Objective Gifford-McMahon (GM) cryocooler without liquid helium has gradually become the primary method to obtain a low-temperature environment, but the typical vibration displacement is about ±14.6 μm at the second-cold stage when the compressor is operated at 50 Hz. This vibration is still too high for some applications, such as optical interference, cryogenic microwave oscillators, X-ray phase-contrast imaging, and other precision systems that require submicron-level vibration control on the sample holder. We have developed a vibration-free cryostat using GM cryocooler years ago and measured the vibrations of the sample holder using the high-speed microscopic vision method. However, a more accurate method is needed to analyze its vibration to provide reference data for further reducing the vibration of the sample holder. Moreover, the direct contact measurement method will destroy the eigenfrequency of the system, resulting in the deviation of results from the real value. Therefore, the non-contact vibration measurement methods, such as the doppler method, triangle method, and holographic interferometry, are needed to analyze the vibration of the sample holder of the cryostat. This paper presents a novel vibration-measuring method for the measurement of the vibration amplitude of the cryocooler based on the Fraunhofer double-slit interference principle. This method not only has a high resolution, but also has the ability to measure the vibration of distant objects, and is especially suitable for cryostat vibration measurement and analysis.
Methods The laser is divided into two beams by the beam splitter after collimation. Beam 1 and beam 2 are used as the reference and signal lights, respectively. First, beam 1 and beam 2 pass through the slit, respectively, to generate slit light. Then, they are reflected by mirror 1, which is fixed, and mirror 2, which is mounted on the vibration object to be measuring and pass through the slit again. Finally, the two beams focus on the focal plane by focusing the lens on generating interference fringes, acquired by the plane-array charge-coupled device (CCD). The light intensity distribution of the fringes at the focal plane is similar to that of Fraunhofer diffraction (Fig.1) when assuming that the two-slit beams are parallel to each other and there is a specific interval between the two-slit beams after passing through the spectroscope. Because the position of the interference fringe is related to the phase of the two-slit beams, we can obtain vibration information about the sample holder by acquiring the position of maximum intensity of the interference fringe. Furthermore, the factors influencing measurement results are investigated to avoid a significant amount of experimental work.
Results and Discussions The resolution of displacement measurement is affected by the parameters of the optical system under the same displacement speed and the same CCD sampling rate through Eq. (6) and Eq. (9). Increasing the focal lengths of the focusing lens, decreasing the slit width and the slit spacing can improve the resolution of the measurement. However, the intensity of light will decrease(Fig.4 and Fig. 5). We conclude that the appropriate slit spacing, slit width and focal length according to the actual situation of CCD are chosen. In this paper, the focal length of the focusing lens is 150 mm, and the size of a single-pixel of the CCD is 13.5 μm. By adjusting the parameters of the optical system, the number of pixels in a cycle is set at around 40, the maximum sampling rate of CCD is 3000 frame/s and the laser wavelength is 532 nm. Hence, the resolution of this device is about 6.65 nm theoretically. The results show that this method can accurately obtain the submicron-level vibration of vibrating objects, and the resolution can reach 10 nm (Table 1). Finally, the vibration curve of the vibration-free cryostat is measured using the optical system (Fig. 9).
Conclusions The current study proposes a novel vibration measuring method for measuring the vibration amplitude of the cryocooler based on the Fraunhofer double-slit interference principle. The factors influencing measurement results are investigated, and the performance of the system is evaluated using a commercial PZT. The results show that the precision of the device can reach 10 nm in the 50--1000 nm vibration range. Furthermore, the vibration of the sample holder of the GM cryocooler after vibration reduction is measured and analyzed with this vibration measuring device. Measured results show that the vibration amplitude of the sample holder is reduced from ±15 to ±0.3 μm. However, the vibration spectrum of the cryostat shows a frequency of 1 Hz, indicating that, whereas the vibration reduction method effectively inhibits vibration transfer from cold head to sample holder, there is still a large optimization space. As a result, this work provides considerable support for further optimization of the vibration level of the cryocooler.