Method and device for measuring the coefficient of liquid expansion

Abstract

The application discloses a kind of liquid expansion coefficient measurement method and device.The method comprises: laser emits laser, passes through lens expansion, passes through beam splitter BS and is divided into measuring light and reference light;Measuring light passes through mirror adjustment light path length, again with vertical direction 45 ° mirror reflection into the mirror M7 on the water surface in refrigeration box, after M7 reflection, along the original light path returns to BS;Reference light passes through compensation plate PCP, then, after passing through polaroid PL1, it is polarized, with vertical direction 45 ° mirror reflection into the mirror M8 on the bottom plate in refrigeration box, after M8 reflection, along the original light path returns to BS;Two beams of light are combined at BS, after passing through polaroid PL2 and diaphragm DP adjustment contrast ratio removes stray light and enters sCMOS camera, obtains non-local interference fringe distribution, using center light intensity analysis algorithm, obtains liquid level height variation rate and temperature variation rate, and further obtains the expansion coefficient of liquid and uncertainty.

Description

Technical Field

[0001] This invention relates to a device for measuring the coefficient of thermal expansion of a liquid, specifically a method and device for measuring the coefficient of thermal expansion of a liquid based on a Michelson nonlocal interferometer. Background Technology

[0002] Thermal expansion refers to the phenomenon of an object expanding in volume due to a change in temperature. Thermal expansion is ubiquitous in our daily lives, playing a crucial role in everything from rising sea levels and melting polar glaciers to bridge design and the evaluation of steel performance grades. Currently available devices for measuring the coefficient of thermal expansion of liquids include those using capillary tubes (Chinese Patent CN201610458450.4), burettes (Chinese Patent CN202220139671.6), or force sensors (Chinese Patent CN103728336A) to measure liquids above room temperature, and those using U-tube densitometers (Chinese Patent CN105548244A) to measure the coefficient of thermal expansion of liquids. The burette-based device for measuring the coefficient of thermal expansion has a temperature graduation of 0.5℃, resulting in low accuracy. The device based on the apparent weight method (Chinese Patent CN201120375047.8) connects the detector and measuring equipment with a rigid rod, which prevents control over the liquid temperature. The force sensor-based measurement did not provide detailed parameters or measurement temperature, and it was impossible to control the temperature below room temperature. The measurement method based on the U-tube vibrating density meter did not take into account association, therefore it had a large error when measuring the thermal expansion coefficient of liquids with strong association, and was completely unsuitable for measuring the thermal expansion coefficient of water.

[0003] In summary, current liquid expansion coefficient measuring devices either can only measure liquids above room temperature or have methodological defects, resulting in a narrow range of applications. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a device for measuring the coefficient of thermal expansion of liquids, comprising a float, a Michelson nonlocal interferometer, and a liquid homogenization cooling device. Using this invention and its method, accurate measurement of the coefficient of thermal expansion of liquids at different temperatures can be achieved.

[0005] According to one aspect of the present invention, a method for measuring the coefficient of thermal expansion of a liquid is provided, specifically comprising the following steps:

[0006] S1, the laser emits a laser beam, which is expanded by lenses L1, L2, and L3, and then split into a measurement beam and a reference beam by the beam splitter BS;

[0007] S2, the measured light passes through mirrors M3, M4, M5, and M6 to adjust the optical path length, and then is reflected by mirrors at a 45° angle to the vertical direction into mirror M7 on the water surface in the cooling box CC. After being reflected by M7, the light returns to BS along the original optical path.

[0008] S3, the reference light passes through the compensation plate PCP, then is polarized by the polarizer PL1, and is reflected by the mirror at 45° to the vertical direction into the mirror M8 on the bottom plate of the cooling box CC. After being reflected by M8, it returns to BS along the original optical path.

