JPS6326426B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method and apparatus for measuring the shape of regular or irregular planar patterns. The plane pattern referred to here is anything other than symbols, characters, and figures.
Contains a projection image of a three-dimensional object onto a two-dimensional plane.

The present invention will be described as being applied to shape measurement of an enlarged projected image of irregularly shaped powder or granular material onto a two-dimensional plane.

Conventionally, the projected area, maximum diameter, and peripheral length of the silhouette are measured as characteristic values representing the geometrical shape of a powder silhouette, and the equivalent area diameter and perimeter equivalent diameter are determined using an equivalent circle or rectangle as a reference. This was taken as the characteristic value of the powder. However, when the shape of the silhouette moves away from the standard shape of a circle or rectangle, such characteristic values lose their meaning in representing the shape. For quality control of product powders, manufacturing process improvements, and process selections, we do not rely on a specific standard shape to obtain shape characteristic values, but instead use true shape characteristic values that numerically represent the shape of the powder or granule itself. There is a need for measurement of something that can be called . In order to meet this demand, it has been proposed to measure the Fourier coefficients of the outline of a plane pattern and use this as the shape characteristic value of the plane pattern. Determination of shape characteristic values of a plane pattern by Fourier transformation will be explained with reference to FIGS. 1 and 2.

As shown in FIG. 1a, the plane pattern is scanned in the x and y directions, and the intersection coordinates (x _i , y _i ) between the scanning line and the plane pattern contour are determined. FIG. 1b shows these coordinate points, and the numbers attached to the coordinate points indicate the order in which the scan line meets the contour. In principle, this plane pattern can be expressed as a set of inclination angles (argument angles with respect to a certain standard tangent) of tangents to the contour at each coordinate point, but in order to find the argument function of the outline, first select an arbitrary coordinate point. Let the starting point be (x ₀ , y ₀ ), the point closest to this starting point in the counterclockwise direction be (x ₁ , y ₁ ), and then the point closest in the counterclockwise direction to this point (x ₁ , y ₁ ) be (x ₂ , y ₂ ), and then repeat this operation one after another to rearrange the point sequence of (x _i , y _i ) counterclockwise (see Figure 2).

Letting the angle change at the coordinate point (x _i , y _i ) be Δφ _i , the argument function _i can be obtained from the following equation.

_i = _i 〓 ^k=1 △ _k (1) If the distance between the i-th and i+1-th coordinate points from the starting point is △l _i , the contour length L becomes L= _o 〓 ⁱ⁼¹ △l _i . Set t=2πl _i /L, l _i = _i 〓 ^j=1 △l _i , and normalize equation (1) by the circular argument function t to obtain the periodic function of 2π ^* _(t) , that is, equation (2). obtain.

^* _(t) = _i −t (2) When this is expanded into a Fourier series, it becomes as shown in equation (3). ^* _(t) = μ ₀ + _∞ 〓 ^k=1 A _k cos (k _t − α _k ) (3) The coefficient A _k is invariant to the movement, rotation, and mirroring of the particle image, and also depends on the position of the starting point. It does not change even if the value is changed, and it takes regular values for specific geometric shapes such as circles and rectangles, so it is suitable as an index for pattern recognition. However, this coefficient determination requires complicated numerical processing, so in order to speed up and simplify the processing, it is necessary to rely on fast Fourier transform. However, for fast Fourier transformation, the number of coordinate points n
requires 2 ^N pieces (N is usually 9 or 10,
Therefore, n is 512 or 1024), and this specific number of coordinate points can be acquired by x-y using a television camera or machine.
This cannot be guaranteed with scanning methods. Conventionally, when more coordinate points than the specified number are obtained using the x-y scanning method, the coordinate points are selected and extracted so that the number of coordinate points becomes the specified number, and new coordinate points are created. When a problem arises, sampling interpolation processing is used to determine the coordinate value by interpolating from the coordinates of the original coordinate point. If fewer coordinate points than the specified number were obtained using the x-y scanning method, the scanning pitch was changed and the pattern was swept again, followed by the sampling interpolation process described above. This and the aforementioned counterclockwise rearrangement of the coordinate points resulted in almost prohibitive complexity. In the case of a glass pen, in which a person visually traces the coordinate points of the outline, the rearrangement of the coordinate points remains unchanged, but sampling interpolation processing is necessary, and although the complexity is reduced compared to the x-y scanning method, However, the complexity associated with sampling interpolation processing has made it difficult to employ Fourier coefficients as shape characteristic values of plane patterns.

The purpose of the present invention is to take 2 ^N coordinate points of the contour of a plane pattern in one direction, determine the argument function _i of the tangent to each coordinate point, normalize it, perform fast Fourier transform, and use the coefficients to calculate the plane pattern. The object of the present invention is to provide a method for determining a shape, thereby eliminating the need for rearrangement of coordinate points and sampling interpolation processing that were conventionally required.

This purpose, according to the present invention, is to rotate either the CCD image sensor of the linear array or the flat pattern to be measured using one point on the contour as the center of rotation, and one point on the contour as the starting point. is intermittently rotated in one direction at a step angle of 2π/n, and the argument _function i of the tangent to each of the n polar coordinate points (r _i , θ _i ) on the contour from the tangent at the starting point This is achieved by determining the normalization function ^* _i = _i −θ _i of this argument function, and then fast Fourier transforming the normalization function * i = i −θ i and determining the shape of the plane pattern from its coefficients.

