Detection method for measuring high reflectivity uniformity of curved surface reflection optical element capable of being mathematically described based on cavity ring-down technology

Abstract

The invention discloses a detection method for measuring the reflectivity uniformity of a curved-surface high-reflection optical element capable of being mathematically described based on an optical cavity ring-down technology, and the method comprises the steps: carrying out the modeling of the surface shape of the curved-surface high-reflection optical element capable of being accurately and mathematically described, and obtaining a two-dimensional transverse position coordinate (x, y) of a measured point on a curved surface; y) and other quantities (a longitudinal position coordinate z, a pitch angle # imgabs0 # and a deflection angle alpha) required to be synchronously adjusted; the positioning control system has five freely adjustable dimensions, namely three position coordinates and two angle dimensions; two-dimensional transverse position scanning is carried out on the element through a control program, and meanwhile, residual dimensions are adjusted to realize longitudinal position and angle compensation, so that reflectivity space distribution of high-reflection optical elements with different calibers and different surface shapes along with the change of scanning positions is obtained; for a sample with an unknown surface shape, a high-precision contourgraph can be used for measuring the surface shape contour and fitting to obtain an accurate mathematical description of the surface shape, and the reflectivity uniformity of any curved surface can be measured by changing the mathematical relationship between the regulating variable and the surface shape position function in a control program.

Description

Technical Field

[0001] The invention relates to the field of high reflectivity distribution measurement for curved reflective optical elements, and in particular to a method for measuring the reflectivity uniformity of a curved high reflective optical element that can be mathematically described based on an optical cavity ring-down technology. Background Art

[0002] Curved high-reflective optical elements, including spherical, aspherical, and free-form high-reflective optical elements, are key components in high-performance laser systems such as high-power laser systems, laser gyroscopes, and gravitational wave detection devices. Reflectivity uniformity, as an important characterization parameter of high-reflective optical elements, will not only directly affect the output energy of the laser system, but also its non-uniformity will introduce local loss and scattering, resulting in intensity non-uniformity, wavefront distortion, and performance degradation of the corresponding laser system. For example, in a laser gyroscope, the non-uniformity of the reflectivity of the resonant cavity mirror will lead to the laser gyroscope locking effect, which will have a huge impact on the linearity and stability of the laser gyroscope output. In high-power laser applications, the non-uniformity of the reflectivity of the focusing mirror will lead to changes in the beam intensity distribution and wavefront distortion, causing serious system safety issues. Therefore, it is of great significance to detect the reflectivity uniformity of curved high-reflective optical elements.

[0003] Cavity ring-down technology is the most commonly used method for accurately measuring reflectivity above 99.9%. This technology evaluates the loss of the cavity or the reflectivity of the test mirror by measuring the decay time of the light intensity captured in the cavity. This technology is insensitive to the power fluctuation of the light source and therefore has ultra-high measurement accuracy. At present, reports on the measurement of high reflectivity by cavity ring-down technology are mostly concentrated on planar reflective elements (CN202211232772.9 "A method for measuring the uniformity of reflectivity of large-aperture reflective optical elements based on large-size laser beams and planar array detection", CN201911352648.4 "A method for high-resolution imaging measurement of reflectivity distribution of high-reflectivity optical elements") The above patents use cavity ring-down technology combined with two-dimensional scanning to achieve high-reflectivity and high-resolution imaging measurement of large-aperture planar high-reflectivity elements. However, for curved high-reflectivity optical elements, due to the off-axis characteristics of the curved surface, traditional two-dimensional scanning is not suitable for detecting the uniformity of reflectivity of curved high-reflectivity optical elements. In recent years, there have been reports on the measurement of spherical high-reflection optical elements. (CN202410162026.X "A method for measuring the uniformity of reflectivity in a small area of ​​a spherical high-reflection optical element based on cavity ring-down technology") This patent determines the scanning range by observing the change in the output mode of the ring-down cavity, and realizes the measurement of the uniformity of reflectivity in a small area of ​​a spherical high-reflection optical element. (GWTruong, G.Winkler, T.Zederbauer, et al.Near-infrared scanning cavity ringdown for optical loss characterization of supermirrors[J].Optics Express, 2019, 27(14): 19141-19149.) In this paper, the spatial variation of optical loss of a spherical substrate super-reflection optical element with an aperture of 8 mm was measured by adjusting the cavity mirror with 4 degrees of freedom, but the problem of cavity length consistency was not considered during the measurement process.(Gutierrez N, Degallaix J, et al. Optical characterization of high performance mirrors based on cavityringdown time measurements with 6degrees of freedom mirror positioning[J]. Review of Scientific Instruments, 2023, 94(10): 105113.1-105113.10.) This paper also performs 6-degree-of-freedom adjustment on the cavity mirror, realizing the measurement of the spatial variation of the reflectivity of spherical high-reflectivity optical elements with an aperture of up to 30 mm. However, it uses PHD active frequency stabilization technology to lock the resonant frequency of the laser and the resonant cavity, which is technically complex and costly.

