Design and Analysis of a Telescope Optical Path Length Stability Measurement Scheme
Objective An optical telescope is a crucial component of the space gravitational wave laser interferometer system,with its optical path length stability required to meet the picometer level.Therefore,it is significant to design a feasible measurement scheme for evaluating the optical path length stability of the telescope.Laser interferometry has become the predominant method for measuring optical path length stability owing to its high measurement precision and strong anti-interference capability.In this study,a measurement scheme for the optical path length stability of an off-axis four-reflection telescope is designed based on the Fabry-Perot interferometer.The noise analysis and measurement of each component in the scheme are performed to assess the feasibility of this scheme.Methods A measurement scheme for the optical path length stability of the telescope is designed based on the Fabry-Perot interferometer.A resonant cavity is formed on the telescope by adding two high-reflectivity mirrors in a vacuum heat and vibration isolation system.The Pound-Drever-Hall(PDH)frequency-locking technique is utilized to lock the laser frequency to the resonant frequency of the telescope cavity,converting the optical path length variations within the telescope into laser frequency variations.The influence of absolute laser frequency and free spectral range on the measurement of optical path length stability is analyzed by utilizing their derivatives in the measurement principle formula.To assess the noise within the entire measurement loop,a low-precision cavity is employed as a substitute for the telescope cavity,and the measurement laser is locked to the low-precision cavity with a similarly low precision.Subsequently,the external noises in the scheme,including the reference system,beat frequency measurement,residual amplitude modulation,and electronic noise,are measured.The impact of these external noises on the measurement of optical path length stability is analyzed,and the primary noise source limiting the measurement accuracy is identified.Results and Discussions The noise allocation requirements for each component in the measurement scheme within the frequency band of 1 mHz to 0.1 Hz are listed in Table 1.The influence of the absolute laser frequency and free spectral range on the measurement of optical path length stability is analyzed by utilizing their derivatives in the measurement principle formula.When the optical path noise and free spectral range change by 1 GHz and 0.25 MHz,respectively,they correspond to optical path length variations of 10 pm and 60 mm,respectively,both of which significantly exceed the optical path length stability measurement requirements.At these values,their impacts on optical path length stability are determined to be 3.5×10-6 pm/Hz1/2 and 5×10-3 pm/Hz1/2,respectively.The overall measurement of electronic noise introduced in the measurement scheme reveals that the electronic noise is 0.2 mV/Hz1/2(Fig.5),which is below the specified requirement of 0.238 mV/Hz1/2.The frequency stability of the ultra-stable laser is shown in Fig.6.However,the optical path noise of 1 pm/Hz1/2 corresponds to a frequency noise of 94 Hz/Hz1/2.Therefore,the frequency noise of the ultra-stable laser is more than one order of magnitude smaller than the telescope requirement,making it suitable to be a frequency reference source.The beat frequency measurement device exhibits a noise level of 1 Hz/Hz1/2(Fig.7),which is two orders of magnitude lower than the specified requirement,indicating that it will not be a limiting noise source for the measurements.The residual amplitude modulation(RAM)noise of the electro-optic phase modulator is determined to be 5 mV/Hz1/2(Fig.8),which exceeds the requirement by one order of magnitude and becomes the primary noise source in the current scheme.In the future,the impact of RAM noise can be mitigated through methods such as active temperature control and active voltage bias on the crystal.Conclusions In this study,the off-axis four-reflection telescope is transformed into a resonant cavity by adding two highly reflective mirrors in the vacuum heat and vibration isolation system.A measurement scheme for assessing the optical path length stability of the telescope was designed based on the Fabry-Perot interferometer.The PDH frequency-locking technique is employed to measure the optical path length changes within the telescope cavity by converting them into laser frequency variations.The influence of the measurand changes and external noise on the measurement of optical path length stability is analyzed in the measurement scheme.Experimental results demonstrated that the absolute laser frequency and free spectral range variations had a negligible impact on the measurement of optical path length stability,both being less than 1 pm/Hz1/2.Within the frequency band of 1 mHz to 0.1 Hz,the electronic,beat frequency measurement,and residual amplitude modulation noises in the measurement scheme are equivalent to optical path noise of 0.14,0.01,and 3.57 pm/Hz1/2,respectively.Therefore,the residual amplitude modulation noise emerged as one of the limiting factors in achieving picometer-level optical path length stability in telescope measurements,necessitating further studies on noise suppression techniques.
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