JP6159956B2 - Method for analyzing shape of machined surface of lens and execution program thereof - Google Patents

Description

  The present invention relates to a method for analyzing a processed surface shape of a lens, which can analyze the processed surface shape of a lens without actually measuring it, and an execution program thereof.

As a problem when processing a spectacle lens, a prominent power deviation called “navel” may occur. The power deviation is a state in which the refractive power changes discontinuously due to the disturbance of processing, and such a lens is defective and must be checked and eliminated. One of such trouble checking means and Patent Document 1 are listed.
In Patent Document 1, a plurality of light beams are incident from one lens surface, the displacement due to refraction for each light beam when emitted from the other lens surface is mapped using a mapping device, and refractive power data at each mapping point is recorded. Is obtained and analyzed to check for defective products.

JP 2012-123139 A

However, it is very time-consuming to check defective products using a mapping device for all lenses, and it takes time to check if the number of mapping devices is small. Therefore, such problems can be solved if it is possible to analyze and evaluate in advance whether or not the actual check is necessary. In addition to determining whether or not to use the mapping device, it is also desirable to analyze the lens processing state in advance to prevent defective products from being shipped.
The present invention has been made paying attention to such problems existing in the prior art. An object of the present invention is to provide a method of analyzing a processed surface shape of a lens and an execution program thereof that can analyze the processed surface shape of the lens by using a probability density function without actually measuring it.

In order to solve the above problem, means 1 is a method for analyzing a processed surface shape of a lens using a probability density function, wherein a predetermined probability density function is optimized based on shape data of a plurality of existing lenses. obtained by applying the shape data of a new lens to optimize the probability density function to create a unique probability density function of the shape of the new lens lens, sudden in the processing surface of the new lens on the basis of the specific probability density function The main point is to analyze the typical frequency deviation .
Further, in the means 2, the probability density function has a predetermined parameter in addition to the structure of the means 1, and the predetermined probability density function is obtained by obtaining the maximum likelihood estimator of the parameter using the shape data of a plurality of existing lenses as a variable. The gist is to optimize.
Further, in addition to the configuration of the means 2, the means 3 defines the parameter with one or a plurality of lens conditions set for each of a plurality of existing lenses and a coefficient given for the same lens condition, and the maximum likelihood of the coefficient The gist is that the maximum likelihood estimator of the parameter is calculated by obtaining the estimator, and the intrinsic probability density function is set using the calculated parameter.

Further, in addition to the configuration described in any one of the means 1 to 3, the means 4 integrates the shape data of the lens within a predetermined range in the intrinsic probability density function, and analyzes the processing surface of the lens based on the integration value. The gist.
Further, in the means 5, in addition to the configuration described in any one of means 1 to 4, the shape data of the lens is a processing state point given to each lens according to the processing state of the processing surface of the lens. And
Further, the gist of the means 6 is that in addition to the configuration described in any one of the means 1 to 4, the lens shape data is an inset value.
Further, the gist of the means 7 is to use the following function as a probability density function in addition to the configuration described in any of the means 1 to 5.
The gist of the means 8 is an analysis program for executing the lens analysis method according to any one of the means 1 to 7.

In such a configuration, a predetermined probability density function is optimized based on the shape data of a plurality of existing lenses, and an optimized probability density function is obtained. Then, the shape data of the new lens is applied to the optimized probability density function to create an intrinsic probability density function. In other words, a probability density function (optimized probability density function) with little statistical error is created based on multiple existing lenses, and the optimized probability density function is applied to a new lens. Thus, a new probability density function specific to the lens (inherent probability density function) is created. At this time, since a certain occurrence probability for the shape data of the intrinsic probability density function is based on the shape data of a plurality of existing lenses, the occurrence probability is objective. Therefore, it is possible to analyze the new lens by verifying the probability of occurrence of the new lens shape data from the intrinsic probability density function, and it is possible to evaluate the analysis result as necessary.
More specifically, the occurrence probability may be integrated with respect to the lens shape data within a predetermined range in the intrinsic probability density function, and the processed surface of the lens may be analyzed based on the integrated value. The predetermined range is preferably performed on the tail side of the distribution without including an average.

