CN112378367B - Method for measuring surface shape and position of multi-free-form surface reflector distributed in inner cavity - Google Patents

Method for measuring surface shape and position of multi-free-form surface reflector distributed in inner cavity Download PDF

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CN112378367B
CN112378367B CN202011223913.1A CN202011223913A CN112378367B CN 112378367 B CN112378367 B CN 112378367B CN 202011223913 A CN202011223913 A CN 202011223913A CN 112378367 B CN112378367 B CN 112378367B
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李泽骁
张效栋
朱琳琳
董禹初
房长帅
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Tianjin University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/20—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring contours or curvatures, e.g. determining profile
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M11/00—Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
    • G01M11/02—Testing optical properties
    • G01M11/0242—Testing optical properties by measuring geometrical properties or aberrations
    • G01M11/025—Testing optical properties by measuring geometrical properties or aberrations by determining the shape of the object to be tested

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Abstract

The invention relates to a method for measuring the surface shape and position of a multi-free-form surface reflector distributed in an inner cavity, wherein a measured workpiece comprises the inner cavity and at least one multi-free-form surface reflector in the inner cavity respectively, an adopted measuring system comprises a moving device, a point measuring head, a data acquisition processing system, a standard inner cylindrical surface and a standard plane, wherein the moving device is provided with an X-axis moving guide rail, a Y-axis moving guide rail, a Z-axis moving guide rail and a rotating main shaft; the point measurement measuring head is positioned in the inner cavity and can aim at the measured surface within a certain included angle range to obtain the distance from the endpoint of the point measurement measuring head to the aimed point on the measured surface; the data acquisition and processing system is connected with the point measurement probe and can acquire and process measurement data; the point measurement measuring heads are used for measuring the multiple free-form surface reflectors distributed in the inner cavity, three-dimensional point cloud data of the multiple free-form surface reflectors are obtained, and surface shape accuracy and position accuracy of the multiple free-form surface reflectors are evaluated.

Description

Method for measuring surface shape and position of multi-free-form surface reflector distributed in inner cavity
Technical Field
The invention belongs to the technical field of mechanical manufacturing, and relates to a method for measuring the surface shape and the position of a plurality of reflectors distributed in an inner cavity with high precision by utilizing a motion device and a point measurement probe, in particular to a method for measuring the three-dimensional data of a plurality of free-form surface reflectors distributed in the inner cavity and evaluating the surface shape precision and the position precision of the reflectors.
Background
The free-form surface optical system is a system which integrates and installs multiple free-form surfaces together to realize specific optical performance, and the imaging quality of the optical system can be improved. The method has important application value in the fields of aerospace, national defense safety, scientific exploration, information interaction, space-time perception and the like, wherein the multi-free-form-surface reflectors distributed in the inner cavity are typical free-form-surface optical system structures. Because the free-form surface optical system is an optical system with multiple lenses in coordination, the final performance of the free-form surface optical system is not only dependent on the surface shape precision of a single free-form surface, but also limited by the position precision of multiple free-form surfaces to a great extent.
At present, the non-contact optical measurement method has the advantages of high precision, rapidness, no damage and the like, and is a main measurement method. The non-contact detection form of the optical free-form surface which is widely concerned at present mainly comprises point, line and surface measurement. Different measuring principles and methods have advantages and disadvantages and are respectively suitable for different processing stages or different forming processes.
The current research and invention mainly aims at the measurement of a single free-form surface reflector and the evaluation of the measurement data of the single free-form surface reflector, and the measured geometric quantity is mainly used for evaluating the surface shape precision of the free-form surface. For multi-free-form optical elements, whether they are based on planar substrates or more, measurements can be made using measurement equipment that is commercially available today, as in two free-form mirrors on the same substrate (Zhu J, Hou W, Zhang X, et al. design of a low F-number of free form off-axis of the three-mirror system with a rectangular field-of-view [ J ]. Journal of optics,2015,17(1): 015605.). On the other hand, in addition to the conventional surface shape measurement evaluation, the multi-free-form surface measurement requires high-precision measurement of the position of each free-form surface. The multi-surface position measurement usually needs to additionally add a reference plane, and the spatial position deviation amount of the measured three-dimensional data and the reference plane is calculated to obtain the processing position quality of the multi-free-form surface. However, the above measurement method is simple in structure for surface shape measurement, and mostly performs scanning measurement through coordinate points on a planar substrate, and then performs machining surface shape evaluation, and the evaluation of the position depends on an additional reference surface (e.g. plane, spherical) standard (patent CN 201710254739.9). In the measurement research of the multi-free-form surface reflector with the inner cavity, the traditional multi-free-form surface reflector measurement method with the planar substrate is not suitable due to the space constraint of the inner cavity.
