JP4781920B2 - Shape measurement method - Google Patents

Description

  The present invention scans the probe in the X or Y coordinate direction on the measurement surface of a measurement object, in particular, a lens such as a single lens or a lens array, or a lens molding die, so that the probe is in the XY coordinate position. The present invention relates to a method and an apparatus for measuring the shape of a measurement surface based on the Z coordinate data sequence, and measuring the shape of the measurement surface by detecting the boundary position of the measurement object. It is about how to do it.

  In recent years, in a liquid crystal display (LCD) used for a projector or the like, a lens array is used for condensing light on each liquid crystal pixel to improve light use efficiency. Although it can be said that such a lens array has already reached the industrial level as a manufacturing method, its evaluation method has not yet been established.

As an apparatus used for evaluation of a lens array, there is one disclosed in Japanese Patent Laid-Open No. 2000-155071 (Patent Document 1). FIG. 25 is a diagram illustrating a schematic configuration of the focal length measurement apparatus described in Patent Document 1. In this apparatus 301, it is possible to optically determine the focal length D (≈height deviation) and the interfocal distance of each cell of the lens array. That is, the light emitted from the light source 302 is collected by the lens array 303, and the light that has spread again after being collected is collected by the measurement lens 304, passes through the ND filter 305, and then forms an image on the photodetector 306. Let While moving the lens array 303 in the direction of the optical axis L by the actuator 307, a position where the amount of light received by the photodetector 306 becomes maximum and minimum is obtained, and from the relative distance difference between the lens array 303 and the measurement lens at that time The focal length of the lens array 303 is obtained.
JP 2000-155071 A

  However, in the apparatus of Patent Document 1, when each lens cell of the lens array (hereinafter sometimes simply referred to as a cell) is spherical, the eccentricity (or inclination) can be obtained from the design shape. When the lens is an aspherical surface, there is a problem that the inclination and decentration of the optical axis from the design shape cannot be extracted. The reason will be described below.

  26A and 26B are conceptual diagrams in a case where each lens cell of the lens array has a spherical shape and there is an eccentricity (or inclination) from the design shape 105. FIG. FIG. 26A shows a case where the tilt amount is calculated by optical measurement, and FIG. 26B shows a case where the eccentricity is calculated by an optical method. Since the amount of inclination 106 (or the amount of eccentricity 107) with the design formula 105 of the optical axis of the lens coincides with the optical axis 101 as the actual lens shape 104, the mold correction can be easily performed. That is, in the case of a spherical lens, there is no problem in measurement using this optical method.

  On the other hand, FIGS. 27A and 27B are conceptual diagrams in the case where each lens cell of the lens array has an aspherical shape and there is eccentricity and inclination from the design shape 115. 27A shows a case where the tilt amount A or the eccentric amount A is calculated by optical measurement, and FIG. 27B shows a case where the actual optical axis is compared with the optical measurement of FIG. 27A. As shown in FIG. 27B, since the tilt and the eccentricity are actually mixed at the same time, the optical axis 111 as the lens shape 114 of the aspherical lens has the tilt amount A116 and the eccentric amount A117 calculated from the focal position. It does not coincide with the inclination amount B118 and the eccentricity amount B119 with the design formula 115. That is, there is a problem that mold correction cannot be performed accurately based on the measurement result.

  2. Description of the Related Art In recent years, optical devices such as projection lenses that use a single lens unit in which a plurality of lenses spread in a plane are used. In order to improve the accuracy of optical devices, it is necessary to make the lens aspherical. In this case, however, the optical method cannot separate the inclination and decentering of the lens optical axis with respect to the reference design shape. There was a problem that it was difficult to correct the mold.

  The present invention solves the above-mentioned conventional problems. A three-dimensional measuring machine measures a single lens or a lens mold such as a lens array composed of a plurality of lenses as a measurement object. Thus, the present invention provides a method for measuring the shape of the measurement object by detecting the boundary position of the measurement object.

  In order to solve the above technical problem, the present invention provides a shape measuring method having the following configuration.

According to the first aspect of the present invention, the probe is scanned in the biaxial plane coordinate direction on the measurement surface of the measurement object having a plurality of geometric boundaries between the characteristic feature portion and the non-feature portion on the surface. The height coordinate data at the coordinate position is continuously obtained, and the measurement data corresponding to the biaxial plane coordinate and the height coordinate is obtained for a plurality of measurement points on the biaxial plane coordinate, and the measurement data is measured based on the measurement data. a shape measuring method for measuring the shape of the surface,
The coordinate value of at least one of the biaxial plane coordinates at the target measurement point on any i-th two-axis plane coordinate, the height coordinate value (P (i), Z (i)), and the target measurement point Between the measured values ((P (i-1), Z (i-1)) regarding the i-1th point continuous upstream in the scanning direction, the value of the second-order partial differential value C in dP (i) is It asked Me,
It is determined whether or not the value of C related to the (i-1) th point is larger than a predetermined threshold value. If the value of C is larger than the predetermined threshold value , each position of the i-1th measurement point is detected as boundary position of the measured object is a boundary between the feature portion and the non-characteristic part of the shape of the measured object,
Based on the detected boundary position and the design data of the measurement object, divided into a first divided area and a first boundary gray area divided for each characteristic part of the measurement object,
For the two divided first divided areas, the positions of the vertices of the first divided areas are detected, and based on the straight line connecting the vertices of the two first divided areas and the design data of the measurement object Detecting the tilt angle deviation and the rotation angle deviation of the measurement object with respect to the design data of the measurement object, and correcting the tilt angle deviation and the rotation angle deviation of the measurement data,
Based on the corrected measurement data of the measurement object and the design data of the measurement object, the image is subdivided into a second divided area and a second boundary gray area divided for each characteristic portion of the measurement object,
Wherein for the second divided area, characterized by a Turkey to calculate the shape difference between the measurement data and the design data, provides a shape measuring method.

  In the above configuration, the measurement unit scans the measurement surface of the measurement object on two-axis plane coordinates such as XY orthogonal plane coordinates, and obtains height coordinates such as Z coordinates at the two-axis plane coordinate positions. Then, the boundary calculation unit detects the boundary position based on the value of at least one axis of the biaxial plane coordinates and the value of the height coordinate in the value. Here, the boundary position means a position that is a boundary between a characteristic feature portion and a non-feature portion in the shape of the measurement object. The distinction between the non-characteristic part and the characteristic part is appropriately determined according to the purpose of the measurement, and does not mean a part indicating the use or function of the measurement object, but on the measurement surface. The part where the tendency of the shape changes can be set as the boundary position.

