Development of laser interferometric high-precision ...

Development of laser interferometric high-precision geometry monitor for JASMINE Yoshito Niwa∗ a ,Koji Araia ,Akitoshi Uedaa ,Masaaki Sakagami b ,Naoteru Goudaa , Yukiyasu Kobayashia , Yoshiyuki Yamadac , Taihei Yanoa a National

Astronomical Observatory Japan, National Astronomical Observatory Japan 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, JAPAN ; b Kyoto University, Cosmology and Gravity group Dept. of Fundamental Science Fac. of Integrated Human Studies Kyoto University Kyoto 606-8501, JAPAN ; c Kyoto University, Theoretical Astrophysics Group Department of Physics, Kyoto University Kyoto 606-8502, JAPAN ABSTRACT

The telescope geometry of JASMINE should be stabilized and monitored with the accuracy of about 10 to 100 picometer or 10 to 100 picoradian in root-mean-square over about 10 hours. For this purpose, a high-precision interferometric laser metrology system is employed. One of useful techniques for measuring displacements in extremely minute scales is the heterodyne interferometrical method. Experiment for verification of multi degree of freedom measurement was performed and mirror motions were successfully monitored with three degree of freedom. Keywords: JASMINE, Astrometry, Metrology, Interferometer, Galaxy, Infrared

1. INTRODUCTION 1.1. High-precision geometry monitor for JASMINE telescope Next-generation astrometry satellite missions will measure parallaxes, positions with the accuracy of 10 microarcsec. So the optical component of their telescope should be stabilized and its fluctuations should be monitored with high accuracy. In JASMINE(Japan Astrometry Satellite Mission for Infrared Exploration) which is one of next generation astronomical satellite missions astronomical parameter is derived by the frame linking method, and It is necessary to suppress fluctuations of frame expansion or distortion according to the temperature changing during the observation as much as possible; the telescope geometry, the distance of primary mirror to secondary mirror and the angle between two mirrors, should be stabilized with the accuracy of about 10 to 100 pm or 10 to 100 prad in root-mean-square over about 10 hours; moreover, the fluctuations should be monitored with such accuracy.

1.2. Concept of high-precision geometry monitor For this purpose, a high-precision interferometric laser metrology system is employed. Fig.1 shows a example of monitoring telescope geometry with two or more sets of displacement measurement system by using laser interferometers. One of the available techniques for measuring the longitudinal and angular fluctuations is a method known as the goptical heterodyne interferometry h using a heterodyne Mach-Zehnder laser interferometer. One of the advantages of the technique is that precision distance measurement signals can be detected without light pathlength control with actuators; traditional interferometers (Fabry-Perot cavities, Michelson on dark fringe) require an actuator to keep the interferometer at a specified operating point to measure some fluctuations with high accuracy. So, this technique makes it possible to measure displacements of two or more degree of freedom with no complex control system; therefore, displacements in some parts of telescope can be measured simultaneously using a number of laser interferometers. Additionally, this technique enables wide dynamic range

Space Telescopes and Instrumentation 2008: Optical, Infrared, and Millimeter, edited by Jacobus M. Oschmann, Jr., Mattheus W. M. de Graauw, Howard A. MacEwen, Proc. of SPIE Vol. 7010, 70104L, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.788734 Proc. of SPIE Vol. 7010 70104L-1 2008 SPIE Digital Library -- Subscriber Archive Copy

Telescope geometry monitor

Distortion monitor Infrared detector

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Figure 1. Illustration of interferometric geometry monitor for JASMINE telescope

measurements: more than micrometer. Then, this method seems to be practical, thinking about that the monitor device will be used on the space orbit where it cannot be repaired or adjusted by person’s hand. The principle of heterodyne Mach-Zehnder laser interferometer operation is illustrated in Fig.2 and Fig.3. The laser beam is split into two parts by beam splitter and each beam are separately frequency-shifted by an acoust-optical modulator(AOM). The two AOM driving frequencies differ by constant amount, the heterodyne frequency fh , which is of the order of 10 kHz. After traveling different paths, the two beams are recombined by beam splitter and a fringe pattern is produced. A photodetector can receive the fringe pattern and generate an electrical beat signal; the beat frequency is equal to the heterodyne frequency fh . The time dependence of the heterodyne signal is given by cos(2πfh t +

2πL ) λ

(1)

where L is the pathlength difference and λ is the laser wavelength. The differential fluctuations δL caused in the pathlength, the amount of them appears as a phase change δφ of that heterodyne signal, which is given by δφ =

2πδL λ

(2)

The phase change δφ will be measured electronically with respect to a phase reference signal derived from another interferometer, which is not subject to the pathlength fluctuations; the reference interferometer is set up on especially stable environment. The amount of the displacement of 10 pm corresponds to about 10−4 rad in terms of the phase change, and such a phase stability is required for the reference signal for JASMINE.

∗

E-mail:[email protected]

Proc. of SPIE Vol. 7010 70104L-2

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Figure 3. Heterodyne Mach-Zehnder laser interferometer: typical photodetector electrical beat signal. Differential pathlength variation δL translates into a phase variation δφ of that heterodyne signal.

