An infrared (IR) thermograph is a radiometer that

Chapter 12, Problem 12.85

(choose chapter or problem)

An infrared (IR) thermograph is a radiometer that pro-vides an image of the target scene, indicating theapparent temperature of elements in the scene by ablackwhite brightness or bluered color scale. Radia-tion originating from an element in the target scene isincident on the radiation detector, which provides a sig-nal proportional to the incident radiant power. The signalsets the image brightness or color scale for the imagepixel associated with that element. A scheme is proposedfor field calibration of an infrared thermograph having aradiation detector with a 3- to 5-?m spectral bandpass.A heated metal plate, which is maintained at 327C andhas four diffuse, gray coatings with different emissivi- ties, is viewed by the IR thermograph in surroundingsfor which Tsur?87C. a) Consider the thermograph output when viewingthe black coating, ?o?1. The radiation reaching thedetector is proportional to the product of the black-body emissive power (or emitted intensity) at thetemperature of the surface and the band emissionfraction corresponding to the IR thermograph spec-tral bandpass. The proportionality constant isreferred to as the responsivity, R(?V?m2/W). Writean expression for the thermograph output signal, So,in terms of R, the coating blackbody emissivepower, and the appropriate band emission fraction.Assuming R?1?V?m2/W, evaluate So(?V).(b) Consider the thermograph output when viewing oneof the coatings for which the emissivity ?cis lessthan unity. Radiation from the coating reaches thedetector due to emission and the reflection of irradia-tion from the surroundings. Write an expression forthe signal, Sc, in terms of R, the coating blackbodyemissive power, the blackbody emissive power ofthe surroundings, the coating emissivity, and theappropriate band emission fractions. For the diffuse,gray coatings, the reflectivity is ?c?1??c.(c) Assuming R?1?V?m2/W, evaluate the thermo-graph signals, Sc(?V), when viewing panels withemissivities of 0.8, 0.5, and 0.2.(d) The thermograph is calibrated so that the signal So(with the black coating) will give a correctscale indication of Ts?327C. The signals fromthe other three coatings, Sc, are less than So.Hence the thermograph will indicate an apparent(blackbody) temperature less than Ts. Estimate thetemperatures indicated by the thermograph for thethree panels of part (c).