J. Eur. Opt. Society-Rapid Publ. 21, 32( 2025) 25
Figure 4. Bode diagram of the comb filter,( a) the amplitude response,( b) the phase response.
Figure 5. Experimental setup.
the limitation of optical bread board size, some mirrors are used to steer the beam into the homemade EOM( d = 3 mm, W = 3mm, l = 70 mm) and the interferometer. The reference arm length is designed minimum due to the external EOM configuration. The interferometer flame is made of low expansion steel( Nippon Chuzo, LEX-ZERO) to eliminate the effect of temperature fluctuation. A DM( Thorlabs, DMP40 / M) which is a multi-segmented piezo driven deformable mirror, is utilized in 2D in-plane displacement. Although the DM has 40 segments, an area of 8 segments located in the center of the DM is targeted due to the beam diameter. PM movements generated by PZT driven linear stage are also measured in performance inspection and 2-D in-plane displacement. DM and PM were exclusively utilized in experiments. The interferometer, DM, PM with linear stage and HSC( Photron, FASTCAM Mini AX200 AOFT1) are located on the breadboard which is also made of low expansion steel. The breadboard is placed on the anti-vibration table. Conditions on experiments are shown in Table 2. To design the bandwidth higher than WFS, the modulation frequency is selected to 5 kHz, leading to the frame rate of 60 kHz and pixel area of( 128, 128) or( 256, 256)( equal to area of 2.56 mm 2.56 mm or 5.12 mm 5.12 mm).
4 Results
In this section, some measurement results are discussed. We conduct 2-D in-plane displacement measurements using plane mirror movement and mirror deformation as
demonstrative measurements. Triangular waveform movement of PM with the amplitude of 400 nm and frequency of 5 Hz is shown Figure 6. LissajousdiagramusingI cos and I sin at( 60, 60) pixel in HSC is shown in Figure 6a. In Figure 6a, a circular Lissajous diagram is obtained by adjusting the voltage V EOM using equation( 3), itmeans that the estimation of the modulation index m shown in equation( 3) and Appendix is valid. The demodulated single point displacement from Lissajous diagram at( 60, 60) pixel is shown in Figure 6b. The 2-D in-plane results are shown in Figure 6c. Figure 6 shows that the 2D in-plane displacement of the entire PM surface can be measured. Periodic interpolation uncertainties are observed in the demodulated displacements in Figure 6b. Determining the cause of this is the future challenge.
We examine whether partial deformation of DM surface can be measured. As shown in Figure 7a, the DM surface is divided into 8 circumferential sections, with each section protruding 125 nm and its protrusion varying in a roulette-like fashion. Figure 7b shows the deformation of the DM surface. In Figure 7b, the yellow area in the figure shows that the protruding part( 120 nm displacement) rotates with time. From Figure 7b, it can be seen that the time-varying surface deformation can be measured by the proposed method.
In the resolution inspection measurements, small movement of PM and noise floor are measured. To verify the effectiveness of the pre-filter, a comparison was made between using it and not using it. The filter condition is described in the above section. The result of mirror movement which is a square waveform with the amplitude of