JP2793931B2 - Light two-dimensional measuring method, surface roughness measuring method and measuring device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a measuring method for two-dimensionally measuring and calculating the position and spread of light, such as a laser beam, and as one application example of this light spread measuring method. Measure the surface roughness of the surface of the object to be measured, such as a metal plate, using the reflected light of a laser beam or LED, etc.
The present invention relates to a surface roughness measuring method for measuring and calculating with a two-dimensional optical sensor such as D and a measuring device therefor.

[0002]

2. Description of the Related Art Many optical measurement methods using a laser or the like require measurement of the position and spread of light.
Conventionally, for example, the position of the laser beam is determined by using the half-width midpoint of the one-dimensional light intensity distribution curve of the laser or the position of the maximum intensity determined by the binarization method. The half width of a one-dimensional light intensity distribution curve is most widely used to determine the spread of the light. The surface roughness of the surface of an object to be measured, such as a metal plate, is generally measured by a so-called stylus type in which a stylus is slid in contact with the surface of the object. The above-mentioned optical non-contact measurement method is used as a method for solving the problem of the stylus type such as rubbing and measurement time.

That is, the surface of an object to be measured is irradiated with light, and the half-value width and the standard deviation indicating the spread of the reflection intensity distribution curve of the reflected light from the object surface are determined by a single unit such as a phototransistor or a CdS element. Is determined by moving the optical sensor. Although such a measurement method has the advantage of not damaging the surface of an object, the measurement of the full width at half maximum and the standard deviation of the reflected light intensity distribution curve requires measurement of the entire distribution curve, and therefore simply requires the measurement. It is necessary to move the optical sensor having one structure in the measurement area, and there is a problem that the configuration becomes complicated and measurement time is required.

The inventor has already approximated the vicinity of the peak of the reflected light intensity distribution curve with a one-dimensional Gaussian function for the purpose of solving such a problem, and has standard deviation of this Gaussian function (this is called a Gaussian curve parameter). The method for determining the surface roughness of the object surface by calculating
No. 843 (JP-A-3-211406).
This method measures the intensity distribution of reflected light from the object surface with a one-dimensional optical sensor, approximates the vicinity of the peak of the intensity distribution curve with a one-dimensional Gaussian function, and sets a Gaussian curve parameter representing the spread of the Gaussian function to a predetermined value. The surface roughness of the object surface is obtained by calculating from three or more measurement points of the reflection intensity using an arithmetic expression, and comparing the Gaussian curve parameter with the center line average roughness data associated in advance.

[0005]

However, although the above method has an advantage that the measurement time of the surface roughness is considerably shortened by the calculation, the method of measuring the one-dimensional distribution of light by the linear light receiving element array is used. With respect to the intensity distribution in the two-dimensional spread of light inherently, it has been necessary to repeat the measurement calculation by changing the arrangement position of the optical sensor itself. Therefore, in order to measure the two-dimensional distribution by this method, not only does the device such as a mechanical drive mechanism for the object to be measured become complicated, but also the number of measurement steps from the step of receiving the reflected light to the arithmetic processing is required. In addition, there is a problem that the measurement time is required.

[0006] The present invention has been made as a result of repeated research and experiments by the present inventors to solve the above problems, and an object of the present invention is to provide a measurement capable of simultaneously measuring the two-dimensional position and spread of light. It is another object of the present invention to provide a two-dimensional light measuring method that can realize this measurement by simple data processing. Another application of the method for measuring the spread of light is to provide a method and a measuring apparatus for simultaneously measuring the surface roughness of an object surface in two orthogonal directions.

[0007]

According to the present invention, light reflected from a light source or a reflector is detected by a two-dimensional optical sensor such as a CCD as x and y coordinate values corresponding to the light intensity distribution. The light intensity distribution on the xy plane is approximated by a two-dimensional Gaussian function, and the x-
Digital data based on the outputs of the plurality of light receiving pixel arrays arranged on the y plane is taken as x, y coordinate data of the two-dimensional Gaussian function, and the x, y coordinates of the main axis of the Gaussian function are obtained by a predetermined arithmetic expression. Determining the position of the light and determining each standard deviation of the two-dimensional Gaussian function with respect to x and y coordinates, thereby determining the spread of the light in two directions orthogonal to each other on the xy plane. I do.

The present invention also provides a method for obtaining the x, y coordinates or the respective standard deviations of the x, y coordinates of the principal axes of the two-dimensional Gaussian function quickly by deriving a very simple arithmetic expression, thereby obtaining the light of light. It is characterized by an arithmetic method that can calculate the two-dimensional position and spread with an inexpensive device.

