JP2001318025A - Method and device for evaluating shape of lens face - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a shape evaluating method applicable for an optional lens face and having high correletion with an optical characteristic, by estimating the optical characteristic based on a shape-measured result, and by evaluating lens performance based thereon. SOLUTION: This method is constituted of a shape measuring process for measuring a contour shape of a measured subject, a shape error extracting process for finding a shape error of a deviation deviated from a design shape, a partial curvature finding process for finding a partial curvature in a each lens height based on the shape error, and a focal point shifting amount estimating process for finding a curvature proportional constant of an optical-axis-directional focal point shifting amount in an image plane per a unit curvature in the each lens height, to estimate the focal point shifting amount based thereon and the partial curvature. The shape error extracting process is constituted of an attaching error correcting process for finding the deviation from the design shape after translational-rotational coordinate transformation is conducted for all or partial coordinate data, so as to find the optimum values of translational values and rotational angles in the all or the partial to minimize a square-sum thereof, and a design shape separation process for finding a difference. form the design shape after the optimized translational and rotational transformation are conducted.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for evaluating the shape of a lens.
It is effective for use in evaluating plastic lenses.

[0002]

2. Description of the Related Art In recent years, an optical element having an aspherical shape has been used as an optical component in an optical writing device used for digital copying or a laser printer. The following is an example of the aspherical expression.

(Equation 1) Where h is the lens height, C is the paraxial curvature, k is the conic constant,
e _i is the coefficient of the polynomial. Such an optical element is realized mainly by a plastic lens manufactured by injection molding.

FIG. 4 shows an optical writing device that has been conventionally used. In brief, the configuration is such that a light beam emitted from a semiconductor laser 1 is transmitted through a collimator lens 2 and irradiated on a polygon motor 3.
The light flux reflected and deflected depending on the rotation angle of the polygon motor passes through the scanning lens 4 and is collected near the image plane 5.

The effective range of the scanning lens surface used in such an apparatus is several tens mm to several hundred mm in the deflection direction of the polygon motor (hereinafter, main scanning direction), while it is perpendicular to this direction (hereinafter, sub scanning direction). In the scanning direction), the distance is about 10 mm. When such a lens is manufactured by injection molding of plastic, a deviation from a design value due to the influence of uneven shrinkage of the resin (hereinafter referred to as “shape error”) occurs. Therefore, it is important to evaluate the shape error. The method is to measure the profile of the surface (generating line) passing through the design origin in the longitudinal direction using a stylus-type profile shape measuring device. Generally, the shape error is evaluated. As a shape measuring device, for example, Rank Taylo
r FORM TALYSURF by Hobson is known.

[0005] To evaluate whether the shape error is sufficiently small, see JP-A-6-129944 and JP-A-7-3930.
No. 5541, that is, one in which the paraxial radius of curvature of the aspheric surface is optimized so as to minimize the sum of squares of the shape error (hereinafter, best fit R), A method is known in which a difference from a spherical equation (hereinafter, a shape error) is used as an evaluation parameter. However, as the amount of aspherical surface, which is the difference between the design shape and the spherical surface, increases, the correlation between the evaluation parameters of the best fit R and the shape error and the optical performance decreases, and the performance is rejected by optical simulation or the like. When the tolerances are assigned so as not to be inconsistent, there is a problem that even if the shape evaluation is rejected, some optical characteristics pass.

[0006] On the other hand, Japanese Patent Application Laid-Open No. Hei 9-1997 discloses an example in which an evaluation parameter having a higher correlation with optical characteristics is proposed.
There is one described in JP 89713. This finds the second derivative of the approximation function of the shape error, the second derivative by the difference between adjacent coordinate data, and the difference between these two values, and attempts to guarantee the lens performance by keeping the difference within a specific range. Things. However, this method merely shows empirically that the correlation with the optical characteristics is higher than that of the conventional method, based on actual production examples, and how effective is it for lens surfaces other than the production examples. There is a problem that is unknown.

[0007]

Accordingly, the present invention estimates the optical characteristics from the shape measurement results and evaluates the lens performance based on the results, so that the present invention can be applied to an arbitrary lens surface and the correlation with the optical characteristics can be obtained. It is an object of the present invention to provide a shape evaluation method with high quality.

