An infrared (IR) thermograph is a radiometer that provides an image of the target scene, indicating the apparent temperature of elements in the scene by a black-white brightness or blue-red color scale. Radia- tion originating from an element in the target scene is incident on the radiation detector, which provides a sig- nal proportional to the incident radiant power. The signal sets the image brightness or color scale for the image pixel associated with that element. A scheme is proposed for field calibration of an infrared thermograph having a radiation detector with a 3- to 5-µ,m spectral bandpass. A heated metal plate, which is maintained at 327°C and has four diffuse, gray coatings with different emissivi- ties, is viewed by the IR thermograph in surroundings for which Tsur = 87°C.

(a) Consider the thermograph output when viewing the black coating, so = 1. The radiation reaching the detector is proportional to the product of the black- body emissive power (or emitted intensity) at the temperature of the surface and the band emission fraction corresponding to the IR thermograph spec- tral bandpass. The proportionality constant is referred to as the responsivity, R(µ,V · m2/W). Write
an expression for the thermograph output signal, So, in terms of R, the coating blackbody emissive power, and the appropriate band emission fraction. Assuming R = 1 µ,V · m2/W, evaluate So (µ,V).

(b) Consider the thermograph output when viewing one of the coatings for which the emissivity sc is less than unity. Radiation from the coating reaches the detector due to emission and the reflection of irradiation from the surroundings. Write an expression for the signal, Sc, in terms of R, the coating blackbody emissive power, the blackbody emissive power of the surroundings, the coating emissivity, and the appropriate band emission fractions. For the diffuse, gray coatings, the reflectivity is pc = 1 - sc.

(c) Assuming R = 1 µ,V · m2/W, evaluate the thermo- graph signals, Sc (µ,V), when viewing panels with emissivities 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 correct scale indication of Ts = 327°C. The signals from the other three coatings, Sc, are less than So. Hence the thermograph will indicate an apparent (blackbody) temperature less than Ts. Estimate the temperatures indicated by the thermograph for the three panels of part (c).