Further, the present invention is an application of the above-described method for obtaining the spread of a two-dimensional light intensity distribution curve measured using the standard deviation of a two-dimensional Gaussian function. Irradiation, reflected light from the object surface is received by a plurality of light receiving pixel rows arranged on an xy plane in a two-dimensional optical sensor such as a CCD,
The reflected light intensity distribution on the y plane is represented by approximating a two-dimensional Gaussian function, and based on digital conversion data corresponding to the output of the light receiving pixel array of the two-dimensional optical sensor, each of the x- and y-coordinates of the two-dimensional Gaussian function is determined. Of the reflected light intensity distribution curve is determined by this standard deviation,
Thereby, the surface roughness of the object surface in two directions perpendicular to each other is simultaneously obtained.

Further, the surface roughness measuring device according to the present invention comprises:
An irradiation light source for irradiating light to an object surface to be measured, a two-dimensional optical sensor such as a CCD arranged at a position capable of receiving reflected light from the object surface, and an xy plane in the two-dimensional optical sensor And an analog / digital converter for converting an analog signal output from the plurality of light receiving pixel columns arranged into a digital signal into a digital signal, and corresponding to the roughness of the object surface based on the digital data converted by the analog / digital converter. The reflected light intensity distribution curve is approximated by a two-dimensional Gaussian function at the x, y coordinates, and the x, y
The standard deviation for the coordinates is obtained by a predetermined arithmetic expression,
Calculating means for calculating the roughness of the object surface based on the standard deviation.

[0011]

According to the above two-dimensional light measuring method, light reflected from a light source or a reflector is received by a two-dimensional optical sensor such as a CCD, and the intensity distribution of the light in the xy plane is two-dimensional Gaussian. Digital data representing the light intensity corresponding to the output of the light receiving pixel array of the two-dimensional optical sensor is taken in as x, y coordinate data of the two-dimensional Gaussian function, and the x, y coordinates of the main axis of the Gaussian function are approximated by a function. Is obtained by a predetermined arithmetic expression, and the respective standard deviations of the two-dimensional Gaussian function with respect to the x and y coordinates are obtained by a predetermined arithmetic expression, so that the position or spread of light on the xy plane can be easily determined. It is possible to ask. Further, according to the surface roughness measuring method and the measuring apparatus as described above, the reflected light reflected on the surface of the object to be measured is received by a two-dimensional optical sensor such as a CCD, and the analog / digital conversion data as the detection result is obtained. Is approximated by a two-dimensional Gaussian function at the x and y coordinates, and a standard deviation of the Gauss function with respect to the x and y coordinates is calculated by a calculation means. The surface roughness of the object surface as a measurement target can be easily obtained by calculating the surface roughness of the object based on the formula and calculating the surface roughness based on the standard deviation. In other words, using a diagram or an expression representing the relationship between the standard deviation and the roughness value such as the center line average roughness measured by a stylus type surface roughness measuring device using a surface roughness standard test piece or the like in advance, The surface roughness can be obtained from the standard deviation obtained optically by the above method.

[0012]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The two-dimensional light measuring method according to the present invention focuses on the fact that the actual light intensity of a laser beam or the like has a two-dimensional Gaussian distribution theoretically, and this light intensity distribution is measured by a CCD. While measuring with such a two-dimensional optical sensor, a two-dimensional Gaussian function representing a light intensity distribution is obtained using digital data corresponding to the outputs of a plurality of light receiving pixel arrays arranged on the xy plane of the two-dimensional optical sensor. To determine the two-dimensional position and spread of light from the position and standard deviation of the principal axis of the two-dimensional Gaussian function in the xy plane, and in particular, to quickly calculate the two-dimensional Gaussian function by the least squares method The formula is derived so that the two-dimensional position and spread of light can be obtained by calculating the main axis and standard deviation of the two-dimensional Gaussian function without requiring an expensive high-speed arithmetic processing device.

Further, the surface roughness measuring method and the measuring apparatus according to the present invention, based on the principle of the above-described two-dimensional light measuring method, also reflect light reflected from the surface by irradiating the surface of the object to be measured with light. Light is received by a two-dimensional light sensor such as a CCD, and the light intensity distribution of the reflected light is approximated by a two-dimensional Gaussian function using digital data corresponding to the output of the light receiving pixel array of the two-dimensional light sensor. X,
The respective standard deviations in the y coordinate are obtained by calculation by the calculating means, and based on the two-dimensional standard deviations, the spreads of the reflected light intensity distribution curves in two directions orthogonal to each other are numerically derived. The surface roughness in two orthogonal directions can be easily measured.

