Two-dimensional Fourier-transform techniques for the analysis of hook interferograms

Hook interferometry is widely used for the measurement of atomic oscillator strengths and atomic energy level populations. The application of Fourier-transform techniques to the analysis of hook interferograms leads to greater precision in the determination of hook separations and is of particular benefit to the detection of small spatial population density gradients in the medium under investigation.     

Fourier-transform spectroscopy: new methods and applications: introduction by the feature editors

We are pleased to introduce this special issue of papers on Fourier-transform spectroscopy, which grew out of a recent topical meeting sponsored by the Optical Society of America. The topical meeting welcomed all researchers who practice the art of Fourier-transform spectroscopy in the laboratory, in the atmosphere, and in space. The power and the wide applicability of Fourier-transform spectroscopy unite these fields with a common mathematical and instrumental bond. The meeting probed each of these areas in depth, bringing out new ideas for instrumentation, analysis, and applications. There was a strong sentiment at the meeting that the quality of papers and posters was exceptionally high and that it would be important for future progress in the field to have the results of this meeting captured in print. This special issue is the fruit of that effort.     

Fourier-transform method of data compression and temporal fringe pattern analysis

Temporal fringe pattern analysis is invaluable in studies of transient phenomena but necessitates large data storage for two essential sets of data, i.e., fringe pattern intensity and deformation phase. We describe a compression scheme based on the Fourier-transform method for temporal fringe data storage that permits retrieval of both the intensity and the deformation phase. When the scheme was used with simulated temporal wavefront interferometry intensity fringe patterns, a high compression ratio of 10.77 was achieved, with a significant useful data ratio of 0.859. The average root-mean-square error in phase value restored was a low 0.0015 rad. With simulated temporal speckle interferometry intensity fringe patterns, the important paremeters varied with the modulation cutoff value applied. For a zero modulation cutoff value, the ratio of data points and the compression ratio values obtained were roughly the same as in wavelength interferometry, albeit the average root-mean-square error in the phase value restored was far higher. By increasing the modulation cutoff value we attained significant reduction and increase in the ratio of data points and the compression ratio, respectively, whereas the average root-mean-square error in the restored phase values was reduced only slightly.     

Fourier-transform laser spectroscopy

The development of microphotonic sensors based on Fourier-transform laser spectroscopy (FT-LS) is discussed. The application demonstrated is for measurement of vapors from the hydrocarbon fuels JP-8, diesel fuel, and gasoline. The two-laser prototype FT-LS sensor used for our research employs distributed-feedback lasers in the near-infrared spectral region (1.3- and 1.7-microm wavelength). An extension of this research to multilaser arrays is discussed. We believe that this is the first measurement of middle-distillate fuel-vapor concentrations using this optical mixing technique.     

Hybrid sampling approach for imaging Fourier-transform spectrometry

A new approach to interferogram sampling is demonstrated for Fourier-transform spectrometry. Sampling of the infrared channel is triggered at equidistant optical path differences while samples are time-referenced with a high-resolution digital clock. This hybrid method exploits the advantages of both time and position-sampling techniques. It minimizes the dataload while allowing a postcorrection scheme to remove sampling errors. It is therefore highly adapted to imaging spectrometers designed for massively parallel spatial sampling. Also, this technique is particularly interesting for spectrometers equipped with an integrating detector, such as a CCD camera, since it can account for the inevitable delay caused by camera integration.     

Static Fourier-transform ultraviolet spectrometer for gas detection

We report the design, construction, and evaluation of a static Fourier-transform ultraviolet spectrometer. The spectrometer is based on Wollaston prisms that form an interferogram in the spatial domain, which is recorded with a detector array. We demonstrate the application of the spectrometer to gas detection. Using a deuterium light source, we measured a detection limit, with a 1-s integration time, for hydrogen sulfide and sulfur dioxide, corresponding to 0.2 ppm over a 5-m path length.     

