White-light Fizeau interferometer

A white-light Fizeau interferometer is described. Commonly, white-light fringes can be produced only by using a virtual wedge instrument such as a Michelson interferometer. By use of a series arrangement of a Fabry-Perot interferometer in front of a two-beam Fizeau interferometer, white-light fringes can be produced. For white-light fringes to be obtained, the thickness of the air gap between the Fizeau plates has to be adjusted to the same thickness as the air gap between the Fabry-Perot plates (or in more general terms to a rational multiple of this value). The contrast of the two-beam type of Fizeau fringes depends on the reflectivity of the Fabry-Perot plates.     

Use of the fast Fourier transform method for analyzing linear and equispaced Fizeau fringes

The Fourier transform method is applied to analyze the initial phase of linear and equispaced Fizeau fringes. We develop an algorithm for high-precision phase measurement by using the Fourier coefficient that corresponds to the spatial frequency of the Fizeau fringes, and we describe methods for determining the fringe carrier frequency. Errors caused by carrier frequency fluctuation and data truncation are studied theoretically and by computer simulation. To demonstrate the method we apply it to the real-time calibration of a piezoelectric transducer mirror in a Twyman-Green interferometer.     

Fringe-imaging Mach-Zehnder interferometer as a spectral analyzer for molecular Doppler wind lidar

The theoretical performance of a Mach-Zehnder interferometer used as a spectral analyzer for wind-speed measurement by direct-detection Doppler lidar is presented. The interferometer is optimized for the measurement of wind velocity from the signal that is backscattered by the molecules. In the proposed fringe-imaging Mach-Zehnder (FIMZ) interferometer, a pattern of equally spaced linear fringes is formed and detected by two conventional detector linear arrays. Assuming a pure molecular signal with Gaussian spectral profile, an analytic expression for the standard deviation of the measurement error is obtained and compared with the Cramer-Rao lower bound given by an ideal spectral analyzer (ISA) in the case of shot-noise-limited signal. The FIMZ measurement error is shown to be 2.3 times that of the ISA and is comparable with the error given by previously developed multichannel spectral analyzers that are based on Fabry-Perot interferometers that, in contrast, have the disadvantages of producing unequally spaced circular fringes and requiring dedicated detectors. The optimal path difference for a FIMZ operating at 355 nm is approximately 3 cm. The interferometer is shown to match important lidar beam étendues without significant performance reduction.     

Measurements of the phase shift on reflection for low-order infrared Fabry-Perot interferometer dielectric stack mirrors

A simple technique based on a Fizeau interferometer to measure the absolute phase shift on reflection for a Fabry-Perot interferometer dielectric stack mirror is described. Excellent agreement between the measured and predicted phase shift on reflection was found. Also described are the salient features of low-order Fabry-Perot interferometers and the demonstration of a near ideal low-order (1-10) Fabry-Perot interferometer through minimizing the phase dispersion on reflection of the dielectric stack. This near ideal performance of a low-order Fabry-Perot interferometer should enable several applications such as compact spectral imagers for solid and gas detection. The large free spectral range of such systems combined with an active control system will also allow simple interactive tuning of wavelength agile laser sources such as CO(2) lasers, external cavity diode lasers, and optical parametric oscillators.     

Fabry-Perot interferometer based Mie Doppler lidar for low tropospheric wind observation

Similar in principle to recent implementations of a lidar system at 355 nm [Opt. Lett. 25, 1231 (2000), Appl. Opt. 44, 6023 (2005)], an incoherent-detection Mie Doppler wind lidar at 1064 nm was developed and deployed in 2005 [Opt. Rev. 12, 409 (2005)] for wind measurements in the low troposphere, taking advantage of aerosol scattering for signal enhancement. We present a number of improvements made to the original 1064 nm system to increase its robustness for long-period operation. These include a multimode fiber for receiving the reference signal, a mode scrambler to allow uniform illumination over the Fabry-Perot interferometer, and a fast scannable Fabry-Perot interferometer for calibration and for the determination of outgoing laser frequency during the wind observation. With these improvements in stability, the standard deviation of peak transmission and FWHM of the Fabry-Perot interferometer was determined to be 0.49% and 0.36%, respectively. The lidar wind measurements were validated within a dynamic range of +/-40 m/s. Comparison experiments with both wind profiler radar and Vaisala wiresonde show good agreement with expected observation error. An example of 24 h continuous observations of wind field and aerosol backscatter coefficients in the boundary layer with 1 min and 30 m temporal and spatial resolution and 3 m/s tolerated wind velocity error is presented and fully demonstrates the stability and robustness of this lidar.     

Theory for the measurement of the linear and nonlinear refractive indices of double-clad fibers using an interferometric technique

Multiple-beam Fizeau fringes are formed across a liquid silvered wedge when it is illuminated by a collimated beam of monochromatic light. Inserting the fiber into the liquid silvered wedge causes the fringes to shift across the fiber region with respect to the fringes at the liquid region. Fringe shift is a function in the geometry of the different regions of the fiber and the refractive index profile of the fiber. In this paper, theoretical models for the fringe shift across double-clad fibers (DCFs) with rectangular, elliptical, circular, and D-shaped inner cladding are developed. An algorithm to reconstruct the linear and nonlinear terms of the refractive index profile of the DCF is outlined. Numerical examples are provided and discussed.     