[0008]

Means taken to solve the problem include a shape measuring step for measuring the contour shape of the object to be measured and a shape error extracting step for obtaining a shape error which is a deviation from the design shape. And a partial curvature derivation process of obtaining a partial curvature at each lens height from the shape error, and a curvature proportionality coefficient which is a defocus amount in an optical axis direction on an image plane per unit curvature at each lens height, and It is configured to include a defocus amount estimation step of estimating the defocus amount from the partial curvature. Further, after the shape error extraction process performs translation and rotation coordinate conversion on all or a part of the coordinate data, a deviation from the design shape is obtained, and a part or all of the translation is performed so as to minimize the sum of squares. It is configured to include a mounting error correction process for obtaining the optimal values of the amount and the rotation angle, and a design shape separation process for obtaining the difference from the design shape after the optimized translation and rotation conversion. In addition, the partial curvature derivation process is configured to divide the shape error data and obtain a curvature when each divided data is least-squares approximated to a spherical surface. In addition, the partial curvature derivation process divides the shape error data, performs a least square approximation of each divided data to a polynomial, and calculates the square
The double was configured to be a partial curvature. Further, the partial curvature derivation process approximates the shape error to a polynomial, and obtains the value of the second derivative. Further, the defocus amount estimation process obtains the defocus amount in the optical axis direction on the image plane corresponding to the lens height when the sample shape error is superimposed only on the target lens surface with respect to the lens surface design value by optical simulation, Find the partial curvature of the sample shape error, find the partial curvature proportional coefficient that is the amount of defocus per unit curvature corresponding to each lens height, approximate the relationship as a function and save each parameter A partial curvature proportionality coefficient is obtained by solving an approximation function using the stored parameters, and an image plane defocus amount derivation process of deriving a defocus curve on an image plane using the obtained coefficient is configured. In addition, the defocus amount estimation process optically calculates the image height corresponding to the lens height when the sample shape error is superimposed only on the target lens surface with respect to the lens surface design value, and the defocus amount in the optical axis direction on the image surface. Calculated by simulation, approximating the relationship between lens height and image height as a function and storing each parameter, and calculating partial curvature of sample shape error, partial curvature proportional to the amount of defocus per unit curvature at each lens height Finding the coefficients, the function of approximating the relationship with the lens height and saving each parameter is defocus estimation preparation process, and the image height and partial curvature proportional coefficient are found by solving the approximation function using the saved parameters, An image plane defocus amount deriving process for deriving a defocus curve on the image plane using this is configured. Also, the sample shape error is
The shape was spherical. The sample shape error was defined as a parabolic shape. Further, the process of approximating the relationship between the image height of the first surface of the lens to be evaluated and the defocus amount by a model formula, and the process of approximating the relationship between the image height of the second surface of the lens and the defocus amount by a model formula. It is configured to include a process and a process of obtaining the total defocus amount of the lens by calculating the sum of these two model expressions. A shape measuring means for measuring a contour shape of the object to be measured; a shape error extracting means for obtaining a shape error by subtracting a design shape from the measured shape; and a part for deriving partial curvatures at a plurality of lens heights from the shape error. A curvature deriving unit and a defocus amount estimating unit that obtains a proportional coefficient of a defocus amount on an image plane per unit curvature at each lens height, and derives a defocus amount at each lens height from this and a partial curvature. Configured.