[0009] S4, the two beams of light are combined at BS, and after passing through polarizer PL2 and aperture DP to adjust the contrast and remove stray light, they enter the sCMOS camera to obtain the non-local interference fringe distribution. Using the central light intensity analysis algorithm, the rate of change of liquid level and the rate of change of temperature are obtained, and the expansion coefficient and uncertainty of the liquid are further obtained.

[0010] Specifically:

[0011] Near the optical axis, the intensity distribution of the nonlocal interference fringes in the Michelson interferometer is as follows:

[0012]

[0013] In equation (1), r1 is the optical path length of the measurement light from the laser beam waist position to the sCMOS camera, r2 is the optical path length of the reference light from the laser beam waist position to the sCMOS camera, r is the radius of a point on the pattern at the sCMOS camera from the center, I0 is the light intensity at the center of the interference ring, and λ is the wavelength of the laser.

[0014] Furthermore, when r << r1 and r << r2, then Therefore, the interference pattern extends from the center of the circle to a given radius. The sum of light intensity at each location W r0 satisfy:

[0015]

[0016] Therefore, the sum of the light intensities at the center of the pattern Interference, reference optical path difference between the two arms The relationship is approximately trigonometric, and the displacement change can be calculated by measuring the change in light intensity at the center of the pattern.

[0017] When the light intensity is less than the maximum grayscale value of the sCMOS camera, the relationship between light intensity and grayscale value is approximately linear. By reading the grayscale value of the sCMOS camera frame by frame, the relationship between light intensity and time can be obtained.

[0018] Furthermore, the volume expansion of the liquid is converted into the displacement change of the interferometer arm of the Michelson interferometer. In the case of no phase change in the liquid, the definition of the liquid's expansion coefficient is given by... And given Δa=Δ(r1-r2), the coefficient of expansion of the liquid is:

[0019]

[0020] In equation (3), A is the surface area of ​​the liquid, V is the volume of the liquid, T is the temperature of the liquid, Δa is the displacement of the water surface, Δt is the time interval during measurement, and ΔT is the temperature change during measurement.

[0021] The central light intensity analysis algorithm analyzes the obtained non-local interferometric pattern change video and temperature change data over time, and derives the thermal expansion coefficient and variance of the liquid under test within this temperature range.

[0022] The central light intensity analysis algorithm approximates the rate of change of liquid level height within the measurement time by linearly fitting the solved displacement data. Based on the given temperature data, the algorithm approximates the rate of change of temperature within the measurement time by linear fitting.

[0023] According to another aspect of the present invention, the present invention provides a measuring device for the coefficient of thermal expansion of a liquid, specifically comprising:

[0024] A laser (LASER) is used to emit laser light.

[0025] Lenses L1, L2, and L3 are used to expand the laser beam emitted by the laser.

[0026] Beam splitter (BS) is used to split the expanded laser beam into a measurement beam and a reference beam.

[0027] Reflectors M3, M4, M5, and M6 are used to adjust the optical path length of the measuring light, and then reflect it through a reflector at a 45° angle to the vertical direction into a reflector M7 on the water surface in the cooling box CC. After being reflected by M7, the light returns to BS along the original optical path.

[0028] After the reference light passes through the compensation plate PCP, it is then polarized by the polarizer PL1, and reflected by the mirror at a 45° angle to the vertical direction into the mirror M8 on the bottom plate of the cooling box CC. After being reflected by M8, it returns to BS along the original optical path.

[0029] Two beams of light are combined at BS, and after passing through polarizer PL2 and aperture DP to adjust the contrast and remove stray light, they enter the sCMOS camera to obtain the non-local interference fringe distribution. Using the central light intensity analysis algorithm, the rate of change of liquid level and the rate of change of temperature are obtained, and the expansion coefficient and uncertainty of the liquid are further obtained.

[0030] Advantages and positive effects of this invention compared to existing technologies:

[0031] 1. The device of this invention is suitable for different liquids and is easy to clean;

[0032] 2. The device of the present invention can reach a minimum cooling temperature of -2°C when the room temperature is 19°C, and can monitor the temperature uniformity in real time;

[0033] 3. The device of the present invention can accurately measure the expansion coefficient of liquids below room temperature;

[0034] 4. The algorithm developed in this invention can monitor nonlinear displacements occurring within half a wavelength, with an error rate of approximately 2%. This method can be directly applied to Michelson interferometers. Attached Figure Description

[0035] Figure 1 A schematic diagram of the liquid expansion coefficient measuring device is shown.

[0036] Figure 2 A schematic diagram of the refrigeration device is shown;

[0037] Figure 3 This diagram illustrates the algorithm flow for central light intensity analysis.

[0038] Figure 4 (a) shows an example of the interference pattern and the central light intensity selection area, and (b) shows the measurement data and results of the displacement of the interferometer arm mirror over time.

[0039] Figure 5 A schematic diagram showing how water temperature changes over time at different locations. Detailed Implementation

[0040] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0041] Figure 1 This is a schematic diagram of a precise liquid expansion coefficient measurement device according to the present invention. A laser emits a laser beam, which is expanded by lenses L1, L2, and L3, and then split into a measurement beam and a reference beam by a beam splitter BS. The measurement beam is adjusted in length by reflectors M3, M4, M5, and M6, and then reflected by a reflector at a 45° angle to the vertical direction into a reflector M7 on the water surface in the cooling tank CC. After reflection by M7, it returns to BS along the original optical path. The reference beam passes through a compensation plate PCP, is polarized by a polarizer PL1, and is reflected by a reflector at a 45° angle to the vertical direction into a reflector M8 on the bottom plate of the cooling tank CC. After reflection by M8, it returns to BS along the original optical path. The two beams are combined at BS, and after contrast adjustment by polarizer PL2 and aperture DP to remove stray light, they enter an sCMOS camera to obtain a non-local interference fringe distribution. Using a central light intensity analysis algorithm, the rate of change of liquid level height and the rate of change of temperature are obtained, and the expansion coefficient and uncertainty of the liquid are further obtained. Specifically:

[0042] Near the optical axis, the intensity distribution of the nonlocal interference fringes in the Michelson interferometer is as follows:

[0043]

[0044] In equation (1), r1 = 270 cm is the optical path length of the measurement light from the laser beam waist to the sCMOS camera, r2 = 316 cm is the optical path length of the reference light from the laser beam waist to the sCMOS camera, r < 4.4 cm is the radius of a point on the pattern at the sCMOS camera from the center, I0 is the light intensity at the center of the interference ring, and λ is the wavelength of the laser. Therefore, the interference pattern extends from the center of the circle to a given radius. The sum of light intensity at position satisfy:

[0045]

[0046] Therefore, the sum of the light intensities at the center of the pattern, W r0 Interference, reference optical path difference between the two arms The relationship is approximately trigonometric, and the displacement change can be calculated by measuring the change in light intensity at the center of the image. When the light intensity is less than the maximum grayscale value of the sCMOS camera, the relationship between light intensity and grayscale value is approximately linear. By reading the grayscale values ​​of the sCMOS camera frame by frame, the change in light intensity over time can be obtained.

[0047] A float with a mirror is placed on the liquid surface, converting the liquid's volume expansion into a displacement change in the interferometer arm of a Michelson interferometer. The coefficient of liquid expansion is defined as follows: [Formula omitted for brevity]. And given Δa=Δ(r1-r2), the coefficient of expansion of the liquid is:

[0048]

[0049] In the formula, A is the surface area of ​​the liquid, V is the volume of the liquid, T is the temperature of the liquid, Δa is the displacement of the water surface, Δt is the time interval during measurement, and ΔT is the temperature change during measurement.

[0050] like Figure 2 As shown Figure 1Detailed structure of the cooling chamber. The specific structure of the cooling chamber includes: a silicon dioxide SL with an internal vacuum chamber VC forming its outer side; a low thermal conductivity plate LTCP forming its bottom and inner side; a 5mm thick high thermal conductivity metal plate HTCP laid on the low thermal conductivity plate at the bottom; soft insulation material SP laid on the brass cooling ring CR, the metal plate HTCP, and the inner side; and a low thermal conductivity cover plate TL covering the top of the cooling chamber. A reference arm mirror M8 is placed on a steel plate. The brass cooling ring CR inside the cooling chamber is connected to an external water-cooled semiconductor refrigeration chip SR. There are two holes on the top of the cooling chamber that allow laser penetration, with a 0.5mm thick, 5cm diameter quartz disc SD fixed at the top of each hole. Hot melt adhesive is used to seal the joints of the cooling chamber. Two thermocouple thermometers Th1 and Th2 are placed in a beaker to monitor the temperature changes at both points in real time. A submersible water pump is also placed in the beaker. The mirror float M7 is made of material with a coefficient of thermal expansion of less than 10. -7 K -1 The quartz glass air chamber is made with a mirror. The mirror is coated with a 30nm zinc oxide film to prevent fogging at low temperatures.

[0051] Preferably, rigid polyurethane composite panels are selected as LTCP and TL;

[0052] Preferably, 304 stainless steel plate is selected as HTCP;

[0053] Preferably, closed-cell foamed rubber and plastic sponge is selected as SP;

[0054] Experiment 1 was conducted using a precise liquid expansion coefficient measuring device. The device's measurement accuracy and temperature uniformity were assessed.

[0055] Based on the precise liquid expansion coefficient measuring device of the present invention, the present invention also relates to a central light intensity analysis algorithm. The specific process of the central light intensity analysis algorithm is as follows: Figure 3The algorithm can analyze the obtained non-local interferometric pattern change video and temperature change data over time, and obtain the thermal expansion coefficient and variance of the liquid under test within this temperature range. The algorithm is mainly divided into four parts: temperature processing, selection area determination, video processing and calculation results. In the temperature processing part, by giving the USB thermometer data address, the start time of reading and the total reading time, linear fitting can be performed and the temperature change rate during the measurement time can be approximately calculated. Then, the selection area determination part is entered. This part needs to determine the selection area to be analyzed based on the image of the first frame after inputting the video address, and copy the parameters into the video processing part. According to the approximate linear relationship between the gray value of the pattern received by the sCMOS camera and the light intensity, the light intensity can be approximately calculated by summing the center gray value of the given pattern. Then, according to equation (2), the distance of the liquid surface where the float is located from the beginning of the video can be calculated. For wavelength variations exceeding one wavelength, the displacement data is obtained by first finding the peak, then finding the valley between each pair of peaks, and finally performing an inverse trigonometric function on the data between adjacent peaks and valleys. For wavelength variations less than one wavelength, the distances between mirrors M3 and M4, and mirrors M5 and M6, need to be adjusted to change the optical path difference between the interference arm and the reference arm. This allows for the accumulation of grayscale values ​​at the moments of strongest and darkest light intensity at the center of the image. The resulting light intensity data is then subjected to an inverse trigonometric function transformation to obtain the displacement data.

[0056] The algorithm approximates the rate of change of liquid level height within the measurement time by linearly fitting the solved displacement data. Combining the results of the temperature processing section and equation (3), the algorithm can calculate the thermal expansion coefficient of the liquid under test and its uncertainty (P = 99.73%).

[0057] A helium-neon laser with a wavelength of 632.8 nm was used as the light source. Video of the interferometer arm moving at a rate of 0.1 mm / s was captured using a high-speed camera (20000 FPS). The pattern is shown below. Figure 4 As shown in (a), the area within the black circle is the selection region. The high-speed camera is only used during verification; the implementation example uses an sCMOS camera.

[0058] Using the above-mentioned central light intensity analysis algorithm, the change of the central light intensity of the interference fringes with time is processed to obtain the relationship between displacement and time, such as... Figure 4 As shown in (b), the displacement rate calculated using the center intensity method is 946 ± 2 μm / s (confidence probability P = 99.73%). Subtracting the measured data from the fitted straight line reveals a measurement deviation of approximately 7 nm within a wavelength range. This indicates that the intensity method has strong anti-interference capabilities and good durability.

[0059] like Figure 5The diagram shows the water temperature changes over time at different locations. Three thermocouples were used to detect the temperature at the top, middle, and bottom of the beaker, respectively. The water temperature inside the beaker was approximately uniform within about 90 seconds.

[0060] Experiment 2 was conducted using a precise liquid expansion coefficient measuring device to measure the expansion coefficient of water.

[0061] A helium-neon laser with a wavelength of 632.8nm is used as the light source. Turn on the cooler and wait for the water temperature to drop below the target temperature, then turn it off. Turn on the water pump and run it for approximately 2 minutes, then turn it off. After waiting approximately 1 minute and 30 seconds, turn on the cooled camera (RNRT-20C) to record video. (Use as follows...) Figure 3 The algorithm process analyzes the recorded video.

[0062] The test was conducted when the water surface displacement exceeded one wavelength. The corresponding light intensity change was read using the central light intensity method: peaks and troughs were found in the time-intensity data and converted into displacement. Linear fitting was then performed to calculate the displacement rate, which in turn yielded the thermal expansion coefficient of water at a specific temperature. At the start of the test, the water temperature was 12.60℃, and at the end, it was 12.40℃. Using the aforementioned central light intensity analysis algorithm, the displacement rate of the central light intensity was found to be 68.73±0.08nm / s. The cooling rate of the refrigeration device was -7.19±0.46mK / s, and the calculated thermal expansion coefficient of water was (1.18±0.18)*10. -5 K -1 (P = 99.73%). The reference value for the coefficient of water expansion is (1.20 ± 0.01) * 10⁻⁶ at 12.40–12.60℃. -4 K -1 This is consistent with the experimental results. The data processing method for other displacements greater than one wavelength is the same as described above, as detailed in Table 1.

[0063] Table 1. Coefficients of water expansion measured at different temperatures (confidence probability 99.73%)

[0064]

[0065]

[0066] When testing water surface displacement less than one wavelength, the corresponding light intensity change was read using the central light intensity method: The optical path difference (i.e., the distance between M3 and M4, and M5 and M6) was adjusted to obtain the grayscale values ​​of the maximum and minimum light intensities at the image center. An inverse trigonometric function transformation was then performed on the light intensity data to calculate the displacement rate, thereby determining the coefficient of thermal expansion of water at a specific temperature. At the start of the test, the water temperature was 3.20℃, and at the end, it was 3.40℃. Using the aforementioned central light intensity analysis algorithm, the displacement rate of the central light intensity was found to be 7.85±0.36nm / s, the cooling rate of the cooling device was 8.15±1.14mK / s, and the coefficient of thermal expansion of water was calculated to be -(1.18±0.17)*10. -5 K -1 (P = 99.73%), when the temperature is between 3.20 and 3.40℃, the reference value for the coefficient of water expansion is -(1.04 ± 0.16) * 10⁻⁶. -5 K -1 This is consistent with the experimental results. The data processing method for other displacements less than one wavelength is the same as described above, as detailed in Table 2.

[0067] Table 2. Coefficients of water expansion measured at different temperatures (confidence probability 99.73%)

[0068]

[0069] Overall, the measured value of the coefficient of water expansion deviates from the accepted value by approximately 10%. -7 -10 -6 K -1 .

[0070] The above embodiments are provided merely for the purpose of describing the present invention and are not intended to limit the scope of the invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications made without departing from the spirit and principles of the invention should be covered within the scope of the invention.