2. DEVELOPMENTAL STATUS OF GEOMETRY MONITOR We have already started to develop laser interferometric high-precision length monitor aiming for measuring JASMINE telescope geometry displacements. The procedure of development is as follows.

• Step1: We prove it is able to measure two or more degree of freedom without contradiction. • Step2: We prove it is able to measure displacements with the accuracy of 10 pm in RMS over 10 hours. • Step3: We measure the stability of the structure of 1m scale with the accuracy of 10 pm in RMS over 10 hours.

We completed step1 as of 2007, and plan to proceed step2 and step3 in 2008. So, the experimental result on step1 is described in this paper.


3. STEP1: DEMONSTRATION OF MONITORING MIRROR MOTIONS 3.1. Experimental layout We performed demonstration experiment of monitoring mirror motions of 3-degrees of freedom; the distance between the target mirror, which was mounted to 0.5 m high structure and optical bench was measured using four heterodyne Mach-Zehnder laser interferometers set up on the optical bench. A sketch of optical configuration is shown in Fig.4 and picture of optical system set up is shown in Fig.5. The optical system was set up on the laser bench of 300 mm ~ 300 mm and the optical bench of 600 mm ~ 600 mm. The total length of the optical path is 2.5 m. The input laser is Nd:YAG laser of 1064 nm wavelength. Two lasers with the frequency difference of 50kHz are generated by AOMs (Acousto-Optical Modulator) on the laser bench. Each beam is split off and interfered to provide some signals on the optical bench. 600mm

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Figure 4. A sketch of optical configuration for monitoring mirror motions of 3-degrees of freedom.

The optical bench contains five separate interferometers: • Interferometer for detecting phase reference signal. • 4 sets of interferometers for monitoring mirror motions. Optical path length fluctuations can be read out from the phase difference between one of four heterodyne interferometer signals and reference signal. The phase differences are measured using digital phase comparator(IC 4046). We can reconstruct the target mirror 3 DOF motions with the information of four optical path lengths.


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Figure 5. Optical configuration set up for monitoring mirror motions of 3-degrees of freedom.

3.2. Experimental result Target mirror motions were monitored with three degrees of freedom to demonstrate heterodyne interferometers operations: length, pitch and yaw motions were measured with four beams from interferometers. First, target mirror were given 3 DOF motions: longitudinal one at 1 Hz, pith one at 2.3 Hz and yaw one at 3.3 Hz, at the same time by PZT actuator which was calibrated beforehand and optical path length fluctuations at the four points on target mirror caused by the such motion was measured using four heterodyne interferometers. Fig.6 shows each interferometer output length sensing signal. Obviously, we could not presume target mirror motions from one information on each channel alone as Fig.6 shows; then, using reconstruction matrix which could be calibrated or known from information about location on the mirror where four beams reflected we could reconstruct its 3 DOF motions. Fig.7 shows successfully reconstructed 3 DOF mirror motions. It was also confirmed to be able continuously to monitor the displacement more than one micro meter. Fig. 8 shows the transfer function for reconstruction system which was measured to evaluate the accuracy of this monitoring procedure. Off-diagonal elements mean the amount of the coupling between each degrees of freedom. The amount of reconstruction error is less than JASMINE requirement. So , it seems that there is no problem even if this measuring method is adopted as JASMINE geometry monitoring system.


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Figure 6. Four heterodyne interferometer measured values when the target mirror was moved with 3 DOF: length, pitch, yaw, by PZT actuator.


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Figure 7. Results of reconstruction of three degree of freedom motion with four heterodyne interferometer measurement signals. The angular displacement is shown as a longitudinal one at the point on the target mirror where beam was reflected.

reconstruction Length Measured JASMINE value requirement L

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Figure 8. The transfer functions for reconstruction system. JASMINE requirement is calculated by one dimensional simulation of the thermal structure of JASMINE telescope model.

4. PRE STEP2: REFERENCE SIGNAL PHASE STABILIZATION We need an ultrastable phase reference signal to measure a light pathlength variation with high accuracy, which is equal to requirement of JASMINE, and the phase of heterodyne signal derived from reference interferometer was stabilized by a feedback control system, which is known as the gphase-locked loop h. Fig.9 shows reference signal phase stability. By now, the phase stability level of 1.77×10−4 rad was reached in root-mean-square over


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10 hours; it is equivalent to about 30 pm in terms of measurable pathlength displacements. Its noise level almost reaches the JASMINE mission requirement.

Figure 9. Reference signal phase stability. The smooth line shows the measured value for root-mean-square from 1Hz to each frequency.

5. CONCLUSIONS The laser metrology using heterodyne Mach-Zehnder interferometer is one of the available techniques for measuring the telescope geometry displacements. One of advantages of this technique is that it possible to measure displacements of two or more degree of freedom with no complex control system; therefore, displacements in some parts of telescope can be measured simultaneously using a number of laser interferometers. To verify this advantage, we performed demonstration of monitoring mirror motions with 3 DOF using four heterodyne interferometers. As a result it was confirmed to be able to successfully reconstruct mirror motions which were given by PZT actuator; moreover, it seems that we can monitor mirror motions with more than three degree of freedom without complex systems.

ACKNOWLEDGMENTS This research is supported by colleagues by JASMINE working group.

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