JP5009840B2 - Optical device design support method and recording medium - Google Patents

Description

  The present invention relates to a design support technology for an optical device such as an optical writing unit installed in an electrophotographic image forming apparatus such as a copying machine or a laser printer, and in particular, reduces the influence of mechanical behavior on optical performance. Optical equipment design support method and optical equipment design support program that can perform optimal optical structure using optical path analysis and mechanical system analysis methods, taking into account deformation of optical components used It relates to the medium.

In general, it is necessary to design an optical device such as an optical writing unit provided in a copying machine or a laser printer in consideration of the influence of the mechanical behavior of the optical device on the optical performance. In the case of the optical writing unit, for example, deformation of the housing, vibration, etc. can be cited as factors that cause spot position deviation, and it is necessary to design the entire unit and each optical device constituting the unit so as not to be affected by the influence. For this purpose, it is necessary to verify in advance how much the spot position is shifted when a factor causing positional deviation occurs in the entire unit.
The invention of Patent Document 1 creates a mechanical system analysis model of an optical instrument, an optical system analysis model, and initial values of mechanical characteristic parameters, and substitutes the initial values of the mechanical characteristic parameters into the mechanical system analysis model to deform the optical component. Calculate the optical performance when the optical component is deformed using the optical system analysis model, compare with the optical performance at rest calculated in advance, and determine whether the difference is within the allowable value . If the value is not within the allowable value, obtain the change in optical performance, perform the optimization calculation based on the result, perform the optimization calculation of the mechanical property parameter, and obtain the value of the mechanical property parameter by the optimization calculation. The process of changing to is repeated until it falls within the allowable value.

In addition, the invention of Patent Document 2 actually measures the frequency and amplitude of an optical component in order to analyze the influence of the vibration of the optical component constituting the optical device on the performance of the optical device. A finite element method simulation model is created based on the vibration frequency and amplitude information, and the calculated simulation model is used to calculate the vibration. The deformation state of the calculated optical component due to vibration is unique to the three-dimensional space. The shape function is approximated by a shape function capable of expressing the shape (curved surface fitting), and the characteristics related to the performance of the optical apparatus are calculated based on the shape function. In the curved surface fitting, a shape function is expressed by a polynomial of spatial variables x, y, and z, and each coefficient of the polynomial is obtained by a least square method from a deformation state discretely calculated by a simulation model, and curved surface fitting is performed.
Further, in the invention of Patent Document 3, the shape of the optical system designed based on the design formula by the optical design tool is input to the deformation analysis tool, the mechanical or thermal behavior is examined, and a more optimal optical is determined from the deformation method. When searching for the shape of a system, in modeling a deformation analysis tool, a coarsely generated model is corrected based on a design formula, and a simulation result is obtained by numerically analyzing the corrected model.
Japanese Patent No. 3788674 Japanese Patent No. 3595775 JP 2005-172545 A

However, the conventional method for fitting an optical surface has the following problems. That is, in Patent Documents 1 and 2, in order to accurately predict the optical performance by fitting the optical surface of the numerical model calculated in the vibration analysis process to a curved surface and using the fitting surface directly in the optical calculation process, the fitting surface The accuracy of is important. For this reason, in the numerical model in the vibration analysis process, there is a problem that the surface corresponding to the optical surface must be positioned with sufficient accuracy so as to be an actual optical surface.
Moreover, in patent documents 1-3, the calculation result data in a vibration analysis process become enormous. For example, the finite element analysis model needs a large number of nodes. For this reason, if the position information of each node after a predetermined time is recorded, the data becomes enormous. In addition, since position information of nodes that are not important for vibration analysis is required, there is a problem that the time required for calculation in the vibration analysis process becomes enormous.
Further, in Patent Documents 1 to 3, the absolute position including both the shape of the optical surface (mm order) and the deformation amount (nm order) is detected. There is a problem that the calculation is easily affected by rounding errors.
An object of the present invention is to provide a design support method for an optical apparatus that can solve the above-described problems.