In view of the above analysis, the presently disclosed techniques suffer from the following drawbacks: firstly, the surface shape measurement of the free-form surface reflector is basically evaluated by point measurement on a plane substrate, and a technical means for measuring the free-form surface reflector under the space constraint condition with an inner cavity is lacked; secondly, the position measurement and evaluation of the multi-free-form surface reflector depend on an additional reference, the measurement structure is complex, and measurement errors are easy to generate. Therefore, a high-precision, complete and reliable surface shape and position measurement and evaluation method is needed, which is used for measuring three-dimensional information of the multi-free-form-surface reflector distributed in the inner cavity, measuring the surface shape on the basis of overcoming the space constraint limitation of the inner cavity, obtaining the three-dimensional distribution information of the multi-free-form-surface reflector, and researching the evaluation method of the surface shape precision and the position precision of the multi-free-form-surface reflector under the condition of no additional reference.
Disclosure of Invention
The present invention aims to provide a method for measuring the surface shape and position of a multi-free-form surface reflector distributed in an inner cavity, which aims at overcoming the defects of the prior art. According to the distribution characteristics of the motion devices, the motion devices with the point measuring heads capable of rotating and translating are constructed under the condition of the space distribution constraint of the inner cavity, the multi-free-form-surface reflectors distributed in the inner cavity are subjected to three-dimensional point measurement, and the surface shape precision and the position precision of the multi-free-form-surface reflectors are evaluated under the condition of no reference. In order to achieve the purpose, the invention adopts the technical scheme that:
a method for measuring the surface shape and position of a multi-free-form surface reflector distributed in an inner cavity comprises a workpiece to be measured, a measuring system and a measuring system, wherein the workpiece to be measured comprises the inner cavity and at least one multi-free-form surface reflector in the inner cavity, the measuring system comprises a moving device, a point measuring head, a data acquisition and processing system, a standard inner cylindrical surface and a standard plane, and the moving device is provided with an X-axis moving guide rail, a Y-axis moving guide rail, a Z-axis moving guide rail and a rotating main shaft; the point measurement measuring head is positioned in the inner cavity and can aim at the measured surface within a certain included angle range to obtain the distance from the endpoint of the point measurement measuring head to the aimed point on the measured surface; the data acquisition and processing system is connected with the point measurement probe and can acquire and process measurement data; the point measurement measuring heads are used for measuring the multiple free-form surface reflectors distributed in the inner cavity, three-dimensional point cloud data of the multiple free-form surface reflectors are obtained, and surface shape accuracy and position accuracy of the multiple free-form surface reflectors are evaluated. The method comprises the following steps:
(1) respectively installing a point measurement measuring head, a standard inner cylindrical surface and a standard plane on a moving device, wherein the standard plane is vertical to a Z-axis moving guide rail, the axis of the standard inner cylindrical surface is parallel to the Z-axis moving guide rail, Cartesian coordinates X (0) and Y (0) of the center of the standard inner cylindrical surface are respectively set as the origin of coordinates of an X-axis moving guide rail and a Y-axis moving guide rail, and the direction of the point measurement measuring head is vertical to the Z-axis moving guide rail and can be driven by a rotating main shaft to rotate;
(2) calibrating a measuring system formed by the moving device and the point measuring head to obtain an original point Z (0) of a guide rail for moving the measuring system along the Z axis and the rotating radius R of the point measuring headrotAnd the included angle theta between the connecting line of the point measurement measuring head and the center point of the standard cylindrical surface and the horizontal direction0The method comprises the following steps:
step 1: controlling the Z-axis moving guide rail to enable the point measuring head to be aligned with the edge of the standard plane, recording the position coordinate Z (0) of the Z-axis moving guide rail at the alignment moment, namely when the data acquisition processing system acquires the measured data, and taking the coordinate as the original point of the measuring Z-axis moving guide rail;
