Simple, real-time method for removing the cyclic error of a homodyne interferometer with a quadrature detector system

The cyclic error of a homodyne interferometer is caused mainly by phase mixing due to the imperfection of polarizing optical components such as polarizing beam splitters. In Appl. Opt. 43, 2443 (2004), we concentrated on the relationship between these imperfect optical characteristics and the cyclic error and found the preamplifier-gains condition for removing the cyclic error. Here we demonstrate the cyclic error correction method experimentally and show that the method can be applied in real time. We obtained 0.04-nm cyclic errors, with a standard deviation above 5 microm.     

Passive directional discrimination in laser-Doppler anemometry by the two-wavelength quadrature homodyne technique

We report a method for passive optical directional discrimination in laser-Doppler anemometers. For this purpose frequency-shift elements such as acousto-optic modulators, which are bulky and difficult to align during assembly, have traditionally been employed. We propose to use a quadrature homodyne technique to achieve directional discrimination of the fluid flow without any frequency-shift elements. It is based on the employment of two laser wavelengths, which generate two interference fringe systems with a phase shift of a quarter of the common fringe spacing. Measurement signal pairs with a direction-dependent phase shift of +/- pi/2 are generated. As a robust signal-processing technique, the cross-correlation technique is used. The principles of quadrature homodyne laser-Doppler anemometry are investigated. A setup that provides a constant phase shift of pi/2 throughout the entire measurement volume was achieved with both single-mode and multimode radiation. The directional discrimination was successfully verified with wind tunnel measurements. The complete passive technique offers the potential of building miniaturized measurement heads that can be integrated, e.g., into wind tunnel models.     

Optical activity measurement by use of a balanced detector optical heterodyne interferometer

What we believe to be a novel amplitude sensitive optical heterodyne polarimeter in which a Zeeman laser is associated with balanced detector detection was set up. The aim was to measure the optical activity of a quartz crystal with a Cornu depolarizer at high accuracy. The features of this novel polarimeter, which include the use of a two-frequency laser that ensures the accuracy of the measurement, are discussed. Furthermore, the detection sensitivity of the optical activity of a quartz crystal was measured as 8.5x10(-10). To our knowledge, this is the highest sensitivity obtained for optical activity measurement of a quartz crystal when the error of the measurement is also analyzed.     

Lidar-signal compression by photomultiplier gain modulation: influence of detector nonlinearity

The application of photomultiplier gain modulation to the compression of wide-dynamic-range lidar signals is investigated in relation to the effect of the gain level on anode-signal linearity. Gain reduction is achieved by the coupling of modulation signals through either multidynode or focus-grid gating networks. This technique facilitates signal recovery and prevents detector nonlinearity and dynode damage caused by high near-field lidar signals. The measurements were performed in the current mode primarily on a 50-mm-diameter, 12-stage photomultiplier (EMI 9214) with a bialkali photocathode. With 3- or 4-dynode-based modulation made at a photomultiplier voltage of 1300 V and a gain of 1 x 10(7), signals of ~6 mA can be maintained at the 1% linearity limit from 100% to 0.2% modulation, corresponding to a 500-fold reduction in the lidar-signal dynamic range. A significant advantage to dynode modulation is that it preserves the shot-signal-to-noise ratio of the incoming signal, which is not true for focus-grid modulation or external predetection schemes such as controlled obscuration or Pockels-cell modulation that attenuate the as-yet unamplified signal.     

Fiber bragg grating strain sensor demodulation with quadrature sampling of a mach-zehnder interferometer

A simple and highly sensitive phase-demodulation technique is proposed, and its use for a fiber Bragg grating strain sensor is experimentally demonstrated. Sampling a phase-modulated Mach-Zehnder output with controlled time delay produced two quadrature data streams that have relative quadrature phase difference (90 degrees ). The Bragg wavelength-dependent phase information is extracted by application of digital arctangent function and phase unwrapping to the quadrature signals. By use of this technique with a reference grating, strain sensing at as much as a 30-kHz sampling rate was obtained with strain resolution of 3.5 microstrains and 6 nanostrains/ Hz in quasi-static and dynamic strain measurements, respectively.     

Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating

We present a new type of quadrature phase-shifting interferometer, which utilizes wave plates, a diffraction grating, and two lasers with different wavelengths, in order to acquire two sets of two quadrature fringe patterns in each wavelength formed on a single image sensor. This method for calculating with four phase-shifted fringe patterns gives us the phase sum and difference distributions between the phases in two wavelengths. This is also substantiated by results of our experiments.     

A note on the measurement of phase space observables with an eight-port homodyne detector

It is well known that the Husimi Q-function of the signal field can actually be measured by the eight-port homodyne detection technique, provided that the reference beam (used for homodyne detection) is a very strong coherent field so that it can be treated classically [see e.g. Leonhardt, U.; Paul, H. Phys. Rev. A 1993, 47, R2460–R2463]. Using recent rigorous results on the quantum theory of homodyne detection observables [Kiukas, J.; Lahti, P. J. Mod. Opt., in press (see arXiv:0706.4436v1 [quant-ph])], we show that any phase space observable, and not only the Q-function, can be obtained as a high amplitude limit of the signal observable actually measured by an eight-port homodyne detector. The proof of this fact does not involve any classicality assumption.     

