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1、Calculation and optimisation of the maximum uncertainty in infrared temperature measurements taken in conditions of high uncertainty in the emissivity and environment radiation valuesFrancisco Javier Meca Meca*, Francisco Javier Rodr? guez Sanchez, Pedro Mart? n SanchezDepartment of Electronics, Uni
2、versidad de Alcal? a a, Alcal? a a de Henares, 28871 Madrid, SpainReceived 24 July 2001AbstractThis paper develops a method that enables the most suitable range of wavelengths to be ascertained in which to take infrared temperature measurements of surfaces in the open air in conditions in which high
3、 uncertainty exists in the environmental radiation and emissivity values. The optimisation criterion adopted for the error is that of achieving the narrowest possible band of maximum uncertainty. The results demonstrate that it is possible to cancel out the solar radiation contribution to the maximu
4、m uncertainty present in the measurement whilst still working in short wave- lengths where this radiation is very intense and, therefore, optimise the band of uncertainty produced by emissivity and environment radiation. ? 2002 Elsevier Science B.V. All rights reserved.PACS: 07.20.D; 61.80.B; 78.30K
5、eywords: Infrared; Temperature; Emissivity; Uncertainty; Wavelength1. IntroductionIn infrared non-contact temperature measure- ment, part of the energy radiated by the surface measured is captured by the sensor and convertedinto an electrical value. The captured energy is composed of three contribut
6、ions: Energy emitted by the surface depending on its temperature and emissivity. Energy reflected on the surface, proceeding from the other surfaces in the environment locatedwithin its field of view. This energy is a function of the temperature and emissivity of the surfacesin the environment, the
7、reflectivity of the surfaceInfrared Physics fax: +34-9188-56591.1350-4495/02/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII: S1350-4495(02)00125-1measured, of the relative view factors between the various surfaces and atmospheric absorp- tion. Energy emitted by the column
8、 of air between the surface measured and the sensor system.Complete modelling of all of the factors men- tioned is highly complicated. Even assuming thatthe scenario is fully known, it is very difficult tocalculate all of the necessary coefficients, the so- lution usually being to simplify the probl
9、em. If the surface measured is highly emissive, its temperature is greater than the temperature of the other surfaces in the environment, and if the distance between the surface and the measuring instrument is short, then the problem can be sim-plified. The final error diminishes as the relation- sh
10、ip between the energy emitted and the energyreflected by the surface measured increases. Thesimplification adopted is usually drastic. It is as- sumed that the environment is made up of a low number of surfaces of unit emissivity and known temperatures. The error produced by this ap- proximation is
11、a function, among other things, of the range of wavelengths used in the measurement. Therefore, it is necessary to carry out a detailed study of the application in order to attain the greatest possible accuracy permitted by the afore- mentioned approximation. This paper proposes a method that enable
12、s the most suitable range of wavelengths to be ascer- tained in which the maximum uncertainty pre- sent in the estimated temperature is minimised. In many applications, this optimisation criterion is more appropriate than reducing the average error value. An example of this is the measurement of the
13、 temperature of greasing boxes, wheels and brake disks of a train in motion 1, where it issufficient to simply detect if the temperature of the elements exceeds a series of pre-established safety thresholds, the precise temperature value not being of great importance. The method considers that both
14、the emissivity of the surface measured and the radiation of the surfaces in the environment are known to a given level of maximum uncertainty, that solar radiation may be incident on the surface measured and that the emission of the column of air between thesurface and the measuring instrument is ne
15、gligible (short distance B, the minimum value of the function is ob- tained for the highest real emissivity and the maximum for the lowest.oIk;TOR o?RB ? A ?2R12Assuming that the condition where A B is met, the expressions used to calculate the maximumand minimum value of the error in the temperatur
16、e estimated are those indicated in (13) and (14), re- spectively. It may be observed that the uncertainty contribution as a consequence of the solar radia-tion is nullified in one case and strongly attenuated in the other, which means that the uncertainty in the measurement is determined by the uncertainty in the emissivity and environment radiation. As the uncertainty due to these items diminishes as the wavelength does, it may be deduced that it is advisable to work with t
