JP3402995B2 - Shape analyzer - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention is obtained by measuring an object to be measured having a curved shape such as an aspherical lens with a precision measuring machine such as a three-dimensional measuring machine, a contracer or an aspherical lens measuring machine. The present invention relates to a shape analysis device that identifies the curved shape of the measurement target from measurement data.

[0002]

2. Description of the Related Art In designing an aspherical lens, it is important to analyze the curved shape of the lens surface of a prototype or a finished lens. This curve shape is identified from the measurement data by a conic curve or the like. However, in general, it is often the case that the curve shape of the aspherical lens cannot be accurately represented only by the equation of the conic curve, and this is supplemented by a correction polynomial. That is, the height x1, x2, ..., Xn of the lens surface at each position h1, h2, ..., Hn in the horizontal direction by the coordinate measuring machine or the contracer is measured data (hj,
xj), C is the curvature, K is the conic curve constant, Pi is the correction polynomial coefficient, m is the degree of the correction polynomial, and H is
= H1, h2, ..., Hn and X = x1, x2, ..., xn, the curve shape can be expressed as in the following formula (1) (however, formula in the reference coordinate system without rotation and translation) .

[0003]

[Equation 1]

The first term on the right side of the above equation (1) is an equation showing a conic curve, and the second term is a correction polynomial. C, K, P
The curve shape can be identified by accurately obtaining i.

[0005]

[Problems to be Solved by the Invention] However, in the past,
For the reasons described below, C, K, and Pi could not be obtained accurately. That is, the first term on the right side of the equation (1) can be transformed as shown in the equation 2.

[0006]

[Equation 2]

Here, in √ of the equation (2),

[0008]

[Equation 3]

When expanded using, the following expression (4) is obtained.

[Equation 4]

By substituting the equation (4) into the equation (1), the following equation (5) is obtained.

[0011]

[Equation 5]

As is clear from the coefficient (C / 2 + P2) of H ^{2 in} the equation (5), the curvature C and the correction polynomial coefficient P 2 have a dependency relationship, and C and P 2 cannot be obtained at the same time. Even when trying to obtain the curvature C, the second term on the right side of the equation (1) exerts a great influence on the data at the position distant from the center in the H direction, so that the first term on the right side is affected, and the curvature C is accurately determined. I can't. Therefore, there is a problem that the curved shape cannot be identified with high accuracy.

The present invention has been made in view of the above points, and an object of the present invention is to provide a shape analysis apparatus capable of accurately identifying a curved shape.

[0014]

A shape analysis apparatus according to the present invention comprises a measurement data storage means for storing measurement data obtained by measuring the curved shape of an object to be measured having a curved shape, and the measured data. It has a curve shape identification calculation means for executing a calculation process for identifying a curve shape from the measurement data stored in the storage means, and a calculation result output means for outputting the curve shape identified by the curve shape identification calculation means. In the shape analysis device, the measurement data storage means stores measurement data obtained as a distance from the reference axis at each position of a specific reference axis, and the curve shape identification calculation means is the Of the measurement data stored in the measurement data storage means, only the measurement data in the central portion of the range from the start point to the end point in the reference axis direction is used as the secondary multiple.
Find the optimal conic curve in the term expression and narrow down the curve shape
After that, the optimum conic curve in the irrational expression is obtained , and then the correction polynomial is obtained from all the measurement data stored in the measurement data storage means to identify the curve shape of the measured object. Characterize.

According to the shape analysis apparatus of the present invention, of all the measured data from the starting point to the ending point in the reference axis (H axis) direction, the central portion where the influence of the second term on the right side of the equation (1) does not appear significantly. The conical curve, that is, the first term on the right side of the equation (1) is obtained using only the measurement data in, and then the correction polynomial, that is, the second term on the right side of the equation (1) is obtained using all the measurement data. Therefore, the curve shape can be accurately identified.

More specifically, the optimum conic curve in the quadratic polynomial expression is obtained from the measurement data of the central portion, and
Converts a polynomial expression of degree to an irrational expression. By once obtaining the curve of the quadratic polynomial expression, the processing time for calculating the curve of the irrational expression can be shortened. Then, the optimum conic curve in the irrational expression is obtained by using the obtained irrational expression as an initial value, and the optimum conic curve in the obtained irrational expression is transformed into the standard form and coordinate conversion is performed, and the coordinates to be the standard form are obtained. By obtaining the correction polynomial using all the measurement data in the system, the curve shape can be identified with high accuracy.

[0017]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a diagram showing the configuration of a shape measuring system including a shape analyzing apparatus according to an embodiment of the present invention. This system includes a shape measuring machine 1, a computer 3 and a printer 4 as a shape analyzing apparatus that analyzes the measurement data obtained by the shape measuring machine 1 to identify the curved shape of the aspherical lens 2 that is an object to be measured.
It consists of and. The shape measuring machine 1 uses a contour tracer in this example, but a three-dimensional measuring machine or another aspherical lens measuring machine may be used. A column 12 extending in the vertical direction is fixed to the table 11 of the shape measuring machine 1, and a slider 13 is mounted on the column 12 so as to be vertically movable. The slider 13 has a stylus arm 1
4 is installed. The stylus arm 14 is driven in the horizontal (H) direction, and the stylus 15 provided at the tip of the stylus arm 14 traces the lens surface of the aspherical lens 2 in the H direction, thereby increasing the height of the lens surface at each position in the H axis direction. The size X is obtained as the measurement data.