Fourier-transform phase-shifting interferometry

Phase-shifting interferometry is a preferred technique for high-precision surface form measurements, but the difficulty in handling the intensity distortions from multiple-surface interference has limited the general use of the technique to interferometer cavities producing strict two-beam interference. I show how the capabilities of phase-shifting interferometry can be extended to address this problem using wavelength tuning techniques. The basic theory behind the technique is reviewed and applied specifically to the measurement of parallel plates, where surfaces, optical and physical thickness, and homogeneity are simultaneously obtained. Basic system requirements are derived, common error sources are discussed, and the results of the measurements are compared with theory and alternative measurement methods.     

Fast line-shape correction procedure for imaging Fourier-transform spectrometers

An instrument line-shape correction method adapted to imaging Fourier-transform spectrometers is demonstrated. The method calibrates all pixels on the same spectral grid and permits a direct comparison of the spectral features between pixels such as emission or absorption lines. Computation speed is gained by using matrix line-shape integration formalism rather than properly inverting the line shape of each pixel. A monochromatic source is used to characterize the spectral shift of each pixel, and a line-shape correction scheme is then applied on measured interferograms. This work is motivated by the emergence of affordable infrared CCD cameras that are currently being integrated in imaging Fourier-transform spectrometers.     

Practical wavelength calibration considerations for UV-visible Fourier-transform spectroscopy

The intrinsic wavelength scale in a modern reference laser-controlled Michelson interferometer-sometimes referred to as the Connes advantage-offers excellent wavelength accuracy with relative ease. Truly superb wavelength accuracy, with total relative uncertainty in line position of the order of several parts in 10(8), should be within reach with single-point, multiplicative calibration. The need for correction of the wavelength scale arises from two practical effects: the use of a finite aperture, from which off-axis rays propagate through the interferometer, and imperfect geometric alignment of the sample beam with the reference beam and the optical axis of the moving mirror. Although an analytical correction can be made for the finite-aperture effect, calibration with a trusted wavelength standard is typically used to accomplish both corrections. Practical aspects of accurate calibration of an interferometer in the UV-visible region are discussed. Critical issues regarding accurate use of a standard external to the sample source and the evaluation and selection of an appropriate standard are addressed. Anomalous results for two different potential wavelength standards measured by Fabry-Perot interferometry (Ar II and (198)Hg I) are observed.     

Solid-block stationary Fourier-transform spectrometer

A solid-block stationary Fourier-transform spectrometer (SBSFTS) is described that is applicable to a wide range of portable, moderate-resolution instrumentation needs that include the detection of temporally variant signatures. The SBSFTS is a low-cost, extremely rugged stationary Fourier-transform spectrometer based on the combination of three standard prism types. The SBSFTS uses a source-doubling, square-and-triangle common-path topology that is mechanically rugged, simple to align, and virtually immune to alignment perturbation. Its alignment stability makes it suitable for use in a variety of hostile operating environments. When coupled to a fiber-optic input, the spectrometer can be constructed in an extremely compact form. Experimental results have demonstrated the design and the performance of the spectrometer.     

High-resolution multimodulation Fourier-transform spectroscopy

High-resolution double-modulation Fourier-transform (FT) spectroscopy (FTS) is demonstrated for what is, to our knowledge, the first time. Two high-resolution FT interferograms are simultaneously recorded. The first one is nonselective and contains all the spectral information from the observed source, and the other one is made of the samples that are sensitive to only a specific source modulation. General formulations and practical recording procedures are given for phase- and intensity-modulated spectra. The advantage of selectivity is illustrated by velocity-modulated emission spectra of the Dv = 1 sequence of the Doppler-shifted ArH(+) ion. It is also shown that for a source perturbation of small amplitude, only the product of intensity x shift can be retrieved from the selective line shapes obtained in a phase-modulated laser or FT spectra. Thanks to the multimodulation FTS approach, the intensity and the shift of the transitions are measured in a single experiment.     