That is, since the intensity distribution curve of the reflected light from the surface of the object spreads as the surface roughness increases, the surface roughness is measured by the so-called light scattering method, from which the surface roughness can be measured approximately. In the measurement method, similar to the theory of the two-dimensional measurement method of light, the light intensity distribution is theoretically a two-dimensional Gaussian function, so that the reflected light has almost the same function type, The light intensity distribution is measured by a two-dimensional optical sensor such as a CCD, and a two-dimensional Gaussian function representing the light intensity distribution is used.

The details of the two-dimensional light measuring method, the surface roughness measuring method, and the measuring device according to the present invention will be described below based on the calculation theory and experiments. The measurement method of the present invention basically uses the two-dimensional Gaussian function to determine the coordinates of the main axis and the standard deviation in the x and y coordinates of x-y corresponding to the intensity distribution of light received by a two-dimensional optical sensor such as a CCD. Since it is obtained by arithmetic processing based on digital data with respect to the coordinates of the y plane, it can be configured in common as a device for confirming the method, so that the measurement target is a He-Ne laser beam and an LED light source reflected by the surface of the metal test piece. The light will be described.

FIG. 1 is a block diagram showing the most basic embodiment capable of implementing the light two-dimensional measuring method of the present invention and functioning as a surface roughness measuring device. In this figure, an experimentally added visual device CRT for visually confirming the light intensity distribution is connected, but is not directly related to the measuring method of the present invention. In FIG.
Reference numeral 1 denotes an irradiation light source for irradiating light to the surface of an object to be measured. The irradiation light source 1 has an LED light source 2 therein. Reference numeral 4 denotes a metal test piece arranged as a test material of an object to be measured. Light from the irradiation light source 1 is applied to the surface of the test piece 4 and light corresponding to the surface roughness of the test piece 4 is obtained from the reflected light. This is to obtain an intensity distribution.

Reference numeral 5 denotes a CCD video camera,
The reflected light reflected on the surface of the sample is transmitted through the translucent plastic plate 6 and the intensity distribution of the reflected light is measured. Here, test piece 4
The diameter of the circular light illuminated on the top is the diameter of LED2 (5 m
m). Reference numeral 7 denotes a point light source of a He-Ne laser beam, and a test piece 4 using the reflected light intensity distribution.
Is provided as an object to be measured for measuring the position and spread of light by two-dimensional measurement of light. Therefore, the test piece 4 with respect to the CCD video camera 5
The relative position of the laser light source 7 may be arbitrarily selected or replaced in each experiment.

Reference numeral 8 denotes an analog / digital converter (hereinafter A / D) connected to the video signal output of the CCD video camera 5.
A video signal received at 512 × 512 pixels corresponding to the xy plane in the CCD video camera 5 is converted into digital data. Therefore, this digital data has a size corresponding to the light intensity distribution at the coordinates (x, y) on the xy plane.
Output as 6-resolution digital data. Also, CC
A predetermined measurement area including the center of the target light to be measured in the light receiving surface of the D video camera 5 can be selected and determined by specifying coordinates, and digital data corresponding to the light intensity distribution in that area can be sampled.

Reference numeral 9 denotes an arithmetic processing unit, which can use a general personal computer, and an A / D converter 8
And calculates various values indicating the position and spread of the light or the surface roughness of the test piece 4 based on an arithmetic expression described later. The arithmetic processing unit 9 incorporates ordinary mechanisms, for example, a memory for temporarily storing and holding digital data from the A / D converter 8, data writing / reading, arithmetic timing, and arithmetic results to the printer 10. And a processor for executing various instructions for printing out.

An image processing device 11 and a CRT 12 for visual confirmation are connected to the video signal output of the CCD video camera 5, and the light intensity distribution measured by the CCD video camera 5 can be converted into an arbitrary visual image. It can be projected by. For example, the image processing device 11 has a built-in data processing function equivalent to that of the arithmetic processing device 9, or a display signal to the CRT 12 is supplied through the arithmetic processing device 9, and the 512 × 512 pixels of the CCD video camera 5 are provided. By converting the data into 256 levels of intensity and performing arithmetic processing, and converting the data into a video signal that matches the display image, the measured light intensity distribution can be displayed as an arbitrary image.