Wedge-plate shearing interferometers for collimation testing: use of a moiré technique

Various optical arrangements of a double-wedge-plate shearing interferometer are presented for checking laser beam collimation. The use of moiré fringes is found to be advantageous for setting the shear fringes parallel to the direction of shear in order to obtain a well-collimated laser beam. The experimental procedure and various details of the interferometer are discussed. A brief summary of a few methods for collimation testing that use a wedge plate is also given. The accuracies achievable with shearing interferometers that use a parallel plate, a wedge plate of small angle, a double wedge having a large wedge angle, a wedge plate of large angle along with two flat mirrors, and a wedge plate having a large angle are compared and summarized.     

Multiple-beam interferometric determination of Poisson's ratio and strain distribution profiles along the cross section of bent single-mode optical fibers

Multiple-beam Fizeau fringes crossing bent single-mode optical fibers immersed in matching liquid reveal the existence of induced birefringence. Changes in the fiber cladding refractive index delta n were measured from the fringe shift to an accuracy of +/- 1 x 10(-4). Mathematical expressions were deduced to evaluate Poisson's ratio and to describe the radial strain distribution profiles of bent optical fibers from the experimental values of the fringe shifts. Experimental results were obtained from microinterferograms. Studying bent fibers by application of Fizeau fringes interferometry provides a nondestructive, accurate, sensitive, and reliable method to measure their parameters and characteristics.     

Three-channel imaging fabry-perot interferometer for measurement of mid-latitude airglow

We have developed a three-channel imaging Fabry-Perot interferometer with which to measure atmospheric wind and temperature in the mesosphere and thermosphere through nocturnal airglow emissions. The interferometer measures two-dimensional wind and temperature for wavelengths of 630.0 nm (OI, altitude, 200-300 km), 557.7 nm (OI, 96 km), and 839.9 nm (OH, 86 km) simultaneously with a time resolution of 20 min, using three cooled CCD detectors with liquid-N(2) Dewars. Because we found that the CCD sensor moves as a result of changes in the level of liquid N(2) in the Dewars, the cooling system has been replaced by thermoelectric coolers. The fringe drift that is due to changes in temperature of the etalon is monitored with a frequency-stabilized He-Ne laser. We also describe a data-reduction scheme for calculating wind and temperature from the observed fringes. The system is fully automated and has been in operation since June 1999 at the Shigaraki Observatory (34.8N, 136.1E), Shiga, Japan.     

Simultaneous determination of the refractive index and wedge angle of an optical wedge plate using a photorefractive holographic interferometer

Abstract

A simple and effective method for simultaneously determining the refractive index and the wedge angle of an optical wedge plate is described. The method is based on a real-time holographic interferometer which uses a photorefractive crystal as the recording and reconstruction medium. The wedge sample under test is inserted into a rectangular cell that is placed in the object light beam of the holographic interferometer. The interference patterns produced before and after a reference liquid is poured into the cell are received by a CCD camera and stored in a computer, respectively. The refractive index and the wedge angle of the wedge sample are determined by measuring the number of fringes falling inside a fixed aperture. The principle of the method is analysed and some experimental results with adequate accuracy are given.     

Method to obtain a clear fringe pattern with a zone-plate interferometer

When a zone-plate interferometer is used, a bright spot appears at the center of the image plane. The spot makes it difficult to analyze the interference fringes. A simple technique that is based on the principle of fringe-intensity reversal is proposed to analyze the fringes efficiently. A zone plate with a phase fraction of π/2 or 3π/2 is used in this technique to diminish the bright spot. Unlike the masking technique, no part of the data on the fringes is lost. The fringes can, therefore, be analyzed completely. The technique is described in detail, and the results of an experiment in which the shape error of a concave mirror was measured with the proposed zone plate is presented. The experimental results agree well with the results obtained with the Fizeau interferometer.     

Comparative signal-to-noise analysis of fibre-optic based optical coherence tomography systems

Several optical coherence tomography (OCT) systems are proposed using optical-fibre components and based around Fizeau sensing interferometers. The theoretical signal-to-noise ratio (SNR) is calculated for each of the proposed configurations, using a constant set of assumed values for illumination and detection parameters. The SNR values obtained are compared with values calculated for typical existing configurations based around Michelson interferometers. Fizeau-based systems incorporating a secondary processing interferometer offer the advantage over current interferometer configurations of down-lead insensitivity, which prevents signal fading and reduces thermal fringe drift. The most basic form of the Fizeau system makes inefficient use of optical power, and has a low SNR compared with the widely used Michelson configuration. However, the results of the analysis described in this paper show that the SNR for more sophisticated Fizeau configurations, incorporating optical circulators and balanced detection systems, can be as high as the value for the most sensitive existing fibre-based OCT systems. Fizeau configurations therefore offer the combined advantages of optimized SNR and down-lead insensitivity, indicating their suitability for use in relatively poorly controlled environments such as in-vivo measurements.     

