When the optical materials generate heat or the ambient temperature changes, they often affect the normal working state of the optical systems. Thus, it is significant to master the thermal performance parameters of the materials for designing optical systems. Among the parameters, thermal expansion coefficient α and temperature coefficient of refractive index dn/dT are the two most commonly employed basic physical parameters. By measuring two of the three parameters including α, γ (temperature coefficient of optical path), and W (thermo-optic coefficient) using interference method, α and dn/dT can be deduced. There are various forms of optical route implementation, among which the “thermal-optic coefficient measurement instrument” based on the Mach-Zehnder (MZ) interferometer features a simple structure and free sample expansion, without additional clamping stress. Thus, we establish a set of instruments using this scheme, analyze the main error sources, and try to suppress or eliminate them. Finally, we conduct verification on quartz glass samples.

In the “thermal-optic coefficient measurement instrument”, the thermo-optic coefficients W can be measured from MZ interference results, and the temperature coefficient of optical path γ can be measured from the Fabry-Perot (FP) interference occurring between the sample end faces. Then α and dn/dT can be calculated from them. The optical path difference of FP interference is the optical path between the front and back surfaces of the sample, which is only related to the interior of the sample and is unaffected by other external factors, leading to high stability. However, the MZ interference optical path is influenced by many factors, including the FP interference effect in the sample, mechanical deformation outside the sample, and temperature drift. Therefore, the main error sources in this testing system are waveform distortion and zero drift phenomena in the MZ interference. Meanwhile, theoretical analysis shows that waveform distortion is caused by the influence of FP interference mixed in MZ interference. The results include two aspects of signal amplitude modulation and the addition of additional phases to the signal phase, which are characterized by small, periodic, and zero mean values. The method of directly measuring phase, such as phase modulation, can be employed to avoid the influence of waveform distortion and obtain the measured Δ[(n-1)L]. The monitoring results of the zero drift effect indicate that there is a significant zero drift during the constant and variable temperature processes of the interferometer. Under the sample length of 10 mm, temperature measurement range of 20-120 ℃, and heating rate of 0.5 ℃ per minute, systematic errors of 2.3×10^-8/℃ and 5.7×10^-7/℃ are yielded respectively. By improving the optical path, the beam is expanded to partially pass through the sample and partially not. The part that does not pass through the sample is called the background interference, whose measured optical path difference represents the zero drift value. The part that passes through the sample is called the sample interference. The measured optical path difference is subtracted from the zero drift to obtain the final measured optical path difference, with subsequent calculations conducted to obtain the thermo-optic coefficient W.

Measurement and verification are performed on quartz glass with low expansion characteristics. The selected sample material Corning 7980 is tested in the temperature range from room temperature to 120 ℃, with a heating rate of 0.5 ℃/min. Comparison among the obtained α and dn/dT and the manufacturer’s data and reference values shows that the results are completely consistent. The maximum deviation between the thermal expansion coefficient and the reference value shall not exceed 5.6×10^-8/℃, and the maximum deviation between the refractive index temperature coefficient and the reference value shall not exceed 7×10^-7/℃.

The “thermal-optic coefficient measurement instrument” based on the MZ interferometer can achieve synchronous measurement of the thermal expansion coefficient and temperature coefficient of the refractive index of optical materials, but there are problems of waveform distortion and zero drift effects. The method of directly measuring optical path difference using phase modulation can eliminate the influence of waveform distortion caused by the FP interference effect. The method of synchronously measuring background interference and sample interference optical path difference can deduct the influence of zero drift effects, and ultimately control the system error caused by zero drift within 3×10^-9/℃. Quartz glass testing indicates that the thermal expansion coefficient and temperature coefficient of refractive index at 632.8 nm are completely consistent with the reference data, which verifies the effectiveness of the error source analysis and suppression methods for the system.