and sidelobe level, the tradeoff between system complexity (channel count/amount of computation) and the appearance of grating lobes, and the issue of signal to noise ratio (SNR) of the processed image. To examine these issues, pulse-echo RF signals were collected for a tungsten wire in degassed water, monofilament nylon wires in a tissue-mimicking phantom, and cyst targets in the phantom. Results show apodization lowers the sidelobes, but only at the expense of lateral resolution, as is the case for classical synthetic aperture imaging. Grating lobes are not significant until spatial sampling is more than one wavelength, when the beam is not steered. Resolution comparable to the resolution at the transducer focus can be achieved beyond the focal region while obtaining an acceptable SNR. Specifically, for a 15-MHz focused transducer, the 6-dB beamwidth at the focus is 157 mum, and with synthetic aperture processing the 6-dB beamwidths at 3, 5, and 7 mm beyond the focus are 189 mum, 184 mum, and 215 mum, respectively. The image SNR is 38.6 dB when the wire is at the focus, and it is 32.8 dB, 35.3 dB, and 38.1 dB after synthetic aperture processing when the wire is 3, 5, and 7 mm beyond the focus, respectively. With these experiments, the virtual source has been shown to exhibit the same behavior as an actual transducer element in response to synthetic aperture processing techniques.     

Focal-length measurement by multiple-beam shearing interferometry

The application of multiple-beam shearing interferometry to lens focal-length measurement is described. A coated shearing plate interferometer was used in transmission to produce sharp multiple-beam fringes that rotate as the collimation of the incoming wave front from the lens under test changes. The test lens was used to collimate light from a point source that was translated longitudinally, and the focal length was determined from the rate of rotation of the fringes as the source moved. This method is simple, accurate, and lends itself to automatic determination of focal length.     

Absolute distance measurement by two-point-diffraction interferometry

We present a point-diffraction interferometer that has been specially devised to perform absolute distance measurements in three dimensions. It is composed of two main parts: One is a target that moves in three dimensions, and the other is a stationary two-dimensional array of photodetectors. The target is made of point-diffraction sources that emit two spherical wave fronts, whose interference is monitored by the photodetectors. Application of a phase-shifting technique allows the phase values of the photodetectors to be precisely measured, which are then fitted to a geometric model of multilateration so as to determine the xyz location of the target by minimization of least-squares errors. Experimental results show that the proposed diffraction interferometer is capable of measuring the xyz coordinates of the target with a volumetric uncertainty of less than 1.0 microm over a working volume of a 100-mm side.