Effects of a nonlinear response of the fourier-transform infrared open-path instrument on the measurements of some atmospheric gases

The response of a Fourier-transform infrared (FTIR) instrument to changes in absorbance is inherently nonlinear for a number of reasons. One is that the interferogram acquired by the FTIR is truncated and then apodized before further processing of the data is accomplished. A commonly used apodization function in open-path FTIR research is triangular apodization, and all the research presented here has been done with that function. We calculated a set of absorption spectra by using the HITRAN database, covering ranges in both concentration and temperature for water, ammonia, and methane. Plots of these data reveal nonlinear results. The commonly used analysis technique, classical least squares, assumes that the response is linear. We describe some of the effects of this nonlinearity and present ways to address these effects.     

Effects of apodization on a holographic demultiplexer based on a photopolymer grating

An investigation of the effects of apodization on a holographic demultiplexer that is based on a photopolymer grating is presented. Uniform and Gaussian apodized gratings are fabricated in a DuPont HRF-150-38 photopolymer. From the theoretical and experimental results, the spectral response of the apodized grating has a larger main lobe but lower sidelobes than those in the uniform-grating case. A 42-channel demultiplexer that is based on the Gaussian apodized grating with an 0.4-nm channel spacing is demonstrated. A cross-talk level of -30 dB and an interchannel uniformity of 1.5 dB are archived in the wavelength range of approximately 1550 nm.     

Reconstruction of fiber grating refractive-index profiles from complex bragg reflection spectra

Reconstruction of the refractive-index profiles of fiber gratings from their complex Bragg reflection spectra is experimentally demonstrated. The amplitude and phase of the complex reflection spectrum were measured with a balanced Michelson interferometer. By integrating the coupled-mode equations, we built the relationship between the complex coupling coefficient and the complex reflection spectrum as an iterative algorithm for reconstructing the index profile. This method is expected to be useful for reconstructing the index profiles of fiber gratings with any apodization, chirp, or dc structures. An apodized chirped grating and a uniform grating with a depression of index modulation were used to demonstrate the technique.     

Effect of apodization on the retrieval of geophysical parameters from fourier-transform spectrometers

The problem of the effect of apodization on the retrieval of geophysical parameters from infrared radiances recorded by Fourier transform spectrometers has been analytically and numerically addressed. Exploiting a matrix representation of apodization, we first derive a general analytical expression for the apodized covariance matrix and then show that apodization, when properly applied, has no effect on retrievals. The methodology has been applied to investigate the effect of Gaussian apodization on the Infrared Atmospheric Sounding Interferometer currently under development at the laboratories of the French Space Agency.     

Apodized pixel lenses in compact shadow-casting correlators

We present a compact two-dimensional shadow-casting correlator that can perform correlation between inputs of size 256 × 256 and a point-spread function of size 32 × 32. A two-dimensional array of mutually incoherent sources is used to encode the point-spread function, and each source is individually steered to improve the light uniformity and the light-utilization efficiency. The geometric optics constraint requires that the shadow region be very close to the input plane. This constraint is removed by the introduction of apodized pixel lenses in the input spatial light modulator. The pixel lenses move the shadow plane to their Fourier plane, and pixel apodization reduces the interchannel cross talk, thereby improving the signal-to-noise ratio. Simulation and experimental results verifying these concepts are presented.     

Defect of focus in two-line resolution with Hanning amplitude filters

In the presence of defocusing the modified Sparrow limits of resolution for two-line objects have been investigated for a diffraction-limited coherent optical system apodized by generalized Hanning amplitude filters. These limits have been studied as a function of different parameters such as intensity ratio, the order of the filter for various amounts of apodization parameter. Results reveal that in some situations the defocusing is effective in enhancing the resolution of an optical system.     

Design of SAW bandpass filters using new window functions

Simple analytical expressions involving Bessel functions are obtained for various window functions. Some of the windows take the form of Kaiser-Bessel and Dolph-Chebyshev functions. The performance of various windows is evaluated with respect to shape factor and sidelobe level. Design data is presented for designing the surface acoustic-wave (SAW) filters using smooth window functions. The design of SAW filters using sin (t)/t-type apodization profile is outlined for various window functions. For given filter specifications, such as center frequency, 3-dB bandwidth, shape factor, and sidelobe level, the design procedure is used to compute the apodized transducer length and apodization profile.     

