A method and device for detecting the profile of a large aperture flat mirror

Abstract

The present application relates to a kind of contour detection method and device of large aperture plane mirror, the present application is changed to three measuring heads by single measuring head, from the position information of single point is changed to the two-dimensional slope information of the center point of measurement sub-region, the three-dimensional profile of large aperture plane mirror is obtained by inversion from the two-dimensional slope information of the center point of obtained sub-region, the influence of single point measurement error caused by the motion error of mechanical moving parts on measurement result is eliminated, measurement range is expanded, measurement precision is improved, the high-precision detection demand of large aperture plane mirror is satisfied.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of optical element detection, in particular to a profile detection method and device for a large-aperture plane mirror. BACKGROUND

[0002] With the development of science and technology, large-aperture optical systems have been widely used in the fields of space optics and astronomical optics. As the return mirror of a large-aperture telescope system, the transmission standard mirror of a large-aperture interferometer and the standard mirror for self-inspection of part of an optical system, the aperture of a large-aperture plane mirror is also increasing. Taking the Thirty Meter Telescope (TMT) project of international cooperation as an example, the three mirrors (M3M) of TMT are an ultra-large-aperture elliptical plane mirror with an aperture size of 3.5m x 2.5m, which has never been seen before.

[0003] In the grinding stage, the surface shape precision of a large-aperture optical plane mirror is in the order of microns or even tens of microns, and at the same time, due to the large roughness value of the mirror surface, the reflectivity of the mirror surface is low, so it is difficult to apply an interferometer splicing or a five-prism scanning detection. At present, optical personnel widely use a three-coordinate measuring instrument to detect the surface shape in the grinding stage, obtain data points by detecting the mirror surface with a high-precision probe, reconstruct the surface shape of the measured mirror surface by the measured discrete data, and then obtain the surface shape error distribution of the measured mirror surface to guide further optical processing.

[0004] A three-coordinate profile measuring instrument uses high-precision mechanical moving parts to ensure its measurement accuracy, does not need additional auxiliary devices, is simple to operate, and is easy to implement. The high-precision probe can move on three mutually perpendicular guide rails, and the displacement measurement systems of the three axes calculate the three-dimensional height (x, y, z) of the large-aperture plane mirror through a data processor or a computer, that is, the surface shape error distribution of the large-aperture plane mirror is obtained. However, the profile detection of a large-aperture optical plane mirror needs a three-coordinate with greater measurement capacity to be implemented. For mechanical moving parts, the increase of the movement stroke means the reduction of the movement precision. As shown in FIG. 1, the probe movement will perfectly "copy" the straightness error of the guide rail, especially the jump in the z direction. Due to the existence of the guide rail error, the actual measurement value of the probe can be expressed as: Figure 1

[0005] Z true =Z surface +a (1)

[0006] wherein Z surf ​is the actual height of the measured surface, and a is the Z-direction runout of the guide rail. According to the measured data of a typical 2m machining range numerical control machine tool, the Z-direction runout a of the guide rail in the full stroke range reaches nearly 20μm, which cannot meet the profile detection precision requirement of the large-aperture mirror polishing stage, especially the fine polishing stage. Therefore, how to eliminate the influence of the guide rail straightness precision on the detection precision is the key to solving the problem. SUMMARY

[0007] An object of the present application is to provide a profile detection method and device for a large-aperture mirror, which can break through the limitation of the long-stroke guide rail movement error in principle, and can achieve high profile detection precision by using a numerical control machining machine tool, thereby realizing in-situ detection of the large-aperture mirror polishing and rough polishing stage, and greatly improving the machining efficiency of the large-aperture mirror.

[0008] In one aspect, the present application provides a profile detection method for a large-aperture mirror, comprising the steps of:

[0009] S1, dividing the measured large-aperture mirror into a plurality of sub-regions;

[0010] S2, using a three-probe measuring instrument to scan the measured large-aperture mirror row by row according to a preset path, and obtaining (x, y, z) information of three measurement points of each sub-region;

[0011] S3, calculating two-dimensional slope information of a center point of each sub-region based on the (x, y, z) information of the three measurement points of each sub-region; and

[0012] S4, performing high-precision surface inversion on the two-dimensional slope information of the center point of the full-aperture sub-region of the measured large-aperture mirror, to obtain a full-aperture three-dimensional profile of the measured large-aperture mirror.