[0004] Based on the above research, this patent introduces a detection method based on the cavity ring-down technology to measure the reflectivity uniformity of the high-reflectivity optical element on the curved surface that can be mathematically described. The mathematical relationship between the position point on the curved high-reflectivity sample and the required adjustment amount is analyzed, and a five-dimensional positioning control system is built. Through the control program, the two-dimensional lateral position scanning of the element is realized while adjusting the remaining dimensions to achieve longitudinal position and angle compensation, thereby obtaining the reflectivity spatial distribution of high-reflectivity optical elements with different calibers and different surface shapes as the scanning position changes. Summary of the invention

[0005] The technical problem to be solved by the present invention is: in view of the problems of the existing detection method for the uniformity of reflectivity of curved surface high-reflectivity optical elements, such as small detection range, inconsistent cavity length, high system cost, and complex technology, a detection method for measuring the uniformity of reflectivity of curved surface high-reflectivity optical elements that can be mathematically described based on optical cavity ring-down technology is proposed. For the curved surface high-reflectivity optical elements with accurate mathematical description of the surface shape, the two-dimensional lateral position coordinates (x, y) of the measured point on the curved surface and other quantities (longitudinal position coordinates z, pitch angle) that need to be synchronously adjusted are analyzed through surface shape modeling. The mathematical relationship between the two-dimensional horizontal position scanning of the element and the deflection angle α is realized by the control program, while adjusting the remaining dimensions to achieve longitudinal position and angle compensation, so as to obtain the reflectivity spatial distribution of high-reflective optical elements with different apertures and different surface shapes as the scanning position changes. The specific implementation steps are as follows:

[0006] Step (1), using a signal generator 1 to apply a square wave signal to the semiconductor laser 2 for modulation, and coaxially couple the light beam emitted by the semiconductor laser 2 into the initial cavity, wherein the initial cavity is a "V"-shaped folded cavity, which is composed of a plane coupling mirror 3 and two identical plano-concave high-reflection cavity mirrors 4 and 5. The light beam is reflected back and forth in the cavity, and the ring-down signal is transmitted and output from the plano-concave high-reflection front cavity mirror 4, and is focused on the detection surface of the photodetector 7 through the focusing lens 6. The photodetector 7 is triggered at the falling edge of the square wave to collect the ring-down signal of the initial cavity, and the ring-down time τ of the initial cavity can be obtained by fitting the ring-down signal according to the single exponential decay function. 0

[0007] Step (2), vertically install the curved high-reflection sample 8 on the five-dimensional positioning control system 9, and add the positioning control system with the sample to be tested to the "V"-shaped folded initial cavity, adjust the rotating table at the bottom of the positioning control system so that the incident angle is the working angle of the sample to be tested, adjust the position of the positioning control system so that the incident light spot is located at the center of the sample, adjust the position of the plano-concave high-reflection rear cavity mirror 10, form a "Z"-shaped folded test cavity and try to keep the length of the initial cavity and the test cavity consistent. Adjust the pitch angle and yaw angle of the two plano-concave high-reflection cavity mirrors 4 and 5 to maximize the amplitude of the ring-down signal of the test cavity, and fit the collected ring-down signal according to the single exponential decay function to obtain the ring-down time τ of the test cavity 1 , ignoring the air loss, the single point reflectivity at the center of the curved high-reflectivity sample 8 is R = exp[(L / cτ 0 -L / cτ 1 )]. (L is the cavity length, c is the speed of light in vacuum).