Self-apodization of low-resolution pixelated lenses

We show that a pixelated lens with appropriate parameters exhibits an apodized point-spread function that originates in the finite size of the pixel's pupil. We evaluate numerically the degree of apodization and the enlargement associated with the point-spread function in terms of the parameters that characterize the pixelated lens.     

A sensor structure for terahertz data-measuring technologies

An integrated terahertz radiation sensor based on apodized and chirped with apodization open resonance microstructures is proposed. It is shown that by choosing the structure and optimizing its structural parameters one can obtain a simple compact receiver of terahertz radiation with an electromagnetic wave conversion efficiency of 91.23% in the 0.55–0.78 THz spectral range.     

Aberration limits for annular Gaussian beams for optical storage

Annularly apodized beams have been suggested for use in optical storage because of their potential to go beyond the conventional spot size and depth-of-focus limits. One concern for such applications is the effects of small aberrations on beams in which the energy is concentrated in a small annular ring. We present calculations and experimental results that show that annular apodization of a Gaussian beam reduces the sensitivity to defocus as well as balanced spherical and coma aberrations. The sensitivity to astigmatism is increased by a small amount.     

Determination of the resolution of a multichannel Raman spectrometer using Fourier transform Raman spectra

The resolution of a grating polychromator for Raman spectroscopy has been simulated by measuring spectra on a Fourier transform (FT) Raman spectrometer and selecting the FT of the apodization function so that the instrument line shape function mimics the triangular spectral slit function of the polychromator. To this end, FT-Raman spectra measured with a nominal resolution of 0.5 cm-1 were modified through the application of sinc2 apodization functions of various widths to simulate spectra measured on a polychromator at lower resolution. The success of this approach was validated using the 1085 cm-1 band of calcite. When the modified FT-Raman spectra were compared with spectra measured on a grating polychromator equipped with slits of widths 100 and 150 microns, the resolution of the polychromator was estimated to be 6.3 and 7.8 cm-1, respectively. This conclusion was verified experimentally by measuring the separation of two bands in the Raman spectrum of BaSO4 at approximately 460 cm-1.     

Porous silicon-based rugate filters

We report an experimental study of porous silicon-based rugate filters. We performed filter apodization, following a half-apodization approach, which successfully attenuated the sidelobes at both sides of the photonic stop band. We achieved successful reduction of interference ripples through the insertion of index-matching layers on the first and last interfaces. An apodized dielectric mirror and a rugate filter are compared: Appreciable differences in the harmonic presence and stop-band performance were observed and are commented on. Bandwidth control when index contrast is modified is also demonstrated. Finally, the possibility of combining different rugate filter designs to attain more complex responses is demonstrated by the achievement of a multi-stop-band filter. Numerical calculations for design optimization and comparison with experimental data are reported too.     

Performance of Apodized Apertures under Partially Coherent Illumination

The performance characteristics of optical systems having apodized apertures and employing partially coherent illumination have been investigated. The pupil function has been taken to be of the form f(x y) = 1 m g (x 2 + y 2), where g is the amplitude shading parameter of the filter. The generalized cross-transfer functions for the system have been calculated for different values of the coherence parameter which is the ratio of the numerical aperture of the condenser to that of the objective. The modulations of periodic targets commonly employed, namely, the sine wave, square wave and triangular wave objects, have also been investigated. It has been shown that for the partially coherent and the incoherent illuminations ( S 1) the apodization improves the low frequency response at a cost of the high frequency response of the system. However, for coherent and near coherent illuminations (     

Analytic diffraction analysis of a 32-m telescope with hexagonal segments for high-contrast imaging

Large segmented telescopes cannot be modeled accurately with fast-Fourier-transform techniques since small features such as gaps between the segments will be inadequately sampled. An analytic Fourier-transform method can be used to model any pupil configuration with straight edges, including tolerance analysis and some types of apodization. We analytically investigated a 32-m segmented primary with 18 hexagonal segments for high-contrast imaging. There are significant regions in the image in which extrasolar planets could be detected. However, the hexagonal profile of the pupil was not as useful as expected. The gaps between the segments, the secondary obscuration, and the secondary spiders must be as small as possible and their edges must be apodized. Apodizing the edges of the individual segments reduced the useful regions in the image since the gaps appeared to be wider.     