  For example, when the object to be measured is a lens, the boundary between the uneven portion on the lens as the characteristic portion and the flat portion as the non-characteristic portion corresponds to this. For example, when the object to be measured is a lens array, a boundary between one lens cell as a characteristic part and another lens cell adjacent to the lens cell as a non-characteristic part corresponds. Further, for example, when there is a measurement object to be peeled off, the boundary between the tooth bottom and the tooth surface, the boundary between the tooth tip and the tooth surface, and the like are applicable.

によりＣの値を算出することができる。 Here, when the values of the second order partial differentiation are defined as dP (i) = P (i) −P (i−1), dZ (i) = Z (i) −Z (i−1),

Can calculate the value of C.

  The threshold value can be set as appropriate. For example, for the C value at each measurement point, the threshold value is a value half the maximum value of the C value for all coordinate values P (i). It can be.

According to a second aspect of the present invention, the calculation of the shape difference between the measurement data and design data,
The coordinate conversion for the RMS minimization is performed by the difference between each second divided region subdivided for each feature portion and the design formula, and the eccentricity dx, dy, the height deviation dz from the design formula is calculated from the coordinate conversion amount. The shape measuring method according to the first aspect is characterized in that the slopes α and β are obtained .

According to a third aspect of the present invention, coordinate transformation of the previous SL RMS minimization conducted RMS minimize changing the R value of the design data to the best-fit R value, the best fit R determined for each feature section A shape measuring method according to a second aspect, comprising displaying on an output device.

According to a fourth aspect of the present invention, the eccentric dx, dy, the height information deviation dz, input to the design parameters of the characteristic part to create a new second design type,
Based on the measurement data converted into the coordinate system for the measurement object, re-divided into a third divided area and a third boundary gray area divided for each characteristic portion of the measurement object ,
A shape measurement method according to a second aspect is provided, wherein a shape difference between measurement data and design data is calculated for the third divided region instead of the second divided region.

According to a fifth aspect of the present invention, by inputting the best-fit R on design parameters in the second design type creates a new third design type,
Based on the measurement data converted into the coordinate system for the measurement object, re-divided into a fourth divided region and a fourth boundary gray region divided for each cell of the lens,
A shape measurement method according to a fourth aspect is provided, wherein a shape difference between measurement data and design data is calculated for the fourth divided region instead of the second divided region.

According to a sixth aspect of the present invention, conversion of the coordinate system relative to the sample of,
The flat surface data the measurement data of all the measured object table surface region to delete the data of only the measured effective surface as a reference surface,
When the measurement object is placed on the jig plate on which the first to third spheres having the same diameter are fixed and the side surface of the measurement object is in contact with the three spheres, one first sphere The direction parallel to the straight line connecting the center and the center of the other second sphere is the converted X _L coordinate axis, the direction parallel to the straight line perpendicular to the reference plane is the Z _L coordinate axis, and the X _L coordinate axis Any one of the first to fifth aspects is characterized in that a direction orthogonal to the Z _L coordinate axis and parallel to a straight line passing through the center of the remaining third sphere is converted into a coordinate system having the Y _L coordinate axis. Two shape measurement methods are provided.

According to the seventh aspect of the present invention, the measurement object is placed on the first to third spheres fixed on the jig plate, and the back surface of the measurement object is used as the reference plane.
On the jig plate to which the first to third spheres are fixed, the center of the first sphere and the second when the measurement object is placed so that the side surface of the measurement object is in contact with the three spheres. The direction parallel to the straight line connecting the centers of the spheres is defined as the X _L coordinate axis, the direction parallel to the straight line orthogonal to the reference plane is defined as the Z _L coordinate axis, and the remaining third third is orthogonal to the X _L coordinate axis and the Z _L coordinate axis. There is provided a shape measuring method according to any one of the first to fifth aspects, characterized in that a direction parallel to a straight line passing through the center of the sphere is converted into a coordinate system having a Y _L coordinate axis.

  According to the present invention, the boundary data of the lens surface can be automatically extracted from the measurement data, and the alignment with the design data of the measurement object can be performed based on the boundary data. The accuracy of the comparison can be increased. Therefore, the shape of the measurement object can be measured with higher accuracy.

  Further, from the extracted boundary data, in the case of a lens array, each divided data and each boundary gray zone can be calculated for each cell. Thereby, the comparison with the design data about the part of the cell can be performed more, and the shape of the part of the optical element can be measured.

  Furthermore, the shape deviation of each lens with respect to the measured object coordinate system of a mold for integrally molding a plurality of lenses or an integrally molded lens array can be evaluated with high accuracy. In particular, since the eccentricity, inclination, height deviation, and best fit R included in the shape error can be quantitatively evaluated, a mold for integrally molding a plurality of lenses can be efficiently fed back to a lens array used for a projector or the like. In this case, a good lens array can be obtained without causing the focus to be blurred or light and dark due to the optical axis deviation or the lens height variation.

Hereinafter, a shape measuring apparatus according to an embodiment for carrying out a shape measuring method of the present invention will be described with reference to the drawings.
FIG. 24A is a perspective view showing a schematic configuration of a shape measuring apparatus as an embodiment for carrying out the shape measuring method of the present invention. In FIG. 24, an oscillation frequency stabilized He-Ne laser 71 for measuring XYZ coordinates is arranged on a stone plate 63 on XY stages 69 and 70, and a probe 65 is placed on a stone plate via a Z stage 64. 63, and is reflected by XYZ reference mirrors 66, 67, 68 having a high flatness of nanometer order by oscillating frequency stabilized He-Ne laser light, and XYZ with ultrahigh accuracy of nanometer order. Coordinates can be measured. The measured result is displayed on the output device 90.

  This shape measuring apparatus obtains a column of Z coordinate data at the XY coordinate position of the measurement probe 65 by scanning the measurement probe 65 in the XY coordinate direction on the measurement surface S of the measurement object. The sequence of Z coordinate data at the XY coordinate positions measured by the measurement probe 65 is subjected to arithmetic processing, and the shape of the measurement surface S is measured.