In order to solve the above problems, the invention described in claim 1 includes a mechanical system analysis model of an optical device to be analyzed, an optical system analysis model, and a storage means for storing a mechanical characteristic parameter used for the mechanical system analysis. And a computer including the mechanical system analysis model, the optical system analysis model, and the mechanical processing parameters appropriately read out from the storage device and performing arithmetic processing, the optical characteristic analysis and the mechanical system analysis of the mechanical characteristics parameters of the optical device. A design support method for an optical device that is calculated and analyzed by the calculation method, wherein the arithmetic processing unit calculates a mechanical behavior state of an optical component by substituting a mechanical characteristic parameter into a mechanical system analysis model of the optical device. a behavior state calculation processing, the arithmetic processing means, based on the results of the mechanical behavior state calculation processing, the optical component of the machine by using an optical system analysis model And optical performance calculation process for analyzing the optical performance of Behavior, said arithmetic processing means, the mechanical behavior state calculated by the mechanical behavior state calculation processing, to extract the spatial distortion characteristics of the optical component, An optical component mechanical behavior state calculation process for calculating a mechanical behavior state of the optical component from the optical component at rest and the spatial distortion characteristic.
According to a second aspect of the present invention, in the optical device design support method according to the first aspect, the optical component mechanical behavior state calculation process represents the spatial distortion characteristic by a mapping transformation function, and the mechanical behavior state A parameter in the mapping transformation function is extracted from the mechanical behavior state calculated by the calculation process.
According to a third aspect of the present invention, in the optical apparatus design support method according to the second aspect, a mechanical behavior state used when extracting a parameter in the mapping transformation function is limited to a part of the optical component. It is characterized by that.

According to a fourth aspect of the present invention, in the optical apparatus design support method according to the third aspect, the mechanical behavior of a part of the optical component used when extracting the parameter in the mapping transformation function is an optical characteristic. It is characterized by using a part limited to the part related to.
According to a fifth aspect of the present invention, in the optical apparatus design support method according to the fourth aspect, the portion related to the optical characteristic is a mirror surface of the optical component.
According to a sixth aspect of the present invention, in the design support method for an optical device according to the fourth aspect, the portion related to the optical characteristics is a lens surface of the optical component and a part of the lens of the optical component. It is characterized by.
The invention according to claim 7 is the design support method for an optical apparatus according to claim 2, wherein the optical performance calculation processing is performed by the mapping transformation function and the mapping transformation function parameter at each time, or the mapping transformation function. The optical performance at the time of mechanical hand behavior of the optical component is analyzed using only the parameters.
According to an eighth aspect of the present invention, in the design support method for an optical apparatus according to the first aspect, the spatial distortion characteristic is calculated before the optical performance calculation process.
The invention described in claim 9 is a computer-readable recording medium having recorded thereon a program for causing a computer to execute the method according to any one of claims 1 to 8.

According to the present invention, the mechanical behavior of the optical surface is expressed by the shape before deformation and the spatial distortion characteristic obtained from the mechanical behavior state. Therefore, if the mechanical behavior can be sufficiently analyzed, the optical performance can be analyzed with high accuracy even if the shape corresponding to the optical surface of the mechanical system analysis model does not conform to the optical surface.
In addition, since the mechanical behavior can be expressed only by the parameters used for expressing the spatial distortion characteristics, the number of data can be reduced.
Furthermore, because the mechanical behavior related to the required optical characteristics is limited, spatial distortion characteristics can be extracted without affecting the behavior of some unimportant optical components, and analysis accuracy can be improved and the number of data can be reduced. Become.

Hereinafter, embodiments of the present invention will be described in detail.
[First Embodiment]
FIG. 1 is an operation flowchart showing a first embodiment of the present invention. In this embodiment, initial setting is performed first (S1). In this initial setting, the mechanical system analysis model of the target optical device, the optical system analysis model, and initial values of the mechanical property parameters used for the mechanical system analysis are created, and these data are stored in a personal computer (hereinafter referred to as a processing means). Are stored in a hard disk device (hereinafter referred to as HDD) as storage means managed by PC. Then, the following processing is executed by the PC. Note that the PC has a program for appropriately reading out a mechanical system analysis model, an optical system analysis model, and mechanical characteristic parameters from the HDD and performing arithmetic processing, and performs various operations according to the program. This program is supplied in a state of being recorded on a computer-readable recording medium such as a floppy (registered trademark) disk or an optical disk, and the PC reads the program data from the recording medium and stores it on the HDD or the like.
First, the deformation state of the optical component is calculated by substituting the initial value of the mechanical characteristic parameter into the mechanical system analysis model (S2, mechanical behavior state calculation process). Next, based on the processing result of S2, it is assumed that the space is distorted from the original shape to the deformed state based on the result of calculating the deformed state of the surface that affects the optical path such as the mirror surface and lens surface of the optical component. Find the spatial distortion from to the deformed state. Further, a deformation state of a surface that affects an optical path such as a mirror surface or a lens surface of the optical component is obtained from the optical surface and spatial distortion (S3, optical component mechanical behavior state calculation process). Next, the optical performance when the optical component is deformed is calculated using the optical system analysis model reflecting this (S4, optical performance calculation processing).