Here, the probability density function is an expression that statistically represents the relationship between a data string and the result thereof as a curve. The probability density function preferably has as high a correlation as possible with the distribution characteristics of the present invention. Specifically, the probability density function expressed by differentiating the general expression of the Weibull distribution as shown by the above equation 1 is good. . In addition, as an example, a normal distribution, a standard normal distribution, a chi-square distribution, a t distribution, or the like can be used.
Here, the optimization of the probability density function means that there is no statistical error in the data, and more specifically, the parameter is set so that there is no error (the maximum likelihood estimator is obtained). . A plurality of methods for optimizing the probability density function are conceivable. For example, it is preferable to obtain the maximum likelihood estimator of the parameters of the probability density function using the shape data of a plurality of existing lenses as variables.
The probability density function parameter is defined by one or a plurality of lens conditions set for each of a plurality of existing lenses and a coefficient given for the same lens condition, and a maximum likelihood estimator of the coefficient is obtained. It is preferable to calculate the maximum likelihood estimator of the parameter, and to set the intrinsic probability density function using the calculated parameter. By defining the probability density function parameters themselves with the lens conditions and their coefficients of the existing lenses as samples, the correlation with the lens shape is given, and the accuracy of the maximum likelihood estimator of the probability density function parameters Will be improved.

Here, the lens shape data is some data based on a predetermined shape formed on the lens surface by processing the lens. From a broad perspective, for example, the lens power itself can be the lens shape data in the first place. In a narrow sense, for example, a sudden power deviation (processing disorder), an inset amount, a length of a progressive zone in a progressive power lens, an addition power, and the like can be mentioned. Lens shape data is a numerical representation of the state of the lens surface produced by such processing. The lens shape data may be acquired as data for the entire region of the processed surface of the lens, or may be a certain region, for example, only near the center of the lens. Processing disturbance is particularly concentrated in the center of the lens and in the vicinity of the lens center, and on the contrary, the processing accuracy is relatively good at the periphery of the lens. Therefore, in order to verify “processing disorder”, it is basically unnecessary to calculate and execute based on the refractive power data at all the mapping points, and it may be performed particularly for a small region near the center of the lens.
There are several methods for digitizing lens shape data. For example, the following method is preferable.
First, a local change amount of the region is calculated based on a difference in refractive power between a plurality of refractive power data included in one continuous region of the lens. Furthermore, the local change amount is calculated for each of a plurality of areas included in one continuous area that is adjacent to each other for each of the plurality of lenses. That is, a plurality of local variations are obtained for a wider region. As a result, a map of the amount of change in the analyzed region is obtained. Then, a correlation pattern is obtained for the local region using the obtained plurality of changes as reference point values. The correlation patterns obtained here are calculated with different patterns if the lens characteristics are different. For the correlation pattern, an evaluation value for the amount of change is obtained for each lens. Then, the principal component analysis is performed using the evaluation value, and the principal component score calculated by the principal component analysis is used as lens shape data. Here, the refractive power data is one of S power data, C power data, or secondary power data derived using both S power data and C power data as parameters, and the secondary power data is the angle of the astigmatic axis. Is preferably a parameter.
It is also possible to use methods other than principal component analysis, such as regression analysis.

  In the present invention, by using the probability density function, it is possible to analyze the processed surface shape of the lens without actually measuring it.

Block diagram explaining the process of the present invention The schematic block diagram of the apparatus for similarly implementing this invention. Explanatory drawing explaining the image which acquires the data of the mapping point in a small area | region in an Example. (A) and (b) are determinants serving as filters for local product-sum operations used in the embodiment. Explanatory drawing of the variation | change_quantity map which mapped the variation | change_quantity of local data to the small area | region S. FIG. Explanatory drawing explaining 35 types of autocorrelation patterns about a 3x3 mask pattern. Intrinsic probability density curves of lenses 1) to 3). 6 is a histogram of the lens analyzed in Example 2.