[0013] In one embodiment of the present application, in the step S2, the three-probe measuring instrument comprises three probes which are arranged at intervals and not on the same straight line, and the angle between adjacent two probes is 60°. The position interval between the three probes is 5-30mm.

[0014] In one embodiment of the present application, in the step S2, the preset path is a grating type scanning path or a spiral type scanning path.

[0015] In an embodiment of the present application, the raster scanning path is a path extending from a first node at one end of the measured large-aperture plane mirror to a second node at the other end of the measured large-aperture plane mirror, wherein the first node and the second node are symmetric about the center of the measured large-aperture plane mirror, wherein the number of meandering bends of the preset path is n, the meandering bend interval is L, and the diameter of the measured large-aperture plane mirror is d, and the number of meandering bends n satisfies: n is an integer value rounded from d / L-2.

[0016] In an embodiment of the present application, in the step S3, the coordinates of the three measurement points of each sub-region are (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) respectively, and the formula of the measured plane of the measured large-aperture plane mirror is

[0017] Ax+By+Cz+D=0 (2)

[0018] then

[0019] A=(y2-y1)×(z3-z1)-(z2-z1)×(y3-y1) (3)

[0020] B=(x3-x1)×(z2-z1)-(x2-x1)×(z3-z1) (4)

[0021] C=(x2-x1)×(y3-y1)-(x3-x1)×(y2-y1) (5)

[0022] then the X and Y direction inclination K of the center point of the sub-region x and K y are respectively

[0023]

[0024]

[0025] In the above formula, A, B, and C are the normal vector of the measured plane of the measured large-aperture plane mirror.

[0026] In an embodiment of the present application, the inversion algorithm used in the step S4 is the Zernike surface profile reconstruction method, and the full-aperture wavefront aberration φ(x, y) is expressed in the form of formula (8) using the Zernike polynomial Z(x, y):

[0027]

[0028] In formula (8), C k is the coefficient of the Zernike polynomial, n is the number of terms of the Zernike polynomial selected in the fitting, and Z k(x, y) is the base of each Zernike, k represents the kth term, k = 1, 2, 3…n, and ε is the remaining part of wave aberration after deducting the Zernike fitting;

[0029] The step S4 comprises the steps of:

[0030] The partial derivatives of formula (8) with respect to x and y are obtained, and the wavefront slope S x and S y The relationship between the Zernike coefficients and the wavefront slope S

[0031]

[0032]

[0033] The above formula (9) and (10) are rewritten in matrix form:

[0034]

[0035] In formula (11), N is the total number of sampling points, and n is the number of Zernike polynomials;

[0036] Formula (11) is simplified as:

[0037] ZC = S (12)

[0038] In formula (12), Z is the derivative of each Zernike term in the x and y directions, C is the coefficient matrix of each Zernike term, and S is the slope matrix of each point X and Y in the wavefront;

[0039] The coefficients are obtained according to the least square method:

[0040] C = (Z T Z) -1 Z T S (13)

[0041] In formula (13), Z T is the transpose of Z;

[0042] For a large-diameter plane mirror, most of the surface shape information is contained in the Zernike term, so the ε in formula (8) can be ignored. The coefficient matrix obtained by formula (13) is directly substituted into formula (8) to obtain the full-aperture three-dimensional profile of the measured large-diameter plane mirror.

[0043] The application also provides a profile detection device of a large-aperture plane mirror, which is used in the profile detection method of the large-aperture plane mirror.

[0044] In an embodiment of the application, the angle between two adjacent probes of the three-probe measuring instrument is 60°. The position interval between the three probes is 5-30 mm.

[0045] In an embodiment of the application, the adjusting mechanism is arranged on the side of the machine tool gantry close to the measured large-aperture plane mirror, and the three-probe measuring instrument moves along the preset path to scan the measured large-aperture plane mirror row by row through the linkage of the adjusting mechanism and the machine tool gantry.