As a specific example, a case where the optical performance of the writing unit is analyzed will be described.
FIG. 2 conceptually shows the main part of the writing unit and the photosensitive member. On the housing 101 of the writing unit 100, a polygon mirror 102, lenses 103A and 103B, mirrors 103C and 103D, and a polygon mirror 102 are provided. Each polygon motor 104 to be driven is disposed at a predetermined position. In the writing unit 100 as described above, the housing 101 vibrates due to the vibration force of the polygon motor 104, thereby causing a problem that the spot position P of the laser beam L irradiated onto the photosensitive member 200 is shifted. First, the housing 101, the optical component 103, and the like are converted into a finite element analysis model. Then, the optical path until the laser beam L emitted from the laser light source S reaches the spot position P through each optical component 103 is modeled for an optical path analysis program (optical performance calculation program). Next, the deformation state of the optical component 103 or the like is calculated by finite element analysis (corresponding to S2 in FIG. 1).
From this result, a mapping conversion function (spatial distortion) is obtained based on the pre-deformation shape and deformation state of the optical surface such as the optical component 103 (corresponding to S3 in FIG. 1). Information that affects the optical path of the laser beam L, such as the angle of the laser beam L emitted from the laser light source S, the deformation state of the surface that affects the optical path such as the mirror surface and lens surface of the optical component 103, is reflected in the optical path analysis program. . Specifically, this optical path analysis program is used to determine the position of the deformed state, the normal vector at that position, etc. using the mapping transformation function for any point on the optical surface required during the calculation, and the spot The position Pf is obtained (corresponding to S4 in FIG. 1). As described above, the direction / variation amount in which the spot position P of the laser beam L irradiated onto the photosensitive member 200 is shifted is obtained.

Next, the case where the deformation state of the optical surface is obtained from the spatial distortion will be described. Based on the finite element analysis model 300 of the pre-deformation shape of the optical surface shown in FIG. 3, using the result of obtaining the deformation state 301 of FIG. 4, the spatial distortion 302 ( (Conceptual diagram) is extracted. Based on this spatial distortion 302 (FIG. 6) and the pre-deformation optical surface 303 in FIG. 7, the deformation state 304 (FIG. 8) of the optical surface is obtained.
The above explanation is an example in the case of obtaining the deformation state of the optical surface, but when dealing with the optical path passing through the inside of the optical component such as a lens, the optical path analysis considering the optical characteristics of the distortion state inside the optical component is required. There is a case. In this case, the deformation state of the object for which the spatial distortion is obtained is taken into consideration inside the lens.
Focusing on optical characteristics important for ray tracing, spatial distortion may be extracted using a deformed state limited to an optical surface necessary for optical path analysis or the inside thereof. For example, in the case of the lens 400 shown in FIG. 9, spatial distortion may be extracted by limiting to the optical surface 401 related to the optical path important for optical path analysis excluding the fastening portion 403 and the inside 402 (white part).

ここで、Ｔは多項近似式の係数マトリックスである。有限要素解析モデル・光学面の節点がｍ個あった場合、式（１）、式（２）から式（３）を導出できる。

・・・（３）
多項近似式係数Ｔを求めるためには、式（３）に例えば、ガウスの消去法等の計算アルゴリズムを用いればよい。
なお、第１の実施形態では光学部品の変形状態を、有限要素解析を例に説明したが、光学部品の変形状態の解析方法はこれに限られるものではない。
例えば、機械特性を離散的に近似して解析するシミュレーション解析、光学面の各個所の振動を計測した実験データ、また、振動特性（固有振動数、減衰比、モードシェイプ）をモーダル解析により求め、動的挙動を予測する時間応答計算結果（参考文献：機械のモーダル・アナリシス、大久保信行著、中央大学出版、Ｐ１１５）、モード合成法（同Ｐ１３７）、および有限要素解析と連成した解析手法（同Ｐ１５８）等を用いることが可能である。また、シミュレーション解析に使用する機械特性パラメータは経験値、および実験により抽出した値を用いてもよい。空間歪みを表現する方法として写像変換関数に多項近似式の具体例を上げたが、区間毎に多項近似式を当てはめる方法（例：スプライン関数）、モーフィング手法等、変形前形状を基に変形状態へ到る関係を表現可能な関数、手法であれば具体例に限るもではない。 Next, as a specific example, the case of obtaining spatial distortion will be described. Spatial distortion is expressed by a mapping transformation function. Specifically, using the equation (1), the coordinates x, y, z before deformation of the optical surface are put into the mapping transformation function f, and the coordinates x ′, y ′, z ′ in the deformed state are obtained. When an nth-order polynomial approximate expression is used for the mapping conversion function, the mapping conversion function f is expressed by Expression (2).

