Study on the number and spacing of calibration points for high-precision NTC thermistors across the ocean temperature range

Marine monitoring often requires the temperature measurement accuracy to be less than 1 mK. A series of regularly arranged temperature points is taken to calibrate the equation expressing resistance-temperature characteristics under ocean conditions. Seventy-two negative temperature coefficient thermistors underwent coincident measurement procedures with nine equally spaced points from -5 to 35 °C in a high-precision thermostatic water bath, followed by calibration using Lagrange interpolation and least-squares fitting methods. Ten of these thermistors, with average interpolation errors below 0.1 mK and calibration uncertainty estimated at 0.6 mK (
k
= 2), were used to study the impact of the number and placement of calibration points on interpolation error, aiming to enhance measurement precision across the ocean temperature range. The results reveal that the standard deviation for the 10 thermistors using six unequally spaced points was only 20% higher than when using nine equally spaced points. However, the standard deviation for five equally spaced points nearly doubled, with a maximum difference of 0.1 mK, still achieving sub-millikelvin accuracy. By adjusting the calibration points near both ends of the range, the optimal placement for five calibration points was found to minimize temperature deviation and adhere to the Chebyshev criterion. This ideal distribution, determined through sequential calculations, contributes to improved calibration precision.