[0046] In an embodiment of the application, the profile detection device of the large-aperture plane mirror further comprises a mechanical support structure for placing the measured optical mirror.

[0047] The application changes the single-probe three-coordinate measuring instrument into a three-probe measuring instrument, and changes the traditional measurement of the coordinate height value of a single point into the measurement of the three-point coordinate values of a sub-area surface. Since the motion error a of the three probes simultaneously affects the z values of the three measurement points, the motion error does not affect the two-dimensional slope of the center point of the sub-area formed by the three measurement points. Therefore, the application calculates the two-dimensional slope information of the center point of the sub-area through the three-point coordinates, and inverses the three-dimensional surface shape through the two-dimensional slope information of the center points of the full-aperture sub-area, so that the influence of the motion error can be avoided, and the high-precision detection of the profile of the large-aperture plane mirror can be realized.

[0048] Further purposes and advantages of the application will be fully apparent from the following description and drawings. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 It is a schematic diagram of the working principle of the traditional single-probe three-coordinate measuring instrument.

[0050] Figure 2 It is a flowchart of the profile detection method of the large-aperture plane mirror.

[0051] Figure 3 It is a schematic diagram of the distribution of the three probes of the three-probe measuring instrument.

[0052] Figure 4 It is a schematic diagram of the scanning path of the large-aperture plane mirror in the detection of the application.

[0053] Figure 5The structure diagram of the profile detection device of the large-aperture plane mirror. DETAILED DESCRIPTION

[0054] The following description is provided so that others skilled in the art can have the best

[0055] It should be understood by those skilled in the art that, in the disclosure of the present application, the terms "vertical", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like indicate the orientation or positional relationship shown in the drawings, which are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore the above terms cannot be understood as a limitation of the present application.

[0056] It can be understood that the term "one" should be understood as "at least one" or "one or more", that is, in one embodiment, the number of one element can be one, and in another embodiment, the number of the element can be multiple, and the term "one" cannot be understood as a limitation on the number.

[0057] In the description of the present application, it should be noted that, unless otherwise explicitly specified and limited, the terms "mounting", "connecting", "connecting" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected or can communicate with each other; it can be directly connected, or indirectly connected through an intermediate medium, it can be the internal communication of two elements or the interaction relationship between two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0058] As Figures 2 to 5 The profile detection method and device of the large-aperture plane mirror according to a preferred embodiment of the present application are specifically illustrated.

[0059] As Figure 2 The profile detection method of the large-aperture plane mirror of the present application includes the steps of:

[0060] S1, dividing the measured large-aperture plane mirror into a plurality of sub-regions;

[0061] S2, using a three-probe measuring instrument to scan the measured large-aperture plane mirror row by row according to a preset path to obtain (x, y, z) information of three measuring points of each sub-region;

[0062] S3, calculating two-dimensional slope information of a center point of each sub-region based on (x, y, z) information of the three measuring points of each sub-region; and

[0063] S4, performing high-precision surface inversion on the two-dimensional slope information of the center points of the full-aperture sub-regions of the measured large-aperture plane mirror to obtain a full-aperture three-dimensional profile of the measured large-aperture plane mirror.

[0064] It can be understood that a traditional single-probe three-coordinate measuring instrument only has one probe to measure the z value of a single point, and there is a guide rail Z direction bounce amount, that is, the single probe has a motion error, which seriously affects the large-aperture plane mirror profile detection precision. Therefore, the single probe is changed to a three-probe measuring instrument in the present application, and the large-aperture optical plane mirror is divided into multiple sub-regions, the coordinates of the three measuring points of the multiple sub-regions are measured, and the two-dimensional slope information of the center point of the sub-region is calculated based on the coordinates of the three measuring points to obtain the full-aperture three-dimensional surface shape of the large-aperture plane mirror. The influence of the motion error is avoided. The surface error distribution of the large-aperture optical plane mirror can also be obtained from the slope of each sub-region.