A method for two-dimensionally measuring light and a method for measuring the surface roughness of the test piece 4 using the measuring apparatus having the above configuration will be described.
First, an arithmetic expression for measuring the position and spread of light as a basic theory of the present invention is obtained. In the present invention, CC
A two-dimensional Gaussian function by the least squares method for expressing the light intensity distribution on the xy plane by x and y coordinates by a two-dimensional optical sensor such as D is obtained. The light intensity distribution I (x, y) on the xy plane is represented by the following two-dimensional Gaussian function. I (x, y) = Aexp (−ax ² + bx−cy ² + dy) (1) where A, a and b are positive constants, and b and d are arbitrary constants. In order to apply the least squares method, taking the logarithm of both sides of equation (1), Z = lnI (x, y) = − ax ² + bx−cy ² + dy + e (2) where e = lnA. Assuming that the x and y coordinates of the principal axes of the Gaussian function of the equation (1) are p _x and p _y , p _x = b / (2a), p _y = d / (2c) (3) The standard deviation of the Gaussian function of the formula (1) with respect to the x and y coordinates is calculated as follows: σ _x = 1 / √ (2a), σ _y = 1 / √ (2c) (4) Given by That is, equation (1) representing the light intensity distribution
Of the main axis representing the position of the two-dimensional Gaussian function and the standard deviation representing the spread can be obtained from the coefficients a, b, c, and d of equation (1).

A feature of the present invention is that the intensity distribution of light is captured as digital data corresponding to the x and y coordinates on the xy plane by a two-dimensional optical sensor, and is approximated by a two-dimensional Gaussian function. The coordinates of the principal axis of are calculated as the position of light, or the two-dimensional Gaussian function x,
The standard deviation of the y coordinate is determined as the spread of light, and the surface roughness of the object is determined on the basis of the standard deviation. since having the characteristics also that led quickly determine arithmetic expression dimensional Gaussian function that has not been used in the measurement, the coordinate p _x of the main shaft in the above formula (3), p _y and equation (4) below A method for obtaining an arithmetic expression that can easily obtain the standard deviations σ _x and σ _y by the least square method will be described. First, the x and y coordinates of one pixel of a plurality of light receiving pixel arrays arranged on the xy plane of the two-dimensional optical sensor are represented by (x _i ,
y _j ) (i, j = 1 to n), and the light intensity data (digital conversion data) based on the output of this pixel is I (x _i ,
y _j ). Here, n is the number of pixels in the x and y directions of the two-dimensional optical sensor, or the number of light intensity data in the x and y directions used when calculating the coefficient of the equation (1) by the least square method. n × n pieces of data _{I (x i, y j)} (i,
j = 1 to n), the coefficient of equation (1) cannot be directly calculated using the method of least squares. Therefore, equation (2) taking the logarithm of both sides is used, but I (x _i , y _j ) the z of the formula (2) corresponding _{to, z ij = lnI (x i} , y j) when a, n × n pieces of data _{(x i, y j, z} ij) (i, j =
Equations (1) to (n) are obtained by using the least squares method, and the coefficients of the two-dimensional Gaussian function of equation (1) are obtained from the coefficients of equation (2). Although the position of the main axis and the standard deviation of the two-dimensional Gaussian function obtained by using the equations (3) and (4) from the coefficients of the equation (1) obtained by the least square method as described above are considerably complicated equations. by artfully deformed organize this, the position p _x of the spindle, p _y and the standard deviation sigma _x, and a sigma _y can be determined from a simple equation which will be described below.

First, since the light receiving surface of a two-dimensional optical sensor such as a CCD is usually a square, pixels represented by x, y coordinates in an xy plane in n × n areas in the light receiving surface. point _{(x i, y j) (} i, j = 1~n) measurements I (x _i, y _j) of the light intensity z of formula (2) corresponding to the z _ij in the residual sum of squares if _{S, S = ΣΣ (-ax i} 2 + bx i -cy j 2 + dy j + e-z ij) 2 However, Shigumashiguma indicates that taking a double sum from 1 for i and j to n. Next, calculated to the S minimized based on the principle of the least squares _{method, -nα 4 a + nα 3 b} -α 2 β 2 c + α 2 β 1 d + nα 2 e = ζ 21 -nα 3 a + nα 2 b-α _{1 β 2 c + α 1 β} 1 d + nα 1 e = ζ 11 -α 2 β 2 a + α 1 β 2 b-nβ 4 c + nβ 3 d + nβ 2 e = ξ 21 -α 2 β 1 a + α 1 β 1 b-nβ 3 c + nβ 2 d + nβ it can be expressed as _{1 e = ξ 11 -nα 2 a} + nα 1 b-nβ 2 c + nβ 1 d + n 2 e = η. _{However, α 1 = Σx i, α} 2 = Σx i 2, α 3 = Σx i 3, α 4
^{_{= Σx i 4 β 1 = Σy}} j, β 2 = Σy j 2, β 3 = Σy j 3, β 4
^{_{= Σy j 4 ζ 11 = ΣΣx}} i z ij, ζ 12 = ΣΣx i 2 z ij ξ 11 = ΣΣy j z ij, a ^{_{ξ 21 = ΣΣy j 2 z ij}} η = ΣΣz ij.