  Hereinafter, processing performed by the control calculation unit 80 will be described. The control calculation unit 80 has functional blocks as shown in FIG. 24B. These functional blocks are responsible for the processing described later when the following processing is performed.

  FIG. 1 is a flowchart showing an outline of a shape measuring method when a lens array is collectively measured in the shape measuring apparatus of FIG. Each step in FIG. 1 will be described below using another figure.

<Step S1>
The entire surface of the lens array 4 is measured on the measuring machine X _M Y _M Z _M coordinate system, and data of the measurement result is stored in a storage device. FIG. 2 is a diagram showing this state.

With the lens array 4 installed in the measuring machine X _M Y _M Z _M coordinate system 1, the probe 65 is turned on as indicated by the arrow 15 to scan the entire surface of the lens array 4 including the base surface 4b. Three-dimensional measurement data ((X (i), Y (i), Z (i)) is obtained. The three-dimensional measurement data ((X (i), Y (i), Z (i))) The data is stored in the second storage unit 802 of the storage unit 7 in 80. The first storage unit 801 of the storage unit 7 stores the design data of the lens array that is the measurement target. Based on these pieces of information stored in the first storage unit 801 and the second storage unit 802, the following arithmetic processing is performed.

2, three-dimensional measurement data ((X (i), Y (i), Z (i)) captures the data moving the X _M direction as the main direction, a state Y _M direction to move the shift direction shows. hereinafter, extract data for each line in the X _M direction is described as an example how to data processing in X _M Z _M section. However, by scanning the probe 65 in the Y _M direction, Y _M Data processing may be performed on the _ZM plane.

<Step S2>
FIG. 3 shows an example of measurement data of a convex lens having an edge plane portion, partial differential value data of a convex lens having an edge plane portion, and second-order knitting differential value data of a convex lens having an edge plane portion.

Partial differential calculation unit 803 of the control computation unit 80, in the X _M Z _M section, i-th (i is 2 or more) using the measurement data and the i-1 th measurement data in the scanning direction upstream side of, the following Second-order partial differential value data is calculated according to the processing. That is, from the i-th measurement data ((X (i), Z (i)), dX (i) = X (i) -X (i-1), dZ (i) = Z (i) -Z ( i-1) and partial differential value data dZ (i) / dX (i) = {Z (i) -Z (i-1)} / {X (i) -X (i-1)} Thereafter, from the partial differential value data dZ (i) / dX (i), the second order partial differential value data d ² Z (i) / dX ² (i) = {dZ (i) / dX (i) −dZ. (i-1) / dX (i-1)} / {X (i) -X (i-1)} is obtained.

Based on the second-order partial differential value data obtained by the partial differential calculation unit, the threshold setting unit 804 sets the threshold values in the + direction and the − direction of the second-order partial differential value data d ² Z (i) / dX ² (i). Set. Next, the boundary calculation unit 805 determines whether or not the absolute value | d ² Z (i) / dX ² (i) | of the second-order partial differential value data is greater than a predetermined threshold value with respect to the i-th measurement data. Then, data exceeding the threshold is extracted. In the case of FIG. 3, since the Kth and Lth measurement data are points larger than a predetermined threshold value, in the measurement data ((X (i), Z (i)), the K−1th, L− It can be detected that the first position is a boundary.

  Here, the threshold value setting by the threshold value setting unit 804 is determined as follows in the present embodiment. That is, the second-order differential value data shown in FIG. 3 is usually composed of a flat portion and a protruding boundary portion. At this time, for the flat portion, an approximate straight line having a slope of 0 is derived by the least square method, and the approximate curve is set as the origin position. Then, the height width of the data of the second-order differential value data when the value is the highest and the data of the approximate straight line is calculated, and the half of the height width is set as a threshold value.

  FIG. 4 shows an example of measurement data of a concave lens having an edge plane portion, partial differential value data of a concave lens having an edge plane portion, and second-order knitting differential value data of a concave lens having an edge plane portion. By the same processing as in FIG. 3, in the measurement data ((X (i), Z (i)), it is detected that the (K-1) th and (L-1) th data are boundaries.

  FIG. 5 shows examples of measurement data of the convex lens array, partial differential value data of the convex lens array, and second-order partial differential value data of the convex lens array. Also in this case, the measurement data ((X (i), Z (i)) has the (K−1) th, (L−1) th, (M−1) th, and (N−1) th data. Detects a boundary.

  FIG. 6 shows examples of measurement data of the concave lens array, partial differential value data of the concave lens array, and second-order partial differential value data of the concave lens array. Also in this case, the measurement data ((X (i), Z (i)) is K−1, L−1, M−1 and N−1 in the same manner as in FIGS. 3A to 3C. Is detected as a boundary.

The process shown in FIGS. 3 to 6 described above, three-dimensional measurement data ((X (i), Y (i), Z (i)) takes in data moving the Y _M direction as the main direction, X _M direction Is also true when moving in the shift direction, in which case dY (i) = Y (i) −Y (i−1), dZ (from the measurement data ((Y (i), Z (i))). i) = Z (i) −Z (i−1) and partial differential value data dZ (i) / dY (i) = {Z (i) −Z (i−1)} / {Y (i ) −Y (i−1)}, and then from the partial differential value data dZ (i) / dY (i), the second order partial differential value data d ² Z (i) / dY ² (i) = {dZ (i) / dY (i) -dZ (i-1) / dY (i-1)} / {Y (i) -Y (i-1)} is obtained and measured data ((Y (i), Z The boundary in (i)) can be detected.

Further, when scanning in the circumferential direction in the X _M Y _M plane, the boundary in the three-dimensional measurement data ((X (i), Y (i), Z (i)) is obtained by the same method as described above. That is, the boundary position can be detected using the coordinate value related to at least one of the two-axis plane coordinates and the coordinate value related to Z _M.

<Step S3>
The design data stored in the first storage unit 801 is divided into divided data A and boundary gray zones A for each lens cell. FIG. 7 is a diagram for explaining the processing.

As described above, the lens array 4 is installed in the measuring machine X _M Y _M Z _M coordinate system. However, when viewed in the sub-μm order, the lens array 4 is installed with an angular deviation around any axis. . With respect to the coordinates (0,0,0) of the measurement origin 5a, three-dimensional measurement data ((X (i), Y (i), Z (i)) is divided.

  That is, the gray zone A is determined from the boundary data obtained in FIGS. FIG. 8 is a diagram for explaining the process of determining the gray zone A. The determination of the gray zone A is governed by the first data dividing unit 806 of the control calculation unit.