角位移Fabry-Perot干涉测量

提出了一种基于Fabry-Perot板干涉的角位移测量新方法。此方法采用函数近似,只需将初始入射角确定在40°到50°之间,即可由角位移与干涉信号条纹数变化间的函数关系,高精度测量角位移。解决了采用F-P板干涉法测量角位移需精确确定入射光初始角的问题。使用计算机处理采集的干涉信号,对干涉条纹进行细分,实现干涉信号相位测量的高分辨力。理论模拟和实验结果得出本方法可以实现精度为10-5rad数量级的角位移测量。该方法的测量装置采用带尾纤的半导体激光作为光源,由自聚焦透镜准直,出射光束直径为0.5mm,使探测头为小光斑。该装置结构简单,能实现小型化。     

Simple multifrequency and phase-shifting fringe-projection system based on two-wavelength lateral shearing interferometry for three-dimensional profilometry

We propose a simple multifrequency spatial-carrier and phase-shifting fringe-projection system based on two-wavelength lateral shearing interferometry (LSI). In this system a wedge-shaped plate lateral shearing interferometer is used and, owing to the presence of tilt, a finite number of fringes parallel to the direction of the shear appears; hence a significant spatial-carrier frequency is generated at the focus position. We further enhance the spatial-carrier frequency either by changing the wavelength of the laser light or by slight defocusing. A synthetic interferogram with low spatial-carrier frequency is obtained by use of laser light of two wavelengths simultaneously in the lateral shear interferometer. We obtain the phase-shifted fringe patterns from the same setup by simply moving the wedge plate in an in-plane parallel direction, using a linear translator. The fringe projection system was tested for measurement of the three-dimensional shape of a discontinuous object. The present system has many advantages; e.g., it is a common-path interferometry and hence is insensitive to external vibrations, is compact in size, and is relatively inexpensive.     

Fabry-Perot etalon aperture requirements for direct detection Doppler wind lidar from Earth orbit

The design of Fabry-Perot etalons for direct detection Doppler wind lidar from a satellite is considered for two direct detection methods, fringe imaging (multichannel) and double edge. The area solid-angle product of the etalon for each technique is derived and shown to be inherently larger, for a given etalon aperture, for the fringe imager than for the double-edge Doppler analyzer. Modeling of the Doppler measurement accuracy of a spaceflight direct detection wind lidar shows that a very large optical aperture, 2 m or more, is necessary. Optical throughput matching to a 2-m collector requires, for the fringe-imaging Doppler analyzer, an etalon with 60 mm aperture, whereas the double-edge technique would require two etalons of 200 mm aperture, or a split-aperture etalon of 400 mm working aperture. Because the two direct detection methods have been shown to have practically identical intrinsic sensitivities (measurement accuracies per unit signal), this difference in etalon dimensions may be a significant selection consideration.     

Real-time polarization state measurement based on a birefringent crystal wedge

Abstract

We present a method of single-shot polarization state measurement based on a birefringent crystal wedge. The phase delay and amplitude angle of detected light are encoded into two groups of fringes through the interference in a crystal wedge and further decoded by fringe position locations. This method has the merit of real-time measurement, a compact set-up and simple calibration. The principle, set-up, calibration and error analysis are presented in details. In the end, a single-shot measurement set-up with 80 kHz temporal resolution is demonstrated to investigate the molecule dynamic behaviour in a TN liquid crystal under a rectangular voltage.     

Rayleigh-Mie Doppler wind lidar for atmospheric measurements. II. Mie scattering effect, theory, and calibration

A theoretical and experimental study is conducted for the direct-detection Doppler Lidar developed by the Service d'Aéronomie du Centre National de la Recherche Scientifique. Thanks to a specific design, the double-edge technique that applies primarily to Rayleigh scattering can also be employed in presence of aerosols backscatter. We focus on a careful estimate of the particle-induced error on the wind measurements. With a theoretical model for the Fabry-Perot interferometer and two sets of calibration measurements, the true spectral properties of the interferometer and the calibration curves are recovered. Furthermore, the particle-induced error is estimated for varying values of the scattering ratio at 532 nm. When applied to real atmospheric signals, this error is shown to be negligible. A comparison between ancillary data and the wind and backscatter ratio as retrieved from the Doppler lidar signals confirms our estimate.     

Compensation of spacer-thickness variations in a holographic Fabry-Perot filter

The fabrication of a solid, holographically recorded Fabry-Perot interferometer that uses plate glass for the spacer has recently been reported. The component produced sharp, circular Fabry-Perot fringes in spite of its use of a plate-glass spacer. We develop a general theoretical characterization of such a component that accounts for its low sensitivity to spacer-thickness variations. We use the Kogelnik theory of volume holograms to calculate the phase change on reflection from the mirrors. This phase change results from the position of the fringes formed throughout the two holographic media during the recording process. An expression for the wavelength location of the transmission peak versus spacer-thickness variation is derived that agrees with the current experimental information available.     

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.