Here, assuming that the intervals in the x and y directions of each pixel on the light receiving surface of the two-dimensional sensor are all equal to ε, the above α and β are respectively α _m = β _m (m = 1 to 4). Become equal. Also, the origins of the x and y coordinates are x _i , y _j (i, j =
Mean value x _a of 1 to n), the x and y coordinates after moving to y _a, is represented by the same symbols x, y and hitherto for simplicity, x = x-x _a, y = y _{-y a p x = x a +} b / (2a), a _{p y = y a + d /} (2c) ··· (5). The values of the standard deviations σ _x and σ _{y in} Equation (4) do not change due to such parallel movement of the coordinates. Therefore, when the coordinates are translated in this manner, α ₁ = β ₁ = 0 and α ₃ = β ₃ = 0. By substituting this condition into the above equation, the following equation is obtained. ^{_{-Nα 4 a-α 2 2 c}} + nα 2 e = ζ 21 -α 2 2 a-nα 4 c + nα 2 e = ξ 21 -nα 2 a-nα 2 c + n 2 e = η b = ζ 11 / nα 4, d = ξ ₁₁ / nα ₂ Here, assuming that t _i = x _i / ε, t _i = i− (n + 1) / 2 (i = 1, 2,...)
·, N), and the each result alpha ₂ and _{α 4, α 2 = Σx i} 2 = ε 2 Σt i 2 = ε 2 Σ (i- (n + 1) / 2) 2 α 4 = Σx i 4 = ε ^{_{4 Σt i 4 = ε 4 Σ}} (i- (n + 1) / 2) 2 to become. This, is calculated using the formula of power sum of a natural ^{_{number, α 2 = n (n 2}} -1) ε 2/12, calculated as ^{_{α 4 = α 2 (3n 2}} -7) ε 2/20.

As described above, the constants a to e of the two-dimensional Gaussian function in equation (1) can be obtained by substituting and rearranging the equations, and substituting these constants into equations (5) and (4). Thus, the x and y coordinates of the main axis of the Gaussian function and two standard deviations can be calculated. In other words, the principal axis of x of the Gaussian function, y coordinate p _x and p _{y are, p x = x a + (} (n 2 -4) (2ζ 1 - (n + 1)) ε) / (10 (6 (n + 1) _{ζ 1 -6ζ 2 - (n +} 1) (n + 2) η)) p y = y a + ((n 2 -4) (2ξ 1 - (n + 1)) ε) / (10 (6 (n + 1) ξ 1 - 6ξ ₁ − (n + 1) (n + 2) η)), and the standard deviations σ _x and σ _y are σ _x = (nε / 2ε (15)) √ ((n ² −1) (n ² -4) / (6 (n + 1) ζ 1 -6ζ 2 - (n + 1) (n + 2) η)) σ y = (nε / 2√ (15)) √ ((n 2 -1) (n 2 -4) / ( _{6 (n + 1) ξ 1} -6ξ 2 - (n + 1) (n + 2) η)) can be obtained as. Where ζ ₁ ,
Each of ζ ₂ , ξ ₁ , and ξ ₂ is ζ ₁ = ΣΣiz _ij , ζ ₂ = ΣΣi ² z _ij ξ ₁ = ΣΣiz _ij , and ξ ₂ = ΣΣi ² z _ij .

The arithmetic expressions for the coordinates p _x and _py and the standard deviations σ _x and σ _y of the main axes of the two-dimensional Gaussian function obtained as described above are calculated very quickly by a general personal computer or other arithmetic device. If this arithmetic expression is set by the arithmetic processing unit 9 in FIG.
Digital data (x _i , y _j ) corresponding to the x and y coordinates from the D converter 8 is input, and the coordinates p _x ,
p _y and the standard deviation sigma _x, can be calculated sigma _y, if printed out the result to the display and or printer 10 in CRT 12, it is possible to check the respective values by the output data.