<Determination procedure of gray zone A>
(1) In the region of the design shape 131 of the cell j, all the points 121 on the boundary of the cell j extracted from the measurement data 130 are extracted, and the Line L group 122a close to the Line L122 and the Line R group close to the Line R123 123a.

  (2) The point having the largest distance 128 in the X direction with Line L in the design data 131 in the Line L group 122a is detected as the AL point 126. Similarly, the X direction from Line R in the Line R group 123a is detected. The farthest distance (not shown) is detected as the AR point 127.

(3) Compare the distance from the line L122 to the AL point 126 with the distance from the Line R123 to the AR point 127, and let the distance from the longest point be _{dj, XMAX} , and the width of the gray zone in the X direction To do.

  (4) The AL point 126 and AR point 127 obtained in (3) are classified into the Line T group 124a close to Line T124 and the Line B group close to Line B. In the case of FIG. 8, only the Line T group 124a is provided.

  (5) The point farthest from Line T124 in Line T group 124a is detected as AT point 132 (in the case of FIG. 8, it is the same point as AR point 127). Although it does not exist in the case of FIG. 8, it has a function of detecting a point farthest from Line B in the Line B group as an AB point.

(6) The distance from Line T124 to AT point 132 and the distance from Line B125 to AB point (none in the case of FIG. 8) are compared, and the distance d _{j, YMAX} to the point having the longest distance is The width of the gray zone.

(7) Using the distance d _{j, xMAX and the} distance d _{j, YMAX} obtained in this way, the periphery of the design shape of the cell j is set as the gray zone A12j, and the inside thereof is set as the divided data A9j. In this way, the boundary gray zone A12j of the cell j and the effective divided data A9j of the cell j can be detected.

  (8) Similarly, the cell j + 1 is divided into the boundary gray zone A12j + 1 and the effective divided data A9j + 1 of the cell j + 1. In this way, the divided data and the boundary gray zone are detected for all lens cells.

<Step S4>
Next, in any two or more cells, translation coordinate conversion for RMS minimization is performed with each divided data A and design formula, and the inter-cell rotation angle γ is calculated from the coordinate conversion amounts dx and dy of each of the two or more cells. (Around Z axis) is calculated. This process is performed by the first coordinate conversion unit 807.

  FIG. 9 is an explanatory diagram of a process of calculating the inter-cell rotation angle γ from the two cells performed by the first coordinate conversion unit. The point that moves to the position of the vertex 17 on the design formula of the cell (1) by the translation coordinate conversion of the RMS minimization corresponds to the vertex 18 on the measurement data of the cell 1. The position of the vertex 18 on the measurement data of the cell 1 can be known from the coordinate conversion amount (dx1, dy1) at this time.

By the same method, the position of the vertex 20 on the measurement data of the cell (5) can also be detected. In FIG. 9, for the cell (1) a cell (5) Since the lined up five cells in the X _M direction, were subjected to detection of the vertex, not particularly this is limited. For example, it is possible to use a cell located at both ends of the X _M direction. In this way, the rotation angle γ around the Z axis of the lens array 4 can be calculated using the information on the position of the vertex.

  Next, the inclination α (around the X axis) and β (around the Y axis) of the entire lens surface are calculated from the data of the edge plane portion of the lens array 4. This process is performed by the first coordinate conversion unit 807. FIG. 10 is an explanatory diagram of the processing. Only the data 5b of the edge plane portion of the lens array is separated based on the data of a predetermined threshold value or more located on the outermost side from the three-dimensional measurement data ((X (i), Y (i), Z (i)). Then, the angle coordinates conversion for minimizing the RMS is performed by the difference from the plane design formula Z = 0, and the tilt angles α and β of the entire lens surface can be calculated.

Using the rotation angles α, β, and γ determined above, the entire surface measurement data in step S1 is converted into the measurement object X _L Y _L Z _L coordinate system. This process is performed by the first coordinate conversion unit 807. FIG. 11 is an explanatory diagram of the conversion process.

  As another method in this step, RMS minimization is performed by moving α (around the X axis), β (around the Y axis), and γ (around the Z axis) between each divided data A on the entire lens surface and the design formula. It is also possible to perform angular coordinate conversion.

<Step S5>
Based on the information obtained in step S4, effective divided data B and boundary gray zone B are calculated for each cell of design data. This process is performed by the second data dividing unit 808 of the control calculation unit 80. FIG. 12 is a diagram for explaining the calculation method. FIG. 13 is a diagram for explaining the process of determining the boundary gray zone B from the boundary data of FIG. The procedure is the same processing as FIG. 8 described in step S3.

Since the boundary of the design equation and the boundary detected in the measurement result are parallel to each other, the design equation is present on the measuring machine X _M Y _M Z _M coordinate system of FIGS. Thus, it becomes possible to obtain a larger effective divided data of each cell, and it is possible to improve the analysis accuracy in each step described later.

FIG. 14 is an example of comparison between the divided data B of each cell and the design formula in the state of FIG. Reference numeral 23a shown in the upper diagram is the divided data B and gray zone B data of each cell after conversion into the measured object X _L Y _L Z _L coordinate system, and reference symbol 22a shown in the middle diagram is a design formula for each lens. Reference numeral 24b shown in the lower diagram is information showing the result of subtracting the Z value in the lower diagram from the Z value in the upper diagram.

  As shown in the lower diagram, when the region 22b of the gray zone B is included, there is an error due to a lateral shift between the measurement object and the design formula. It can be seen that the accuracy of the measurement result is improved by evaluating the area of the divided data B22c excluding the area 22b of the gray zone B.

<Step S6>
FIG. 15 is a diagram for explaining the process of performing coordinate conversion for RMS minimization based on the difference between the divided data and the measurement data in step S6 for each cell on the measurement object X _L Y _L Z _L coordinate system. This process is performed by the second coordinate conversion unit 809. That is, the design formula data and measurement data for each cell are compared, and the translational coordinate conversion amount dZ, the inclination coordinate conversion amount β (or α), and the translational coordinate conversion amount dX (or dY) shown in FIG. 15 are minimized. The two data are approximated as follows. Next, from the coordinate conversion amount for each cell, the eccentricity (translational coordinate conversion amount) dX (or dY) from the design value, the coordinate conversion amount (translational coordinate conversion amount) dZ, and the inclination (coordinate conversion amount) β (or α) increase. Processing to find out the inside. FIG. 16 is a diagram for explaining processing for obtaining the eccentricity dX (or dY), the height deviation dZ, and the inclination β (or α) from the design value from the coordinate conversion amount for each cell.

