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Corrective image deconvolution of smearing caused by extended instrument functions in optical imaging possible by holographic Fourier transform division
This work presents a theoretical framework for the propagation of partially coherent Gaussian radiation in a modified Mach–Zehnder interferometer designed for Fourier transform spectroscopy (FTS) applications. Using the Wigner function formalism, we analytically propagate the radiation through the system and benchmark our approach by comparing the resulting interference pattern and interferogram with previous works in the diffraction limit. Our analysis reveals that the transverse coherence length requirement of the incident light field for detectable modulation is less stringent than previously assumed. Additionally, we provide theoretical demonstrations of FTS performance across various wavelengths using the proposed setup. These findings underscore the potential of this interferometer to achieve high-resolution FTS in the soft X-ray regime.
Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature, an unstable Fredholm integral equation of the first kind is solved. Fourier transform techniques are used to invert the integral after it is placed into a cross correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system are included. The instability of the ill-posed Fredholm equation is examined and a restoration procedure is included which smooths the resulting oscillations. With the recent availability and advances of fast Fourier transform (FFT) techniques, the method presented becomes very attractive in the evaluation of large quantities of data.
PDP-9 assembly language program and algorithm for fast Fourier transform
Fourier transform of focussed diffraction pattern to describe coherent optical systems with lenses
Optical imaging systems achieving aperture synthesis by lensless Fourier transform holography, noting X ray astronomy, ultrasonic and space applications
Fourier transform representation by approximations of ideal lens in coherent optical systems
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Fourier Transform Infrared Spectroscopy (FTIR) has been used to characterize inductively coupled CF4 plasmas in a GEC Reference Cell in-situ In examining these FTIR spectra, several assumptions and approximations of FTIR analysis are addressed. This includes the density dependence of cross-sections, non-linear effects in the addition of overlapping bands and the effect of spatial variations in density and temperature, This analysis demonstrates that temperatures extracted from MR spectra may provide a poor estimate of the true neutral plasma temperature. The FTIR spectra are dominated by unreacted CF, accounting for 40-60% of the gas products. The amount of CF4 consumption is found to have a marked dependence on power, and is nearly independent of pressure in the range of 10-50 mtorr. Small amounts of C2F6 are observed at low power. Also observed are etching products from the quartz window SiF4 COF2 and CO which occur in approximately equal ratios and together account for less than 10% of the gas. The concentrations of these species are nearly independent of pressure. CFx radicals are below the detection limit of this apparatus (approx. 1012/cc).
A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.
An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.
Researchers from a broad spectrum of scientific and engineering disciplines are increasingly using scattering-type near-field infrared spectroscopic techniques to characterize materials non-destructively with nanoscale spatial resolution. However, a sub-optimal understanding of a technique's implementation can complicate data interpretation and act as a barrier to entering the field. Here the key detection and processing steps involved in producing scattering-type near-field nanoscale Fourier transform infrared spectra (nano-FTIR) are outlined. The self-contained mathematical and experimental work derives and explains: i) how normalized complex-valued nano-FTIR spectra are generated, ii) why the real and imaginary components of spectra qualitatively relate to dispersion and absorption respectively, iii) a new and generally valid equation for spectra which can be used as a springboard for additional modeling of the scattering processes, and iv) an algebraic expression that can be used to extract an approximation to the sample's local extinction coefficient from nano-FTIR. The algebraic model for weak oscillators is validated with nano-FTIR and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectra on samples of polystyrene and Kapton and further provides a pedagogical pathway to cementing some of the technique's key qualitative attributes.
Explicit inverse Fourier transformation of rational function with new theorem
Multispectral and multitemporal digital imagery spatial registration using fast Fourier transform techniques, applying to earth resources satellite imagery preprocessing
A detailed and complete description of Winograd's discrete Fourier transform algorithm (DFT) is presented omitting all proofs and derivations. The algorithm begins with the transfer of data from the input vector array to the working array where the actual transformation takes place, otherwise known as input scrambling and output unscrambling. The third array holds constraints required in the transformation stage that are evaluated in the precomputation stage. The algorithm is made up of several FORTRAN subroutines which are not to be confused with practical software algorithmic implementation since they are designed for clarity and not for speed.
The NASA New Millennium Program's Geostationary Imaging Fourier Transform Spectrometer (GIFTS) requires highly accurate radiometric and spectral calibration in order to carry out its mission to provide water vapor, wind, temperature, and trace gas profiling from geostationary orbit. A calibration concept has been developed for the GIFTS Phase A instrument design. The in-flight calibration is performed using views of two on-board blackbody sources along with cold space. A radiometric calibration uncertainty analysis has been developed and used to show that the expected performance for GIFTS exceeds its top level requirement to measure brightness temperature to better than 1 K. For the Phase A GIFTS design, the spectral calibration is established by the highly stable diode laser used as the reference for interferogram sampling, and verified with comparisons to atmospheric calculations.
This paper presents the design and implementation of the Discrete Fourier Transform (DFT) algorithm on a reconfigurable processor system. While highly applicable to many engineering problems, the DFT is an extremely computationally intensive algorithm. Consequently, the eventual goal of this work is to enhance the execution of a floating-point precision DFT algorithm by off loading the algorithm from the computing system. This computing system, within the context of this research, is a typical high performance desktop computer with an may of field programmable gate arrays (FPGAs). FPGAs are hardware devices that are configured by software to execute an algorithm. If it is desired to change the algorithm, the software is changed to reflect the modification, then download to the FPGA, which is then itself modified. This paper will discuss methodology for developing the DFT algorithm to be implemented on the FPGA. We will discuss the algorithm, the FPGA code effort, and the results to date.
The geosynchronous-imaging Fourier transform spectrometer (GIFTS) engineering demonstration unit (EDU) is an imaging infrared spectrometer designed for atmospheric soundings. It measures the infrared spectrum in two spectral bands (14.6 to 8.8 microns, 6.0 to 4.4 microns) using two 128 128 detector arrays with a spectral resolution of 0.57/cm with a scan duration of approx. 11 seconds. From a geosynchronous orbit, the instrument will have the capability of taking successive measurements of such data to scan desired regions of the globe, from which atmospheric status, cloud parameters, wind field profiles, and other derived products can be retrieved. The GIFTS EDU provides a flexible and accurate testbed for the new challenges of the emerging hyperspectral era. The EDU ground-based measurement experiment, held in Logan, Utah during September 2006, demonstrated its extensive capabilities and potential for geosynchronous and other applications (e.g., Earth observing environmental measurements). This paper addresses the experiment objectives and overall performance of the sensor system with a focus on the GIFTS EDU imaging capability and proof of the GIFTS measurement concept.