Therefore, when the light intensity distribution of the irradiation light of the laser light source 7 is examined by the CCD video camera 5,
In each of the light receiving pixels corresponding to the x and y coordinates of the xy plane (square as a whole) in the CD video camera 5, x-y
A video signal that changes in accordance with the light intensity distribution of the laser light source 7 on the y-plane is output. The video signal is converted into a digital signal having 256 steps of intensity change in the A / D converter 8 and supplied to the arithmetic processing unit 9. You. Suppose that a light receiving pixel array arranged on the xy plane of the CCD video camera 5 has 512 × 51 pixels.
If it has two pixels, its x and y coordinates (x _i ,
y _j ), digital data changed to light intensities distributed in i, j = 1 to 512 can be obtained, but distribution in a specific area centered on the main axis of the light source 7 (most of the distribution curve can be covered) Area, or an area that only covers the vicinity of the spindle)
By setting a specific measurement window by specifying coordinates forming an arbitrary square of the y-coordinate and processing digital data in the window, the light intensity distribution in that area can be obtained.

As an experimental sample, a He—Ne laser beam was used as the laser light source 7 in FIG.
When the distribution of the irradiation light is captured, the light intensity distribution I (x, y) at the x, y coordinates is as shown in FIG. The lower tail of this distribution curve indicates the spread of square area data in the xy plane in the two-dimensional optical sensor, and sampling of data excluding such a tail area (background) is performed at the x, It can be selected by specifying the y coordinate.

The position of the principal axis and the standard deviation of the two-dimensional Gaussian function calculated by the above equation using all the data obtained from the light intensity distribution as shown in FIG. Each light receiving pixel interval ε of 5
The following values could be obtained by expressing as a unit. Position of the main shaft _{p x = 255, p y =} 258 the standard deviation _{σ x = 11.6, σ y =} 10.9 or more as the main axis of the two-dimensional Gaussian function obtained x, y
Since the coordinates Px, Py and the standard deviations σ _x , σ _y are close to the principal axis and the standard deviation of the light intensity distribution curve of the experimental sample light source captured by the CCD video camera 5, this value is This indicates the position and spread of the light from the sample light source.

According to the above measuring method in the present invention,
Although the two-dimensional position and spread of the light can be measured quickly, using the above-described arithmetic expression, the sampling data of the square measurement area whose sampling data is captured by a two-dimensional optical sensor such as the CCD video camera 5 can be obtained. Since all are targets, there may be some errors due to the background of the distribution curve, but it can be regarded as an approximated light intensity distribution. For example, even when measuring the roughness of an object surface, the reflected light intensity distribution Is calculated in the same manner, the measurement based on the values of the standard deviations σ _x and σ _y becomes possible. Further, in the measurement method using the above arithmetic expression, data of a square measurement formula is used, but only data within an ellipse cut by a plane parallel to the xy plane may be selected and obtained. If the calculation becomes complicated, a more accurate standard deviation can be obtained.

Next, in the measuring apparatus shown in FIG.
A method of measuring a detection target by the CD video camera 5 as reflected light corresponding to the surface roughness of the test piece 4 will be described. When the light from the LED light source 2 in the irradiation light source 1 is condensed by the lens 3 and is irradiated on the test piece 4, the test piece 4
Is reflected by the CCD video camera 5 with the intensity distribution of light corresponding to the surface roughness on the reflecting surface. Since the reflected light intensity distribution at this time can be approximated and represented by a two-dimensional Gaussian function in the same manner as in the above-described theory of two-dimensional measurement of light, a standard deviation of two axes orthogonal to each other in the two-dimensional Gaussian function is obtained. Thus, the spread of the reflected light intensity distribution curve in two directions orthogonal to each other can be evaluated, and the surface roughness can be obtained using the standard deviation of the Gaussian function.

The theory of the measuring method will be described below.
First, when the reflected light intensity distribution I (x, y) is represented by a two-dimensional Gaussian function, I (x, y) = Aexp (−ax ² + bx + cy ² + dy + exy) (6) where A, a, c Is a positive constant, and b, d, and e are arbitrary constants. Next, taking the natural logarithm of the equation (6), which upon the z, z = lnI (x, y) = - ax 2 + bx-cy 2 + dy + exy + f ··· (7) However, the f = lnA. To determine the coefficients of the equation (7), n pieces of measurement _{(x i, y i, z} i) (i = 1~
The least squares method is applied to n). When the two-dimensional Gaussian function of the equation (6) is cut by a plane parallel to the xy plane, an ellipse is obtained.
When ≠ 0, the main axis of the ellipse is generally inclined with respect to the x and y axes as shown in FIG.

