An optimal piecewise Chebyshev fitting method to calibrate cryogenic temperature sensors

An optimal piecewise Chebyshev fitting method (OPCFM) for calibration of cryogenic temperature sensors (especially the negative temperature coefficient resistors) is presented. Compared with other common fitting equations, Chebyshev polynomials give the best fitting performances at low temperature range of 14.5-40K. Based on least squares Chebyshev fitting method, the OPCFM is good at finding the best overlapping field and optimal coefficient power to minimize standard deviation at each segment. The experimental results demonstrated that this method can minimize its standard deviation at cryogenic temperature range and keep deviation below 1mK at 18K in most cases. Using the same original data, the OPCFM shows better performances on the whole temperature range (14.5-300K) compared with original Chebyshev fitting method used in ten commercial cryogenics temperature sensors' certificates of calibration. The results prove that our proposed OPCFM can enhance the calibrated accuracy of cryogenic sensors, which has a significant promotion for improving temperature measurements at cryogenics.