This measurement data is loaded into the computer 3 and used for shape analysis. The computer 3 realizes the function as shown in FIG. 2 by a predetermined shape analysis program. That is, the measurement data storage means 21 stores the measurement data from the shape measuring machine 1. The curve shape identification calculation means 22 identifies the curve shape of the lens surface of the aspherical lens 2 from the measurement data by the calculation described later. The calculation result output means 23 displays or prints out information regarding the identified curve shape.

FIG. 3 is a flow chart showing the processing in the curve shape identification calculation means 22. This processing is roughly divided into the conical curve portion determination processing (S1 to
S4) and the correction polynomial part determination process (S5) in the equation (1). The conical curve part determination process further includes quadratic polynomial determination (S1) and irrational formula determination (S2-
S4). Hereinafter, each step will be described in detail.

First, the optimum conic curve in the quadratic polynomial expression is obtained from the measured data (S1). The measurement data used at this time is, as shown in FIG. 4, centered on the n0th measurement data, which is the central portion in the H direction, out of the n measurement data, and n1 in the range of ± Δh from that data. The n2th measurement data is used from the second measurement data. The measurement data to be used is, for example, about 20 to 30% of all the measurement data, and specifically, the distance from the center of the data,
Specify by the ratio from near the center of the data, the range on the window of the screen, etc. Now, H = h _n1 , h _{n1 + 1} ,
, H _n2 , X = x _n1 , x _{n1 + 1} , ..., X _n2, and a quadratic polynomial F (H, X) of H and X is defined as follows.

[0021]

[Equation 6]

However, a ² + b ² + c ² + p ² + q ² + r ² = 1
And At this time,

[0023]

[Equation 7]

A, b, c, p,
Determine q and r. To do this, expand equation (7),
When a, b, c, p, q, and r are arranged, the following equation (8) is obtained.

[0025]

[Equation 8]

Here, M is a 6 × 6 non-negative symmetric matrix. The minimum eigenvalue of M is λ, and the eigenvector at that time is v
If you add (→ on top),

[0027]

[Equation 9]

From the above, a, b, c, p, q and r are obtained. At this time, ± in the equation (9) is determined so that c becomes nonnegative.

The quadratic polynomial thus obtained is
Although it is close to the equation representing the conic section, the conic section cannot be accurately represented only by a quadratic polynomial. Then, the obtained quadratic polynomial is then converted into an irrational expression (S
2). That is, the quadratic polynomial F obtained as described above
When (H, X) is arranged with respect to X, the following expression (10) is obtained.

[0030]

[Equation 10]

When c ≠ 0 and the equation (10) is solved for X, the equation (11) is obtained.

[0032]

[Equation 11]

Here again,

[0034]

[Equation 12]

Putting it another way, X can be expressed as in equation (13).

[0036]

[Equation 13]

In the equation (13), the sign of ± is added before √, but the data does not match in any case, and only + or − matches. Therefore,
The measurement data (hα, xα) in the range of n1 to n2 is (13)
Substitute into the formula to determine the sign of ±. If the code is sign, the equation (13) becomes the equation (14).

[0038]

[Equation 14]

Next, let Q (H) be the right side of equation (14), and
Using a, b, p, q, and r obtained earlier as initial values, the following (1
The minimum value of S (a, b, p, q, r) in the equation (5) is obtained by the nonlinear least squares method, and the optimum conic curve in the irrational expression is obtained (S3). Since the initial values a, b, p, q, and r are close to the solution to be calculated, the solution can be obtained with a small number of calculations.

[0040]

[Equation 15]

The optimal conic curve X = Q (H) in the irrational expression shown in the following equation (16) by the solutions a, b, p, q, and r of the nonlinear least squares method thus obtained is given by It transforms into a standard form. (S4).

[0042]

[Equation 16]

FIG. 5 is a flowchart showing the procedure for obtaining the standard form. First, in order to simplify the transformation to the standard form, the equation (16) is transformed again into an implicit function representation of a quadratic polynomial (S11). That is, by shifting the right side aH + b of the equation (16) to the left side, squaring both sides, and rearranging H and X,

[0044]

[Equation 17]

It becomes like. Here, the coefficient of the equation (17) is changed to

[0046]

[Equation 18]

Replacing as shown in the equation (17),
It is expressed as in equation (19).

[0048]

[Formula 19]

Next, the equation (19) is transformed into the standard form (S).
12). That is, the inclination of the curve with respect to the coordinate systems H and X is θ,
If u and v are the parallel movement amounts in the H and X directions,

[0050]

[Equation 20]

By the coordinate conversion by, it is possible to conform to any of the following standard forms on the conversion coordinate system.