Spatial coherence of the nonlinearly generated second harmonic portion of backscatter for a clinical imaging system

Correlation-based approaches to phase aberration correction rely on the spatial coherence of backscattered signals. The spatial coherence of backscatter from speckle-producing targets is predicted by the auto correlation of the transmit apodization (Van Cittert-Zernike theorem). Work by others indicates that the second harmonic beam has a wider mainlobe with lower sidelobes than a beam transmitted at 2f. The purpose of this paper is to demonstrate that the spatial coherence of backscatter for the second harmonic is different from that of the fundamental, as would be anticipated from applying the Van Cittert-Zernike theorem to the reported measurements of the second harmonic field. Another objective of this work is to introduce the concept of the effective apodization and to verify that the effective apodization of the second harmonic is narrower than the transmit apodization. The spatial coherence of backscatter was measured using three clinical arrays with a modified clinical imaging system. The spatial coherence results were verified using a pseudo-array scan in a transverse plane of the transmitted field with a hydrophone. An effective apodization was determined by backpropagating these values using a linear angular spectrum approach. The spatial coherence for the harmonic portion of backscatter differed systematically and significantly from the auto correlation of the transmit apodization.     

Sidelobe suppression in ultrasound imaging using dual apodization with cross-correlation

This paper introduces a novel sidelobe and clutter suppression method in ultrasound imaging called dual apodization with cross-correlation or DAX. DAX dramatically improves the contrast-to-noise ratio (CNR) allowing for easier visualization of anechoic cysts and blood vessels. This technique uses dual apodization or weighting strategies that are effective in removing or minimizing clutter and efficient in terms of computational load and hardware/software needs. This dual apodization allows us to determine the amount of mainlobe versus clutter contribution in a signal by cross-correlating RF data acquired from 2 apodization functions. Simulation results using a 128 element 5 MHz linear array show an improvement in CNR of 139% compared with standard beamformed data with uniform apodization in a 3 mm diameter anechoic cylindrical cyst. Experimental CNR using a tissue-mimicking phantom with the same sized cyst shows an improvement of 123% in a DAX processed image.     

Spatial coherence of backscatter for the nonlinearly produced second harmonic for specific transmit apodizations

To be successful, correlation-based, phase-aberration correction requires a high correlation among backscattered signals. For harmonic imaging, the spatial coherence of backscatter for the second harmonic component is different than the spatial coherence of backscatter for the fundamental component. The purpose of this work was to determine the effect of changing the transmit apodization on the spatial coherence of backscatter for the nonlinearly generated second harmonic. Our approach was to determine the effective apodizations for the fundamental and second harmonic using both experimental measurements and simulations. Two-dimensional measurements of the transverse cross sections of the finite-amplitude ultrasonic fields generated by rectangular and circular apertures were acquired with a hydrophone. Three different one-dimensional transmit apodization functions were investigated: uniform, Riesz, and trapezoidal. An effective apodization was obtained for each transmit apodization by backpropagating the values measured from within the transmit focal zone using a linear angular spectrum approach. Predictions of the spatial coherence of backscatter were obtained using the pulse-echo Van Cittert-Zernike theorem. In all cases the effective apodization at 2f was narrower than the transmit apodization. We demonstrate that certain transmit apodizations result in a greater spatial coherence of backscatter at the second harmonic than at the fundamental.     

Correction of phase distortion in spatial heterodyne spectroscopy

The detailed analysis of measured interferograms generally requires phase correction. Phase-shift correction methods are commonly used and well documented for conventional Fourier-transform spectroscopy. However, measured interferograms can show additional phase errors, depending on the optical path difference and signal frequency, which we call phase distortion. In spatial heterodyne spectroscopy they can be caused, for instance, by optical defects or image distortions, making them a characteristic of the individual spectrometer. They can generally be corrected without significant loss of the signal-to-noise ratio. We present a technique to measure phase distortion by using a measured example interferogram. We also describe a technique to correct for phase distortion and test its performance by using a simulation with a near-UV solar spectrum. We find that for our measured example interferogram the phase distortion is small and nearly frequency independent. Furthermore, we show that the presented phase-correction technique is especially effective for apodized interferograms.     

Admittance matrix of a surface acoustic wave interdigital transducer

The admittance matrix of a surface acoustic wave interdigital transducer (IDT) is derived from the impulse response model and circuit theory. It is shown, that Y(23)=Y(13) for a symmetrical IDT and Y(23)-Y(13) for an antisymmetrical one. A simple algorithm for the input admittance calculation of apodized IDTs is given. The proposed algorithm is also capable of analyzing withdrawally weighted, withdrawally weighted and apodized, and unapodized IDTs. Calculations of an apodized IDT input admittance are compared with measurements.