A note on the general class of blackbody fractional functions

Johnson

2014

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The detected thermal contrast is a recently defined figure of merit introduced to describe the overall performance of a detector detecting radiation from a thermal source. We examine the detected thermal contrast for the case where the target emissivity can be assumed to be a function of the temperature and independent of the wavelength within a narrow wavelength interval of interest. Exact expressions are developed to evaluate the thermal contrast detected by both thermal and quantum detectors for focal-plane radiation detecting instruments. Expressions for the thermal contrast of a blackbody, an intrinsic radiative quantity of a body independent of the detection process, and simplified expressions for the detected thermal contrast for target emissivities which are well approximated by the grey body approximation are also given. It is found the contribution in the detected thermal contrast consists of two terms. The first results from changes occurring in the emissivity of a target with temperature while the second results from purely radiative processes. The size of the detected thermal contrast is found to be similar for the two detector types within typical infrared wavelength intervals of interest, contradicting a result previously reported in the literature. The exact results are presented in terms of a polylogarithmic formulation of the problem and extend a number of approximation schemes that have been proposed and developed in the past.

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Section: Actinometric Casementioning

confidence: 80%

Exact expressions for thermal contrast detected with thermal and quantum detectors

Johnson

2014

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“…(10) recently led two authors to mistakenly define it as a new fractional function, 60 something it is not. 36 …”

Section: Actinometric Casementioning

confidence: 99%

“…35,36 In terms of fundamental constants, the Stefan-Boltzmann constants can be shown to be equal to D 2 5 k 4 B =.15c 2 h 3 / and q D 4 k 3 B .3/=.c 2 h 3 / respectively. …”

Section: Ideal Thermal Detectormentioning

confidence: 99%

“…To facilitate the analytic treatment, a mathematical approach based on the recently introduced polylogarithmic formulation developed by the author is used. 35,36 Using such an approach we are able to develop closed-form expressions for the detected thermal contrast for either detector type in terms of the special function known as the polylogarithm function. 37 These represent a significant computational advance over previously used approximate schemes that have been developed in the past to calculate the detected thermal contrast.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the relative merits of the 3-5 μm and the 8-12 μm spectral bands using detected thermal contrast

2015

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The two most important atmospheric transmission bands in the infrared occur at 3-5 µm and 8-12 µm respectively. For a given infrared detector a common question that continues to be asked is, of the two spectral bands, which, if any, gives the better performance? While seemly an innocent enough question, the literature attests it has not been without controversy. Conflicting and often contradictory results have been given that tend to reflect the predilections of the proponent rather than any sort of measured consideration based on technical factors likely to affect performance. In this study an analysis designed to assess the relative merits of infrared detectors operating in the 3-5 µm and 8-12 µm spectral bands based on the recently defined figure of merit known as the detected thermal contrast is undertaken. The detected thermal contrast attempts to describe the overall performance of the sequence of events from the initial emission of thermal radiation at the surface of a target to the final measurable output signal seen in the detecting instrument. Under ideal limiting conditions typical of those found for many industrial and scientific applications, by considering targets whose spectral emissivities vary as a function of both wavelength and temperature, exact expressions based on the recently introduced polylogarithmic formulation of the problem are developed for both thermal and quantum detectors. It is found the 3-5 µm waveband for either detector type gives better performance while differences between the two types of detectors is not as significant as one might initially expect. The work not only extends upon a number of approximate schemes that have been proposed and developed in the past where target emissivities as a function of the temperature have been used, it also challenges a number of previously reported results.

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Comparison of the relative merits of the midwave and longwave infrared bands for various target types using detected thermal contrast

2015