<Step S7>
FIG. 17 is a diagram for explaining a process for obtaining the best fit R by RMS minimizing by changing the approximate radius R of the measurement data with respect to the divided data B after coordinate transformation for RMS minimization for each cell in step S6. It is. That is, the coordinate conversion word three-dimensional measurement data 36 is compared with the design formula data 32, the two data are arranged so as to be closest to each other, and the best fit R is calculated. Here, the best fit R performs a process of obtaining R (radius) for fitting by the least square method between the design data and the measurement data after coordinate transformation. Since the lens array 4 is an aspheric lens, it includes an approximate radius R, a conic coefficient, and an aspheric coefficient. However, the fitting process is performed by a least square method that changes only the approximate radius R.

<Step S8>
The above processing is performed for each cell, and the eccentricity amounts dx and dy, the height shift amount dz, and the inclinations α and β are obtained for each cell. FIG. 18 is a configuration example of an information table of the eccentricity amounts dx and dy, the height shift amount dz, and the inclinations α and β for each cell. The information table includes information on the design optical axis position, the actual optical axis position, the best fit R, the PV value of the difference between the measurement data and the design formula, and the RMS value. The information table is stored in the third storage unit 811.

<Step S9>
Next, the amount of eccentricity obtained in step S7 is input as a design parameter for each cell, a new design formula is created, and divided data C is created by dividing the measurement data in step S4. This process is performed by the third data dividing unit 812. FIG. 19 is a diagram illustrating a process for creating the divided data C obtained by dividing the measurement data in step S4 by inputting the amount of eccentricity obtained in step S7 into the design parameters of each cell to create a new design formula. Compared with FIG. 12, since the amount of eccentricity in the XY direction obtained from the measurement data is input to the design parameter of each cell, the vertex on the measurement data and the design vertex are matched. Therefore, the boundary gray zone C of each cell is reduced to a level that can be almost ignored, and the maximum effective divided data C can be larger than the divided data B of FIG. These data are output to the output device 90 via the result creation unit 813.

In FIG. 20, the eccentricity obtained in step S8 is input to the design parameters of each cell to create a new design formula, and the difference between the divided data C obtained by dividing the measurement data in step S1 and the measurement data is output to the output device. It is like a graph. Reference numeral 23 in the upper diagram is measurement data after conversion into the measured object X _L Y _L Z _L coordinate system obtained in step S4, and reference symbol 22b in the middle diagram represents the amount of eccentricity obtained in step S7 for each cell. The reference numeral 24a in the lower diagram shows a result of subtracting the Z value in the lower diagram from the Z value in the upper diagram. In the lower figure, the boundary gray zone C is reduced to a level that can be almost ignored. Therefore, it can be seen that the error due to the boundary gray zone is almost negligible compared to FIG.

<Step S10>
In FIG. 21, the best fit R obtained in step S9 is input as a design parameter to the design equation obtained in step S9 to create a new design equation, and the divided data C obtained by dividing the measurement data in step S1 and the design equation It is a figure which shows the example of the graph which output-displayed the difference. Reference numeral 23 in the upper diagram is measurement data after conversion into the measured object X _L Y _L Z _L coordinate system obtained in step S4, and reference symbol 22b in the middle diagram is obtained in step S7 from the design equation obtained in step S8. The reference numeral 24a in the lower diagram shows a result of subtracting the Z value in the lower diagram from the Z value in the upper diagram. In the lower diagram, since the data for each cell is generally flat, each lens height deviation is much easier to understand than in FIG.

  In steps S8 and S9, the dZ (height deviation) of each cell obtained in step S8 can be input as a design parameter for evaluation. With this evaluation, the focal length can be evaluated.

In step S4, the measurement object X _L Y _L Z _L coordinate system obtained by the first coordinate conversion unit 807 can be obtained by another method. Two methods will be described below.

<First Modification of Construction Method of Measurement Object X _L Y _L Z _L Coordinate System>
FIG. 22 is a diagram showing a construction example of the measurement object X _L Y _L Z _L coordinate system based on the edge surface reference and the outer side surface reference. Calculate tilt angles α (around the X axis) and β (around the Y axis) from the data on the edge plane of the lens array measurement data, and calculate a rotation angle γ (around the Z axis) from the outer side of the lens array. It shows that an array object X _L Y _L Z _L coordinate system is constructed.

  In the outer reference jig A50a, the second plate 53 and the third plate 54 are fixed on the first plate 51, and a sphere 52d is fixed on the right side of the second plate 53. A sphere 52e and a sphere 52f are fixed in front of the third plate 54.

The sphere 52d of the outer shape reference jig A50a is centered by a super-precision three-dimensional measuring machine shown in FIG. 24 to calculate temporary vertex coordinates, and then measured in the XY directions to obtain three-dimensional measurement data. The minimum square error position is calculated from the design formula. At this time, true vertex coordinates (Xd, Yd, Zd) are calculated. Similarly, true vertex coordinates (Xe, Ye, Ze) and (Xf, Yf, Zf) are calculated for the sphere 52e and the sphere 52f. Further, the best fit R (Br) is calculated from the measurement data, and when the sphere 52e and the sphere 52f are substantially parallel to the X _M axis,
In the case of the sphere 52d, (Xd, Yd, Zd) <-(Xd + Br, Yd, Zd-Br)
In the case of the sphere 52e, (Xe, Ye, Ze) <-(Xe, Ye-Br, Ze-Br)
In the case of the sphere 52f, (Xf, Yf, Zf) <-(Xf, Yf-Br, Zf-Br)
Convert as follows.

Further, an X _L coordinate axis is formed in a direction parallel to a straight line connecting the point (Xf, Yf, Zf) on the sphere F from the point (Xe, Ye, Ze) on the sphere E.

  When the lens array 4 is installed on the outer shape reference jig A50a, the Z bottom surface 4e of the lens array 4 rides on the first plate 51, and the X side surface 4c of the lens array 4 is on the X + side surface of the sphere 52d. The Y side surface 4d of the lens array is configured to contact the Y-side side surface of the sphere 52e and the sphere 52f, and the thickness of the second plate 53 and the third plate 54 is three spheres 52d. , 52e and 52f are designed to be smaller than the diameter.