Correction of detector nonlinearity in Fourier transform spectroscopy with a low-temperature blackbody

The nonlinearity of a mercury cadmium telluride photoconductive detector, an integral part of a modified commercial interferometer used for airborne research, has been analyzed and evaluated against a number of correction schemes. A high-quality blackbody with accurate temperature control has been used as a stable and well-characterized radiation source. The detector nonlinearity was established as a function of scene temperature between 194 and 263 K. Second- and third-order corrections to the measured interferogram have been tested by analyzing the measured signal both within and outside the spectral response region of the detector. A combined correction scheme is proposed that best represents the real nonlinear response of the detector.     

Practical example of the correction of Fourier-transform spectra for detector nonlinearity

HgCdTe photoconductive detectors can display a nonlinear response when illuminated. In interferometric applications, this behavior must be accounted for in the data transformation process to avoid errors in the measurement of the spectral distribution of the incident radiation. A model for the distortion of the interferogram is proposed and applied to solar observations made by the Atmospheric Trace Molecule Spectroscopy (ATMOS) Fourier-transform spectrometer during orbital sunrise and sunset from the Space Shuttle. Empirical estimation of the dc current level is necessary for this instrument, and satisfactory nonlinearity correction is obtained for several of the primary ATMOS optical filters. For ATMOS broadband optical filters that cover more than one half the alias bandwidth, the model is inadequate because of the presence of antialiasing electronic filters within the instrument, and it is necessary to resort to estimation and subtraction of the residual baseline offset. In either case the remaining base line offsets are typically smaller than 1%, which is satisfactory, although offset remains a significant systematic source of error in the estimation of the abundance of telluric and solar constituents from the spectra.     

Effects of infrared detector nonlinearity on thermal diffusivity measurements using the flash method

When using an infrared detector to measure temperature changes as in the case of the flash technique, the effects of detector nonlinearity can have drastic effects on the experimental data. In the flash technique, the detector nonlinearity tends to shift the calculated half-time to larger values, resulting in underpredicted values of thermal diffusivity especially in experiments performed at room temperature. In order to predict the error in the diffusivity calculation, the nonlinear relationship between the detector signal and the temperature change was developed into a Taylor series expansion used in the flash technique's mathematical model. The nonlinear detector model proves to yield accurate correction factors for the presently calculated values of diffusivity. In order to utilize the model, it is necessary to estimate the maximum temperature rise of the back surface and the degree of detector nonlinearity.     

Correction of detector nonlinearity for the balloonborne Michelson Interferometer for Passive Atmospheric Sounding

The detectors used in the cryogenic limb-emission sounder MIPAS-B2 (Michelson Interferometer for Passive Atmospheric Sounding) show a nonlinear response, which leads to radiometric errors in the calibrated spectra if the nonlinearity is not taken into account. In the case of emission measurements, the dominant error that arises from the nonlinearity is the changing detector responsivity as the incident photon load changes. The effect of the distortion of a single interferogram can be neglected. A method to characterize the variable responsivity and to correct for this effect is proposed. Furthermore, a detailed error estimation is presented.     

Wind-velocity lidar measurements by use of a Mach-Zehnder interferometer, comparison with a Fabry-Perot interferometer

We present the first wind-velocity profiles obtained with a direct-detection Doppler lidar that uses a Mach-Zehnder interferometer (MZI) as spectral discriminator. The measurements were performed in the lower stratosphere, between 10 and 40 km in altitude, at the Observatoire de Haute Provence (OHP), France, during nighttime. They are in excellent agreement with those obtained simultaneously and independently with the already validated double Fabry-Perot interferometer (FPI) of the OHP Doppler lidar (mean difference lower than the combined standard deviation). A statistical analysis shows that the random error obtained with this experimental MZI is 1.94 times the Cramer-Rao lower bound and is approximately half of that given by the FPI (both operating in photometric mode). Nevertheless, the present MZI measurements are sensitive to the presence of atmospheric particles and need an additional correction, whereas the OHP FPI is designed to be insensitive to particulate scattering.     

Effects of detector nonlinearity and specimen size on the apparent thermal diffusivity of NIST 8425 graphite

With the use of a graphite thermal conductivity standard it is demonstrated that optical detector non-linearity, coupled with excessive laser pulse energies, is primarily responsible for the anomalous specimen size dependence of the thermal diffusivity measured by the laser-pulse technique. High laser pulse energies also result in an anomalous positive temperature dependence for thin specimens near room temperature, in contrast to the expected negative temperature dependence. Using moderately thick specimens and attenuated laser pulses yields excellent agreement with thermal diffusivity calculated from standard thermal conductivity data.     

Solution of the Poisson equation by differential quadrature

The method of differential quadrature is demonstrated by solving the two-dimensional Poisson equation. The results for three test problems are compared with the exact analytical solutions and the numerical solutions obtained by others for the Galerkin, the control-volume and the five-point finite difference methods. The method of differential quadrature leads to more accurate results for comparable levels of computational effort.     

Improvement in the rejection rate of a nulling interferometer by spatial filtering

We propose applying the techniques of spatial filtering to the concept of interferometric coronography. In such a system, provided that the object being studied is not resolved by the individual apertures of the interferometric array, the beams can be considered as coherent or, more exactly, single mode. Hence spatial filtering allows one to cleanse the beams of imperfections generated by defects on the optical components of the interferometer and thus to obtain very high rejection rates in the destructive output of the interferometer (coronographic output) for an on-axis star. Numerical simulations show that the very stringent constraints on the optical quality of a space IR interferometer aimed at detecting extrasolar planets can be relaxed to values achievable with current technology. In particular, we show that the difficulties induced by dust scattering, small micrometeorite impacts on the primary mirror, and high-frequency ripples of polishing residuals can be eliminated by simple pinhole spatial filtering. The effects, however, will be less dramatic on large-scale defects such as coating defects and pointing errors in the telescopes.