[0065] Specifically, in the step S2, the three-probe measuring instrument shown in Figure 3 is used to measure the three measuring points of the sub-region, the three-probe measuring instrument includes three probes arranged at intervals and not on the same straight line, the angle between adjacent two probes is that is, the angle between adjacent two probes is 120°, and the position interval between the three probes depends on the surface shape state of the to-be-measured surface, and is generally 5-30 mm.

[0066] In this specific embodiment of the present application, in the three-dimensional coordinate system shown in Figure 3 , the three probes of the three-probe measuring instrument are respectively denoted as ProbA, ProbB and ProbC, wherein the angle θ1 between ProbA and the X axis is about , the angle θ2 between ProbB and the X axis is about , and the angle θ3 between ProbC and the X axis is about In some embodiments of the present application, the three probes can also be arranged at other angles, which are not limited in the present application.

[0067] Further, as shown in Figure 4As shown in the step S2, the preset path is a grating type scanning path extending from a first node at one end of the measured large aperture plane mirror to a second node at the other end of the measured large aperture plane mirror, wherein the first node and the second node are symmetric about the center of the measured large aperture plane mirror. Specifically, in the step S2, the first node is E point, the second node is F point, and the scanning direction of the three probe measuring instrument is as shown by the arrow. Figure 4

[0068] It can be understood that, where the number of the roundabout bends of the preset path is n, the roundabout bend interval is L, and the diameter of the measured large aperture plane mirror is d, the number of the roundabout bends n satisfies: n is an integer value after rounding off d / L-2.

[0069] In this specific embodiment of the present application, as shown in the step S2, the diameter d of the measured large aperture plane mirror is 2, and the roundabout bend interval L of the preset path is 0.1. Therefore, the number of the roundabout bends n of the three probe measuring instrument is 2 / 0.1-2=18. If the roundabout bend interval L is 0.3, the number of the roundabout bends n is an integer value after rounding off 2 / 0.3-2, i.e. the number of the roundabout bends n is 5. Figure 4 It should be understood that the number of the roundabout bends of the three probe measuring instrument can also be set to other values according to the surface shape of the measured large aperture plane mirror, and the present application does not limit this.

[0070] It should be understood that, in some embodiments of the present application, the measured large aperture plane mirror can also be divided into a plurality of sub-regions in other ways, and the plurality of sub-regions can also be distributed in other regular manners, such as being scattered in the radial direction with the center point of the measured large aperture plane mirror as the origin, and the three probe measuring instrument can scan in a spiral manner approaching or away from the center point of the measured large aperture plane mirror, i.e. the preset path can be a grating type scanning path or a spiral type scanning path, and the present application does not limit this.

[0071] Further, in the step S3, the three probe measuring instrument is used to simultaneously obtain the coordinates of the three measurement points of the sub-regional plane as (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3), and the two-dimensional slope of the local region can be obtained by the following formula:

[0072] Supposing that the plane formula is

[0073] Ax+By+Cz+D=0 (2)

[0074]

[0075]

[0076] ​​​A = (y2-y1) x (z3-z1) - (z2-z1) x (y3-y1) (3)

[0077] B = (x3-x1) x (z2-z1) - (x2-x1) x (z3-z1) (4)

[0078] C = (x2-x1) x (y3-y1) - (x3-x1) x (y2-y1) (5)

[0079] Then the X, Y direction inclination K of the center point of the sub-region x and K y are respectively

[0080]

[0081]

[0082] In the above formula, A, B, C are normal vectors of the measured plane of the measured large-aperture plane mirror.

[0083] Particularly, at this time, the motion error a of the detection end simultaneously affects the z values of the three measurement points, but does not affect the measured two-dimensional inclination, so that the present application can avoid the influence of the motion error by using the two-dimensional inclination information of the full-aperture sub-region to inverse the full-aperture three-dimensional profile, and a high-precision three-dimensional profile detection result can be obtained.