According to the above arrangement, since the amount of defocus can be estimated from the shape error, the correlation between the shape evaluation result and the optical performance increases. This enables highly accurate lens evaluation and can be applied to various types of lens evaluation. In addition, by correcting an error at the time of mounting the device under test to the jig, it is possible to perform evaluation with higher reproducibility. In addition, the contour shape measurement data is separated into partial data having the same length as the diameter of the approximate light beam, and the curvature is obtained. Evaluation becomes possible. In addition, since the approximation is made to a second-order polynomial, the evaluation can be performed in a shorter time than the spherical approximation. Further, by approximating the shape error to a polynomial, it is possible to reduce the influence of abnormal data in which coordinates due to minute dust or the like on the surface of the object to be measured at the time of shape measurement locally vary greatly. In addition, the proportionality coefficient of the defocus on the image plane per unit curvature is obtained in advance by an optical simulation, and the relationship with the lens height is approximated and stored as an appropriate function, so that the proportionality coefficient at an arbitrary lens height can be calculated. This can be easily obtained, and the evaluation can be performed in less time. In addition, since the relationship between the image height and the amount of defocus on the image plane is obtained, by comparing this with the measurement result of the optical performance of the actual lens, it is possible to examine the evaluation accuracy, correct the proportionality coefficient, etc. it can. Further, if a spherical surface or a parabola is used as the sample shape error, the process of evaluating the curvature of the sample shape can be shortened. Also, by adding the defocus of the first surface and the second surface of the lens, the overall accuracy of the lens itself can be evaluated. For this reason, even if the lens does not fall within the tolerance as a single surface due to the influence of the warpage of the lens or the like, it is possible to perform appropriate comprehensive evaluation such as when the overall accuracy falls within the tolerance.

[0009]

The embodiment of the present invention uses the fact that the amount of defocus in the optical axis direction on the image plane at each lens height of the design shape is approximately proportional to the partial curvature of the shape error of the lens surface near the design shape. Then, a deviation from the design shape is obtained from the measurement result of the contour shape of the object to be measured, the partial curvature is obtained, the amount of focal position shift at an arbitrary lens height is estimated, and the lens is evaluated based on this.

In describing in more detail, first,
A case where all lenses have the ideal shape will be described. At an arbitrary time, depending on the rotation angle of the polygon motor, when a light beam passes through a part of the effective area of the lens at a specific position of each lens, it focuses on a fixed position near the image plane. This can be considered that the optical systems at any time are independent of each other. That is, the focal length and the like of the optical system can be obtained for each lens, and all the lens surfaces are smoothly connected, so that it is considered that the optical characteristics such as the focal length are also smoothly connected. Here, even if the lens is in the ideal state, the focal position at an arbitrary time is accurately shifted from the image plane, but this time, in the ideal state when a slight shape error is added to the ideally shaped lens. In order to consider the amount of deviation from the focal position, this effect is separately considered.

Next, a case where a lens to be evaluated has a shape error will be described. At any time, the shape error is sufficiently small with respect to the design shape, so that the influence of the shape error in the light beam at any time on the optical characteristics is within a range that can be approximated by paraxial theory. Here, in the current scanning optical system, the defocus due to the influence of the shape error,
It has been confirmed by the results of optical simulations that the yield is a bottleneck in the manufacturing process, and that the main factor is the influence of the variation of the partial curvature. Therefore, in this embodiment, the amount of defocus on the image plane due to the influence of the variation of the partial curvature due to the shape error is estimated.

The effect of a shape error before and after an arbitrary lens surface will be considered using Snell's formula. First, Snell's equation in an ideal state is as follows.

(Equation 2) The s the object side imaging position, s _d'image side imaging position, n represents the object-side refractive index, n'the image side refractive index, C _d is the curvature of the lens surface. Then, when the curvature becomes C _r varies by as shape errors in FIG. 1, the image-side focal position s _r'optical contained shape error system is as follows.

[Equation 3] The focal position change _{Δs ′} on the image side is as follows

(Equation 4)

Here, the curvature error ΔC is the curvature C at the design value.
_Since it is sufficiently smaller than _d , the focus variation _{Δs ′} is smaller than the focal length s ′ and is approximately expressed.

(Equation 5) Assuming that the lens system following this lens surface has the designed value, the magnification is also constant, so that the defocus amount on the image surface is also proportional to the curvature error. This proportional coefficient is a constant depending on the design value shape.

Therefore, by calculating the proportional coefficient, which is the amount of defocus on the image plane per unit curvature at an arbitrary lens height, and the curvature error at an arbitrary lens height on each lens surface, the defocus on the image surface is obtained. The amount can be estimated. FIG. 2 shows a processing procedure of the measurement data.