A Z _L coordinate axis parallel to the normal vector 4f of the base surface 4b of the lens array 4 placed on the outer shape reference jig 50a is created.

A coordinate axis perpendicular to the X _L coordinate axis and the Z _L coordinate axis and passing through the coordinate values (Xd, Yd, Zd) on the X + side of the sphere 52d is defined as a Y _L coordinate axis. By doing so, an X _L Y _L Z _L coordinate system based on the surface edge surface portion data and the outer surface of the lens array is constructed.

This external reference jig 50a can be applied not only to the lens array 4, but also to all lens units having a rectangular outer frame. With the X _L Y _L Z _L coordinate system constructed in this way as a reference coordinate system, the evaluation of FIG. 1 obtained previously can be performed.

<Second Modification of Construction Method of Measurement Object X _L Y _L Z _L Coordinate System>
FIG. 23 is an explanatory diagram of a construction example of the measurement object X _L Y _L Z _L coordinate system based on the bottom surface reference and the external surface reference. The tilt angles α (around the X axis) and β (around the Y axis) are calculated from the inclination of the bottom surface 4e of the lens array, the rotation angle γ (around the Z axis) is calculated from the outer side surface of the lens array, and the lens array X _L It illustrates the process of constructing a Y _L Z _L coordinate system.

  Three balls 52a, 52b, and 52c having the same diameter are fixed on the first plate 51 in the outer shape reference jig 50b. A second plate 53 and a third plate 54 are fixed on the first plate 51, and a sphere 52 d is fixed on the second plate 53. A sphere 52e and a sphere 52f are fixed on the third plate 54.

The sphere 52a of the outer shape reference jig 50b is centered by a super-precision three-dimensional measuring machine shown in FIG. 24A to calculate temporary vertex coordinates, and then measured in the XY directions to obtain three-dimensional measurement data. The minimum square error position is calculated from the design formula. At this time, true vertex coordinates (Xa, Ya, Za) are calculated. Similarly, true vertex coordinates (Xb, Yb, Zb) and (Xc, Yc, Zc) are calculated for the sphere 52b and the sphere 52c. From these three coordinates, a normal vector 4g of a plane passing through the vertices of the sphere 52a, sphere 52b, and sphere 52c is calculated and used as the Z _L coordinate axis.

Next, true vertex coordinates (Xd, Yd, Zd), (Xe, Ye, Ze) are also obtained for the sphere 52d, sphere 52e, and sphere 52f in the same manner as the sphere 52a, sphere 52b, and sphere 52c described above. , (Xf, Yf, Zf) are calculated. Furthermore, the best fit R (Br) is calculated from the measurement data, and when the sphere E and the sphere F are substantially parallel to the X axis,
In the case of the sphere 52d, (Xd, Yd, Zd) <-(Xd + Br, Yd, Zd-Br)
In the case of the sphere 52e, (Xe, Ye, Ze) <-(Xe, Ye-Br, Ze-Br)
In the case of the sphere 52f, (Xf, Yf, Zf) <-(Xf, Yf-Br, Zf-Br)
Convert as follows.

Further, an X _L coordinate axis is formed in a direction parallel to a straight line connecting the point (Xe, Ye, Ze) on the sphere 52e and the point (Xf, Yf, Zf) on the sphere 52f. A coordinate axis that is perpendicular to the Z _L coordinate axis and the X _L coordinate axis and that passes through the coordinate values (Xd, Yd, Zd) of the side surface on the X + side of the sphere 52d previously determined is defined as a Y _L coordinate axis. In this way, an X _L Y _L Z _L coordinate system that serves as a reference on the jig is constructed.

  When the lens array is installed on the outer shape reference jig 50b, the Z bottom surface 4e of the lens array rides on the sphere 52a, sphere 52b, and sphere 52c, and the X side surface 4c of the lens array 4 is on the X + side of the sphere 52d. The dimensions of the second plate 53 and the third plate 54 are adjusted in accordance with the thickness of the lens array such that the Y side surface 4d of the lens array is in contact with the side surface and the Y side surface of the sphere 52e and the sphere 52f. Is designed.

  By installing the lens array 4 on the outer shape reference jig 50b, the optical axis positions of the lens array can be calculated with reference to the Z bottom surface 4e, the X side surface 4c, and the Y side surface 4d of the lens array 4.

The external reference jig 50b can be applied not only to the lens array 4, but also to all lens units having a rectangular outer frame. With the X _L Y _L Z _L coordinate system constructed in this way as a reference coordinate system, the evaluation of FIG. 1 obtained previously can be performed.

  The shape measuring method and apparatus according to the present invention uses a three-dimensional shape measuring apparatus having a contact or non-contact type probe, and extracts lens boundary position data from measurement data obtained by measuring a single lens or a lens array at a time. it can.

  In addition to the lens design value information, highly accurate evaluation is possible by eliminating abnormal data in the vicinity of the lens boundary.

  Furthermore, when the measurement object coordinate system of the lens array is used as a reference, the difference between the entire measurement data and the design formula of the entire surface of the plurality of lenses is calculated, and the difference between the individual measurement data of each lens and the design formula is calculated, The difference between the design optical axis position and the actual optical axis position is calculated, and the difference between the individual measurement data and the design formula is calculated by matching each optical axis with the design optical axis. It is possible to calculate a shape parameter.