[0084] That is, the present application measures the sub-aperture according to a row-by-row grating scanning path as shown in FIG. 2, and performs point-by-point scanning measurement, so as to obtain the full-aperture two-dimensional inclination information of the measured surface, and through high-precision surface inversion, the full-aperture three-dimensional profile of the measured large-aperture plane mirror can be obtained. Figure 4

[0085] Specifically, the inversion algorithm used in the step S4 is the Zernike surface profile reconstruction method, and the full-aperture wavefront φ(x, y) can be expressed in the form of formula (8) by using the Zernike polynomial Z(x, y):

[0086]

[0087] In formula (8), C k is the coefficient of the Zernike polynomial, n is the number of terms of the Zernike polynomial selected in the fitting, Z k (x, y) is the basis of each Zernike, k represents the term number, k = 1, 2, 3…n, and ε is the remaining part of the wavefront after deducting the Zernike fitting;

[0088] It is worth mentioning that n can be selected as the first 37 terms to represent the low-order wavefront. ​

[0089] Further, step S4 includes the following steps:

[0090] Taking the partial derivatives of equation (8) with respect to x and y respectively, we obtain the wavefront slope S. x and S y Relationship with Zernike coefficient:

[0091]

[0092]

[0093] In actual testing, sampling and measurement are performed at discrete points, and the number of terms in the Zernike polynomial is finite. Therefore, equations (9) and (10) above can be rewritten in matrix form:

[0094]

[0095] In equation (11), N is the total number of sampling points, and n is the number of terms in the Zernike polynomial;

[0096] Equation (11) can be simplified as follows:

[0097] ZC=S(12)

[0098] In equation (12), Z is the derivative of each Zernike term in the x and y directions, C is the coefficient matrix of each Zernike term, and S is the slope matrix of each point in the wavefront in the X and Y directions.

[0099] The coefficients can be obtained by applying the least squares theorem.

[0100] C=(Z T Z) -1 Z T S (13)

[0101] In equation (13), Z T It is the transpose of Z;

[0102] The coefficient matrix obtained by equation (13) can be directly substituted into equation (8) to obtain the full-aperture three-dimensional profile of the large-aperture plane mirror.

[0103] like Figure 5 As shown, the present invention also provides a contour detection device for a large-aperture plane mirror, which is used for the contour detection method of the large-aperture plane mirror. The contour detection device for the large-aperture plane mirror includes a machine tool gantry, an adjustment mechanism connected to the machine tool gantry, and a three-probe measuring instrument disposed on the adjustment mechanism. The three-probe measuring instrument includes three probes that are spaced apart and not on the same straight line.

[0104] In particular, the angle between two adjacent probes of the three-probe measuring instrument is The position interval between the three probes is 5-30mm.

[0105] It is worth mentioning that the adjustment mechanism is arranged on the side of the machine tool gantry close to the measured large-aperture plane mirror, and the three-probe measuring instrument realizes line-by-line scanning of the measured large-aperture plane mirror along a preset path through linkage movement of the adjustment mechanism and the machine tool gantry.

[0106] In addition, it is also worth mentioning that the profile detection device of the large-aperture plane mirror further comprises a mechanical support structure for placing the measured optical mirror.

[0107] It can be understood that the present application changes the single-probe three-coordinate measuring instrument to a three-probe measuring instrument, and changes the traditional measurement of single-point coordinate height value to the measurement of three-point coordinate values of a sub-area surface. Since the movement error a of the three probes simultaneously affects the z values of the three measurement points, it does not affect the two-dimensional slope of the center point of the sub-area formed by the three measurement points. Therefore, the present application obtains the two-dimensional slope information of the center point of the sub-area through three-point coordinate calculation, and inverts the three-dimensional surface through the two-dimensional slope information of the center point of the full-aperture sub-area. The influence of the movement error can be avoided, so that high-precision detection of the profile of the large-aperture plane mirror can be realized.

[0108] That is, the present application changes the single probe to a three-probe, changes the obtained single-point position information to the obtained two-dimensional slope information of the center point of the measurement sub-area, eliminates the influence of the single-point measurement error a caused by the movement error of the mechanical movement component on the measurement result, expands the measurement range, improves the measurement precision, and meets the high-precision detection requirement of the large-aperture plane mirror.