Here, T is a coefficient matrix of a polynomial approximate expression. When there are m nodes of the finite element analysis model / optical surface, Expression (3) can be derived from Expression (1) and Expression (2).

... (3)
In order to obtain the polynomial approximate expression coefficient T, for example, a calculation algorithm such as Gaussian elimination may be used in Expression (3).
In the first embodiment, the deformation state of the optical component has been described by taking finite element analysis as an example. However, the analysis method of the deformation state of the optical component is not limited to this.
For example, simulation analysis that analyzes by approximating mechanical characteristics discretely, experimental data that measures the vibration of each part of the optical surface, and vibration characteristics (natural frequency, damping ratio, mode shape) are obtained by modal analysis, Time response calculation results to predict dynamic behavior (Reference: Machine modal analysis, Nobuyuki Okubo, Chuo University Press, P115), mode synthesis method (P137), and analysis method coupled with finite element analysis ( P158) and the like can be used. Further, as a mechanical characteristic parameter used for the simulation analysis, an empirical value or a value extracted by experiment may be used. Specific examples of polynomial approximations have been given to mapping transformation functions as a method for expressing spatial distortion. However, deformation states based on pre-deformation shapes, such as methods of applying polynomial approximations to sections (eg, spline functions), morphing methods, etc. It is not limited to a specific example as long as it is a function or method capable of expressing the relation to the end.

また、実施例では光学部品の機械的挙動状態を算出するときに用いる変形前形状の光学面を用いたが、光学面を定義するときに使用する光学式を用いても良い。
以上のように第１の実施形態では、光学面をフィッティングするのではなく、その空間の歪み情報を抽出し、静止時の正確な光学面をこの歪み情報で変形させ、その変形面を光学性能評価計算に用いるようにした。つまり、光学面の機械的挙動を、変形前の形状と、機械的挙動状態から求めた空間歪み特性で表現するようにした。このため、機械的挙動を十分解析できれば、機械系解析モデルの光学面相当の形状が光学面に則していなくとも、光学的性能を精度よく解析することができる。
また、空間歪み特性を表現するために用いたパラメータのみで機械的挙動を表現できるため、データ数を低減することができる。また、必要な光学特性に関わる機械的挙動を限定しているため、重要ではない一部の光学部品挙動に影響されることなく空間歪み特性を抽出でき、解析精度の向上およびデータ数の低減が可能となる。 Further, although the target of the mapping transformation function is x, y, z space, the coordinates may be limited as long as sufficient accuracy can be obtained by the optical performance calculation process. For example, the x coordinate component (optical axis) If sufficient accuracy can be obtained only with the deformed state (direction, etc.), the mapping transformation function f may be obtained by using Equation (4).

In the embodiment, the pre-deformation-shaped optical surface used when calculating the mechanical behavior state of the optical component is used. However, an optical system used when defining the optical surface may be used.
As described above, in the first embodiment, rather than fitting an optical surface, the distortion information of the space is extracted, the accurate optical surface at rest is deformed with this distortion information, and the deformation surface is optical performance. It was used for evaluation calculation. In other words, the mechanical behavior of the optical surface is expressed by the shape before deformation and the spatial distortion characteristics obtained from the mechanical behavior state. Therefore, if the mechanical behavior can be sufficiently analyzed, the optical performance can be analyzed with high accuracy even if the shape corresponding to the optical surface of the mechanical system analysis model does not conform to the optical surface.
In addition, since the mechanical behavior can be expressed only by the parameters used for expressing the spatial distortion characteristics, the number of data can be reduced. In addition, since the mechanical behavior related to the required optical characteristics is limited, spatial distortion characteristics can be extracted without being affected by the behavior of some unimportant optical components, improving analysis accuracy and reducing the number of data. It becomes possible.