The flowchart which shows the outline of the shape measuring method when collectively measuring a lens array in the shape measuring apparatus concerning one Embodiment of this invention. The shape measuring apparatus of FIG. 1, illustration of a process of measuring the entire surface of the lens array on measuring X _M Y _M Z _M coordinate system. The figure which shows the example of the measurement data of the convex lens in which the edge plane part exists, the partial differential value data of the convex lens in which the edge plane part exists, and the second-order knitting differential value data of the convex lens in which the edge plane part exists. The figure which shows the example of the measurement data of the concave lens in which the edge plane part exists, the partial differential value data of the concave lens in which the edge plane part exists, and the second-order knitting differential value data of the concave lens in which the edge plane part exists. The figure which shows the example of the measurement data of a convex lens array, the partial differential value data of a convex lens array, and the 2nd-order partial differential value data of a convex lens array. The figure which shows the example of the measurement data of a concave lens array, the partial differential value data of a concave lens array, and the 2nd-order partial differential value data of a concave lens array. Explanatory drawing of the process which divides | segments design data into each division data A and each boundary gray zone A for every lens cell. The figure explaining the process which determines the gray zone A. FIG. Explanatory drawing of the process which calculates the rotation angle (gamma) between cells from two cells. Explanatory drawing of the process which calculates the inclination (alpha) and (beta) of the lens whole surface from the data of the edge plane part of a lens array. Explanatory drawing of the process which converts whole surface measurement data into the measurement object X _L Y _L Z _L coordinate system. Explanatory drawing of the process which calculates the division data B and boundary gray zone B which are effective for every lens cell for design data. FIG. 13 is a diagram illustrating processing for determining a boundary gray zone B from the boundary data in FIG. 12. The figure which shows the example of the comparison with the division data B of each cell, and a design formula in the state of FIG. The figure for demonstrating the process which carries out the coordinate conversion of RMS minimization by the difference of the division | segmentation data of step S6 for every cell, and a design formula on the measurement object X _L Y _L Z _L coordinate system. The figure for demonstrating the process which calculates | requires the eccentricity from a design value, height shift, and inclination from coordinate transformation amount for every cell. Explanatory drawing of the process which calculates | requires the best fit R with respect to the division | segmentation data B after coordinate conversion of RMS minimization for every cell in step S6. The figure which shows the structural example of the information table of eccentricity dx and dy for every cell, height shift | offset | difference amount dz, and inclination (alpha) and (beta). Explanatory drawing of the process which produces the division | segmentation data C which divided | segmented the measurement data of step S4 using the eccentricity calculated | required by step S7. The eccentricity obtained in step S8 is input to the design parameters of each cell to create a new design formula, and the difference between the divided data C obtained by dividing the measurement data in step S1 and the design formula is displayed on the output device. The figure which shows an example. The best fit R obtained in step S9 is input to the design parameter obtained in step S9 as a design parameter to create a new design equation, and the difference between the divided data C obtained by dividing the measurement data in step S1 and the design equation is output and displayed. FIG. Explanatory drawing of the construction example of the measurement object X _L Y _L Z _L coordinate system by edge surface reference | standard and external side surface reference | standard. Bottom reference, measured X _L Y _L Z illustration of _L coordinate system construction example according outer side reference. The external appearance block diagram of the shape measuring apparatus concerning one Embodiment of this invention. The figure which shows the structure of the functional block of the control calculating part of the shape measuring apparatus of FIG. 24A. The figure which shows schematic structure of the conventional focal distance measuring apparatus. It is a conceptual diagram when each lens cell of the lens array has a spherical shape and there is an eccentricity (or inclination) from the design shape, and is an explanatory diagram when calculating the amount of inclination by optical measurement. It is a conceptual diagram in case each lens cell of a lens array is spherical shape, and there exists eccentricity (or inclination) from a design shape, and explanatory drawing in the case of calculating eccentricity with an optical method. It is a conceptual diagram when each lens cell of the lens array has an aspherical shape and there is eccentricity and inclination from the design shape, and is an explanatory diagram when calculating the inclination amount A or the eccentricity amount A by optical measurement . FIG. 28 is a conceptual diagram in a case where each lens cell of the lens array has an aspherical shape and is decentered and inclined from the design shape, and is an explanatory diagram in a case where the actual optical axis is compared with the optical measurement in FIG. 27A.

Explanation of symbols

4 Lens array 4a Optical axis of each lens 4b Base surface 4c X side surface 4d Y side surface 4e Z side surface 4f Normal vector of base surface 10b of lens array A 4g Normal vector of plane passing through each vertex of sphere 4h Lens array shape 5 Three-dimensional measurement data ((X (i), Y (i), Z (i))
5a Measurement origin (0, 0, 0)
5b Edge data 5c Measurement data (X (i-1), Y (i-1), Z (i-1))
5d Measurement data ((X (i), Y (i), Z (i))
5e Measurement data ((X (i + 1), Y (i + 1), Z (i + 1))
5f Boundary data 6 Three-dimensional measurement data (Xi ', Yi', Zi ') after conversion to the object coordinate system
7 Storage device 8 Design formula boundary 8a Design boundary Xj, 1
8b Design boundary Xj, 2 = Xj + 1, 1
8c Design boundary Xj + 1,2
9 Division data A
9j Effective division data A of cell j
9j1 Valid divided data A of cell j + 1
10 Division data B
10j Effective division data B of cell j
10j1 Valid divided data B of cell j + 1
11 Divided data C
11j Valid divided data C of cell j
11j1 Valid divided data C of cell j + 1
12 Boundary Gray Zone A
12j Boundary gray zone A of cell j
12j1 Boundary gray zone A of cell j + 1
13 Boundary Gray Zone B
13j Boundary gray zone B of cell j
13j1 Boundary gray zone B of cell j + 1
14j Boundary gray zone C of cell j
14j1 Boundary gray zone C of cell j + 1
15 Focus ON
16 Focus OFF
17 Vertex on design formula of cell (1) 18 Vertex on measurement data of cell (1) 19 Vertex on design formula of cell (5) 20 Vertex on measurement data of cell (5) 22a Design formula of each lens 22b Region of gray zone B 22c Region of divided data B 23a Divided data B of each cell and gray zone B data 24b after conversion to the measurement object X _L Y _L Z _L coordinate system 24b Divided data B and design formula of each cell Comparison 30 Optical axis of aspherical lens 31 Three-dimensional measurement data ((X (i), Y (i), Z (i))
32 Design equation 33 Translational coordinate conversion amount dX
33a Translation amount from design value dX
34 Translational coordinate conversion amount dZ
34a Height deviation from design value dZ
35 Inclination coordinate conversion amount β
35a Inclination amount β from design value
36 Three-dimensional measurement data after coordinate transformation 37 Approximate radius of design equation 38 Best fit R
39 RMS minimization 41 cell (1)
42 cells (2)
50a External reference jig A
50b External reference jig B
51 Plate P1
52a Sphere A
52b Sphere B
52c Sphere C
52d Sphere D
52e Sphere E
52f Sphere F
53 Plate P2
54 Plate P3
55b Measured object XLYLZL coordinate system based on edge surface reference and lens array outer side reference 55c Measured object XLYLZL coordinate system based on lens array bottom surface reference and outer side reference 61 Stone surface plate 62 Optical system 63 Stone surface plate 64 Z stage 65 Probe for measurement 66, 67, 68 XYZ reference mirror 69, 70 XY stage 71 Oscillation frequency stabilization He-Ne laser 90 Output device S Measurement surface 101 Optical axis of spherical lens 102 Incident light 103 Focus 104 Actual lens shape 105 Design (ideal) shape 106 Tilt amount 1
107 Eccentricity 1
111 Optical axis of aspheric lens 112 Incident light 113 Focus 114 Actual lens shape 115 Design (ideal) shape 116 Inclination amount 1
117 Eccentricity 1
118 Tilt amount 2
121 Point on the boundary of cell j extracted from measurement data 122 Line L
122a Line L Group 123 Line R
123a Line R Group 124 Line T
124a Line T Group 125 Line B
125a Line B group 126 AL point 127 AR point 128 d _{j, XMAX}
129 d _{j, YMAX}
130 Actual shape of cell j 131 Design shape of cell j 801 First storage unit 802 Second storage unit 803 Partial differentiation operation unit 804 Threshold setting unit 805 Boundary calculation unit 806 First data division unit 807 First coordinate conversion unit 808 Second data division unit 809 Second coordinate conversion unit 810 Data approximation processing unit 811 Third storage unit 812 Third data division unit 813 Result creation unit

