# Zero Drift Infrared Radiation Thermometer Using Chopper Stabilised Pre-Amplifier
## 2 Materials and Methods
### Characterisation of IRTs over Low-Temperature Ranges  
The output voltages of the IRTs were characterised as a function of the temperature of an Ametek Land Instruments, Landcal P80P blackbody source (Ametek Land Instruments, Dronfield, UK). The blackbody source temperature was calibrated prior to characterisation of the IRTs, using an Isothermal Technology Limited, milliK precision thermometer (Isothermal Technology, Southport, UK) and transfer standard Platinum Resistance Thermometer (Isothermal Technology, Southport, UK), which was calibrated at manufacture by an accredited, primary temperature calibration laboratory.  
A 150 mm length of 600 \(\upmu\)m core diameter, ZBLAN fluoride glass fibreoptic coupled blackbody radiation from the calibration thermowell in the blackbody source to the IRTs. The fibreoptic had a numerical aperture of 0.20, transmitting radiation between 0.2 \(\upmu\)m and 4.5 \(\upmu\)m in wavelength. The depth to diameter ratio of the calibration thermowell and the exposed tip of the fibre exceeded 5:1, which afforded high relative emissivity approaching blackbody conditions [27,28].  
The IRT output voltages were measured and recorded using a DMM. The temperature set point of the blackbody source was increased in 10 \({}^{\circ}\)C increments between 20 \({}^{\circ}\)C and 70 \({}^{\circ}\)C and the IRT output voltages characterised against this sequence of temperatures. The IRT output voltages at each source temperature were recorded at intervals of 1 s for a duration of ten minutes per measurement. The configuration of the equipment for undertaking IRT characterisation was the same as presented in Figure 1, except that the fibreoptic was inserted into the blackbody source thermowell and coupled the blackbody radiation onto the photodiode.  
The mean and standard deviation of the output voltages recorded from the IRTs were evaluated to abstract values that were representative of each temperature and the noise. The root mean square (RMS) noise for each IRT was calculated from the characterisation measurements.  
The Wien approximation of [PERSON]'s law enabled evaluation of the ratio between radiances arising from two temperatures to be compared. This leads to the expectation of a linear relationship between the natural logarithm of the IRT output voltage, \(ln(V_{o})\) and the inverse of the absolute temperature of the source object, \(1/T\). The limiting effective wavelength, which is a monochromatic wavelength abstraction  
Figure 1: Schematic diagram illustrating configuration used to test the two infrared radiation thermometers (IRTs) concurrently.  
of the IRT response at different temperatures over a broad wavelength range [29], was calculated from the gradient of the relationship between \(ln(V_{o})\) and 1/\(T\). The practical calibrations of the IRTs were used to determine interpolation curves, according to the method of [PERSON] and [PERSON] [30]. RMS noise was evaluated from the calibration data to provide an IRT noise measurement in terms of the equivalent temperature resolution in K.  
These measurements tested the capability of the IRTs to measure low temperatures likely to be encountered on industrial processes [31] and provided practical calibrations of the IRTs through the temperature range 20 \({}^{\circ}\)C to 70 \({}^{\circ}\)C.