Hereinafter, specific embodiments of the present invention will be described with reference to the drawings.
In the present embodiment, as a premise for optimizing the probability density function, the processing state points as the lens shape data are calculated in advance for the processing state points of a large number of lenses. In the present embodiment, the machining state point is measured and calculated by a system in which a frequency distribution measuring device (lens mapper) 2 as a mapping device for measuring a frequency distribution is connected to a calculation computer 1 as shown in FIG. ing. In this system, a computer 3 for calculation is connected to a monitor 3 as output means and a keyboard 7 as input means for inputting basic lens data of the test lens 5. Examples of the output means include an output means for transferring data to a printer and other devices in addition to the monitor 3. In addition to the keyboard 7, the input means includes a two-dimensional code such as a bar code, a means for inputting data transferred from another device such as another computer or data storage device connected via a LAN, and the like.
The frequency distribution measuring device (lens mapper) 2 includes a light source 10, a beam splitter 11, a screen 12, and a CCD camera 13 as shown in FIG. An analysis device 14 is connected to the CCD camera 13. The test lens 5 is disposed between the light source 10 and the beam splitter 11. The light source 10 emits parallel light rays toward the beam splitter 11. The beam splitter 11 is formed with a large number of through holes arranged regularly and vertically at equal intervals, and a light beam (light beam) passing through the through holes is projected onto the screen 12. This projected light spot is used as a mapping point. The CCD camera 13 captures an image of the mapping point projected on the screen 12.
The analysis device 14 calculates the refractive power for the mapping points of all the lenses based on the positional displacement of the through holes corresponding to the light rays captured by the CCD camera 13 with respect to the respective through hole positions. That is, the refractive power data (S power data, C power data, astigmatism axis data) of the test lens 5 can be obtained for all positions mapped on the lens. Further, the analysis device 14 calculates an equivalent spherical surface value (average power) and secondary power data of J00 and J45 based on the refractive power data. A memory 15 as storage means is provided inside the analysis device 14 and stores refractive power data and secondary power data.
The calculation computer 1 includes a CPU (Central Processing Unit) and its peripheral devices. The CPU obtains optical characteristic data from various programs and the frequency distribution measuring device 2 and performs calculations in the following embodiments for the test lens 5 according to the operation of the operator.

Example 1
(A) Calculation of processing state point of existing lens An example of a processing state point calculation method executed by the calculation computer 1 in the above-described system will be described.
In Example 1, as shown in FIG. 3, mapping point data in a small region S of 5 mm in length and width with the geometric center of the lens as the center is used and calculated as an equivalent spherical value (average power). The number of lenses for which the processing state point was calculated was 15943. This number is the actual number of orders received in the past.
(A-1: Edge treatment)
In order to study the amount of change in the local region of the lens, 3 × 3 vertical and horizontal local data was extracted and a local product-sum operation was performed.
For this local product-sum operation, a vertical filter shown in FIG. 4A and a horizontal filter shown in FIG. 4B were used. These filters are determinants for performing a local product-sum operation by giving an appropriate coefficient to each of 3 × 3 local data, and are Sobel filters used to emphasize image discontinuity in image processing. It is called. Specifically, for example, when these filters are executed on the local data surrounded by L in FIG. 3, the product-sum operation value (fx) of the vertical filter: 1 × (−1) + 1 × 0 + 0.8 × 1 + 1.1 × (−2) + 1.2 × 0 + 3.5 × 2 + 1.4 × (−1) + 1.5 × 0 + 1.6 × 1 = 4.8
Product sum operation value (fy) of horizontal filter: 1 × (−1) + 1 × (−2) + 0.8 × (−1) + 1.1 × 0 + 1.2 × 0 + 3.5 × 0 + 1.4 x 1 + 1.5 x 2 + 1.6 x 1 = 2.2
It becomes.

fx = 4.8 and fy = 2.2. By applying this result to the following equation (2), the amount of change in the local data surrounded by L is 5.3 (the actual data is calculated as a fraction like 5.28...) It is obtained.
FIG. 5 shows the amount of change in the small region S corresponding to FIG. 3 when the amount of change is obtained for the 3 × 3 local data in order by shifting one by one downward and laterally from the local data surrounded by L. Shown in That is, the local area change amount map MP corresponding to the small area S is obtained.

(A-2: Development of higher-order autocorrelation pattern)
The data calculated in A-1 is used. In general, the Nth-order autocorrelation function is defined as follows with respect to N (z ₁ ... Z _n ) displacements around the reference point.

Here, in order to see the local correlation around the reference point, the order is limited to three, and the correlation is examined for a 3 × 3 mask pattern. In this case, 35 patterns are conceivable as shown in FIG. Correlation values in the variation map MP were obtained for these 35 types of patterns. For example, as shown in Equation 4, if the pattern M ₁ is, for example, the frequency value that is a weight is only the reference point, M ₁ = 10.4, and the pattern M ₈ considers the frequency value around the reference point. Is calculated. In this case, M ₈ = 44.6.
Thus, the correlation value about the 3 × 3 mask pattern from M _{1 to} M ₃₅ was obtained for each lens.