Fourier-transform instrument for high-resolution Raman spectroscopy of gases

An instrument is described for recording vibrational-rotational Raman spectra of gases with a resolution of 0.02-0.03 cm(-1). The Raman scattered light is collected by near forward scattering within the cavity of a single-mode, long-term, stabilized Ar-ion laser. The Raman light is analyzed in an ordinary step-scanned Michelson interferometer. To compensate for the low intensity of vibrational-rotational Raman spectra, the interferometer has a beam diameter of 160 mm. The movable mirror, weighing 2.7 kg, is mounted on a smoothly moving sledge, the stepwise motion being performed by three piezotranslators and controlled by three independent He-Ne laser beams. It is shown experimentally that it is possible for one to move the mirror with sufficient precision, using only 13% of the scan time in a typical experiment. In a preliminary spectrum of the fundamental vibration of(14) N(2), the width of the lines has been measured to 0.015 cm(-1).     

Retrievals for the atmospheric chemistry experiment Fourier-transform spectrometer

SCISAT-1, also known as the Atmospheric Chemistry Experiment, is a satellite mission for remote sensing of the Earth's atmosphere, launched on 12 August 2003. The primary instrument on the satellite is a 0.02 cm(-1) resolution Fourier-transform spectrometer operating in the mid-IR (750-4400 cm(-1)). We describe the approach developed for the retrieval of atmospheric temperature and pressure from the troposphere to the lower thermosphere as well as the strategy for the retrievals of volume-mixing ratio profiles of atmospheric species.     

Ghosts and artifacts in Fourier-transform spectrometry

Ghosts in Fourier-transform spectrometry are important for three reasons: they can give rise to spurious coincidences of frequency differences in spectral analysis, distort the phase correction, and set a limit to the attainable signal-to-noise ratio. The various types of ghost, originating from amplitude modulation, phase modulation, and intermodulation, are described and discussed, together with some hardware and software artifacts. Recipes are given for identifying these features and, where possible, avoiding harmful effects from them.     

Extreme-ultraviolet lensless Fourier-transform holography

We demonstrate 100-nm-resolution holographic aerial image monitoring based on lensless Fourier-transform holography at extreme-UV (EUV) wavelengths, using synchrotron-based illumination. This method can be used to monitor the coherent imaging performance of EUV lithographic optical systems. The system has been implemented in the EUV phase-shifting point-diffraction interferometer recently developed at Lawrence Berkeley National Laboratory. Here we introduce the idea of the holographic aerial image-recording technique and present imaging performance characterization results for a 10x Schwarzschild objective, a prototype EUV lithographic optic. The results are compared with simulations, and good agreement is obtained. Various object patterns, including phase-shift-enhanced patterns, have been studied. Finally, the application of the holographic aerial image-recording technique to EUV multilayer mask-blank defect characterization is discussed.     

Compact liquid-crystal-polymer Fourier-transform spectrometer

We present the optical design and realization of a low-resolution liquid-crystal (LC) Fourier-transform spectrometer (FTS). This FTS is based on a polarization interferometer that has a Wollaston prism made of a LC material as a key component. It has a compact design, a good acceptance angle, and low temperature dependence and can be fabricated with cost-effective LC technology. Because the LC is polymerized, it is robust, and the temperature dependence is drastically reduced. The performance of a compact handheld version of the spectrometer and the characteristics (angular dependence, resolution, stray light, and temperature dependence) will be discussed.     

Diffraction and line shape of Fourier-transform spectrometers

The effect of diffraction the instrument line shape of a Fourier-transform spectrometer is studied with an analytical line-shape model. The expression for the instrument line shape of a diffracted point source is obtained. A simple condition on the throughput of the instrument is derived under which diffraction is negligible when compared with the field-of-view-induced line shape. The effect of diffraction is illustrated and compared for various instruments.     

Fourier-transform method of phase-shift determination

A new phase-shifting interferometry analysis technique has been developed to overcome the errors introduced by nonlinear, irregular, or unknown phase-step increments. In the presence of a spatial carrier frequency, by observation of the phase of the first-order maximum in the Fourier domain, the global phase-step positions can be measured, phase-shifting elements can be calibrated, and the accuracy of phase-shifting analysis can be improved. Furthermore, reliance on the calibration accuracy of transducers used in phase-shifting interferometry can be reduced; and phase-retrieval errors (e.g., fringe print-through) introduced by uncalibrated fluctuations in the phase-shifting phase increments can be alleviated. The method operates deterministically and does not rely on iterative global error minimization. Relative to other techniques, the number of recorded interferograms required for analysis can be reduced.