[0109] The technical features of the above embodiments can be combined in any way. In order to make the description simple, not all possible combinations of the technical features in the above embodiments are described, however, as long as the combinations of the technical features do not exist contradictory, they should be considered as the scope of the present application.

[0110] The above embodiments only express the preferred embodiments of the present application, and the description is more specific and detailed, but it cannot be understood as a limitation on the scope of the patent. It should be pointed out that for ordinary skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are within the scope of the present application. Therefore, the protection scope of the present application patent should be subject to the appended claims.

Claims

1. A method of profile detection of a large aperture flat mirror, characterized by, The method comprises the steps of: S1, dividing the measured large-aperture plane mirror into a plurality of sub-regions; S2, using a three-probe measuring instrument to scan the measured large-aperture plane mirror row by row according to a preset path to obtain (x, y, z) information of three measuring points of each sub-region; S3, based on the (x, y, z) information of the three measuring points of each sub-region, calculating two-dimensional slope information of a center point of each sub-region; S4, performing high-precision surface inversion on the two-dimensional slope information of the center points of the sub-regions of the full-aperture of the measured large-aperture plane mirror to obtain a full-aperture three-dimensional profile of the measured large-aperture plane mirror. In the step S2, the preset path is a grating type scanning path or a spiral type scanning path.

2. The method of claim 1, wherein In the step S2, the three-probe measuring instrument comprises three probes which are arranged at intervals and are not on the same straight line, and the angle between two adjacent probes is 60° The position interval between the three probes is 5-30 mm.

3. The method of claim 2, wherein The grating type scanning path is a path extending from a first node at one end of the measured large-aperture plane mirror to a second node at the other end of the measured large-aperture plane mirror through multiple detours, wherein the first node and the second node are symmetric about the center of the measured large-aperture plane mirror, wherein the number of detours of the preset path is n, the detour interval is L, and the diameter of the measured large-aperture plane mirror is d, and the number of detours n satisfies: n is an integer value rounded off from d / L-2.

4. The method of claim 3, wherein In the step S3, the coordinates of the three measuring points of each sub-region are (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3), respectively, and the measured plane formula of the measured large-aperture plane mirror is 5. The method of profile detection of a large-aperture plane mirror according to any one of claims 1 to 4, characterized in that, Ax+By+Cz+D=0 (2) Then A=(y2-y1)×(z3-z1)-(z2-z1)×(y3-y1) (3) B=(x3-x1)×(z2-z1)-(x2-x1)×(z3-z1) (4) C=(x2-x1)×(y3-y1)-(x3-x1)×(y2-y1) (5) In the above formula, A, B, and C are the normal vectors of the measured plane of the measured large-aperture plane mirror. Kx, Ky, Kx, Ky x and K y are respectively The inversion algorithm used in the step S4 is a Zernike surface profile reconstruction method, and the full-aperture wavefront aberration φ(x, y) is expressed in the form of formula (8) using Zernike polynomials Z(x, y):

6. The method of profile detection of a large-aperture flat mirror according to claim 5, wherein The step S4 comprises the steps of: In formula (8), C k is a coefficient of Zernike polynomial, n is the number of terms of Zernike polynomial selected in fitting, Z k (x, y) is a base of each term of Zernike, k represents the term number, k = 1, 2, 3…n, and ε is a residual part of wave aberration deducted from Zernike fitting; Rewriting the above formulae (9) and (10) into a matrix form: Taking partial derivatives of equation (8) with respect to x and y, respectively, gives the wavefront slope S x and S y The relationship between the Zernike coefficients and the wavefront slope S In formula (11), N is the total number of sampling points, and n is the number of Zernike polynomials; Simplifying formula (11) as ZC=S (12) In formula (12), Z is the derivative of each Zernike term in the x and y directions, C is the coefficient matrix of each Zernike term, and S is the slope matrix of each point X and Y in the wavefront; The coefficients are obtained according to the least square method: The coefficient matrix obtained by formula (13) is directly substituted into formula (8) to obtain the full-aperture three-dimensional profile of the measured large-aperture plane mirror. C = (Z T Z) -1 Z T S (13) In formula (13), Z T is the transpose of Z; ​

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