[Second Embodiment]
The mechanical behavior of each optical surface is changed over time, the type of mathematical expression used in the mapping conversion function, such as a polynomial approximation, is selected, and the coefficient is obtained by the method calculated in the first embodiment. In the optical performance calculation process, the optical surface mechanical behavior is set in the same manner as in the first embodiment by using the type and coefficient of the polynomial approximation formula.
As described above, the optical performance for each time, for example, the direction / variation amount in which the spot position P of the laser beam L irradiated onto the photoreceptor 200 is shifted is obtained. When the mapping conversion function is fixed to one in all time zones, the mapping performance is set in advance in the optical performance calculation process, and the optical performance is obtained by setting only the coefficient for each time. Can do. Note that the type and coefficient of the mapping conversion function are selected and extracted in advance before the optical performance calculation process, the type and coefficient of the mapping conversion function are stored, and the optical performance calculation process is performed. At this time, the formula type and coefficient for each time may be called to calculate the optical characteristics.
As described above, in the second embodiment, the mapping conversion function and the coefficient of the mapping conversion function or the parameter of only the coefficient of the mapping conversion function are handled at each time, so that data can be used for evaluating the optical performance at each time. The number can be reduced. In addition, by calculating the spatial distortion characteristics before calculating in the optical performance calculation process, it is possible to efficiently calculate the optical performance particularly at each time.

It is an operation | movement flowchart which shows the 1st Embodiment of this invention. FIG. 2 is a diagram conceptually showing a main part of a writing unit and a photoconductor. It is a figure which shows the finite element analysis model of the shape before a deformation | transformation of an optical surface. It is a figure which shows the finite element analysis model of the shape after a deformation | transformation of an optical surface. It is a conceptual diagram of the spatial distortion from the shape before deformation of the optical surface to the deformation state. It is a conceptual diagram of spatial distortion. It is a figure which shows the optical surface before a deformation | transformation. It is a figure which shows the optical surface after a deformation | transformation. It is the figure which showed the part in connection with an optical path important for an optical path analysis.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 100 ... Writing unit 101 ... Housing 102 ... Polygon mirror 103 ... Optical part 103A, 103B ... Lens, 103C, 103D ... Mirror 104 ... Polygon motor 200 ... Photoconductor 300 ... Finite element analysis model 301 ... Deformed state, 302 ... Spatial distortion, 303 ... Pre-deformation optical surface, 304 ... Deformed state of optical surface, 400 ... Lens, 401 ... Optical surface, 402 ... Inside, 403 ... Fastening part

Claims (9)

A mechanical system analysis model of the optical device to be analyzed, an optical system analysis model, and a storage means for storing a mechanical characteristic parameter used for the mechanical system analysis; from the storage means, the mechanical system analysis model, the optical system analysis model, and A computer including an arithmetic processing unit that appropriately reads out mechanical characteristic parameters and performs arithmetic processing is a design support method for optical equipment that calculates and analyzes mechanical characteristic parameters of optical equipment by optical path analysis and mechanical system analysis,
The arithmetic processing means substitutes a mechanical characteristic parameter into a mechanical system analysis model of the optical device to calculate a mechanical behavior state of an optical component, and a mechanical behavior state calculation process;
The arithmetic processing means , based on the result of the mechanical behavior state calculation process, an optical performance calculation process for analyzing the optical performance at the time of the mechanical behavior of the optical component using an optical system analysis model;
The arithmetic processing means extracts the spatial distortion characteristic of the optical component from the mechanical behavior state calculated by the mechanical behavior state calculation process, and the optical component machine from the optical component at rest and the spatial distortion characteristic Optical component mechanical behavior state calculation processing for calculating a dynamic behavior state;
A design support method for an optical apparatus, comprising:   The optical component mechanical behavior state calculation process represents the spatial distortion characteristic by a mapping transformation function, and extracts parameters in the mapping transformation function from the mechanical behavior state calculated by the mechanical behavior state calculation processing. The optical apparatus design support method according to claim 1.   3. The design support method for an optical apparatus according to claim 2, wherein a mechanical behavior state used when extracting a parameter in the mapping transformation function is limited to a part of the optical component.   4. The optical apparatus according to claim 3, wherein the mechanical behavior of a part of the optical component used when extracting the parameter in the mapping function is limited to a part related to optical characteristics. Design support method.   5. The method of supporting design of an optical apparatus according to claim 4, wherein the part related to the optical characteristic is a mirror surface of the optical component.   5. The optical apparatus design support method according to claim 4, wherein the part related to the optical characteristic is a lens surface of the optical component and a part of the lens of the optical component.   The optical performance calculation processing includes analyzing the optical performance at the time of mechanical hand movement of the optical component using only the mapping conversion function and the mapping conversion function parameter at each time or the mapping conversion function parameter. The method for supporting the design of an optical apparatus according to claim 2, wherein:   2. The design support method for an optical apparatus according to claim 1, wherein the spatial distortion characteristic is calculated before performing the optical performance calculation process.   A computer-readable recording medium having recorded thereon a program for causing a computer to execute the method according to claim 1.

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