The coordinate axes of this ellipse are x ',
When this is newly represented by x and y on the y ′ axis, the following equation (6) is obtained.
Is I (x, y) = Aexp (−αx ² −βy ² ) (8) Here, α and β are positive constants, and α = acos ² θ + csin ² θ−esin θcos θβ = asin ² θ + ccos ² θ−esin θcos θ θ = 0.5 tan ⁻¹ [e / (ca)] (Θ is the inclination of the x ′ axis with respect to the x axis.) According to the theory of statistics, the standard deviations σ _x and σ _y of the equation (8) with respect to the x axis and the y axis are σ _x = 1 / √ (2α), σ _y = 1 / √ (2β) (9) ). From the standard deviations σ _x and σ _y , the spread of the reflected light intensity distribution curve on the x-axis and the y-axis orthogonal to each other can be obtained.

The result of measuring the surface roughness of the test piece 4 with the measuring device shown in FIG. 1 based on the above theory will be described. The test piece 4 used had a center line average roughness Ra of 0.05.
6 kinds of standard surface roughness test pieces ground from 1.6 μm. In FIG. 1, first, light emitted from an LED light source 2 is condensed on a test piece 4 by a lens 3, and the reflected light intensity distribution is measured by a CCD video camera 5 through a translucent plastic plate 6. The video signal output from the CCD video camera 5 is input to the arithmetic processing device 9 through the image processing device 11, and is displayed by the CRT 12 in a predetermined image corresponding to the reflected light intensity distribution. At the same time, in the arithmetic processing unit 9, a two-dimensional light intensity distribution curve is obtained based on digital data obtained by digitally converting the video signal by the A / D converter 8, and the x-axis of a two-dimensional Gaussian function representing the spread of the curve is obtained. And standard deviations σ _x and σ _y with respect to the y-axis were obtained four times for each test piece.

FIGS. 4A to 4D show examples of the reflected light intensity distribution of the test piece 4 measured by the measuring apparatus of FIG. As can be seen from this figure, since the surface roughness due to grinding has directionality, the horizontal cross section of the reflected light intensity distribution curve that can be approximated by a two-dimensional Gaussian function is not circular but elliptical. Also, it can be seen from FIG. 4 that this curve becomes wider as the surface roughness Ra increases.

FIGS. 5 and 6 show the intensity distribution curves of vertical cross sections of the two-dimensional reflected light intensity distribution curves obtained by subtracting the background intensity, using a test piece with Ra = 0.8 μm as an example. The curves shown in these figures are Gaussian functions obtained by using the least squares method on data of 30% or more (70% from the top) of the maximum intensity value Imax. This indicates that the reflected light intensity distribution can be approximated to a Gaussian function with considerable accuracy.

FIG. 7 shows that the maximum value Imax of the reflected light intensity is 30.
5 shows the relationship between the standard deviations σ _x , σ _y on the x-axis and the y-axis obtained from the two-dimensional Gaussian function fitted using data of at least% and using the equation (9) and the surface roughness Ra. From this figure, the standard deviation σ _{y in the} grinding direction has a substantially constant value irrespective of the surface roughness Ra, whereas the standard deviation σ _{x in the} direction perpendicular to the grinding direction increases with the surface roughness Ra. You can see that it is. Standard deviation σ _x and surface roughness R in FIG.
As a result of obtaining an empirical formula indicating the relationship with a, the following formula could be obtained. ^{_{Ra = 21.86 σ x 2 -6.75σ x}} +0.58 ··· (10) Therefore, by using the equation (10), the standard deviation sigma surface roughness of the test piece 4 _x Ra Gaussian function obtained optically Is obtained. As data calculation equation in the arithmetic processing unit 9, the standard deviation sigma _x of the two-dimensional Gaussian function, the equation for sigma _y, the standard deviation sigma _x, by setting the equation for surface roughness Ra based on sigma _y, The surface roughness Ra can be easily and quickly obtained from the standard deviation of the intensity distribution curve of the reflected light from the object surface by the CCD video camera 5 in the measuring apparatus of FIG.

[0038]

As described above in detail, according to the present invention, the position or spread of light necessary for various optical measurements, and as one application example, the surface roughness of the object surface as a measurement object The light and the reflected light on the surface are CC
While measuring with a two-dimensional optical sensor such as D, the light intensity distribution is taken as an approximated two-dimensional Gaussian function, and the coordinates of the main axis and the standard deviation of the two-dimensional Gaussian function are obtained by a predetermined arithmetic expression. It is possible to determine the position and spread of light very easily and quickly, without complicating the measuring device and moving the relative position between the measuring object and the optical sensor as before. At the same time, and it is possible to provide a measurement method and an apparatus having extremely high practical value in this type of optical measurement field. In particular, the present invention captures the spread of two-dimensional light with a two-dimensional optical sensor, approximates this light intensity distribution to a two-dimensional Gaussian function, and derives a simple arithmetic expression to obtain the coordinates of the principal axis of the Gaussian function. And the standard deviation can be quickly obtained, and the two-dimensional position and spread of light can be represented by the coordinates of the main axis and the standard deviation, and furthermore, by a predetermined arithmetic expression using these two standard deviations. The surface roughness of the object in two directions perpendicular to each other can be easily obtained optically, and by measuring these with a two-dimensional spread, an effect that an extremely wide range of use can be achieved is achieved. is there.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a basic structure of a measuring apparatus for performing two-dimensional measurement of light and measurement of surface roughness of an object according to the present invention.