The shape measurement result is output as point sequence data. That is, each point is output as coordinate data in a coordinate system depending on the measuring machine. Here, in order to separate the design shape component from the measurement data, the measurement coordinate system and the coordinate system at the time of designing each lens need to be the same. However, there are problems such as the mounting accuracy of the object to be measured at the time of measurement, and the two cannot be exactly the same. Therefore, coordinate conversion is required to represent the point sequence of the measurement coordinate system in the coordinate system at the time of design. In addition, since this coordinate conversion matrix cannot be directly obtained, it is substituted by converting to a coordinate system having the “minimum error”. This can be realized by optimizing the coordinate transformation matrix so as to minimize the shape error. 2
In the case of dimensional data, the coordinate transformation matrix is a shift s in the optical axis direction.
Optimization of at least two degrees of freedom of sy and θ among three degrees of freedom of x and a shift sy in a direction orthogonal thereto and a rotation angle θ is performed. The actual mounting error correction method is realized by, for example, performing three-dimensional optimization using the sum of squares of the shape error after coordinate conversion as an evaluation function.

As a method of obtaining the partial curvature from the shape error, first, the shape error data is separated into a plurality of point sequences. The length of each partial point sequence in the y-axis direction is preferably near the width of the light beam. Then, each partial point sequence is least-squares-approximately approximated to a spherical surface, and its curvature is obtained. The approximate spherical equation is shown below.

(Equation 6) Here, (x0, y0) is the coordinates of the vertices of the spherical surface, and c is the curvature of the spherical surface. As an actual calculation method, c is obtained by optimizing these parameters by a nonlinear least squares method.

Next, another method for obtaining the partial curvature from the shape error will be described. First, the shape error data is separated into a plurality of point sequences. The length of each partial point sequence in the y-axis direction is preferably near the width of the light beam. Then, each partial point sequence is least-squares approximated to a quadratic polynomial, and a value obtained by doubling the square term is defined as a curvature. As an actual operation method, a linear least square method such as a singular value decomposition method is used.

As still another method for obtaining the partial curvature from the shape error, first, the shape error data is approximated to a polynomial of an appropriate order, and the coefficient of each term is obtained. Next, each coefficient of the second derivative of the approximate polynomial is obtained. The polynomial and its 2
Here is the expression for the first derivative.

Equation 7 Finally, this is solved for multiple lens heights.

A method for estimating the amount of defocus will be described. First, as a preparation stage, an optical simulation is performed at a plurality of deflector angles with a sample shape error of an appropriate model formula added to the design value of a specific lens surface, and the principal ray at each deflector angle and a specific The lens height in the main scanning direction at the intersection with the lens surface and the amount of deviation from the focal point at the design value on the image plane are determined. In addition, the partial curvature of the polynomial shape error at the same lens height is obtained using the above-described method. At each lens height, the amount of defocus is divided by the partial curvature to obtain a partial curvature proportional coefficient, which is the amount of defocus per unit curvature.
By approximating the relationship between the lens height and the partial curvature proportional coefficient to an appropriate function, for example, a polynomial and storing the parameters, it is possible to obtain the proportional coefficient of the defocus amount corresponding to an arbitrary lens height. . With respect to the measurement result of the actual sample, the partial curvature and the proportional coefficient are obtained at a plurality of lens heights, and these are integrated to estimate the defocus amount. FIG. 3 shows a processing procedure of the measurement data.

Next, another method of estimating the amount of defocus will be described. First, as a preparation stage, an optical simulation is performed at a plurality of deflector angles with a sample shape error of an appropriate model formula added to the design value of a specific lens surface, and the principal ray at each deflector angle and a specific The lens height in the main scanning direction at the intersection with the lens surface, the image height on the image plane, and the deviation from the focal point at the design value are obtained. In addition, the partial curvature of the polynomial shape error at the same lens height is obtained using the above-described method. Next, the relationship between the lens height and the image height is approximated by a model formula, for example, a polynomial, and each parameter is stored. Further, a proportional coefficient which is a defocus amount per unit curvature is obtained by dividing the defocus amount at each lens height by the partial curvature. Then, by approximating this to an appropriate function, for example, a polynomial and storing the parameters, it becomes possible to obtain a proportional coefficient of defocus corresponding to an arbitrary lens height. Furthermore, the relationship between the image height and the amount of defocus is derived from the product of the image height, partial curvature, and the proportionality coefficient at a plurality of lens heights with respect to the measurement results of the actual sample.

