J. Eur. Opt. Society-Rapid Publ. 21, 32( 2025) 27
Figure 7. DM displacement like roulette motion,( a) Segment structure of DM and its roulette motion,( b) 2-D in-plane result.
Figure 8. 2 nm displacement at( 60, 60) pixel with comb filter,( a) without filter,( b) with filter.
p is flat at around 0:1nm = ffiffiffiffiffiffi
Hz, while the noise shape with pre-filter decreases with increasing frequency. In the low frequency range from 0.1 Hz to 1 Hz, the noise increases with decreasing frequency. Reducing the noise floor to the theoretical resolution of the HSC is also the future challenge.
We measure air fluctuation in measurement path in case of the fixed plane mirror. A fan is used to generate a wind speed of approximately 1 m / s in a direction perpendicular to the optical axis. The measured 2-D in-plane result is shown in Figure 10a. A single point at( 60, 60) pixel is shown in Figure 10b. The variation of the air turbulence causes tens of nanometer fluctuation. It is known that the air flow configuration to optical path caused fluctuation in displacement measurement, but the relationship between the beam wave front and the displacement had not been revealed. In Figure 10a, from 50 ms ~ 350 ms, the high displacement locations( shown in yellow) appear to move randomly with time. Figure 10b shows that the time variation of the displacement of the central pixel fluctuates approximately 30 nm during 400 ms. Figures 10a and 10b show that the wavefront varies dynamically in time and space, resulting in the observed displacements. The next issue is the extent to which air fluctuations in turbulence can be measured using the proposed method.
Figure 9. Noise floor at( 60, 60) pixel. Black line was without the pre-filter and gray line was with the pre-filter.
5 Conclusion
In this paper, we introduced a SPM interferometer for nanometer order 2-D in-plane displacement measurement. HSC and PC based phase-meter were utilized for 2-D measurement. The configuration of the interferometer and the algorithm of the phase-meter( demodulation) were described. In experiment, displacement measurement with PM was conducted to inspect the noise characteristic and the resolution. PM movement and deformation of DM were