The principle of the present invention will be explained with reference to FIG. Linear array CCD (charge coupled device)
An image sensor is a device in which photoelectric elements are arranged in a straight line, and when this array is exposed to a light image, the photoelectric elements, which are equivalent to a capacitor, store electric charges in accordance with the amount of exposure light. When the photoelectric elements are accessed sequentially, they emit light, thereby obtaining information about their optical images. As shown in Fig. 3, select an arbitrary point O in the plane pattern and move the CCD image sensor 1 counterclockwise around that point.
Rotate intermittently at a step angle of 2π/n. Measure the distances ₁ r _i and ₂ r _i from the center to the contour for each rotation, and calculate π
(180 degrees) to complete the measurement. Or measure one distance from the center to the contour for each rotation and calculate 2π (360
degree) and complete the measurement.

A computer is connected to this image sensor, and the argument function _i of the tangent to each polar coordinate point (r _i , θ _i ) is determined using a predetermined algorithm. Next, the normalization function of this argument function ^* _i = _i − θ _i is determined. This is then subjected to fast Fourier transform, and the coefficients are recorded or displayed as shape characteristic values of the plane pattern.

As shown in Fig. 4, when the radius vectors r _i and r _i+1 at the rotation angles θ _i and θ _i+1 are measured, the angle change between the tangent at the i-th coordinate point and the i+1-th tangent is △ _i can be determined. In this way, the argument i+1 at the _i+1th
is determined from the following equation as the sum of angular changes _Δk from the starting point.

_i = _i 〓 ^k=1 △ _kThis is naturally the same as equation (1), but as already stated, this is normalized using the following equation.

^* _i = _i −θ _iThis ^* _i is not strictly equal to the argument function in equation (2), but the rotation center is within the plane pattern and the pattern contour changes smoothly as the step angle changes. If so, the accuracy is sufficient for pattern graphic recognition.

FIG. 5 schematically shows an apparatus for carrying out the method of the present invention.

An arbitrary point within the plane pattern 5 on the moving table 3 and the center point of the CCD image sensor 1 of the linear array are optically matched. 2 indicates an optical system.
When the reset button 6 is pressed to reset the increment feed counter 8, the Noah gate 14 is opened. Next, the start switch of the start pulse generator 11 is pressed to activate the start pulse generator 11. A pulse signal from the start pulse generator 11 passes through an OR gate 13 and a NOR gate 14 and is applied to the scanning circuit 10 of the image sensor, which is activated to perform the first scan. When the first scan is completed, a signal representing the radius vector at the starting point position and a scan end output signal are output. In response to this scan end output signal, the start pulse generation circuit 7 generates a pulse signal, and in response to this pulse signal, the step feed preset counter 8 counts one count, and the pulse motor drive circuit 9 starts the pulse motor 4. is driven one step to rotate the movable stage 3 by 2π/n relative to the stationary CCD image sensor 1.
Further, the pulse signal from the start pulse generation circuit 7 is delayed by the rotation time of the movable table 3 in the pulse delay circuit 12, and then sent to the OR gate 13 and the NOAH gate 14.
and enters the scanning circuit 10 of the image sensor, which is activated to perform a second scan. If this is repeated a predetermined number of times (n/2 times when measuring ₁ r _i and ₂ r _i in one scan, n times when measuring ₁ r _i in one scan), the increment feed preset Counter 8 generates a stop signal and NOR gate 1
4 is in the closed state. 4' is CCD image sensor 1
This pulse motor is directly connected to the CCD image sensor 1 and is used to keep the moving table 3 stationary and rotate the CCD image sensor 1.

Preferably, the clock pulse generator 15 is a variable frequency clock generator that generates a pulse signal that changes so that the background of the CCD image sensor remains constant even when the amount of light from a light source that illuminates the pattern to be measured is changed. Such a variable frequency clock generator is a voltage frequency converter that responds to the difference between the peak value of the output of the CCD image sensor and some reference value.

[Brief explanation of the drawing]

FIG. 1a shows how a planar pattern is xy scanned, and FIG. 1b shows coordinate points on the contour of the planar pattern. FIG. 2 is an explanatory diagram for arranging coordinate points on the contour of a plane pattern and determining the declination angle at each coordinate point. 3 and 4 are diagrams for explaining the principle of the method of the present invention, and FIG. 5 is a schematic diagram of an apparatus for carrying out the method of the present invention. In the drawing, 1... Linear array CCD image sensor, 2... Optical system, 3... Moving table, 4, 4'... Pulse motor, 5... Planar pattern to be measured, 6... Reset switch, 7... Start pulse generation circuit, 8
... Incremental feed preset counter, 9... Pulse motor drive circuit, 10... CCD image sensor scanning circuit, 11... Start pulse generator, 12... Pulse delay circuit, 13... OR circuit, 14... NOR circuit,
15...Variable frequency clock generator.

Claims (1)

[Claims] 1 One point within the outline of the plane pattern to be measured is the center of rotation, and one point on the outline is the starting point, and either the CCD image sensor of the linear array or the plane pattern to be measured is rotated 2π/n with respect to the other.
determine the argument function _i of the tangent to each of the n polar coordinate points (r _i , θ _i ) on the contour from the tangent at the starting point;
A method for measuring the shape of a plane pattern characterized by fast Fourier transforming the normalization function ^* _i = _i −θ _i of the argument function and determining the shape of the plane pattern from its coefficients.