[0008] Step (3), for a curved sample with an accurate mathematical description of the surface shape, taking a spherical sample as an example, the center of curvature of the spherical sample is taken as the coordinate origin, the Z axis is perpendicular to the sample surface and passes through the center of the sample surface to establish a spherical coordinate system. If the position coordinates, x and y, are known, the depth length required for adjustment can be calculated. Pitch Angle Swing Angle (ρ is the radius of curvature). For surface samples of other shapes, since the curvature of each point on the surface is different and the center of curvature is not at the same point, the entire surface shape cannot be described by a simple spherical coordinate system equation. It is necessary to solve the normal vector of each point on the surface. The required adjustment amount can be obtained by solving the projection component of the normal vector angle between two points along the coordinate axis and the position difference along the optical axis. For surface samples of unknown shape, the profile distribution of the surface shape can be obtained by measuring with a profilometer, and the surface shape can be fitted by selecting an appropriate mathematical function type to obtain an exact mathematical description of the surface shape before calculating the adjustment amount.

[0009] Step (4), write a positioning control program according to the mathematical relationship between the position and the adjustment amount obtained in step (3), and realize the computer positioning control of five dimensions through the driving module 11. In the two-dimensional position scanning process, each time a scanning position point is moved, the longitudinal position and angle of the point are compensated and the optical cavity output signal of the point is collected, and the signal data is transmitted to the computer 13 through the data acquisition card 12. The computer records the sample scanning position information at the same time, and the back-end program fits the optical cavity output signal and calculates the reflectivity, and then maps the reflectivity information to each position point, so as to obtain the spatial distribution of the surface reflectivity of samples with different surface shapes and different calibers.

[0010] The five-dimensional positioning control system consists of three linear electric displacement stages and a two-dimensional electric mirror frame, and a manual rotating stage is installed at the bottom of the device. By designing and processing the mechanical adapter, the coating surface of the sample mounted on the electric mirror frame and the XY plane composed of the linear electric displacement stage coincide with each other, and the center point of the sample coating surface vertically passes through the center of the bottom circular rotating stage. It is ensured that at different working angles, the optical axis always passes through the center point of the sample surface and coincides with the normal line of the center point.

[0011] The single exponential decay function is I(t)=Aexp(-t / τ)+B, A is the amplitude of the ring-down signal, t is the time, τ is the ring-down time, and B is the DC bias.

[0012] Among them, the spatial resolution of reflectivity measurement mainly depends on the laser spot diameter and the position scanning step.

[0013] The present invention has the following advantages: (1) The present invention is based on the optical feedback cavity ring-down technology, which reduces the complexity of the system and improves the coupling efficiency of the light beam to the optical resonant cavity. (2) A five-dimensional positioning control system is used to adjust the depth, pitch and yaw of the curved surface high-reflection sample during the two-dimensional position scanning process, so that the resonant cavity maintains a consistent cavity length during the scanning process and meets the cavity stability conditions. (3) For curved surface high-reflection samples with accurate mathematical descriptions of the surface shape, the spatial distribution of reflectivity of the surface of samples with different surface shapes and different apertures that changes with the scanning position can be obtained. (4) For samples with unknown surface shapes, a high-precision profilometer can be used to measure their surface contours and fit them to obtain an accurate mathematical description of the surface shape. By changing the mathematical relationship between the adjustment amount and the surface shape position function in the control program, the reflectivity uniformity measurement of any curved surface can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a schematic diagram of a system for measuring the uniformity of high reflectivity of curved reflective optical elements based on the cavity ring-down technology of the present invention;

[0015] Figure 2 This is a schematic diagram of the five-dimensional positioning control system of the present invention;

[0016] Figure 3 The surface shape function detected by the present invention is High reflectivity spatial distribution diagram of curved high reflective sample #1;

[0017] Figure 4 The surface shape function detected by the present invention is High reflectivity spatial distribution diagram of curved high reflective sample #2;

[0018] Figure 5 The surface shape function detected by the present invention is High reflectivity spatial distribution diagram of curved high reflective sample #3;

[0019] Figure 1 In the figure: 1 is a signal generator; 2 is a laser; 3 is a plane coupling mirror; 4 is a plano-concave high-reflection front cavity mirror; 5 is an initial cavity plano-concave high-reflection rear cavity mirror; 6 is a focusing lens; 7 is a photodetector; 8 is a curved surface high-reflection sample; 9 is a five-dimensional positioning control system; 10 is a test cavity plano-concave high-reflection rear cavity mirror; 11 is a positioning control drive module; 12 is a data acquisition card; 13 is a computer; DETAILED DESCRIPTION

[0020] Combine the following Figures 1 to 5 The present invention describes a detection method for measuring the reflectivity uniformity of a highly reflective optical element with a curved surface that can be described mathematically based on the cavity ring-down technology.

[0021] Build Figure 1 The curved surface reflectivity uniformity detection system based on the cavity ring-down technology shown in the figure: a signal generator 1 is used to apply a square wave signal to the semiconductor laser 2 for modulation, and the light beam emitted by the semiconductor laser 2 is coaxially coupled to the initial cavity, which is a "V"-shaped folded cavity, consisting of a plane coupling mirror 3 and two identical plano-concave high-reflection cavity mirrors 4 and 5. The light beam is reflected back and forth in the cavity, and the ring-down signal is transmitted and output from the plano-concave high-reflection front cavity mirror 4, and is focused on the detection surface of the photodetector 7 through the focusing lens 6. The photodetector 7 is triggered at the falling edge of the square wave to collect the ring-down signal of the initial cavity, and the ring-down signal is decayed according to the single exponential decay function I(t)=A. 0 exp(-t / τ 0 )+B 0 (A 0 is the initial cavity ring-down signal amplitude, t is time, τ 0 is the initial cavity ring-down time, B 0 The initial cavity ring-down time τ can be obtained by fitting 0

[0022] The curved high-reflection sample 8 is vertically mounted on a five-dimensional positioning control system 9. The five-dimensional positioning control system is as follows: Figure 2As shown, the positioning control system with the sample to be tested is added to the "V"-shaped folded initial cavity, the rotating table at the bottom of the positioning control system is adjusted so that the incident angle is the working angle of the sample to be tested, the position of the positioning control system is adjusted so that the incident light spot is located at the center of the sample, and the position of the plano-concave high-reflection rear cavity mirror 10 is adjusted. At this time, the plane coupling mirror 3, the plano-concave high-reflection front cavity mirror 4, the curved high-reflection sample 8, and the plano-concave high-reflection rear cavity mirror 10 form a "Z"-shaped folded test cavity and try to keep the initial cavity and the test cavity length consistent. Adjust the pitch angle and yaw angle of the two plano-concave high-reflection cavity mirrors 4 and 5 to maximize the amplitude of the ring-down signal of the test cavity, and the collected ring-down signal is decayed according to the single exponential attenuation function I(t)=A 1 exp(-t / τ 1 )+B 1 (A 1 is the amplitude of the test cavity ring-down signal, t is the time, τ 1 is the ring-down time of the test cavity, B 1 The ring-down time τ of the test cavity is obtained by fitting 1 , ignoring the air loss, the single point reflectivity at a certain position of the curved high-reflectivity sample 8 is R = exp[(L / cτ 0 -L / cτ 1 )](L is the cavity length, c is the speed of light in vacuum).

[0023] For curved samples with accurate mathematical descriptions of their surface shapes, take a spherical sample as an example, take the center of curvature of the spherical sample as the coordinate origin, and establish a spherical coordinate system with the Z axis perpendicular to the sample surface and passing through the center of the sample surface. If the position coordinates, x and y, are known, the required depth length can be calculated. Pitch Angle Swing Angle (ρ is the radius of curvature). For other surface samples, since the curvature of each point on the surface is different and the center of curvature is not at the same point, the entire surface cannot be described by a simple spherical coordinate system equation. It is necessary to solve the normal vector of each point on the surface. The required adjustment amount can be obtained by solving the horizontal and vertical angles and the axial position difference between the normal vectors of two points. For surfaces with unknown shapes, the profile distribution of the surface can be obtained by measuring with a profilometer. The surface can be fitted by selecting an appropriate mathematical function type to obtain an exact mathematical description of the surface before calculating the adjustment amount.