step 2: controlling an X-axis motion guide rail, a Y-axis motion guide rail and a rotating main shaft through a motion control module to enable a point measuring head to align with a standard inner cylindrical surface, measuring N points on the standard inner cylindrical surface, wherein N is more than or equal to 3, when a data acquisition and processing system acquires distances L (1), L (2), … … and L (N) from a point measuring head end point to a point aimed at on a measured surface, respectively recording the X-axis motion guide rail position, the Y-axis motion guide rail position and the rotating main shaft angle of the N points, which are respectively marked as X (1), X (2), … …, X (N) and Y (1), Y (2), … …, Y (N), theta (1), theta (2) … … and theta (N),
wherein, i is 1,2,3, … …, n, and R can be obtained by adopting an optimization searching methodrotAnd theta0With an optimized objective function and constraints of
Figure BDA0002763028330000031
s.t.Yc(i)＝y(i)+Rrot sin[θ(i)+θ0]+L(i)sinθ(i)
Yc(i)＝y(i)+Rrot sin[θ(i)+θ0]+L(i)sinθ(i)
Wherein, Xc(i) And Yc(i) The Cartesian coordinates of the ith point on the standard cylindrical surface;
(3) the X-axis motion guide rail, the Y-axis motion guide rail, the Z-axis motion guide rail and the rotating spindle of the motion control device measure the multi-free-form surface reflector distributed in the inner cavity, and the data acquisition and processing system records X-axis motion guide rail coordinates X (i, j), Y-axis motion guide rail coordinates Y (i, j), Z-axis motion guide rail Z (i, j) and rotating spindle coordinates theta (i, j) corresponding to each measurement data point of the multi-free-form surface reflector, wherein i is 1,2,3, … …, NmJ is 1,2,3, … …, M is the number of free-form surface mirrors, NmThe number of the m-th mirror measurement data points is shown, and the Cartesian coordinates X (i, j), Y (i, j) and Z (i, j) of each measurement data point are respectively
X(i,j)＝x(i,j)+Rrot cos[θ(i,j)+θ0]+L(i,j)cosθ(i,j)
Y(i,j)＝y(i,j)+Rrot sin[θ(i,j)+θ0]+L(i,j)sinθ(i,j)
Z(i,j)＝z(i,j)
(4) And (3) evaluating the surface shape error and the position error of the multi-free-form surface reflector according to the acquired Cartesian coordinates of each measurement data point, and adopting the following steps:
step 1: and (3) carrying out coordinate registration calculation on the measurement data of all the free-form surface reflectors and the design model of the multi-free-form surface reflector system together to finish the unification of a measurement coordinate system and a model coordinate system: let the coordinate of the ith measurement data point of the jth mirror be P (i, j), then
P(i,j)＝(X(i,j),Y(i,j),Z(i,j))
The coordinates of the ith model data point of the jth mirror of the multiple freeform mirrors are Q (i, j), and the normal vector there is nq(i, j) is calculated according to the equation of the free-form surface reflector model, P (i, j) and Q (i, j) are rotation and translation modes for searching all coordinates according to the principle that the point distance is nearest, and the search objective function is
Figure BDA0002763028330000032
Wherein R isroughAnd troughRespectively converting a coordinate rotation matrix and a coordinate translation matrix of the measurement data; at this time, for the measured data point P (i, j), the coordinate P of the ith data point of the jth mirror obtained after the translation and rotation is performed1(i, j) is represented by
P1(i,j)＝RroughP(i,j)+trough
Step 2: according to a reference equation of a multi-free-form surface reflector model, calculating the space distance from a measurement data point to a free-form surface reflector along the normal vector direction, and optimizing and calculating a coordinate translation matrix and a coordinate rotation matrix between two coordinate systems through the following objective functions:
Figure BDA0002763028330000041
wherein R isfineAnd tfineA coordinate rotation matrix and a coordinate translation matrix, DR, respectively, unified for the measurement coordinate system and the model coordinate systemfineP1(i,j)+tfine]Is P1(i, j) the distance from the point passing through the coordinate system to the ideal model of the reflector; after the measured coordinate system is unified with the model coordinate system, the obtained coordinate T (i, j) of the ith data point of the jth reflector is the measured number unified with the model coordinate systemAccording to the expression
T(i,j)＝RfineP1(i,j)+tfine
And step 3: and respectively carrying out coordinate registration calculation on the measurement data T (i, j) of each free-form surface reflector and a design model thereof, and setting the measurement data point of the mth free-form surface reflector after passing through a measurement coordinate system and a model coordinate system as T (i, m), wherein the transformation relation of the measurement data point and the ideal model coordinate registration calculation is calculated according to the following objective function:
Figure BDA0002763028330000042
wherein R ismAnd tmRespectively a coordinate rotation matrix and a coordinate translation matrix for coordinate registration calculation of the mth free-form surface reflector, DRm T(i,m)+tm]The distance from the point of T (i, j) after coordinate registration calculation to the ideal model of the reflector; rmAnd tmThe expressions are respectively:
Figure BDA0002763028330000043
tm＝(Δxm,Δym,Δzm)
wherein R ism(i, j) is the element in the ith row and jth column of the coordinate rotation matrix, Δ xm，ΔymAnd Δ zmDisplacement deviation quantities of the mth free-form surface reflector along the X-axis motion guide rail direction, the Y-axis motion guide rail direction and the Z-axis motion guide rail direction are respectively; the measured data after coordinate registration is recorded as Treg(i, j), the data coordinates being obtained by the following transformation:
Treg(i,m)＝RmTreg(i,m)+tm＝(Xreg(i,m),Yreg(i,m),Zreg(i,m))
wherein Xreg(i,m)，Yreg(i, m) and Zreg(i, m) is the m-th free-form surface mirror measurement after coordinate registrationCartesian coordinates;
in this case, the surface shape error is the distance from each point of the measurement data after coordinate registration calculation to the free-form surface mirror model, and the surface shape equation of the mth free-form surface mirror is set to z ═ Fm(x, y), the surface shape error E (i, m) corresponding to each measured data point is
E(i,m)＝Zreg(i,m)-Fm(Xreg(i,m),Yreg(i,m))
The position error of the mth free-form surface reflector is defined as the displacement deviation T between the mth free-form surface reflector and the model surfacemAnd around a certain vector direction V in the model coordinate systemmIs offset by an angle thetam(ii) a Wherein T ismAnd a translation matrix tmIn agreement, i.e.
Tm＝tm
Wherein Δ xm，ΔymAnd Δ zmDisplacement deviation quantities of the mth free-form surface reflector along the X-axis motion guide rail direction, the Y-axis motion guide rail direction and the Z-axis motion guide rail direction are respectively; vmAnd thetamBy rotating the matrix RmCalculated using the following formula:
Figure BDA0002763028330000051
Figure BDA0002763028330000052
drawings
FIG. 1 is a schematic view of a measurement system and a measured object according to the present invention. The movement device of the 1-point measuring head consists of a 2-X axis movement guide rail, a 3-Y axis movement guide rail, a 4-Z axis movement guide rail and a 5-rotating main shaft. And 6, the workpiece to be detected comprises a plurality of free-form surface reflectors distributed in the inner cavity.
FIG. 2 is a schematic structural diagram of a measurement principle in the measurement method according to the present invention;
FIG. 3 is a schematic diagram of the calibration of the measurement system and the determination of the Z-axis motion guide coordinate origin Z (0) using a standard ring gauge according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of the relative position relationship between the point measurement head and the motion device of the present invention: (a) relative position at initial position; (b) is a relative positional relationship when measuring the ith point
Detailed Description
The invention discloses a high-precision measuring and evaluating method for a multi-free-form surface reflector distributed in an inner cavity, which is described by combining the accompanying drawings and an embodiment.
The measuring system used by the high-precision measuring and evaluating method of the multi-free-form surface reflector distributed in the inner cavity is shown in figure 1, wherein a 1-point measuring head and a moving device consist of a 2-X-axis moving guide rail, a 3-Y-axis moving guide rail, a 4-Z-axis moving guide rail and a 5-rotating main shaft. 6, the workpiece to be measured comprises a plurality of free-form surface reflectors distributed in the inner cavity, and the four free-form surface reflectors distributed in the inner cavity, namely the reflector 1, the reflector 2, the reflector 3 and the reflector 4, are selected as the workpiece to be measured in the embodiment without loss of generality. The workpiece to be measured is placed on the Z-axis motion guide rail, the point measurement measuring head is installed on the rotating main shaft, and the direction of the point measurement measuring head is perpendicular to the Z-axis motion guide rail and can rotate along with the rotating main shaft. The measurement principle is as shown in fig. 2, the movement of the X-axis movement guide rail, the Y-axis movement guide rail, the Z-axis movement guide rail and the rotation main shaft in the movement device is controlled by the movement control module, so that the point measurement probe and the workpiece to be measured generate relative movement, the point measurement probe can aim at the surface to be measured within a certain included angle range, and the distance from the endpoint of the point measurement probe to the aimed point on the surface to be measured is obtained. The measurement system is calibrated by means of a standard inner cylindrical surface and a standard plane. When the measured workpiece is measured, the data acquisition and processing system can obtain the X-axis motion guide rail coordinate, the Y-axis motion guide rail coordinate, the Z-axis motion guide rail coordinate and the rotation spindle coordinate, and evaluate the measurement result. The operation flow comprises the following steps:
(1) and respectively installing the point measuring head, the standard inner cylindrical surface and the standard plane on the moving device. As shown in the left side of fig. 3, preferably, the inner wall and the end face of the standard ring gauge are respectively used as a standard inner cylindrical surface and a standard plane, wherein the end face of the standard ring gauge is perpendicular to the Z-axis motion guide rail, the axis of the standard ring gauge is parallel to the Z-axis motion guide rail, cartesian coordinates X (0) and Y (0) of the central axis of the standard ring gauge are respectively set as the origin of coordinates of the X-axis motion guide rail and the Y-axis motion guide rail, and the direction of the point measurement head is perpendicular to the Z-axis motion guide rail and can be driven by the rotating main shaft to rotate;
(2) controlling the Z-axis moving guide rail to enable the point measuring head to be aligned with the edge of the end face of the standard ring gauge, as shown in the right side of the figure 3, the signal intensity of the point measuring head will change suddenly at the aligning moment, and at the moment, the data acquisition and processing system acquires the position coordinate Z (0) of the Z-axis moving guide rail and takes the point as the origin of the Z coordinate of the measuring system;
(3) the relative position of the point measurement head and the movement device is shown in fig. 4. When in the initial position, the relative position of the spot measuring head and the moving device is as shown in FIG. 4(a), and the center of the rotation main shaft is OsThe point measuring head is parallel to the horizontal direction and the included angle between the connecting line of the end point of the point measuring head and the center of the main shaft and the horizontal direction is theta0The distance between the end point and the center of the main shaft is Rrot. Controlling the X-axis motion guide rail, the Y-axis motion guide rail and the rotating main shaft through the motion control module to enable the point measuring head to aim at the standard inner cylindrical surface and measure n points on the standard inner cylindrical surface, wherein when the ith point on the standard inner cylindrical surface of the standard ring gauge is measured, the relative positions of the point measuring head, the rotating main shaft and the standard ring gauge are shown in figure 4(b), and the central point of the rotating main shaft is Os(i) The measuring head endpoint is A (i), and the measuring point is B (i). Measuring the distance L (i) from the measuring head endpoint to the aimed point on the measured surface by using a data acquisition processing system acquisition point, and recording the X-axis motion guide rail position X (i), the Y-axis motion guide rail position Y (i) and the rotation main shaft angle theta (i) at the moment, so that the corresponding Cartesian coordinate of the measuring point of the standard inner cylindrical surface on the standard ring gauge is as follows
Xc(i)＝x(i)+Rrot cos[θ0+θ(i)]+L(i)cos[θ(i)]
Yc(i)＝y(i)+Rrot sin[θ0+θ(i)]+L(i)sin[θ(i)]
Wherein i is 1,2,3, … …, n. R can be obtained by least square methodrotAnd theta0A least squares objective function of
Figure BDA0002763028330000061
(3) The X-axis motion guide rail, the Y-axis motion guide rail, the Z-axis motion guide rail and the rotating main shaft of the control motion device measure the multi-free-form surface reflectors distributed in the inner cavity, a data acquisition and processing system records X-axis motion guide rail coordinates X (i, j), Y-axis motion guide rail coordinates Y (i, j), Z-axis motion guide rail Z (i, j) and rotating main shaft coordinates theta (i, j) corresponding to each measurement data point (M is the number of the free-form surface reflectors, N is the number of the measurement data points of each reflector) of the multi-free-form surface reflectors, and point measurement measuring probe distance L (i, j) from the surface, wherein i is 1,2,3, … …, NmJ is 1,2,3, … …, M is the number of free-form surface mirrors, NmIs the number of mth mirror measurement data points. The Cartesian coordinates X (i, j), Y (i, j) and Z (i, j) of the respective measurement data points are then respectively
X(i,j)＝x(i,j)+Rrot cos[θ(i,j)+θ0]+L(i,j)cosθ(i,j)
Y(i,j)＝y(i,j)+Rrot sin[θ(i,j)+θ0]+L(i,j)sinθ(i,j)
Z(i,j)＝z(i,j)
(4) And carrying out coordinate registration calculation on the measurement data of all the free-form surface reflectors and the design model of the multi-free-form surface reflector system together to finish the unification of the measurement coordinate system and the model coordinate system. Let the coordinate of the ith measurement data point of the jth mirror be P (i, j), then
P(i,j)＝(X(i,j),Y(i,j),Z(i,j))
The coordinates of the ith model data point of the jth mirror of the multiple freeform mirrors are Q (i, j), and the normal vector there is nq(i, j) is calculated according to the equation of the free-form surface reflector model, and P (i, j) and Q (i, j) are obtained by searching all coordinates according to the principle that the point distances are nearestThe rotation and translation modes of (1).