When the sample shape error is a spherical surface having a certain curvature, the partial curvature of the shape error becomes the same at an arbitrary lens height, so that it is not necessary to obtain the partial curvature. In this case, a proportional coefficient is derived by dividing the defocus amount by a constant curvature.

When the sample shape error is a parabolic shape, the partial curvature becomes a constant at all lens heights by using the method for obtaining the second derivative among the above methods. Therefore, it is not necessary to obtain the partial curvature of the sample shape error as in the case of a spherical surface.

As a method of evaluating the amount of defocus, the relationship between the image height and the amount of defocus on the image plane is derived, and when this is evaluated, the effects of the first surface and the second surface of the lens are the same. Is evaluated as field curvature, which is the amount of defocus at
By adding this, it is possible to evaluate the amount of defocus of the lens alone.

By connecting a PC or the like having the above processing functions to the shape measuring instrument, the process of shape measurement can be performed by the PC.
It can be realized by the above software.

[0025]

According to the first aspect of the present invention, the amount of defocus can be estimated from the shape error, and the lens evaluation can be performed based on this. As a result, the correlation between the shape evaluation result and the optical performance increases, leading to an improvement in yield, an increase in the tolerance of various parameters during processing, and a reduction in lens production cost. Further, according to the configuration of the second aspect, it is possible to correct an error when the object to be measured is attached to the jig, and it is possible to repeatedly perform evaluation with high reproducibility. Claim 3
According to the configuration, the contour shape measurement data can be separated into partial data having the same length as the diameter of the approximate light beam, the curvature can be obtained for each, and for a shape error localized in a part of the lens surface, Higher precision shape evaluation becomes possible. According to the configuration of the fourth aspect, the approximation to the quadratic polynomial is more stable than the approximation to the spherical surface, and the evaluation can be performed in a shorter time. Further, according to the configuration of the fifth aspect, by approximating the shape error to a polynomial, the influence of abnormal data in which coordinates due to minute dust or the like on the surface of the object to be measured at the time of shape measurement are locally largely fluctuated. Since the size can be reduced, more stable shape evaluation can be performed. Also,
According to the configuration of claim 6, the proportionality coefficient of defocus on the image plane per unit curvature can be obtained in advance by optical simulation, and the relationship with the lens height can be approximated and stored as an appropriate function. The proportional coefficient at the lens height is easily obtained, and the evaluation can be performed in a shorter time. According to the configuration of claim 7, since the relationship between the image height and the defocus amount on the image plane is finally obtained, this is compared with the actual measurement result of the optical performance of the lens.
The evaluation accuracy can be examined, the proportional coefficient can be corrected, and the like. Further, according to the configuration of the eighth aspect, since the spherical shape is used as the sample shape error, the process of evaluating the curvature of the sample shape is shortened. According to the ninth aspect,
Since a parabola is used as the sample shape error, the process of evaluating the curvature of the sample shape is shortened. Although the second-order terms of the polynomial are pre-installed as a part of the aspherical coefficients of the optical simulator, they are not used in many cases, and can be used simply by inserting a numerical value therein. Therefore, it is not necessary to remodel the simulator, and even if necessary, the range of remodeling can be reduced. According to the configuration of claim 10, the total accuracy of the lens itself can be evaluated by adding the defocus of the first surface and the defocus of the second surface of the lens. For example, a lens that does not fall within the tolerance as a single surface may fall within the tolerance with total accuracy due to the influence of the warpage of the lens, for example, but such a lens can be appropriately evaluated. Therefore, the yield is improved. Further, according to the configuration of the eleventh aspect, a shape evaluation device having a high correlation with optical characteristics is realized.

[Brief description of the drawings]

FIG. 1 is a conceptual diagram when an optical system near a light beam corresponding to a certain rotation angle of a polygon motor is taken out.

FIG. 2 is a flowchart of a defocus amount estimation flowchart.

FIG. 3 is a flowchart of another focus position shift amount estimation.