[0024] The positioning control program is written according to the mathematical relationship between the position and the adjustment amount, and the computer realizes the positioning control of five dimensions through the driving module 11. In the two-dimensional position scanning process, each time a scanning position point is moved, the longitudinal position and angle of the point are compensated and the optical cavity output signal of the point is collected, and the signal data is transmitted to the computer 13 through the data acquisition card 12. The computer records the sample scanning position information at the same time. The back-end program fits the optical cavity output signal and calculates the reflectivity, and then maps the reflectivity information to each position point, so as to obtain the spatial distribution of the surface reflectivity of high-reflectivity samples with different surface shapes and different diameters.

[0025] The reflectivity of three curved surface samples with different surface shapes was repeatedly scanned and measured six times. The scanning results of samples #1, #2, and #3 are as follows: Figure 3 , Figure 4 , Figure 5 As shown. Sample #1 is a high-reflection sample with a spliced ​​surface shape, and the spliced ​​surface shapes are spherical and annular respectively. Sample #2 and sample #3 are spherical high-reflection samples. The average reflectance of the three samples measured repeatedly is 99.9826±2.6x10 -4 %、99.9891±6.7x10 -4 %、99.9837±53x10 -4 %, among which there is a black ring in the reflectivity distribution diagram of sample #1. The reflectivity distribution inside the ring is the reflectivity distribution of the sphere, and the reflectivity distribution outside the ring is the reflectivity distribution of the plane. The ring is located at the junction of two continuous surfaces. This is because the surface shape at the junction suddenly changes and the first-order derivative of the surface shape is discontinuous. The light spot moves to the vicinity of the junction and is dispersed, resulting in the detector not being able to collect effective optical cavity output signals, resulting in a ring-shaped signal-free area, which is in line with mathematical laws. Only two small defects were detected in the coating area of ​​sample #2, and both were located at the edge, indicating that sample #2 has good reflectivity uniformity. There are many defects in the coating area of ​​sample #3, and the reflectivity fluctuations at the defect points cause the standard deviation of sample #3 to be larger, which is in line with the technical characteristics of the optical cavity ring-down technology that the measurement error increases with the decrease of reflectivity.