The searching mode is
Figure BDA0002763028330000071
Wherein R isroughAnd troughThe coordinate rotation matrix and the coordinate translation matrix are respectively converted from the measurement data. At this time, for the measured data point P (i, j), the coordinate P of the ith data point of the jth mirror obtained after the translation and rotation is performed1(i, j) is represented by
P1(i,j)＝RroughP(i,j)+trough
(5) According to a reference equation of a multi-free-form surface reflector model, calculating the space distance from a measurement data point to the free-form surface reflector along the normal vector direction, and setting P1(i, j) spatial distance D [ P ] to free-form surface mirror1(i,j)]. Then, a coordinate translation matrix and a coordinate rotation matrix between the two coordinate systems are calculated through the following objective function optimization:
Figure BDA0002763028330000072
wherein R isfineAnd tfineThe coordinate rotation matrix and the coordinate translation matrix are respectively unified by a measurement coordinate system and a model coordinate system. After the measured coordinate system is unified with the model coordinate system, the obtained coordinate T (i, j) of the ith data point of the jth reflector is measured data unified with the model coordinate system, and the expression is
T(i,j)＝RfineP1(i,j)+tfine
(6) And respectively carrying out coordinate registration calculation on the measurement data T (i, j) of each free-form surface reflector and the design model thereof, and setting the measurement data point of the mth free-form surface reflector after passing through the measurement coordinate system and the model coordinate system as T (i, m), then calculating the transformation relation of the measurement data point and the ideal model coordinate registration calculation according to the following modes:
Figure BDA0002763028330000073
wherein R ismAnd tmRespectively is a coordinate rotation matrix and a coordinate translation matrix which are used for coordinate registration calculation of the mth free-form surface reflector. The expression is as follows:
Figure BDA0002763028330000074
tm＝(Δxm,Δym,Δzm)
wherein R ism(i, j) is the element in the ith row and jth column of the coordinate rotation matrix, Δ xm，ΔymAnd Δ zmDisplacement deviation quantities of the mth free-form surface reflector along the X-axis motion guide rail direction, the Y-axis motion guide rail direction and the Z-axis motion guide rail direction are respectively. Coordinate registration calculated measurement data TregThe (i, m) coordinates are transformed to:
Treg(i,m)＝RmTreg(i,m)+tm＝(Xreg(i,m),Yreg(i,m),Zreg(i,m))
in this case, the surface shape error is the distance from each point of the measurement data after coordinate registration calculation to the free-form surface mirror model, and the surface shape equation of the mth free-form surface mirror is set to z ═ Fm(x, y), the surface shape error E (i, m) corresponding to each measured data point is
E(i,m)＝Zreg(i,m)-Fm(Xreg(i,m)-Yreg(i,m))
The position error of the mth free-form surface reflector is defined as the displacement deviation T between the mth free-form surface reflector and the model surfacemAnd around a certain vector direction V in the model coordinate systemmIs offset by an angle thetam. Wherein T ismAnd a translation matrix tmIn agreement, i.e.
Tm＝tm
Wherein Δ xm，ΔymAnd Δ zmRespectively is the m-thAnd the displacement deviation of the free-form surface reflector along the X-axis motion guide rail direction, the Y-axis motion guide rail direction and the Z-axis motion guide rail direction. VmAnd thetamBy rotating the matrix RmCalculated using the following formula:
Figure BDA0002763028330000081
Figure BDA0002763028330000082
the surface shape error result of the surface can be obtained as E (i, j) according to the mode; the result of the position error of the surface is: the position translation error of the jth free-form surface reflector along each axis of the Cartesian coordinate system is Deltaxj，Δyj，ΔzjThe rotation error being about the vector direction VjIs rotated by an angle thetaj。
The invention relates to a high-precision measuring and evaluating method for multi-free-form surface reflectors distributed in an inner cavity, which is mainly used for measuring the shape and the position of the surface of each element of an optical system under the space constraint, but can also be applied to measuring other shapes and positions with a plurality of surfaces. The point measuring probe adopted by the embodiment adopts an optical probe, and the method can also adopt other types of point measuring probes and is suitable for measuring and evaluating the shapes and the positions of the surfaces of a plurality of elements in situ and offline.

Claims (1)

1. A method for measuring the surface shape and position of a multi-free-form surface reflector distributed in an inner cavity comprises a workpiece to be measured, a moving device, a point measuring head, a data acquisition processing system, a standard inner cylindrical surface and a standard plane, wherein the workpiece to be measured comprises the inner cavity and the four multi-free-form surface reflectors respectively arranged in the inner cavity; the point measurement measuring head is positioned in the inner cavity and can aim at the measured surface within a certain included angle range to obtain the distance from the endpoint of the point measurement measuring head to the aimed point on the measured surface; the data acquisition and processing system is connected with the point measurement probe and can acquire and process measurement data; the method comprises the following steps of measuring the multiple free-form surface reflectors distributed in the inner cavity through a point measurement measuring head to obtain three-dimensional point cloud data of the multiple free-form surface reflectors, and evaluating surface shape accuracy and position accuracy of the multiple free-form surface reflectors, wherein the method comprises the following steps:
(1) respectively installing a point measurement measuring head, a standard inner cylindrical surface and a standard plane on a moving device, wherein the standard plane is vertical to a Z-axis moving guide rail, the axis of the standard inner cylindrical surface is parallel to the Z-axis moving guide rail, Cartesian coordinates X (0) and Y (0) of the center of the standard inner cylindrical surface are respectively set as the origin of coordinates of an X-axis moving guide rail and a Y-axis moving guide rail, and the direction of the point measurement measuring head is vertical to the Z-axis moving guide rail and can be driven by a rotating main shaft to rotate;
(2) calibrating the measuring system to obtain the original point Z (0) of the guide rail for the measuring system to move along the Z axis and the rotating radius R of the point measuring headrotAnd the included angle theta between the connecting line of the point measurement measuring head and the center point of the standard cylindrical surface and the horizontal direction0The method comprises the following steps:
step 1: controlling the Z-axis moving guide rail to enable the point measuring head to be aligned with the edge of the standard plane, recording a position coordinate Z (0) of the Z-axis moving guide rail at the alignment moment, namely when the data acquisition processing system acquires the measured data, and taking the position coordinate as an original point of the measuring Z-axis moving guide rail;
step 2: controlling an X-axis motion guide rail, a Y-axis motion guide rail and a rotating main shaft through a motion control module to enable a point measuring head to align with a standard inner cylindrical surface, measuring N points on the standard inner cylindrical surface, wherein N is more than or equal to 3, when a data acquisition and processing system acquires distances L (1), L (2), … … and L (N) from a point measuring head end point to a point aimed at on a measured surface, respectively recording the X-axis motion guide rail position, the Y-axis motion guide rail position and the rotating main shaft angle of the N points, which are respectively marked as X (1), X (2), … …, X (N) and Y (1), Y (2), … …, Y (N), theta (1), theta (2) … … and theta (N),
wherein, i is 1,2,3, … …, n,r is obtained by an optimized search methodrotAnd theta0With an optimized objective function and constraints of
Figure FDA0003168516600000011
s.t.Yc(i)＝y(i)+Rrotsin[θ(i)+θ0]+L(i)sinθ(i)
Yc(i)＝y(i)+Rrotsin[θ(i)+θ0]+L(i)sinθ(i)
Wherein, Xc(i) And Yc(i) The Cartesian coordinates of the ith point on the standard cylindrical surface;
(3) the X-axis motion guide rail, the Y-axis motion guide rail, the Z-axis motion guide rail and the rotating spindle of the motion control device measure the multi-free-form surface reflector distributed in the inner cavity, and the data acquisition and processing system records X-axis motion guide rail coordinates X (i, j), Y-axis motion guide rail coordinates Y (i, j), Z-axis motion guide rail Z (i, j) and rotating spindle coordinates theta (i, j) corresponding to each measurement data point of the multi-free-form surface reflector, wherein i is 1,2,3, … …, NmJ is 1,2,3, … …, M is the number of free-form surface mirrors, NmThe number of the m-th mirror measurement data points is shown, and the Cartesian coordinates X (i, j), Y (i, j) and Z (i, j) of each measurement data point are respectively
X(i,j)＝x(i,j)+Rrotcos[θ(i,j)+θ0]+L(i,j)cosθ(i,j)
Y(i,j)＝y(i,j)+Rrotsin[θ(i,j)+θ0]+L(i,j)sinθ(i,j)
Z(i,j)＝z(i,j)
(4) And (4) evaluating the surface shape error and the position error of the multi-free-form surface reflector according to the Cartesian coordinates of each measurement data point obtained in the step (3), and adopting the following steps:
step 1: and (3) carrying out coordinate registration calculation on the measurement data of all the free-form surface reflectors and the design model of the multi-free-form surface reflector system together to finish the unification of a measurement coordinate system and a model coordinate system: let the coordinate of the ith measurement data point of the jth mirror be P (i, j), then
P(i,j)＝(X(i,j),Y(i,j),Z(i,j))
The coordinates of the ith model data point of the jth mirror of the multiple freeform mirrors are Q (i, j), and the normal vector at that data point is nq(i, j) is calculated according to the equation of the free-form surface reflector model, P (i, j) and Q (i, j) are rotation and translation modes for searching all coordinates according to the principle that the point distance is nearest, and the search objective function is
Figure FDA0003168516600000021
Wherein R isroughAnd troughRespectively converting a coordinate rotation matrix and a coordinate translation matrix of the measurement data; at this time, for the measured data point P (i, j), the coordinate P of the ith data point of the jth mirror obtained after the translation and rotation is performed1(i, j) is represented by
P1(i,j)＝RroughP(i,j)+trough
Step 2: according to a reference equation of a multi-free-form surface reflector model, calculating the space distance from a measurement data point to a free-form surface reflector along the normal vector direction, and optimizing and calculating a coordinate translation matrix and a coordinate rotation matrix between two coordinate systems through the following objective functions:
Figure FDA0003168516600000022
wherein R isfineAnd tfineA coordinate rotation matrix and a coordinate translation matrix, DR, respectively, unified for the measurement coordinate system and the model coordinate systemfineP1(i,j)+tfine]Is P1(i, j) the distance from the point passing through the coordinate system to the ideal model of the reflector; after the measured coordinate system is unified with the model coordinate system, the obtained coordinate T (i, j) of the ith data point of the jth reflector is measured data unified with the model coordinate system, and the expression is
T(i,j)＝RfineP1(i,j)+tfine
And step 3: and respectively carrying out coordinate registration calculation on the measurement data T (i, j) of each free-form surface reflector and a design model thereof, and setting the measurement data point of the mth free-form surface reflector after passing through a measurement coordinate system and a model coordinate system as T (i, m), wherein the transformation relation of the measurement data point and the ideal model coordinate registration calculation is calculated according to the following objective function:
Figure FDA0003168516600000023
wherein R ismAnd tmRespectively a coordinate rotation matrix and a coordinate translation matrix for coordinate registration calculation of the mth free-form surface reflector, DRmT(i,m)+tm]The distance from the point of T (i, j) after coordinate registration calculation to the ideal model of the reflector; rmAnd tmThe expressions are respectively:
Figure FDA0003168516600000031
tm＝(Δxm,Δym,Δzm)
wherein R ism(i, j) is the element in the ith row and jth column of the coordinate rotation matrix, Δ xm，ΔymAnd Δ zmDisplacement deviation quantities of the mth free-form surface reflector along the X-axis motion guide rail direction, the Y-axis motion guide rail direction and the Z-axis motion guide rail direction are respectively; the measured data after coordinate registration is recorded as Treg(i, j), the measured data coordinates being obtained by the following transformation:
Treg(i,m)＝RmTreg(i,m)+tm＝(Xreg(i,m),Yreg(i,m),Zreg(i,m))
wherein Xreg(i,m)，Yreg(i, m) and Zreg(i, m) are cartesian coordinates of the mth free-form surface mirror measurement data after coordinate registration;
at this time, the surface shape error isTaking the distance from each point of the measurement data to the free-form surface reflector model after coordinate registration calculation as a surface shape error, and setting the surface shape equation of the mth free-form surface reflector as z ═ Fm(x, y), the surface shape error E (i, m) corresponding to each measured data point is
E(i,m)＝Zreg(i,m)-Fm(Xreg(i,m),Yreg(i,m))
The position error of the mth free-form surface reflector is defined as the displacement deviation T between the mth free-form surface reflector and the model surfacemAnd around a certain vector direction V in the model coordinate systemmIs offset by an angle thetam(ii) a Wherein T ismAnd a translation matrix tmIn agreement, i.e.
Tm＝tm
Wherein Δ xm，ΔymAnd Δ zmDisplacement deviation quantities of the mth free-form surface reflector along the X-axis motion guide rail direction, the Y-axis motion guide rail direction and the Z-axis motion guide rail direction are respectively; vmAnd thetamBy rotating the matrix RmCalculated using the following formula:
Figure FDA0003168516600000032
Figure FDA0003168516600000033
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