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1959 |
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Phase Modulation Homodyne Interferometer with Picometer Resolution Using Tunable Laser Diode |
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Optics: Optics / Interferometry |
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Since nanotechnology and ultra-precision engineering have progressed rapidly, a measuring method for length or displacement with resolution of picometer must be required in the near future. Nowadays, the laser interferometry is of the industrial standard. A lot of commercial interferometers are widely used in industries. However, it is very difficult to determine an arbitrary length or displacement with an accuracy of nanometer using the commercial interferometer, because it suffers from the nonlinearity problem of fringe interpolation(1).
A phase modulation homodyne interferometer (PMHI)(2) is proposed by IMGC in 1991. In the PMHI, a phase of an incident light is modulated with an EOM and the output signal of a photodiode at the end of interferometer is demodulated with the modulation signal using a lock-in amplifier. From this configuration, it is possible to determine an optical path difference L of wavelength λ × integer N (mode number) with an accuracy of 10 pm or less using the null-method, because the lock-in demodulation can transfer a dark fringe (in the case, L = λ × N) into a null-cross-point of the lock-in output signal. However, it is impossible to determine an arbitrary length or displacement using this method.
We propose a new length/displacement measurement method using the PMHI and a tunable laser diode (TLD) as a light source, to determine an arbitrary length with resolution of picometer. In the proposed instrument, a displacement of movable mirror in the interferometer can be converted to a frequency shift of the TLD. The measurement procedures are,
1) search some null point of the lock-in output signal by tuning the frequency of the TLD,
2) move the movable mirror, but keep the null point firmly by controlling the frequency of the TLD with some servo loop,
3) measure the frequency shift using the beat frequency between the TLD and a frequency stabilized He-Ne laser.
From the above procedures, a change of the displacement ΔL equals –Δf(L/f), where f and Δf the laser frequency, frequency shift, respectively. In the case, we neglect effects from the changes in mode number and refractive index. We hope that the proposed method has a direct linkage to the frequency standard, and shows no interpolation error. Furthermore, if we can use two TLDs in the PMHI and keep neighboring null points using the above method, there is a prospective possibility of direct determination of the optical path difference L from the frequency difference between the two TLDs.
In this paper, we discuss the principle of the proposed method, the instrumentation and the experimental results. In the experiments, we compare the proposed method with the commercial heterodyne interferometer. We determine an interpolation error (periodic error) of the heterodyne interferometer with an uncertainty of 10 pm level.
1) N. Bobroff, Meas. Sci. Technol. 4 (1993) 907.
2) G. Basile et al., Metrologia 28 (1991) 455.
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