Resolution Enhancement of Spectra
01 May 1970-Journal of the Optical Society of America (Optical Society of America)-Vol. 60, Iss: 5, pp 596-599
TL;DR: In this paper, a numerical method was developed to correct high-resolution infrared spectra for the distortion introduced by the spectrometer, which involves, first, an accurate determination of the response function and, then, deconvolution by a point-successive over-relaxation procedure.
Abstract: A numerical method has been developed to correct high-resolution infrared spectra for the distortion introduced by the spectrometer. The method involves, first, an accurate determination of the spectrometer response function and, then, deconvolution by a point-successive over-relaxation procedure. The method is applied to portions of the Q branches N2O and CH4 near 3.3 μ. The spectra are observed at pressures below 1.0 torr with spectrometer response-function half-widths less than 0.02 cm−1. The deconvolved spectra show an improvement of resolution which approaches the limit set by the Doppler widths of the lines. Line separations measured from the deconvolved spectra are within 0.001 cm−1 of the calculated values. The reduction of line overlap in the deconvolved spectra considerably increases the number of lines whose positions may be accurately measured.
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TL;DR: Parts of image processing are discussed--specifically: the mathematical operations one is likely to encounter, and ways of implementing them by optics and on digital computers; image description; and image quality evaluation.
Abstract: Image processing techniques find applications in many areas, chief among which are image enhancement, pattern recognition, and efficient picture coding. Some aspects of image processing are discussed--specifically: the mathematical operations one is likely to encounter, and ways of implementing them by optics and on digital computers; image description; and image quality evaluation. Many old results are reviewed, some new ones presented, and several open questions are posed.
2,961 citations
TL;DR: In this article, the Fourier self-deconvolution (FDS) method was proposed to resolve overlapped lines that can not be instrumentally resolved due to their intrinsic linewidth.
Abstract: The general theory of Fourier self-deconvolution, i.e., spectral deconvolution using Fourier transforms and the intrinsic line-shape, is developed. The method provides a way of computationally resolving overlapped lines that can not be instrumentally resolved due to their intrinsic linewidth. Examples of the application of the technique to synthetic and experimental infrared spectra are presented, and potential applications are discussed. It is shown that lines in spectra having moderate signal/noise ratios (∼1000) can readily be reduced in width by a factor of 3. The method is applicable to a variety of spectroscopic techniques.
1,213 citations
TL;DR: This chapter has discussed the nature of image formation in three dimensions and dealt with several means to remove contaminating out-of-focus information and developed a method for extremely rapidly and accurately producing an in-focus, high-resolution "synthetic projection" image from a thick specimen.
Abstract: The combination of the specificity provided by fluorescence microscopy and the ability to quantitatively analyze specimens in three dimensions allows the fundamental organization of cells to be probed as never before Key features in this emergent technology have been the development of a wide variety of fluorescent dyes or fluorescently labeled probes to provide the requisite specificity High-quality, cooled charge-coupled devices have recently become available Functioning as nearly ideal imagers or "electronic film," they are more sensitive than photomultipliers and provide extraordinarily accurate direct digital readout from the microscope Not only is this precision crucial for accurate quantitative imaging such as that required for the ratioing necessary to determine intracellular ion concentrations, but it also opens the way for sophisticated image processing It is important to realize that image processing isn't simply a means to improve image aesthetics, but can directly provide new, biologically important information The impact of modern video microscopy techniques (Allen, 1985; Inoue, 1986) attests to the fact that many biologically relevant phenomena take place at the limits of conventional microscopy Image processing can be used to substantially enhance the resolution and contrast obtainable in two dimensions, enabling the invisible to be seen and quantitated Cells are intrinsically three-dimensional This can simply be a nuisance because of limited depth of focus of the microscope or it could be a fundamental aspect of the problem being studied In either case, image processing techniques can be used to rapidly provide the desired representation of the data In this chapter we have discussed the nature of image formation in three dimensions and dealt with several means to remove contaminating out-of-focus information The most straightforward of these methods uses only information from adjacent focal planes to correct the central one This approach can be readily applied to virtually any problem and with most commonly available image processing hardware to provide a substantially deblurred image in almost real time In addition to covering more sophisticated algorithms where the utmost in three-dimensional imaging is required, we have developed a method for extremely rapidly and accurately producing an in-focus, high-resolution "synthetic projection" image from a thick specimen This is equivalent to that produced by a microscope having the impossible combination of a high-NA objective lens and an infinite depth of focus A variation on this method allows efficient calculation of stereo pairs(ABSTRACT TRUNCATED AT 400 WORDS)
702 citations
TL;DR: A communication-theory model for the process of image formation is used and it is found that the most likely object has a maximum entropy and is represented by a restoring formula that is positive and not band limited.