(A-3: Principal component analysis)
Based on the correlation values M _{1 to} M ₃₅ , machining state points are calculated by a principal component analysis technique. The first principal component can be expressed by the following formula.

Here, it is necessary to calculate a (eigenvector) that maximizes the dispersion of the main components of each lens to be examined. That is, the time when the dispersion value becomes the maximum is the first main component. However, if the value of a is increased, the value of Z increases as much as possible. Therefore, a restriction is imposed so that a ₁ + a ₂ +... + A ₃₅ = 1 (condition 1). Table 1 shows the first principal component vector obtained by the calculation. From this table, the value of the first principal component is
_{Z = 0.069271 × 10.4 + ······ a} 7 M 7 + 0.080246 × 44.6 + ······ a 35 M 35
Can be obtained.
In the first embodiment, the value of the first principal component is 200.9025.

  Here, if the average of the first principal component obtained when calculating the eigenvector is B, the first principal component score Y used for the final determination may be expressed as Y = Z−B. it can. A score can be obtained by calculating the second principal component and the like in the same manner. Since it is known that the first principal component indicates “processing disorder”, the score of the first principal component of each of the existing lenses is ranked as a processing state point. It is assumed that the machining state point is not as good as the score is high. In the first embodiment, the processing state points of all 15943 data were distributed between -100 and 250.

(B) Optimization of probability density function The probability density function is optimized based on the lens processing state points obtained above. That is, a predetermined probability density function that is a population distribution is estimated using 15943 data. Here, the above formula 1 is used as a predetermined probability density function. This equation is a differential equation of the Weibull distribution, and has three parameters. Therefore, when the shape of the curve is determined by the parameters, it can correspond well to the probability density of the data. That is, if the shape parameter α, the scale parameter β, and the position parameter γ are determined, the shape of the distribution curve is determined.
Here, first, γ was set to −100 which is the lowest point of the actual machining state point. Note that γ can be changed as appropriate.
Next, the two parameters α and β are defined by the lens conditions of each lens and their coefficients as in the following equation (6). For convenience of calculation, constant terms F and F ′ are provided. As lens conditions, X1: blade point, X2: back base curve, X3: back cross curve, X4: front curve, and X5: refractive index were used.
Here, the blade point is a value uniquely determined by the applicant. When performing lens cutting, a cutting tool called a cutting tool is periodically replaced so that the cutting ability is not lowered. It has been found that the change in the cutting ability of the lens varies depending on the lens material, and the number of sheets that can be processed with one tool differs. Therefore, the points up to the blade replacement are set in advance, and when a certain material is processed, 5 points are added per piece, and when a certain material is processed, 1 point is added per piece. Is going. The point gets higher as you continue to use the blade, and the blade is replaced when the total point exceeds the preset point. Points will be canceled once by the blade exchange.
The back base curve, back cross curve, and front curve are the curve values in each order. Use semi-finished blanks with different table curves for each order. The numerical values used this time are all values obtained by multiplying the value converted to the refractive index of 1.500 by 100. The calculation method of the curve is (n-1) / r. In the above formula, n is the refractive index, and r is the radius of curvature (m). The back base curve and the back cross curve are back curves set according to the client's order. This is also calculated in terms of a refractive index of 1.500.
The refractive index represents a value calculated with 1.5 as 1. That is, when the lens has a refractive index of 1.6, it is calculated as 1.07.

  At this time, the maximum value of the likelihood function is expressed by the following equation of the total product of Equation 7. In order to obtain α and β which maximize this, the log likelihood of L is taken, and the form of addition simplifies the calculation. Here, the values of α and β are determined so that the log likelihood is maximized. That is, the A to E coefficients and constant terms of the lens conditions constituting α and β are determined. For these determinations, coefficients are determined by solving simultaneous equations using a known optimization method, such as Gaussian elimination method or skyline method. Here, it is only necessary to obtain optimized coefficients without finally obtaining α and β (it can be said that α and β are indirectly optimized by the optimized coefficients). The results are shown in Table 2.