FIG. 2 is a distribution diagram three-dimensionally showing a light intensity distribution obtained by measuring light of a laser light source in the present invention as an intensity change curve with respect to xy coordinates.

FIG. 3 is an explanatory diagram of coordinates obtained by cutting a two-dimensional Gaussian function approximating a reflected light intensity distribution of a test piece in a surface roughness measurement of the present invention by a plane parallel to an xy plane.

4 is a distribution diagram three-dimensionally showing the surface roughness of a measurement test piece in the measurement apparatus of FIG. 1 by a reflected light intensity distribution.

5 is a reflected light intensity distribution diagram with respect to the y-axis of a test piece measured by the measuring device of FIG.

FIG. 6 is a reflection light intensity distribution diagram with respect to the x-axis of a test piece measured by the measurement device of FIG. 1;

FIG. 7 is a correlation diagram showing a relationship between a standard deviation with respect to an x-axis and a y-axis and a surface roughness of a test piece.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Irradiation light source 2 LED light source 3 Lens 4 Test piece 5 CCD video camera as a two-dimensional optical sensor 6 Plastic plate 7 Laser light source 8 Analog / Digital converter 9 Arithmetic processing unit 10 Printer 11 Image processing unit 12 CRT

Claims (4)

(57) [Claims] 1. A light measuring method for determining a two-dimensional distribution of light intensity of a laser beam or the like by a non-contact optical system,
The reflected light from the light source or the reflector is detected by a two-dimensional optical sensor such as a CCD as x and y coordinate values corresponding to the light intensity distribution, and the light intensity distribution on the xy plane is calculated. And captures digital conversion data based on the outputs of a plurality of light receiving pixel arrays arranged on the xy plane of the two-dimensional optical sensor as x, y coordinate data of the two-dimensional Gaussian function. , the principal axis of x of the Gaussian function, y coordinate p _x, by obtaining by calculating the p _y, the two-dimensional measurement method of the light and determines the two-dimensional position of the light. 2. A light measuring method for determining a two-dimensional distribution of light intensity of a laser beam or the like by a non-contact optical system,
The light reflected from the light source or the reflector is detected by a two-dimensional light sensor such as a CCD as x and y coordinate values corresponding to the light intensity distribution, and the light intensity distribution on the xy plane is sent to an arithmetic processing unit. And captures digital conversion data based on the outputs of a plurality of light receiving pixel arrays arranged on the xy plane of the two-dimensional optical sensor as x, y coordinate data of the two-dimensional Gaussian function. Standard deviations σ of x and y coordinates of Gaussian function
By calculating and calculating _x , σ _y , the _xy of the light
A two-dimensional measuring method of light, characterized by determining a two-dimensional spread in a plane. 3. A laser or an LE on a surface of an object to be measured.
A light from a light source such as D is irradiated, and a reflected light from the surface of the object is received by a plurality of light receiving pixel rows arranged on an xy plane in a two-dimensional optical sensor such as a CCD.
-The reflected light intensity distribution in the y-plane is taken as a two-dimensional Gaussian function, and each standard in x and y coordinates of the two-dimensional Gaussian function is based on digital conversion data corresponding to the output of the light receiving pixel array of the two-dimensional optical sensor. Deviation σ _x , σ _y
Is determined by a predetermined arithmetic expression to determine the two-dimensional spread of the reflected light intensity distribution curve using the standard deviations σ _x and σ _y , thereby obtaining the surface roughness of the object. Roughness measurement method. 4. An irradiation light source for irradiating a surface of an object to be measured with light such as a laser beam or LED light, and a two-dimensional optical sensor such as a CCD arranged at a position capable of receiving reflected light from the surface of the object. And an analog / digital converter for converting analog signals output from a plurality of light receiving pixel arrays arranged on an xy plane in the two-dimensional sensor into digital signals, and digital data converted by the analog / digital converter. Is approximated by a two-dimensional Gaussian function in the x and y coordinates of the reflected light intensity distribution curve corresponding to the surface roughness of the object surface based on And a calculating means for calculating the roughness of the object surface based on the standard deviation.