Abstract: Given M sampled image values of an incoherent object, what can be deduced as the most likely object? Using a communication-theory model for the process of image formation, we find that the most likely object has a maximum entropy and is represented by a restoring formula that is positive and not band limited. The derivation is an adaptation to optics of a formulation by Jaynes for unbiased estimates of positive probability functions. The restoring formula is tested, via computer simulation, upon noisy images of objects consisting of random impulses. These are found to be well restored, with resolution often exceeding the Rayleigh limit and with a complete absence of spurious detail. The proviso is that the noise in each image input must not exceed about 40% of the signal image. The restoring method is applied to experimental data consisting of line spectra. Results are consistent with those of the computer simulations.
673 citations
01 Apr 1981
TL;DR: It is shown that by predistorting the signal (and later removing this predistortion) it is possible to achieve spectral extrapolation, to broaden the class of signals for which these algorithms achieve convergence, and to improve their performance in the presence of broad-band noise.
Abstract: This paper describes a rather broad class of iterative signal restoration techniques which can be applied to remove the effects of many different types of distortions. These techniques also allow for the incorporation of prior knowledge of the signal in terms of the specification of a constraint operator. Conditions for convergence of the iteration under various combinations of distortions and constraints are explored. Particular attention is given to the use of iterative restoration techniques for constrained deconvolution, when the distortion band-limits the signal and spectral extrapolation must be performed. It is shown that by predistorting the signal (and later removing this predistortion) it is possible to achieve spectral extrapolation, to broaden the class of signals for which these algorithms achieve convergence, and to improve their performance in the presence of broad-band noise.
465 citations
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17,427 citations
TL;DR: In this paper, a Methode wird angegeben, um mit Hilfe der Intensitatsverteilung, welche ein Spektrograph fur vollkommen monochromatisches Licht geben wurde, aus der beobachteten „scheinbaren VerteILung“ die „wahre Verteilings“ zu berechnen.
Abstract: Eine Methode wird angegeben, um mit Hilfe der Intensitatsverteilung, welche ein Spektrograph fur vollkommen monochromatisches Licht geben wurde (die „Apparatsverteilung“) aus der beobachteten „scheinbaren Verteilung“ die „wahre Verteilung“ zu berechnen. Fur die Apparatsverteilung wird ein Ausdruck gegeben, welcher fur sehr viele Falle gultig ist. — Der Fall, das das Prisma eines Prismenspektrographen absorbierend ist, wird diskutiert. Gezeigt wird, das man mit stark absorbierenden Prismen betrachtlich verbreiterte Linien beobachtet, und das man fur die Beobachtung des ausersten Ultravioletts mit einem Quarzspektrographen mit Vorteil sehr scharfe Prismen verwenden kann.
442 citations
TL;DR: In this article, a method for determining the response function of an infrared spectrometer under the usual running condition of partially coherent illumination from a thermal source was developed, which consists of deconvolving observed absorption lines of known Doppler shape.
Abstract: A method has been developed for determining the response function of an infrared spectrometer under the usual running condition of partially coherent illumination from a thermal source. The method consists of deconvolving observed absorption lines of known Doppler shape. Only the sample-gas temperature, molecular weight, absorption-line frequency, and equivalent width are needed to construct the true absorptance profile. The response function of a high-resolution spectrometer has been determined by this method at several frequencies in the 3-μ region. It ranged from 0.014 cm−1 to 0.020 cm−1 in width and was typically 6%–20% narrower than the observed absorption line. The entire process was carried out automatically in the computer, with absorptance data in digital form. A procedure due to P. H. van Cittert, which is often used for resolution enhancement, is shown to be a special case of the more-general and efficient relaxation technique used in this study.
88 citations
TL;DR: In this paper, the authors measured the center frequencies of some absorption lines in the HF fundamental and first-overtone bands and measured the pressure-broadened shapes of some lines.
Abstract: The spectrometer and experimental methods described in a companion paper were used to measure the center frequencies of some absorption lines in the HF fundamental and first-overtone bands and to measure the pressure-broadened shapes of some lines in the fundamental. The centers of both bands were calculated, and strongly J-dependent, pressure-induced line center shifts were measured for the fundamental. A method for correcting the measured shape of a spectral line for the effects of instrumental broadening in order to obtain the “true shape” is explained. It was possible to obtain the true shape of lines whose pressure broadened half-width was as small (0.03 cm−1) as several times the Doppler half-width.It was found that the true line shape could be represented quite satisfactorily by a modified form of the Lorentz expression, i.e., α=α0(Δν)2[|ν−ν0|η+(Δν)2]−1. For spectral lines whose half-width at one-half the maximum percent absorptance was less than 2.25 cm−1, η=2 gave good agreement between the true shape and that predicted by the Lorentz expression. If this width was greater than 3 cm−1 then η=1.85 allowed the best fit to the true line shape. No pressure dependence of η could be measured in the range of pressures used (0–5 atm).
87 citations
TL;DR: In this paper, the frequencies of the tetrahedral fine structure components of the rotational lines of the fundamental ν 3 of CH 4 were derived using the matrix elements derived in the first paper of this series.
84 citations