(C) Examination of processing state of new lens Table 3 shows the lens conditions for specific new lenses 1) to 3). Since α and β are determined by giving the above optimized coefficients to the lens conditions, the intrinsic probability density curves of the lenses 1) to 3) can be created as shown in FIG. At this time, the area surrounded by the horizontal axis and the curve indicates the probability of each lens. In this case, the area of the region where the processing state point is particularly high indicates the probability that the “processing disorder” of the lens is high. Here, when the area of the region with many “processing disturbances” of the processing state points 100 to 250 is calculated for each of the lenses 1) to 3) on the basis of the integral formula of Formula 8, it is as shown in Table 4. Here, since the area of the lens 1) is large, it can be determined that the “processing disorder” is large. Therefore, for new lenses, it is possible to probabilistically determine the “working disorder” of the lens based on the lens conditions alone, set an appropriate threshold, and selectively check a lens with a large area with a mapping device. Improvement of work efficiency can be expected by making it a target.

(D) Validity of probability density curve The validity of the judgment based on such a probability was verified with respect to the similarity with the actually measured data.
First, for the 15943 lens data analyzed this time, the area of processing point 100 or more was obtained and divided into five categories as shown in Table 5 below. And the average of the area whose process state point was 100 or more was calculated about the lens contained for every category. As mentioned above, area means probability. In Table 5, the third column shows the number of sheets belonging to each category.
On the other hand, the number of lenses having a processing state point of 100 or more is calculated based on the blade conditions, the back base curve, the back cross curve, the front curve, and the refractive index values, which are lens conditions, for 15943 lens data. Divided into categories (4th column in Table 5). The fifth column in the probability table 5 based on actual measurement values is a numerical value obtained by dividing the number m of lenses in the third column by the number M of lenses in the fourth column in each category.
Here, when the probability based on the probability density curve is compared with the probability based on the actual measurement value, there is a difference of several percent, but the deviation is small, and the analysis by the above probability density curve shows the actual measurement data well. It can be said that.

(Example 2)
In the second embodiment, a normal distribution is used as the probability density curve as in the first embodiment. In Example 1, the lens surface was analyzed by optimizing the probability density function using the processing state point as the lens shape data. In Example 2, the progressive lens inset was analyzed as the lens shape data. .
When a lens is manufactured with a certain prescription for manufacturing a lens, it is necessary to analyze whether the lens is manufactured as designed and to feed back the analysis result. For example, there is a possibility that the lens is not manufactured as designed due to a mechanical error. Therefore, a lens manufactured by irradiating a manufactured lens with a plurality of light beams, mapping the displacement in light refraction with a power distribution device, and checking the actual refractive power data (lens power data) of the lens. It is possible to analyze (evaluate).
Here, inset means that when the eyeglass lens is worn, if the line of sight is moved from the distance vision state to the near vision state, the eye approaches inside (convergence). In general, a numerical value indicating how much congestion has occurred is measured at the near eye point position, and the amount of convergence in the left-right direction of the eye at this position is used as an inset value. The near eye point position is an inset position from which an inset value is obtained.

When C power and its direction component (astigmatic axis direction) are set as the prescription of the lens to be manufactured, or when C power and astigmatic axis direction are set at the power measurement position for confirming spectacle lens performance As a method for measuring the inset value, for example, there is a method described in the applicant's Japanese Patent Application No. 2012-125603.
On the other hand, when the C power and the direction component (astigmatic axis direction) are not set as the prescription of the lens, or the C power and the astigmatic axis direction are not set at the power measurement position for confirming the spectacle lens performance. Based on the refractive power data measured by the power distribution device, it is sufficient to measure the astigmatism at a certain position and the average power by S power and C power.
In Example 2, the probability density function was optimized based on the design values and the values measured by any one of these methods for the inset value data of 42453 lenses. That is, a predetermined probability density function, which is a population distribution, was estimated using 42453 data. First, assuming that the difference between the design value and the measured value is the x-axis and the number of lenses is the y-axis, the distribution is relatively normally distributed as shown in the histogram of FIG. Therefore, in Example 2, the following equation (9) was used as a predetermined probability density function. Since this equation is a normal distribution equation and has two parameters, an average value and a variance value, it can correspond well to the established density of data when the shape of the curve is determined by the parameters.