Claims (9)

The probe is scanned in the biaxial plane coordinate direction on the measurement surface of the measurement object having a plurality of shape boundaries between the characteristic feature portion and the non-feature portion on the surface, and the height coordinate data at the biaxial plane coordinate position is continuously obtained. in Te calculated, the obtained two measurement data axial plane coordinates and a height coordinate is corresponding for a plurality of measurement points on the 2-axis plane coordinates, based on said measurement data, the shape measuring method for measuring the shape of the measurement surface There ,
The coordinate value of at least one of the biaxial plane coordinates at the target measurement point on any i-th two-axis plane coordinate, the height coordinate value (P (i), Z (i)), and the target measurement point Between the measured values ((P (i-1), Z (i-1)) regarding the i-1th point continuous upstream in the scanning direction, the value of the second-order partial differential value C in dP (i) is It asked Me,
It is determined whether or not the value of C related to the (i-1) th point is larger than a predetermined threshold value. If the value of C is larger than the predetermined threshold value , each position of the i-1th measurement point is detected as boundary position of the measured object is a boundary between the feature portion and the non-characteristic part of the shape of the measured object,
Based on the detected boundary position and the design data of the measurement object, divided into a first divided area and a first boundary gray area divided for each characteristic part of the measurement object,
For the two divided first divided areas, the positions of the vertices of the first divided areas are detected, and based on the straight line connecting the vertices of the two first divided areas and the design data of the measurement object Detecting the tilt angle deviation and the rotation angle deviation of the measurement object with respect to the design data of the measurement object, and correcting the tilt angle deviation and the rotation angle deviation of the measurement data,
Based on the corrected measurement data of the measurement object and the design data of the measurement object, the image is subdivided into a second divided area and a second boundary gray area divided for each characteristic portion of the measurement object,
Wherein for the second divided area, characterized by a Turkey to calculate the shape difference between the measurement data and the design data, the shape measuring method. d P (i) = P ( i) -P (i-1), when defined as dZ (i) = Z (i ) -Z (i-1),

The shape measuring method according to claim 1, wherein the value of C is calculated by: The pre SL threshold, said about the value of C at each measurement point, characterized by a value of 1 for 2 minutes of the maximum value of the values of C for all the coordinate values P (i) with a threshold value, according to claim 1 Or the shape measuring method of 2. Calculating a shape difference between the measurement data and design data,
The coordinate conversion for the RMS minimization is performed by the difference between each second divided region subdivided for each feature portion and the design formula, and the eccentricity dx, dy, the height deviation dz from the design formula is calculated from the coordinate conversion amount. 4. The shape measuring method according to claim 1 , further comprising : obtaining inclinations α and β. Coordinate conversion before Symbol RMS minimization,
Conducted RMS minimize changing the R value of the design data in the best-fit R value comprises displaying the best fit R determined for each feature portion on the output device, it claim 4, wherein Shape measurement method. The eccentric dx, dy, the height information deviation dz, input to the design parameters of the characteristic part to create a new second design type,
Based on the measurement data converted into the coordinate system for the measurement object, re-divided into a third divided area and a third boundary gray area divided for each characteristic portion of the measurement object ,
The shape measuring method according to claim 4 , wherein a shape difference between measurement data and design data is calculated for the third divided region instead of the second divided region. Enter the best-fit R on design parameters in the second design type creates a new third design type,
Based on the measurement data converted into the coordinate system for the measurement object, subdivided into a fourth divided area and a fourth boundary gray area divided for each characteristic portion of the measurement object ,
The shape measuring method according to claim 6 , wherein a shape difference between measurement data and design data is calculated for the fourth divided region instead of the second divided region. Conversion to the coordinate system with respect to the measured object,
The flat surface data the measurement data of all the measured object table surface region to delete the data of only the measured effective surface as a reference surface,
When the measurement object is placed on the jig plate on which the first to third spheres having the same diameter are fixed and the side surface of the measurement object is in contact with the three spheres, one first sphere the direction parallel with the line connecting the centers of the other one second sphere and X _L coordinate after conversion, the linear parallel direction orthogonal to the reference plane and Z _L coordinate axis, the X _L coordinate axis and converting the linear direction parallel passing through the center of Z _L and perpendicular to the axes remaining one third sphere coordinate system with Y _L coordinate, any one of claims 1 to 7 The shape measuring method described in 1. Install the measurement object on the first to third spheres fixed on the jig plate and use the plane behind the measurement object as the reference plane.
On the jig plate to which the first to third spheres are fixed, the center of the first sphere and the second when the measurement object is placed so that the side surface of the measurement object is in contact with the three spheres. the direction parallel with the line connecting the center of the sphere and X _L coordinate axis, a straight line parallel to a direction perpendicular to the reference plane and Z _L coordinate axis, the X _L coordinate axis Z _L and perpendicular to the axes remaining one third The shape measuring method according to claim 1, wherein the shape measuring method is converted into a coordinate system having a direction parallel to a straight line passing through the center of the sphere as a Y _L coordinate axis.

Images