Curved tube correction factors for indirect measurements with a radiation thermometer

To measure surface temperature, a radiation guide in the form of a curved tube with a specular wall is used to couple thermal energy between a target surface and a radiometer. The relationship between the radiometer output and the target temperature depends on a correction factor, CF, which is a function of the tube temperature and another factor CFS. The term CFS, determined by the shape and reflectivity of the tube, is computed by a ray-trace technique. Calculations show how the factor CFS depends both on the ratio of tube length-to-diameter and length-to-bend radius. A particular gold-plated tube in conjunction with a radiometer having a narrowband filter at 7.9 microm is used to verify the relationship between surface temperature and radiometer output. Surface temperatures in the 0-100 degrees C range are measured for various fixed wall temperatures. There is good agreement between the measured and the calculated values.