Claims

1. A method for measuring the coefficient of thermal expansion of a liquid, characterized in that, The device for measuring the coefficient of liquid expansion includes a float, a Michelson nonlocal interferometer, and a liquid homogenization cooling device; the reflector M7 acts as the float, and the liquid has a coefficient of expansion of less than 10. -7 K -1 The quartz glass gas chamber is made with a mirror coated with a 30nm zinc oxide thin film. The measurement method specifically includes the following steps: S1, the laser emits a laser beam, which is expanded by lenses L1, L2, and L3, and then split into a measurement beam and a reference beam by a beam splitter BS; S2, the measured light passes through mirrors M3, M4, M5, and M6 to adjust the optical path length, and then is reflected by mirrors at a 45° angle to the vertical direction into mirror M7 on the water surface in the cooling box CC. After being reflected by M7, the light returns to BS along the original optical path. S3, the reference light passes through the compensation plate PCP, then is polarized by the polarizer PL1, and is reflected by the mirror at 45° to the vertical direction into the mirror M8 on the bottom plate of the cooling box CC. After being reflected by M8, it returns to BS along the original optical path. S4, the two beams of light are combined at BS, and after passing through polarizer PL2 and aperture DP to adjust the contrast and remove stray light, they enter the sCMOS camera to obtain the intensity distribution of non-local interference fringes. Using the central light intensity analysis algorithm, the rate of change of liquid level and the rate of change of temperature are obtained, and the expansion coefficient and uncertainty of the liquid are further obtained. when At that time, ; Interference pattern from the center of the circle to a given radius The sum of light intensities at a position of 1.4 cm satisfy: （2） in The optical path length of the measurement light from the laser beam waist to the sCMOS camera. Let r be the optical path length of the reference beam from the laser beam waist to the sCMOS camera, and r be the radius of a point on the pattern at the sCMOS camera from the center. The intensity of the nonlocal interference fringes in a Michelson interferometer near the optical axis. The light intensity at the center of the interference ring, The wavelength of the laser; Therefore, the sum of the light intensities at the center of the pattern Interference, reference optical path difference between the two arms The approximation is a trigonometric function relationship, and the displacement change is calculated by measuring the change in light intensity at the center of the pattern; Converting the volume expansion of a liquid into the displacement change of the interferometer arms of a Michelson interferometer, the definition of the liquid's expansion coefficient is given by the formula in the case of no phase change in the liquid. ,as well as The coefficient of expansion of the liquid is obtained as follows: （3） In equation (3), A is the surface area of ​​the liquid, V is the volume of the liquid, and T is the temperature of the liquid. For the displacement of the water surface, The time interval during measurement. This represents the temperature change during measurement.

2. The method for measuring the coefficient of liquid expansion according to claim 1, characterized in that, Near the optical axis, the intensity of the nonlocal interference fringes of the Michelson interferometer The distribution is as follows: （1）。 3. The method for measuring the coefficient of liquid expansion according to claim 1, characterized in that, When the light intensity is less than the maximum grayscale value of the sCMOS camera, the relationship between light intensity and grayscale value is approximately linear. By reading the grayscale value of the sCMOS camera frame by frame, the relationship between light intensity and time can be obtained.

4. The method for measuring the coefficient of liquid expansion according to claim 1, characterized in that, The central light intensity analysis algorithm analyzes the obtained non-local interferometric pattern change video and temperature change data over time, and derives the thermal expansion coefficient and variance of the liquid under test within this temperature range.

5. The method for measuring the coefficient of liquid expansion according to claim 1, characterized in that, The central light intensity analysis algorithm is mainly divided into four parts: temperature processing, selection area determination, video processing, and calculation results. In the temperature processing part, by giving the USB thermometer data address, the start time of reading, and the total reading time, linear fitting is performed to approximately calculate the rate of temperature change during the measurement time. Then, the selection area determination part is entered. After inputting the video address, the selection area to be analyzed needs to be determined based on the image of the first frame, and the parameters are copied into the video processing part.

6. The method for measuring the coefficient of liquid expansion according to claim 1, characterized in that, Based on the fact that the gray value of the image received by the sCMOS camera is approximately linearly related to the light intensity, the light intensity is approximately calculated by summing the center gray value of the given image. Then, the distance between the liquid surface where the float is located and the change at the beginning of the video is calculated according to the formula (2).