Claims

1. A detection method for measuring the reflectivity uniformity of a highly reflective optical element on a curved surface that can be mathematically described based on the cavity ring-down technology, the implementation steps of which are as follows: Step (1), using a signal generator 1 to apply a square wave signal to the semiconductor laser 2 for modulation, and coaxially coupling the light beam emitted by the semiconductor laser 2 into the initial cavity, wherein the initial cavity is a "V"-shaped folded cavity, which is composed of a plane coupling mirror 3 and two identical plano-concave high-reflection cavity mirrors 4 and 5. The light beam is reflected back and forth in the cavity, and the ring-down signal is transmitted and output from the plano-concave high-reflection front cavity mirror 4, and is focused on the detection surface of the photodetector 7 through the focusing lens 6. The photodetector 7 is triggered at the falling edge of the square wave to collect the ring-down signal of the initial cavity, and the ring-down time τ0 of the initial cavity can be obtained by fitting the ring-down signal according to the single exponential decay function. Step (2), vertically install the curved high-reflection sample 8 on the five-dimensional positioning control system 9, and add the positioning control system with the sample to be tested to the "V"-shaped folded initial cavity, adjust the bottom rotating table of the positioning control system so that the incident angle is the working angle of the sample to be tested, adjust the position of the positioning control system so that the incident light spot is located at the center of the sample, adjust the position of the plano-concave high-reflection rear cavity mirror 10, form a "Z"-shaped folded test cavity and try to keep the initial cavity and the test cavity length consistent. Adjust the pitch angle and yaw angle of the two plano-concave high-reflection cavity mirrors 4 and 5 to maximize the amplitude of the ring-down signal of the test cavity, fit the collected ring-down signal according to the single exponential decay function to obtain the ring-down time τ1 of the test cavity, and ignore the air loss. The single-point reflectivity at the center of the curved high-reflection sample 8 is R=exp[(L / cτ0-L / cτ1)]. (L is the cavity length, c is the speed of light in vacuum). Step (3), for a curved sample with an accurate mathematical description of the surface shape, taking a spherical sample as an example, the center of curvature of the spherical sample is taken as the coordinate origin, the Z axis is perpendicular to the sample surface and passes through the center of the sample surface to establish a spherical coordinate system. If the position coordinates, x and y, are known, the depth length required for adjustment can be calculated. Pitch Angle Swing Angle (ρ is the radius of curvature). For surface samples of other shapes, since the curvature of each point on the surface is different and the center of curvature is not at the same point, the entire surface shape cannot be described by a simple spherical coordinate system equation. It is necessary to solve the normal vector of each point on the surface. The required adjustment amount can be obtained by solving the projection component of the normal vector angle between two points along the coordinate axis and the position difference along the optical axis. For surface samples of unknown shape, the profile distribution of the surface shape can be obtained by measuring with a profilometer, and the surface shape can be fitted by selecting an appropriate mathematical function type to obtain an exact mathematical description of the surface shape before calculating the adjustment amount. Step (4), write a program according to the mathematical relationship between the position and the adjustment amount obtained in step (3), and realize the computer positioning control of five dimensions through the driving module 11. In the two-dimensional position scanning process, each time a scanning position point is moved, the longitudinal position and angle of the point are compensated and the optical cavity output signal of the point is collected, and the signal data is transmitted to the computer 13 through the data acquisition card 12. The computer records the sample scanning position information at the same time, and the back-end program fits the optical cavity output signal and calculates the reflectivity, and then maps the reflectivity information to each position point, so as to obtain the spatial distribution of the surface reflectivity of samples with different surface shapes and different calibers.

2. According to claim 1, a detection method for measuring the reflectivity uniformity of a highly reflective optical element with a mathematically describable curved surface based on the cavity ring-down technique, characterized in that: The five-dimensional positioning control system consists of three linear electric translation stages and a two-dimensional electric mirror frame, and a manual rotating stage is installed at the bottom of the device. By designing and processing mechanical adapters, the coating surface of the sample mounted on the electric mirror frame and the XY plane composed of the linear electric translation stage coincide with each other, and the center point of the sample coating surface vertically passes through the center of the bottom circular rotating stage. It is ensured that at different working angles, the optical axis always passes through the center point of the sample surface and coincides with the normal line of the center point.

3. The detection method for measuring the reflectivity uniformity of a highly reflective optical element with a mathematically describable curved surface based on the cavity ring-down technique according to claim 1, characterized in that: The single exponential decay function is I(t)=Aexp(-t / τ)+B, where A is the amplitude of the ring-down signal, t is time, τ is the ring-down time, and B is the DC bias.

4. According to claim 1, a detection method for measuring the reflectivity uniformity of a highly reflective optical element with a mathematically describable curved surface based on the cavity ring-down technique, characterized in that: For highly reflective samples with an accurate mathematical description of their surface shape, the spatial distribution of their surface reflectivity that varies with the scanning position can be obtained by surface modeling and writing a positioning control program.

5. The detection method for measuring the reflectivity uniformity of a highly reflective optical element with a mathematically describable curved surface based on the cavity ring-down technique according to claim 1, characterized in that: For samples with unknown surface shapes, a high-precision profilometer can be used to measure their surface contours and fit them to obtain an accurate mathematical description of the surface shape. By changing the mathematical relationship between the adjustment amount and the surface position function in the control program, the reflectivity uniformity measurement of any curved surface can be achieved.

6. The detection method for measuring the reflectivity uniformity of a highly reflective optical element with a mathematically describable curved surface based on the cavity ring-down technique according to claim 1, characterized in that: The spatial resolution of reflectivity measurement depends mainly on the laser spot diameter and the position scanning step size.

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