# Optical Filters to Determine Variations in Radiometers

A 6µm cut-on filter is often used to control the spectral bandpass of infrared radiometers equipped with thermopile detectors. The cut-on tolerance of these filters is typically ±1µm.

The substrate transmission determines the cut-off wavelengths, and is normally silicon or germanium.

The calibration of a radiometer against a linearizing network is affected by the deviation of cut-on wavelength in a fashion that is uncorrectable by a single gain adjustment.

## Analysis

This analysis is on the basis of integrating the Planck function, and involves calculations for a radiometer measuring a temperature range of 0-200°C. In addition, the radiometer is temperature compensated for ambient temperature effects.

It is assumed that the bandpass of the filter is a square ending at 15.5µm. The filter also has a transmission of 1.0 across the pass band (average transmission is typically in the range of 60-80%). Furthermore, the specimen is assumed to be an ideal blackbody emitter. The results of these estimations are summarized in Table 1.

Table 1. Calculated energy for three spectral bandpasses ending at 15.5μm

Temp. Transmitted Energy from Cut-on to15.5mm (mW/cm2sr)
°C Cut-on Wavelength: 5μm 6μm 7μm
0 5.16 5.00 4.69
25 8.11 7.74 7.14
50 12.05 11.34 10.26
100 23.44 21.32 18.61
200 62.59 53.25 43.68

The results during normalization of each column to its value at 200°C are presented in Table 2. The normalization process is similar to the calibration of the radiometer against a 200°C blackbody.

Table 2. Energy normalized to 1.0 at 200°C for each cut-on wavelength

Temp. Normalized Transmitted Energy from Cut-on to15.5mm
°C Cut-on Wavelength: 5μm 6μm 7μm
0 0.0824 0.0939 0.1074
25 0.1296 0.1454 0.1635
50 0.1925 0.2130 0.2349
100 0.3745 0.4004 0.4261
200 1.0 1.0 1.0

The chart depicted in Figure 1 may be applied for the development of a meter scale, which would be divided into °C for temperatures between 0 and 200°C.

If the 6µm filter cut-on wavelength was the basis of the meter scale and the calibration of the radiometer was at 200°C, then the temperature indication would be 37.5°C and 17°C with a 5µm and 7µm cut-on filter, respectively.

## Conclusion

This article has demonstrated the non-linearities that may be come across in the calibration of a radiometer, which uses a cut-on filter for limiting the sensed thermal radiation’s spectral bandwidth.

This information has been sourced, reviewed and adapted from materials provided by Dexter Research.

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