7. The method for measuring the coefficient of liquid expansion according to claim 6, characterized in that, For wavelength variations exceeding one wavelength, the displacement data is obtained by first finding the peak, then finding the valley between each pair of peaks, and finally performing an inverse trigonometric function on the data between adjacent peaks and valleys. For wavelength variations less than one wavelength, the distances between mirrors M3 and M4, and mirrors M5 and M6, need to be adjusted to change the optical path difference between the interference arm and the reference arm. This allows for the accumulation of grayscale values ​​at the moments of strongest and darkest light intensity at the center of the image. The resulting light intensity data is then subjected to an inverse trigonometric function transformation to obtain the displacement data.

8. The method for measuring the coefficient of liquid expansion according to claim 1, characterized in that, The central light intensity analysis algorithm approximates the rate of change of liquid level height within the measurement time by linearly fitting the solved displacement data. Based on the given temperature data, the algorithm approximates the rate of change of temperature within the measurement time by linear fitting.

9. A measuring apparatus for implementing the method for measuring the coefficient of thermal expansion of a liquid according to any one of claims 1-8, characterized in that, Specifically, it includes: A laser (LASER) is used to emit laser light. Lenses L1, L2, and L3 are used to expand the laser beam emitted by the laser. Beam splitter (BS) is used to split the expanded laser beam into a measurement beam and a reference beam. Reflectors M3, M4, M5, and M6 are used to adjust the optical path length of the measuring light, and then reflect it through a reflector at a 45° angle to the vertical direction into a reflector M7 on the water surface in the cooling box CC. After being reflected by M7, the light returns to BS along the original optical path. After the reference light passes through the compensation plate PCP, it is then polarized by the polarizer PL1, and reflected by the mirror at a 45° angle to the vertical direction into the mirror M8 on the bottom plate of the cooling box CC. After being reflected by M8, it returns to BS along the original optical path. Two beams of light are combined at BS, and after passing through polarizer PL2 and aperture DP to adjust the contrast and remove stray light, they enter the sCMOS camera to obtain the non-local interference fringe distribution. Using the central light intensity analysis algorithm, the rate of change of liquid level and the rate of change of temperature are obtained, and the expansion coefficient and uncertainty of the liquid are further obtained.

10. The measuring device for the coefficient of liquid expansion according to claim 9, characterized in that, The refrigeration box includes: The silica SL of the vacuum chamber VC forms the outer side of the refrigeration box, and the low thermal conductivity plate LTCP forms its bottom and inner side. A high thermal conductivity metal plate HTCP is laid on the low thermal conductivity plate at the bottom. The brass cooling ring CR, the metal plate HTCP and the inner side are all covered with soft insulation material SP, and the top of the refrigeration box is covered with a low thermal conductivity cover plate TL.

11. The measuring device for the coefficient of liquid expansion according to claim 10, characterized in that, The refrigeration unit also includes: A reference arm mirror M8 is placed on a steel plate, and the brass cooling ring CR inside the cooling box is connected to the external water-cooled semiconductor cooling chip SR.

12. The measuring device for the coefficient of liquid expansion according to claim 11, characterized in that, There are two holes on the top of the cooling box that can be penetrated by a laser, and a 0.5mm thick, 5cm diameter quartz disc SD is fixed on the top of the holes.

13. The measuring device for the coefficient of liquid expansion according to claim 11, characterized in that, The joints of the refrigeration box are sealed with hot melt adhesive. There are two thermocouple thermometers, Th1 and Th2, in the beaker to monitor the temperature changes at the two locations in real time. A submersible water pump is also placed in the beaker.

14. The measuring device for the coefficient of liquid expansion according to claim 10, characterized in that, The low thermal conductivity plate (LTCP) and the low thermal conductivity cover plate (TL) are made of rigid polyurethane composite board; 304 stainless steel plate is used as HTCP; and closed-cell foamed rubber and plastic sponge is used as SP.

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