The two parameters of the average value and the dispersion value are defined by the lens condition of each lens and its coefficient as shown in the following equation (10). For convenience of calculation, constant terms E and E ′ are provided. Four lens conditions were used: X1: blade point, X2: back base curve, X3: back cross curve, and X4: inset value. The lens conditions were changed slightly from those in Example 1. Since the description is the same as that of the first embodiment, the description is omitted.
Then, as in the first embodiment, the total product from the first lens to the 42453th is set, and the average value and the dispersion value are obtained so that the total product becomes maximum. That is, the A to D coefficients and the constant terms that constitute the average value and the variance value are determined. For these determinations, coefficients are determined by solving simultaneous equations using a known optimization method, such as Gaussian elimination method or skyline method. Table 6 shows the average value and the variance value that maximize the total product.
Since the probability density function is optimized for the inset value as described above, the “processing disorder” of the lens can be determined probabilistically only by the lens conditions as in the first embodiment, and an appropriate threshold value is set. A lens having a large area can be selectively checked by the mapping apparatus.

It should be noted that the present invention can be modified and embodied as follows.
As the probability density curve, a standard normal distribution, chi-square distribution, t distribution, etc. can be used in addition to the differential expression of the Weibull distribution and the normal distribution.
The analysis content in each of the above embodiments is the degree of processing irregularity and the amount of inset, but an analysis on other lenses may be performed.
-The number and types of the lens conditions can be changed as appropriate.
A differential expression of Weibull distribution may be applied to the second embodiment.
The above-mentioned optimization method for the parameters of the probability density curve is an example.
In each of the above embodiments, the equivalent spherical value (average power) is used as the secondary power data acquired at the mapping point position, but other refractive power data and secondary power data can be freely used. .
In each of the above embodiments, in order to examine the amount of change in the local region of the lens, 3 × 3 vertical and horizontal local data is extracted and a local product-sum operation is performed. However, patterns other than 3 × 3, for example, 2 It is also possible to take local data at x5, 4x4, etc.
In each of the above-described embodiments, the change amount is manifested using the Sobel filter. However, this is only an example, and other functions and matrices are used as filters in order to emphasize and acquire the change amounts in the vertical and horizontal directions. That is free.
In each of the above-described embodiments, the amount of change is obtained for the 3 × 3 local data in order by shifting the local data surrounded by L one by one in the downward and horizontal directions. In other words, the change amount is obtained while overlapping the local regions by 1/3. However, if the accuracy is not so required, the change amount may be obtained for the adjacent regions so as not to overlap each other by shifting by two. .
In addition, it is free to implement in a mode that does not depart from the spirit of the present invention.

  11: CPU that executes calculation of optimization of probability density function.

Claims (8)

A method of analyzing a processed surface shape of a lens using a probability density function, wherein a predetermined probability density function is optimized based on shape data of a plurality of existing lenses, and a new lens is added to the obtained optimized probability density function. A characteristic probability density function for the lens shape of a new lens is created by applying the shape data of the lens, and a sudden frequency shift in the processed surface of the new lens is analyzed based on the characteristic probability density function. To analyze the processed surface shape of the lens.
2. The probability density function has a predetermined parameter, and the predetermined probability density function is optimized by obtaining a maximum likelihood estimator of the parameter using shape data of a plurality of existing lenses as a variable. 4. A method for analyzing a processed surface shape of a lens according to 1.
The parameter is defined by one or a plurality of lens conditions set for each of a plurality of existing lenses and a coefficient given to the lens condition, and a maximum likelihood estimation of the parameter is obtained by obtaining a maximum likelihood estimator of the coefficient. 3. The method of analyzing a processed surface shape of a lens according to claim 2, wherein the quantity is calculated, and the intrinsic probability density function is set using the calculated parameter.
4. The integral processing is performed on the lens shape data within a predetermined range in an intrinsic probability density function, and the processing surface of the lens is analyzed based on the integration value. Method for analyzing the processed surface shape of lenses.
The shape data of the lens is a processing state point given to each lens according to a processing state of the processing surface of the lens, and the processing surface shape of the lens according to any one of claims 1 to 4. Analysis method.
The lens shape data analysis method according to claim 1, wherein the lens shape data is an inset value.
6. The method for analyzing a processed surface shape of a lens according to claim 1, wherein the following function is used as a probability density function.

  An analysis program for executing the lens analysis method according to claim 1.