[0052]

[Equation 21]

Therefore, the most suitable standard form among the standard forms of circle, ellipse, hyperbola and parabola, and θ,
u and v are determined by arithmetic processing. Here, as an example, when considering the case of fitting to a circle, as shown in FIG. 6A, case 1 in which the data exists on the upper side of the circle, and as shown in FIG. Case 2 that exists in. Therefore, the curve portion where the data is present is (H, X) (both are attached to the top, and so on) = (0,
In 0), the curve is translated so as to contact the H axis (S13). That is, in the case of Case 1, since it is necessary to translate the X axis to the + side as shown in FIG. 7A, the equation of the curve is transformed into the equation (22).

[0054]

[Equation 22]

By transforming this as follows,
Standard form is required.

[0056]

[Equation 23]

In the case of Case 2, it is necessary to translate the X axis to the − side by r as shown in FIG. 7B, so the equation of the curve is transformed into the equation (24).

[0058]

[Equation 24]

By modifying this as follows,
Standard form is required.

[0060]

[Equation 25]

Accordingly, the conic curve constant K = 1 and the curvature C = -1 / r in the case 1 and the conic curve constant K = 1 and the curvature C = 1 / r in the case 2 are obtained.

Next, a correction polynomial is obtained in the standard coordinate system (S5). That is, measurement data (hα, xα)
The conversion data obtained by performing the coordinate conversion of the equation (20) and the above-described parallel movement on (α = 1, 2, ..., N) is (hα, xα)
(If both are marked with-), the correction polynomial coefficient Pi is determined so that the following expression (26) is minimized.

[0063]

[Equation 26]

Since the above equation (26) is a quadratic equation for Pi, the minimum value can be easily obtained by solving simultaneous linear equations. By performing such processing, a small amount of data is processed in the first half conic curve calculation processing, and a rough curve is calculated by a quadratic polynomial before the irrational expression is calculated. The processing time is also shortened, and the curved shape of the aspherical lens can be identified efficiently and highly accurately as a whole.

[0065]

As described above, according to the present invention, the conical curve is obtained by using only the measurement data in the central portion of the range from the start point to the end point in the reference axis (H axis) direction among the measurement data. After that, since the correction polynomial is obtained by using all the measurement data, there is an effect that the curve shape can be identified efficiently and accurately.

[Brief description of drawings]

FIG. 1 is a diagram showing a configuration of a timekeeping measurement system to which a shape analysis apparatus according to an embodiment of the present invention is applied.

FIG. 2 is a functional block diagram of a shape analysis system in the system.

FIG. 3 is a flowchart showing a processing flow of the shape analysis system.

FIG. 4 is a diagram for explaining measurement data used in the same shape analysis process.

FIG. 5 is a flowchart showing a procedure of processing for transforming a curve into a standard shape in the same shape analysis processing.

FIG. 6 is a diagram for explaining parallel movement of a curve according to the standard form.

FIG. 7 is a diagram for explaining parallel movement of a curve.

[Explanation of symbols]

1 ... Shape measuring machine, 2 ... Aspherical lens, 3 ... Computer, 4 ... Printer, 11 ... Table, 12 ... Column, 1
3 ... Slider, 14 ... Stylus arm, 15 ... Stylus, 21 ... Measurement data storage means, 22 ... Curve shape identification calculation means, 23 ... Calculation result output means.

─────────────────────────────────────────────────── ─── Continuation of front page (56) References JP-A-3-33635 (JP, A) JP-A-7-83653 (JP, A) JP-A-10-62142 (JP, A) (58) Field (Int.Cl. ⁷ , DB name) G01B 21/20

Claims (2)

(57) [Claims] 1. A measurement data storage means for storing measurement data obtained by measuring the curve shape of an object to be measured having a curve shape, and a curve shape is identified from the measurement data stored in the measurement data storage means. A shape analysis device having a curve shape identification calculation means for executing calculation processing for performing the calculation, and a calculation result output means for outputting the curve shape identified by the curve shape identification calculation means, wherein the measurement data storage means is The measurement data obtained as a distance from the reference axis at each position of a specific reference axis is stored, and the curve shape identification calculation means is one of the measurement data stored in the measurement data storage means. Obtain the optimum conic curve in the quadratic polynomial expression from only the measured data in the central part of the range from the start point to the end point in the reference axis direction, and calculate the curve shape.
Determine the optimum conic in unreasonable type representation then narrowed down, its
After that, the shape analysis device is characterized in that the curve shape of the object to be measured is identified by obtaining a correction polynomial from all the measurement data stored in the measurement data storage means. 2. The curve shape identification calculation means obtains an optimum conic curve in a quadratic polynomial expression only from the measurement data in the central portion stored in the measurement data storage means, and the quadratic polynomial expression is an irrational expression. Converted to the expression, the obtained irrational expression is used as an initial value to find the optimum conic curve in the irrational expression, and the optimum conic curve in the irrational expression obtained is transformed into the standard form and the coordinates are converted to the standard form. The shape analysis apparatus according to claim 1, wherein the correction polynomial is obtained in a coordinate system that is