FIG. 4 is a schematic diagram of an optical writing device. Description of reference numerals in FIGS. 1 to 4 1... Semiconductor laser 2... Collimator lens 3... Polygon motor 4. .Scanning lens 5 ...

Claims (11)

[Claims] 1. A shape measurement step for measuring a contour shape of an object to be measured, a shape error extraction step for obtaining a shape error which is a deviation from a design shape, and a partial curvature for obtaining a partial curvature at each lens height from the shape error. A derivation process and a defocus amount estimating process of calculating a curvature proportionality coefficient, which is a defocus amount in the optical axis direction on the image plane per unit curvature at each lens height, and estimating the defocus amount from the partial curvature. A method for evaluating a lens surface shape, characterized in that: 2. The method according to claim 2, wherein the shape error extracting step performs a translation and rotation coordinate conversion on all or a part of the coordinate data, obtains a deviation from the design shape, and minimizes the sum of squares. Alternatively, it is characterized by a mounting error correction process for obtaining an optimum value of all translation amounts and rotation angles, and a design shape separation process for obtaining a difference from a design shape after the optimized translation and rotation conversion. The method for evaluating a lens surface shape according to claim 1. 3. The partial curvature deriving step divides the shape error data and obtains a curvature when each divided data is least square approximated to a spherical surface.
Evaluation method of lens surface shape. 4. The method according to claim 1, wherein the partial curvature deriving step divides the shape error data, performs a least square approximation of each divided data to a polynomial, and sets a double of the square term as a partial curvature. The method for evaluating a lens surface shape according to claim 2. 5. The lens surface shape evaluation method according to claim 1, wherein said partial curvature derivation step approximates a shape error to a polynomial and obtains a value of a second derivative thereof. 6. The defocus amount estimating step includes calculating a defocus amount in an optical axis direction on an image plane corresponding to a lens height when a sample shape error is superimposed only on a target lens surface with respect to a lens surface design value. Calculate by simulation, find the partial curvature of the sample shape error, find the partial curvature proportional coefficient, which is the amount of defocus per unit curvature corresponding to each lens height, and approximate this relationship as a function and save each parameter Estimation preparation process and the partial curvature proportionality coefficient are obtained by solving an approximation function using the stored parameters,
2. An image plane defocus amount deriving step of deriving a defocus curve on an image plane by using this.
6. The method for evaluating a lens surface shape according to claim 5. 7. An image height corresponding to a lens height when a sample shape error is superimposed only on a target lens surface with respect to a lens surface design value, and a focus in an optical axis direction on the image surface. The amount of shift is obtained by optical simulation, the relationship between the lens height and the image height is approximated to a function, and each parameter is stored.The partial curvature of the sample shape error is obtained, and the defocus amount per unit curvature at each lens height is obtained. A defocus estimation preparation step of obtaining a partial curvature proportional coefficient, approximating the relationship with the lens height as a function, and saving each parameter,
Finding the image height and the partial curvature proportionality coefficient by solving an approximation function using the stored parameters, and using this to derive an out-of-focus curve on the image plane, comprises an image plane defocus amount derivation process. Claim 1 to Claim 5
Evaluation method of lens surface shape. 8. The method according to claim 6, wherein the sample shape error is a spherical shape. 9. The method according to claim 6, wherein the sample shape error is a parabolic shape. 10. The process of approximating the relationship between the image height of the first surface of the lens to be evaluated and the defocus amount by a model formula, and the relationship between the image height of the second surface of the lens and the defocus amount by a model formula. 10. The method for evaluating a lens surface shape according to claim 1, comprising a step of approximating by: and a step of calculating a total defocus amount of the lens by calculating a sum of the two model expressions. 11. A shape measuring means for measuring a contour shape of an object to be measured, a shape error extracting means for obtaining a shape error by subtracting a design shape from the measured shape, and a partial curvature at a plurality of lens heights from the shape error. Derived partial curvature deriving means, and a defocus amount estimating means for obtaining a proportional coefficient of defocus amount on an image plane per unit curvature at each lens height, and deriving a defocus amount at each lens height from this and the partial curvature A lens surface shape evaluation apparatus characterized by having: