Method and device for detecting the surface shape of a small-curvature-radius mirror

Abstract

This invention relates to a method and apparatus for detecting the surface shape of a small radius-of-curvature mirror. It utilizes a combination of a long-range surface profiler (LTP) and a computational hologram (CGH) assembly. Specifically, a CGH module and its position adjustment mechanism are added between the optical head of the LTP and the mirror under test. The CGH acts as a wavefront converter, using the CGH and its position adjustment mechanism to convert the wavefront shape of the measurement beam emitted by the laser from a planar wavefront to a wavefront matching the surface shape of the mirror under test, thereby achieving the detection of the surface shape of a small radius-of-curvature mirror. This invention achieves high-precision detection of the surface shape of curved mirrors by adding a corresponding auxiliary measurement component, the computational hologram (CGH), to the long-range surface profiler (LTP).

Description

Technical Field

[0001] This invention belongs to the field of optical detection technology and relates to a method and apparatus for detecting the surface shape of a small radius of curvature reflective mirror. Background Technology

[0002] With the development of synchrotron radiation sources and free-electron lasers, the requirements for the surface accuracy of curved mirrors used in such large scientific facilities are constantly increasing. The surface accuracy of curved mirrors is an important indicator affecting the quality of the light source. Therefore, there is an urgent need for a method and device for accepting and testing the surface quality of high-precision curved mirrors.

[0003] Long-Range Surface Profiler (LTP) has achieved high accuracy in the inspection of plane mirrors. Its measurement principle utilizes the displacement angle conversion principle of a Fourier lens for slope measurement. When measuring a plane mirror, the light beam that strikes the surface is reflected back, passes through a Fourier lens, and is captured by a CCD camera. However, when measuring curved mirrors, if the radius of curvature of the mirror is small, the reflected beam will diverge, changing from a circular beam to an elliptical beam. If the cross-sectional size of the reflected beam exceeds the size of the CCD detection window, LTP will be unable to perform the measurement. In actual measurement, the shape of the light spot on the CCD camera is as follows... Figure 1 As shown, during the measurement process, the slope difference between two adjacent points is determined by analyzing the position of the centroid of the light spot. When the measurement beam directly illuminates the curved mirror, the light spot on the CCD appears as follows: Figure 1 As shown in the right figure, the inability to accurately determine the centroid position of the light spot will lead to inaccurate measurement results. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a method and device for detecting the surface shape of a small radius of curvature mirror. By adding a corresponding auxiliary measurement component, namely the computational holographic GH, to the long-range surface shape meter (LTP), high-precision detection of the surface shape of curved mirrors can be achieved.

[0005] Technical solution of the present invention:

[0006] Firstly, this invention provides a method for detecting the surface shape of a small radius-of-curvature mirror. This method utilizes a long-range surface profiler (LTP) and a computational hologram (CGH) assembly. Specifically, a CGH module and its position adjustment mechanism are added between the optical head of the LTP and the mirror under test. The CGH acts as a wavefront converter, using the CGH and its position adjustment mechanism to convert the wavefront shape of the measurement beam emitted by the laser from a planar wavefront to a wavefront matching the surface shape of the mirror under test, thereby enabling the detection of the surface shape of a small radius-of-curvature mirror. The small radius of curvature refers to less than 1 meter, and can reach 10-20 mm.

[0007] Specifically, for curved mirrors with different curvatures, different CGH parameters can be used to achieve high-precision surface shape measurement of mirrors with small curvature radii, where high precision refers to repeatability of less than 30 nanoradians.

[0008] Specifically, the CGH is a variable line spacing grating; the CGH parameter refers to the linear density distribution of the variable line spacing grating, which is determined by the height of the CGH placement position from the surface of the mirror under test and the sagittal radius of the mirror under test.

[0009] In particular, when combining CGH and LTP, an angle is designed between the front and back surfaces of the quartz substrate of CGH. There is no mandatory requirement for the angle. After multiple experiments, 0.5° was selected to avoid stray light caused by reflection from the front and back surfaces of CGH from entering the detector system of LTP and interfering with the positioning of the measurement spot, thus avoiding stray light interference.

[0010] Specifically, the included angle described in CGH is designed based on the wavefront distribution of the LTP incident beam, so that the wavefront of the beam after passing through CGH matches the surface shape of the mirror under test. At the same time, by adjusting the linear density distribution parameters, other diffraction orders cannot return to the LTP detector system.

[0011] Specifically, the CGH's position adjustment mechanism is designed to allow movement in the X, Y, and Z directions and rotation around the X, Y, and Z axes, achieving a six-degree-of-freedom adjustment function. A combined mirror frame is mounted on the CGH. The two linear displacement platforms in the position adjustment mechanism enable linear movement along the X and Z axes, respectively. The mirror frame 3 in the combined mirror frame slides inside the slot 4 to move along the Y axis. The slot 4 rotates 360° in the mirror frame's frame 5 to achieve rotation around the Z axis. The three adjustment knobs of the frame 5 enable rotation around the X and Y axes. Through the adjustment of six degrees of freedom, the wavefront passing through the CGH is matched with the surface of the mirror to be tested.

[0012] Secondly, the present invention provides an apparatus for detecting the surface shape of a small radius of curvature mirror, comprising a long-range surface shape analyzer (LTP) and a computational hologram (CGH) assembly. A CGH module and its position adjustment mechanism are added between the optical head of the LTP and the mirror to be tested. The CGH is equivalent to a wavefront converter. The CGH and the adjustment mechanism are used to convert the wavefront shape of the measurement beam emitted by the laser from a planar wavefront to a wavefront matching the same as the surface shape of the mirror to be tested, thereby realizing the detection of the surface shape of a small radius of curvature mirror.

[0013] The advantages of this invention compared to the prior art are:

[0014] (1) This invention achieves high-precision detection of mirror surface with small curvature radius by adding an auxiliary measuring element CGH and its adjustment mechanism to the long-range surface shape instrument.

[0015] (2) This invention will greatly expand the measurement range of the long-range surface shape measuring system, enabling it to detect not only planar surfaces and curved reflector surfaces with large radii of curvature, but also cylindrical and toroidal reflector surfaces with small radii of curvature. It can detect the meridional surface shape of toroidal surfaces with sagittal radii of tens of millimeters, with measurement repeatability better than tens of nanoradians (RMS), meeting the high-precision detection requirements for large-size curved reflector surfaces. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 The images show the light spot shapes on a CCD camera when measuring plane mirrors and curved mirrors. The left image shows the light spot shape on a CCD camera when measuring a plane mirror, and the right image shows the light spot shape on a CCD camera when measuring a curved mirror.

[0018] Figure 2 This is a schematic diagram illustrating the principle of CGH ray tracing.

[0019] Figure 3 CGH working principle diagram;

[0020] Figure 4 This is a schematic diagram showing the possible values ​​of the included angle γ;

[0021] Figure 5 A 3D model of the CGH frame module;

[0022] Figure 6 This is a schematic diagram of the device structure of the present invention;

[0023] Figure 7 These are the optical path diagrams when measuring curved mirrors using CGH, where (a) is the optical path diagram without CGH and (b) is the optical path diagram with CGH.

[0024] Figure 8 For measuring the actual object;

[0025] Figure 9 This is a schematic diagram of the measurement results for three sets of slope values. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0027] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0028] like Figure 1 As shown, the shape of the light spot on the CCD camera during the actual measurement process is as follows: Figure 1 As shown in the left figure, during the measurement process, the slope difference between two adjacent points is determined by analyzing the position of the centroid of the light spot. When the measurement beam directly illuminates the curved mirror, the light spot on the CCD appears as follows: Figure 1 As shown in the right figure, the inability to accurately determine the centroid position of the light spot leads to inaccurate measurement results. This invention addresses this problem by combining a Long Range Surface Shape Analyzer (LTP) and a Computational Hologram Array (CGH). Specifically, a CGH module and its position adjustment mechanism are added between the optical head of the LTP and the mirror under test. The CGH acts as a wavefront converter, using the CGH and its position adjustment mechanism to convert the wavefront shape of the measurement beam emitted by the laser from a planar wavefront to a wavefront matching the surface shape of the mirror under test, thereby enabling the detection of the surface shape of mirrors with small curvature radii.

[0029] In this embodiment of the invention, a small radius of curvature refers to less than 1 meter, which can reach 10-20 mm.

[0030] In this embodiment of the invention, a small radius-of-curvature reflector is defined as one whose radius is small in only one direction and large in another, such as a cylindrical mirror or a toroidal mirror. The LTP and CGH combination measures the slope error in the direction with the larger radius.

[0031] When using LTP to measure curved mirrors, the beam divergence can cause measurement failures. Therefore, auxiliary measuring elements are needed to modify the beam wavefront to match the shape of the mirror under test, making the beam shape the same as when measuring plane mirrors. Lenses and CGHs are optical elements that can modify the beam wavefront. Although both CGHs and lenses act as compensators, their compensation principles are significantly different. CGHs primarily utilize the diffraction effect of light. The micro-nano structures on the CGH surface cause the plane wavefront to diffract, transforming it into a corresponding cylindrical wavefront upon reaching the measured surface, thus achieving zero-point compensation detection. The manufacturing precision of CGHs is easier to control than that of lenses, and their errors are easier to calibrate. Therefore, after extensive research and experimentation, the applicant chose CGHs to modify the measurement beam wavefront.

[0032] Through the embodiments of this invention, the measurement range of the long-range surface profiler system will be greatly expanded. It will no longer be limited to detecting planar surfaces and curved reflector surfaces with small curvatures; it will also be able to detect cylindrical surfaces with large curvatures and hyper-curved reflector surfaces. It can measure the meridional surface shape of a toroidal surface with an arc radius of 89.7 mm, with a measurement repeatability better than 30 nrad (RMS), meeting the high-precision measurement requirements for large-size curved reflector surfaces.

[0033] This invention adds a CGH (Conductivity, Heat, and Growth) component to the existing LTP (Light Targeting) system, enabling it to measure the surface shape of curved mirrors, such as hypersurfaces, along the meridional direction. For curved mirrors with different curvatures, high-precision measurements can be achieved by simply replacing the CGH component with one of different parameters. This invention does not require altering the original optical path structure of the LTP system; by adding a CGH component below the LTP optical head, the CGH converts the planar wavefront of the measurement beam into a wavefront identical to the surface shape of the mirror under test, achieving high-precision measurement of the meridional surface shape of a hypersurface with a sagittal radius of 89.7 mm. The measurement repeatability is better than 30 nrad (RMS). This invention economically and efficiently expands the functionality of existing LTP systems.

[0034] The core of CGH (Cyclic High-Growth Light) in altering the wavefront shape of a beam lies in controlling the phase function. This is typically achieved using optical design software to perform ray tracing on the beam passing through the CGH, in order to reconstruct the wavefront's phase function Ψ with high accuracy. CGH (x,y). For example... Figure 2 As shown, SUT is the reflector under test, and the plane wavefront is transformed into a wavefront that matches the reflector under test after passing through CGH.

[0035] Figure 2 A schematic diagram of the CGH ray tracing principle shows that any ray passing through any point on the CGH surface and incident on the surface of the mirror under test should be the normal at that point. The phase of the ray passing through the ray tracing point K is the phase difference of the optical path between the ray KA and the on-axis reference ray K0A0, which can be expressed as:

[0036]

[0037] Among them: Ψ CGH (x,y) represents the phase difference of the incident light before and after passing through the CGH, i.e., the modulation phase function of the light by the CGH; Ψ asphere (K) is the transformed aspherical wave that matches the surface shape of the mirror under test; opl(K0A0) is the optical path from K0 to A0.

[0038] The embodiments of the present invention are mainly aimed at cylindrical mirrors and toroidal mirrors with large radius of curvature in the meridional direction. The deformation of the light spot in the meridional direction is negligible. Therefore, when designing the CGH, it is only necessary to consider modulating the wavefront shape of the measurement beam in the sagittal direction from a plane to a cylinder.

[0039] This invention does not require altering the original optical path structure of the LTP system. It only requires adding a CGH module between the LTP optical head and the mirror to be measured. The CGH acts as a wavefront converter, transforming the wavefront shape of the measurement beam emitted by the laser from a planar plane to a wavefront that matches the surface shape of the mirror under test. This enables the surface shape measurement of mirrors with small curvature radii. The working principle of the CGH is as follows: Figure 3 As shown. Where h is the distance from CGH to the upper surface of the lens under test, ρ is the radius of the sagittal direction of the lens under test, and θ is the +1st order diffraction angle of the measurement beam after modulation by CGH.

[0040] The CGH parameters need to be determined based on the height of its placement relative to the surface of the mirror under test and the sagittal radius of the mirror. In this embodiment of the invention, the CGH is essentially a variable-pitch grating, and the line density distribution at different positions of the CGH can be calculated using the grating equation:

[0041] n2sin(θ0)+n1sinθ=mλN

[0042] In this system, the CGH is placed perpendicular to the optical path with an incident angle θ0 = 0, the air refractive index n1 = 1, the quartz refractive index n2 = 1.4699, m is the diffraction order of the CGH used in the measurement, which is taken as +1 order according to the design, and the wavelength of the measurement beam λ = 402 nm. θ is the +1 order diffraction angle of the measurement beam after modulation by the CGH. Figure 3 As shown, the value of θ is related to the sagittal radius ρ of the mirror under test and the distance h from CGH to the upper surface of the mirror. The equation for calculating θ is:

[0043]

[0044]

[0045] Where x is the coordinate along the direction of linear density variation of CGH, and N is the linear density of the measurement beam at a certain point on CGH.

[0046] For toroidal and cylindrical mirrors with different parameters, their sagittal radii vary. Therefore, a corresponding curvature radius detector (CGH) needs to be designed for each mirror to achieve surface shape measurement. Knowing the sagittal radius of curvature ρ of the mirror under test and the distance h from the CGH placement position to the upper surface of the mirror, the CGH linear density distribution can be obtained by substituting these values ​​into the above formula.

[0047] For cylindrical mirrors, just like for toroidal mirrors, the CGH linear density distribution can be obtained by only considering the radius of curvature in the sagittal direction.

[0048] It is important to note that during the CGH fabrication process, in order to prevent stray light reflected from the front and back surfaces of the CGH substrate from entering the CCD, an angle γ is designed on the front and back surfaces of the substrate, as shown in Figure 4. The optimal value of this angle γ is approximately 0.5°, which was determined through repeated experiments. This angle can effectively deflect stray light out of the CCD detection range.

[0049] The consistency between the actual position and the design value of the CGH in the measurement optical path affects its diffraction wavefront accuracy. Furthermore, to ensure that the linear density of each CGH is within a range suitable for manufacturing, the CGH's position adjustment mechanism needs to allow movement in the X, Y, and Z directions and rotation around the X, Y, and Z axes. To achieve this six-degree-of-freedom adjustment function, this embodiment of the invention designs a combined frame around the CGH installation, the three-dimensional model of which is shown below. Figure 4 As shown, this CGH frame module, while satisfying six degrees of freedom, has a compact structure and small size, making it easy to install and debug, and effectively connecting the LTP optical head to the CGH.

[0050] from Figure 5 As can be seen, linear displacement platforms 1 and 2 achieve linear movement along the X and Z axes, respectively; the mirror frame 3 slides inside the slot 4 to achieve movement along the Y axis; the slot 4 can rotate 360° within the mirror frame 5, achieving rotation around the Z axis; and the three adjustment knobs on the mirror frame 5 achieve rotation around the X and Y axes. Through adjustments of these six degrees of freedom, the wavefront passing through the CGH can be matched with the surface of the mirror under test.

[0051] like Figure 6 The diagram shown is a schematic diagram of the overall device structure of an embodiment of the present invention. A CGH module and its position adjustment mechanism are added between the optical head of the LTP and the mirror under test. The guide rail, autocollimator and optical head constitute a conventional LTP.

[0052] The mirror under test is placed on the guide rail. The optical head emits a beam of light that shines on the mirror under test. After being reflected back to the CCD by the mirror, the measurement is completed. During this process, an autocollimator is used to monitor the attitude of the optical head to avoid errors caused by vibration of the guide rail.

[0053] like Figure 7 As shown, (a) is the optical path diagram inside the optical head when LTP directly measures a curved mirror, which has the problem of divergence when the measurement beam returns to the CCD. (b) is the optical path diagram inside the optical head when measuring a curved mirror with the addition of CGH, where the measurement beam can be focused into a circular spot after returning to the CCD. The function of the beam expander is to enlarge the diameter of the parallel input beam to a larger parallel output beam; the function of the beam splitter is to illuminate the mirror under test with the incident beam, while allowing the returning beam to pass through into the FT lens; the function of the FT lens is to focus the returning beam onto the CCD system to form a circular spot.

[0054] This invention was used to inspect a cylindrical reflector with an arc radius of 89.7 mm and a length of 150 mm. The measurement position was the generatrix at the center of the mirror. The actual measurement is shown in the figure below. Figure 8 As shown.

[0055] To verify the consistency of measurements on the cylindrical mirror after adding a CGH to the LTP system of this embodiment, the tilt angle between the cylindrical mirror and the horizontal plane was adjusted so that the measurement beam illuminated different positions of the optical elements in the CGH and LTP systems. Measurements were taken at the same position of the cylindrical mirror at three different tilt angles. The repeatability of the measurement system was verified by the consistency of these three sets of slope values. The three sets of slope curves and the slope curve after subtracting the fitted value are shown below. Figure 9 As shown in (a) and (b).

[0056] First, the average of the three sets of slope data is taken as the reference data. Then, the average slope value is subtracted from each of the three slope values ​​to obtain the deviation between the three slope values ​​and the average value. The root mean square values ​​of the three slope deviations are 26.6 nrad, 24.4 nrad, and 36.7 nrad, respectively, with a root mean square value of 29.3 nrad. The measurement results show that using the average of the three sets of measurement data achieves a measurement repeatability of 29.3 nrad.

[0057] Figure 9 The three sets of slope measurement results demonstrate that the repeatability of the present invention can reach below 30 nrad when detecting mirrors with small curvature radii, achieving high-precision detection of the surface shape of mirrors with small curvature radii.

[0058] 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 detecting the surface shape of a reflective mirror with a small radius of curvature, characterized in that: This is achieved by combining a long-range surface profiler (LTP) and a computational hologram (CGH) assembly. Specifically, a CGH module and its position adjustment mechanism are added between the optical head of the LTP and the mirror under test. The CGH acts as a wavefront converter, using the CGH and its position adjustment mechanism to convert the wavefront shape of the measurement beam emitted by the laser from a planar wavefront to a wavefront matching the same as the surface shape of the mirror under test, thereby enabling the detection of the surface shape of mirrors with small curvature radii. When combining CGH and LTP, an angle is designed on the front and back surfaces of the quartz substrate of CGH to prevent stray light caused by reflection from the front and back surfaces of CGH from entering the detector system of LTP and interfering with the positioning of the measurement spot. The included angle mentioned in CGH is designed based on the wavefront distribution of the incident beam of LTP, so that the wavefront of the beam after passing through CGH matches the surface shape of the mirror under test. At the same time, by adjusting the linear density distribution parameters, other diffraction orders cannot return to the detector system of LTP. The linear density distribution at different locations of the CGH was calculated using the grating equation: Wherein, the CGH is placed perpendicular to the optical path at the incident angle. , The refractive index of air, λ is the refractive index of quartz, m is the CGH diffraction order used in the measurement, and m is taken as +1 order according to the design. The wavelength of the measurement beam is λ = 402 nm. It measures the +1st order diffraction angle of the beam after CGH modulation. Value and the sagittal radius of the mirror under test and the distance from CGH to the upper surface of the mirror Related to calculation The equation is: Where x is the coordinate along the direction of linear density variation of CGH, and N is the linear density of the measurement beam at a certain point on CGH.

2. The method for detecting the surface shape of a small radius-of-curvature reflective mirror according to claim 1, characterized in that: For curved mirrors with different curvatures, different CGH parameters can be used to achieve high-precision surface shape measurement of mirrors with small curvature radii. The high precision refers to repeatability of less than 30 nanoradians.

3. A method for detecting the surface shape of a small radius-of-curvature reflective mirror according to claim 1 or 2, characterized in that: The CGH is a variable line spacing grating; the CGH parameter refers to the linear density distribution of the variable line spacing grating, which is determined by the height of the CGH placement position from the surface of the mirror under test and the sagittal radius of the mirror under test.

4. The method for detecting the surface shape of a small radius-of-curvature reflective mirror according to claim 1, characterized in that: The CGH's position adjustment mechanism allows for movement in the X, Y, and Z directions and rotation around the X, Y, and Z axes, achieving a six-degree-of-freedom adjustment function. A combined mirror frame is mounted on the CGH. Two linear displacement platforms in the position adjustment mechanism enable linear movement along the X and Z axes, respectively. The mirror frame within the combined mirror frame slides within a slot, enabling movement along the Y axis. The slot rotates 360° within the mirror frame's frame, achieving rotation around the Z axis. Three adjustment knobs on the frame enable rotation around the X and Y axes. Through this six-degree-of-freedom adjustment, the wavefront passing through the CGH is matched to the surface of the mirror under test.

5. An apparatus employing the method for detecting the surface shape of a small radius-of-curvature reflective mirror as described in claim 1, characterized in that: The system includes a long-range surface profiler (LTP) and a computational hologram (CGH) assembly. A CGH module and its position adjustment mechanism are added between the optical head of the LTP and the mirror under test. The CGH is equivalent to a wavefront converter. The CGH and the adjustment mechanism are used to convert the wavefront shape of the measurement beam emitted by the laser from a planar wavefront to a wavefront matching the same as the surface shape of the mirror under test, thereby realizing the surface shape detection of mirrors with small curvature radii.

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