JP2006153810A - Optical characteristics-analyzing system for optical equipment - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an optical characteristics-analyzing system for quickly verifying influence to optical characteristics due to water absorption of each component composing an optical system, by finding the material characteristics necessary for optical characteristics analysis of an optical component in a short time. <P>SOLUTION: The optical characteristics-analyzing system at least comprises a diffusion constant acquisition means 1 for calculating a diffusion constant of a component material composing the optical system, for which the diffusion constant is unknown, an optical system model generating means 2 for generating a numerical analysis model necessary for numerical analysis by a finite element method, and an optical characteristics-calculating means 3 for calculating the optical characteristics. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a system for analyzing optical characteristics of an apparatus having optical components.

  In designing optical equipment, it is necessary to consider the influence of the installation environment of the optical equipment on the optical characteristics. In particular, when the optical system of an optical device includes plastic parts, the plastic parts have higher water absorption than glass parts, so the optical characteristics of the plastic parts are high in a high humidity environment. It is necessary to verify at the design stage how it changes due to water absorption.

  Therefore, in recent optical equipment design, the optical characteristics are calculated in consideration of the water absorption effect on the optical system obtained by numerical analysis, and it is verified whether the optical characteristics of the optical system design plan meet the design specifications. After that, the optimum mechanical and optical design parameters are determined.

Patent Document 1 discloses an optical characteristic analysis system that simulates changes in characteristics of resin optical elements over time due to water absorption.
JP 2004-012249 A

  In recent years, there has been a demand for shortening the development period of optical equipment products, so the numerical characteristics can be used to verify the optical characteristics of the design proposal before prototyping. It is hoped that.

  However, in the conventional optical property analysis system, the material properties necessary for the analysis model used for the analysis method such as the finite element method analysis must be measured. The measurement itself took time, and it was difficult to shorten the development period.

  In particular, in order to verify the effect of water absorption on the plastic parts that make up the optical system, it is necessary to have a water diffusion constant for each plastics material as a material property. May take more than a month.

  Further, since the diffusion constant has temperature dependence, it is necessary to measure the diffusion constant at a plurality of temperatures. As described above, since it is not possible to take sufficient time to actually measure the diffusion constant within the limited development period, it is difficult to verify the design plan by numerical analysis sufficiently and quickly at present. .

  The present invention has been made in view of the above-mentioned problems, and a problem to be solved is to obtain material characteristics necessary for analyzing optical characteristics of a device having an optical component in a short period of time, and an optical system. It is an object to provide an optical characteristic analysis system capable of quickly verifying the influence of water absorption on each part constituting the optical characteristic on water.

  In order to solve the above-described problem, an optical characteristic analysis system for an optical device according to the present invention provides a molecule of the component material arranged in an arbitrary rectangular parallelepiped region with respect to the component material constituting the optical system whose diffusion constant is unknown. And stable configuration data is read from a stable configuration storage means for storing a stable configuration in which the potential energy between atoms constituting the water molecule is substantially constant, and the motion of the water molecule for a predetermined time is read from the stable configuration by a molecular dynamics method. Diffusion constant acquisition means for calculating a diffusion constant from the displacement amount of the water molecule obtained by analysis and storing it in a diffusion constant storage means, and a numerical analysis model necessary for numerical analysis by the finite element method by dividing the optical system into meshes And the optical system model generation means for storing in the numerical analysis model storage means, the optical under a predetermined humidity environment using the diffusion constant and the numerical analysis model An optical property calculation means for calculating an optical property from a refractive index distribution obtained by calculating a water absorption distribution of the optical system, and a deformed optical surface shape obtained by calculating a displacement amount of the optical system caused by the water absorption distribution. At least.

  According to the present invention, the diffusion constant obtaining means can accurately determine the diffusion constant of the component material constituting the optical system whose diffusion constant is unknown, so the water absorption distribution calculated using this diffusion constant is also accurate. Further, it is possible to obtain the displacement amount of the optical system caused by water absorption, that is, the shape of the optical surface after deformation, from the water absorption distribution.

  Moreover, the optical characteristics based on the influence of the deformation of the optical surface caused by water absorption can be obtained from the refractive index distribution and the optical surface shape without being affected by the measurement environment considered when the optical system is actually measured and the variation of the test piece. It becomes possible to grasp changes accurately.

  In order to solve the above-mentioned problem, the present invention relates to a component material constituting an optical system whose diffusion constant is unknown, and atoms constituting the molecules of the component material and water molecules arranged in an arbitrary rectangular parallelepiped region. A diffusion constant acquisition processing step for calculating a diffusion constant from a displacement amount of the water molecule obtained by tracking the movement of the water molecule for a predetermined time by molecular dynamics analysis from a stable arrangement in which the potential energy between the two is substantially constant; An optical system model generation processing step for generating a numerical analysis model necessary for numerical analysis by a finite element method by dividing the optical system into meshes, and using the numerical analysis model and the diffusion constant under a predetermined humidity environment Optical characteristics are obtained from a refractive index distribution obtained by calculating a water absorption distribution of the optical system and a deformed optical surface shape obtained by calculating a displacement amount of the optical system caused by the water absorption distribution. An optical characteristic calculation processing step of leaving, may be an optical characterization method of the optical device to be executed by at least the information processing apparatus.

  As described above, according to the present invention, material characteristics necessary for analyzing optical characteristics of a device having optical components are obtained in a short period of time, and the influence of water absorption of each component constituting the optical system on the optical characteristics is determined. It is possible to provide an optical characteristic analysis system that can be quickly verified.

Hereinafter, embodiments of the present invention will be described with reference to FIGS. 1 to 6.
FIG. 1 shows a principle diagram of an optical characteristic analysis system according to the present embodiment.
The optical characteristic analysis system shown in the figure generates a diffusion constant acquisition means 1 for calculating a diffusion constant of a component material constituting an optical system whose diffusion constant is unknown, and a numerical analysis model necessary for numerical analysis by a finite element method. Optical system model generation means 2 for performing the calculation, optical characteristic calculation means 3 for calculating the optical characteristics, and information storage means 4 for storing stable arrangement data and the like.

  The diffusion constant obtaining unit 1 includes a first molecular arrangement calculating unit 5 that calculates a stable arrangement (first stable arrangement) of the component material in order to calculate a diffusion constant of the component material constituting the optical system; A second molecular arrangement calculating means 6 for calculating a stable arrangement (second stable arrangement) when water molecules are arranged in the stable arrangement of the water molecule, and a water molecule after a predetermined time with respect to the second stable arrangement. And a diffusion constant calculating means 7 for calculating a diffusion constant from the displacement.

  The first molecular arrangement calculating means 5 is means for obtaining a stable state (first arrangement) of the component materials constituting the optical system, and the second molecular arrangement calculating means 6 is used for the first stable arrangement. This is means for obtaining a stable state (second stable arrangement) when water molecules are arranged.

  The first molecular arrangement calculation means 5 sets an arbitrary rectangular parallelepiped region (cuboid cell) for the component material constituting the optical system, and further determines the orientation of the molecule of the component material using a random number in this region. Then, until the potential energy between the atoms constituting the molecules of the component material becomes substantially constant at a predetermined temperature, the movement of the molecules is analyzed by the molecular dynamics method to obtain the first stable arrangement, and the stable arrangement storage means 8 is stored. Remember.

  The second molecular arrangement calculating means 6 arranges water molecules using random numbers in the first stable arrangement of the component material read from the stable arrangement storage means 8, and the potential energy between atoms constituting the water molecules at a predetermined temperature. The molecular motion is analyzed by the molecular dynamics method until a second stable configuration is obtained and stored in the stable configuration storage means 8 until.

  The diffusion constant calculating means 7 analyzes the movement of water molecules for a predetermined time from the second stable arrangement by the molecular dynamics method, and calculates the displacement amount of the water molecules from the second stable arrangement. Then, the average value of the square sums of the calculated displacement amounts of water molecules is divided by a predetermined time to obtain a diffusion constant, which is stored in the diffusion constant storage means 9.

  The optical system model generation means 2 generates the three-dimensional shape data of the optical system, divides the mesh, generates a finite element method analysis model necessary for analysis by the finite element method, and stores it in the numerical analysis model storage means 10.

  The optical characteristic calculation means 3 performs analysis by the finite element method using the diffusion constant read from the diffusion constant storage means 9 and the finite element method analysis model read from the numerical analysis model storage means 10, and the component after a predetermined time has passed. The refractive index distribution is obtained by calculating the water absorption distribution of the material. Furthermore, based on this water absorption distribution, the displacement amount of the part material caused by water absorption is calculated to obtain the optical surface shape. Then, the optical characteristics of the optical system are calculated from the refractive index distribution and the optical surface shape.

  Here, the analysis method used in this embodiment, that is, the analysis method based on the molecular dynamics method or the finite element method is a generally used method. Therefore, detailed description in this embodiment is omitted.

  Moreover, the optical characteristic analysis system according to the present embodiment is realized by a general information processing apparatus. That is, a CPU for performing numerical analysis, a volatile memory for storing data necessary for numerical analysis, an input device for inputting data, an output device for outputting data, a program and data This is realized by an information processing apparatus (in the following description, simply referred to as “analysis apparatus”) including at least an external recording apparatus for recording.

  Therefore, the diffusion constant acquisition unit 1, the optical system model generation unit 2, and the optical characteristic calculation unit 3 shown in the figure can be realized mainly by causing a CPU provided in the analysis apparatus to execute a program describing a predetermined process. Is possible.

  The information storage unit 4 can be realized by a volatile memory (for example, RAM, hereinafter simply referred to as “memory”) or an external storage device (for example, a magnetic disk) provided in the analysis apparatus.

  Note that the main subject of the processing of the optical characteristic analysis system according to the present embodiment described below is the CPU, but in order to simplify the explanation, the diffusion constant acquisition means 1, the optical system model generation means 2, and the optical characteristic calculation means. 3 will be described as the processing subject.

FIG. 2 is a flowchart illustrating processing of the optical characteristic analysis system according to the present embodiment.
The processing of the optical characteristic analysis system shown in the figure includes a diffusion constant acquisition process S10 for calculating the diffusion constant of the component material constituting the optical system, an optical system model generation process S20 for generating an analysis model of the optical system, and a diffusion constant. An optical system characteristic calculation process S30 for calculating optical characteristics from the diffusion constant obtained in the acquisition process S10 and the analysis model obtained in the optical system model generation process S20.

In addition, although the diffusion constant acquisition process S10 which concerns on a present Example demonstrates the case where a plastics material is used as a component material which comprises an optical system, it is not the meaning limited to this.
First, in step S11 of the diffusion constant acquisition process S10, the operator of the optical characteristic analysis system arbitrarily sets a rectangular parallelepiped region (cuboid cell) to be a calculation region from the input means provided in the analyzer, and the initial arrangement is set therein. The plastics material molecules that are the objects of diffusion whose orientation is specified according to random numbers are arranged, and relational expressions such as equations of motion (hereinafter referred to as “molecular dynamics analysis model”) are set between the plastics molecules.

  FIG. 3 shows an example of a basic cuboid cell (cuboid cell) used in the present embodiment. In the basic rectangular parallelepiped cell 20 shown in the figure, the lengths of the respective sides are set to Lx, Ly, and Lz, respectively, and N plastics molecules are arranged in the rectangular parallelepiped cell. In this embodiment, a rectangular parallelepiped cell is used, but a cubic cell (that is, a cell of Lx = Ly = Lz) may be used.

  Therefore, the barycentric coordinates (Xi, Yi, Zi) for any plastic molecule i can be given by the following equation.

  Furthermore, if the rotation angle α around the X axis, the rotation angle β around the Y axis, and the rotation angle γ around the Z axis of each plastics molecule are determined by random numbers, the orientation of each plastics molecule can be expressed by the following equation: Can be given.

  Then, as calculation conditions for molecular dynamics analysis, a temperature T at which a diffusion constant is to be calculated, a periodic boundary condition for each surface of the rectangular parallelepiped region, and potential energy between atoms constituting the plastics molecule are set.

For example, the algorithm shown in FIG. 4 is given to the periodic boundary condition for each surface of the rectangular parallelepiped region.
That is, when the plastic molecule in the state a in the basic cuboid cell 20 at the time t becomes the state b in the adjacent cuboid cell beyond the boundary of the basic cuboid cell 20 after the time Δt, the cuboid cell The plastic molecule is handled as the state c in the basic rectangular parallelepiped cell 20 corresponding to the state b in the inside.

  Therefore, the periodic boundary condition for each surface of the rectangular parallelepiped cell can be given by the following equation.

Thus, by setting the periodic boundary condition on each surface of the rectangular parallelepiped cell, the influence of the boundary portion of the rectangular parallelepiped cell can be eliminated.
Further, the potential energy φ between atoms constituting the plastics molecule is given by the following Lennard-Jones potential type empirical potential function equation where r is the distance between atoms, ε is the energy parameter, and σ is the length parameter. be able to.

  Here, considering that the plastics material is an amorphous body, the size of the rectangular parallelepiped cell needs to be larger than that of the molecule forming the crystal structure. It shall be large enough to represent the structure.

  Plastics molecules placed in a rectangular parallelepiped cell can be placed regularly, but in order to reduce the dependence of the initial placement in molecular dynamics analysis, the orientation of plastics molecules is determined according to random numbers. Is preferable.

The number of plastics molecules is the number corresponding to the mass calculated from the density of the plastics material and the volume of the rectangular parallelepiped, and the stable structure of these plastics molecules has already been obtained through experimental methods such as X-ray crystal structure analysis. It is determined by an analytical method such as a molecular mechanics method and a molecular orbital method.

Furthermore, during the molecular dynamics analysis, the plastics molecule is treated as a rigid body without giving freedom of deformation inside the plastics molecule.
In the present embodiment, the empirical potential function of the Lennard-Jones potential type shown in the equation (4) is used to calculate the potential energy between atoms. However, the present invention is not limited to this. For example, The potential energy between atoms may be calculated more accurately by using a molecular orbital method or the like.

  When the above settings are made by the operator in step S11, the diffusion constant acquisition means 1 stores the molecular dynamics analysis model in the information storage means 4 and also stores it in advance in an external storage device (not shown) provided in the analysis apparatus. From the set of programs, a program in which an analysis algorithm corresponding to the setting is written is loaded into the memory, and the process proceeds to step S12.

  In step S12, the diffusion constant acquisition unit 1 analyzes the motion of the plastics molecule at the temperature T at which the diffusion constant is to be calculated by the molecular dynamics method, and calculates the position of the plastics molecule at regular time intervals. That is, the diffusion constant obtaining unit 1 calculates the position of the plastics molecule by calculating the molecular dynamics analysis model given in step S11 under the conditions of the equations (1) to (3).

  At the same time, the diffusion constant acquisition means 1 sequentially calculates and monitors the potential energy in the rectangular parallelepiped cell from the equation (4). Then, the calculation is continued until the potential energy φ is sufficiently reduced to become a substantially constant value, and the stable arrangement (first stable position) of the plastics molecule is obtained.

  Here, for example, when the displacement amount Δφ (t + Δt) of potential energy after the lapse of Δt from the potential energy φ (t) at an arbitrary time t is 1% or less, the potential energy may be determined to be substantially constant.

  When the stable arrangement of the plastics molecules is calculated, the diffusion constant obtaining unit 1 moves the process to step S13 and arranges the water molecules in the space between the plastics molecules in the rectangular parallelepiped cell according to random numbers.

  Similar to step S12, the molecular dynamics analysis tracks the movement of water molecules in a rectangular parallelepiped cell additionally arranged with water molecules at temperature T, and the water molecules whose potential energy in the rectangular parallelepiped cell becomes a substantially constant value. Is determined (second stable position).

  Also in this case, in the same manner as the diffusion target molecule arrangement calculation process S12, for example, when the displacement amount Δφ (t + Δt) of the potential energy after the lapse of Δt from the potential energy φ (t) at an arbitrary time t is 1% or less. It can be determined that the potential energy is almost constant.

  Here, if an overlap occurs between water molecules, the potential energy calculation may diverge during the molecular dynamics method analysis. Therefore, it is desirable to arrange so that there is no overlap between molecules.

  The number of water molecules to be arranged is a number corresponding to about 0.05% of the mass of the plastics in the rectangular parallelepiped cell, with a standard that the general saturated water absorption rate of the plastics material is not exceeded.

  The structure of the water molecule is a rigid body based on the apparent absence of internal rotation in the molecule, and each water molecule is calculated to facilitate the distinction between plastics molecules and water molecules. Should be numbered.

  Furthermore, the calculation of the potential energy between the atoms composing the water molecule and between the atoms composing the plastics molecule and the atom composing the water molecule is similar to that between the atoms composing the plastics molecule. It is assumed to be performed by a static potential function.

  When the stable positions (second stable positions) of the plastics molecule and the water molecule in the basic rectangular parallelepiped cell are calculated by the above process, the diffusion constant obtaining unit 1 moves the process to step S14.

  In step S14, the diffusion constant obtaining unit 1 uses the obtained stable arrangement of water molecules as a reference arrangement, and again analyzes the movement of water molecules within a predetermined time under the condition of the temperature T, starting from this reference arrangement. The position di (t) of the molecule i is calculated sequentially.

  Then, the arrangement of water molecules after the elapse of an arbitrary time t is taken out, and the displacement amount Δdi (t) = di (t) − from the position di (0) of each water molecule i in the reference arrangement according to the numbering of the water molecules. Find di (0).

  When the displacement amount of the water molecule is calculated, the diffusion constant obtaining unit 1 moves the process to step S15, and calculates the average value of the sum of squared displacements from the displacement amount Δdi (t) obtained in the water molecule displacement calculation process of step S14. To do.

That is, the squares of the displacement amounts Δdi (t) of all water molecules obtained by the process of step S14 are integrated, and the average value thereof is calculated.

Ask for. And the calculated mean square displacement

Is substituted into Einstein's relational expression shown below to calculate the diffusion constant D.

  As described above, the numerical calculation of the diffusion constant is performed for all temperature conditions for which the temperature dependence of the diffusion constant is to be grasped, and for all the components whose diffusion constant is unknown among the components that make up the optical system. To do.

  Then, after calculating diffusion constants for all component materials constituting the optical system in the diffusion constant acquisition process S10, the diffusion constants are quoted in step S22 (finite element method analysis model generation process) in the overall model generation process S20 of the optical system. By doing so, the change in the optical characteristics in consideration of the deformation of each part due to water absorption and the change in the refractive index inside the optical part is obtained.

  In step S21, the optical system model generation means 2 uses the function of the three-dimensional shape modeler to generate the three-dimensional shape data of the component materials constituting the optical system and the parts holding the component materials, and stores them in the information storage means 4. Remember.

  In this embodiment, the case where the optical system model generating means 2 has the function of a three-dimensional shape modeler will be described. The three-dimensional shape data of the component material and the component holding the component material are generated and stored in an external storage device or the like, and in step S21, the three-dimensional shape data is simply read from the external storage device or the like, and information storage means 4 may be stored.

FIG. 5 shows an example of the three-dimensional shape data of the optical system generated by this embodiment.
The optical system shown in the figure is composed of lenses 11 to 13 having convex optical surfaces and a lens support component 14 for supporting the lenses 11 to 13.

  When the three-dimensional shape data is generated by the process of step S21, the optical system model generation unit 2 moves the process to step S22, reads the shape data generated by the process of step S21 from the information storage unit 4, and further, Represents the material properties (for example, diffusion constant, elastic modulus, density, etc.) necessary to calculate the deformation of each part caused by water absorption and the refractive index change inside the optical part, and the holding state of each part constituting the optical system. The optical component holding condition and the water absorption condition representing the water absorption surface of the optical system are read from an external storage device or the like.

  At this time, the diffusion constant calculated numerically in the diffusion constant acquisition process S10 is cited and set for each component. Further, as shown in FIG. 6, discrete data required for numerical analysis by the finite element method is performed by dividing the entire part into meshes with fineness that can ensure sufficient accuracy in post-processing optical system characteristic calculation processing S30. (Hereinafter referred to as “mesh data”) is generated and stored in the numerical analysis model storage means 10.

  When the numerical analysis model is generated, the optical system model generation unit 2 shifts the processing to step S23, reads the mesh data of the optical component generated in S22 from the numerical analysis model storage unit 10, and optically analyzes the mesh data. Only the nodes belonging to the surface are extracted, and a local coordinate system having the optical axis direction as the Z axis is set for each optical surface.

  Further, the coordinate values in the X direction and Y direction other than the optical axis direction for the extracted nodes are substituted into the design formula of the optical system prepared in advance to calculate the correct Z direction coordinate value located on the design surface. The mesh data is updated by replacing the coordinate value in the optical axis direction of the node belonging to the optical surface with the coordinate value in the optical axis direction calculated according to the equation.

  For example, FIG. 7 shows an optical surface (approximate surface) 18 before correction and an optical surface (design surface) 16 after correction, and nodes (shown in FIG. 7) belonging to the optical surface of the lens 11 shown in FIG. Only the circle drawn with a broken line is extracted from the mesh data, and local coordinates 19 with the optical axis direction as the Z axis are set for the extracted nodes 15 (the coordinates of the nodes 15 at this time are, for example, (X0, Y0). , Z0)).

  Then, an X coordinate value (= X0) and a Y coordinate value (= Y0) of the node 15 are substituted into a design formula representing the design surface 16 prepared in advance to obtain a Z coordinate value (the Z coordinate value at this time is, for example, The obtained Z coordinate value (= Z1) is set as a new Z coordinate value of the node 15 (therefore, the coordinate of the corrected node 17 is updated to (X0, Y0, Z1)).

By performing the above processing on all the nodes belonging to the optical surface extracted from the mesh data, the corrected optical surface 16 is corrected to mesh data that matches the design surface.
When the optical system model is generated by the processes in steps S21 to S23, the analysis apparatus moves the process to step S31.

  In step S31, the optical characteristic calculation unit 3 configures an optical system using the diffusion constant D acquired in the diffusion constant acquisition process S10, the numerical analysis model generated in the optical system model raw process S20, and the following diffusion equation. The diffusion of water under a specific humidity environment for each part is calculated by the finite element method, and the water absorption distribution ρ (t, x at the position x = (Xi, Yi, Zi) inside each part after a certain time has elapsed. ) Is calculated.

Here, ρ (t, x) represents the water absorption amount at the coordinates (Xi, Yi, Zi) at time t.
When the calculation of the water absorption distribution ρ (t, x) is completed, the optical characteristic calculation unit 3 moves the process to step S32, and uses the numerical analysis model to deform the parts generated based on the water absorption distribution calculated in step S31. The quantity is calculated by the finite element method.

Then, only the nodes belonging to the optical surface are extracted from the obtained deformation amount, and the coordinates of the deformed optical surface are calculated by adding the extracted deformation amount to the design value.
Further, as in FIG. 7, local coordinates having the optical axis direction as the Z coordinate are set for the calculated coordinates of the optical surface after deformation, and can be used in the optical characteristic calculation processing in step S33 using the least square method. An optical surface shape is generated by converting the optical surface into a functional form.

Further, the water absorption distribution obtained in step S31 is converted into a refractive index distribution in accordance with a relational expression such as a linear expression representing a correlation between a water absorption coefficient and a refractive index prepared in advance.
Further, the obtained point sequence data of the refractive index distribution may be further converted into a function format approximating the refractive index distribution for use in the optical characteristic calculation processing in step S33.

  When the optical surface shape and the refractive index distribution are generated, the optical property calculating unit 3 moves the process to step S33, and uses the function expressing the deformed optical surface shape calculated in step S32 to obtain the optical surface shape information. In addition, the refractive index distribution inside the optical component changed by water absorption is also replaced. Then, the optical characteristics shown in FIG. 8 are calculated from the function representing the deformed optical surface shape and the refractive index distribution. .

  The optical characteristic shown in the figure is a modulation transfer function (MTF: Modulation Transfer Function) of the lens shown in FIG. As shown in the figure, it can be seen that the focus focal position (FOC) shifts from the center position due to the effect of water absorption.

When material properties other than the refractive index distribution required for optical property calculation change with water absorption, the optical property calculation may be performed by replacing the material property information with the changed material property.
In the present embodiment, an example has been shown in which the plastics molecule is treated as a rigid body in the diffusion constant acquisition process S10. This is because the calculation amount in the molecular dynamics method analysis is reduced and the diffusion constant is calculated in a short time. Therefore, if an analysis apparatus that can withstand large-scale calculations can be used, the calculation of the stable structure of plastics molecules may be included in the molecular dynamics analysis without imposing this rigid body condition.

  Further, in the present embodiment, the stable arrangement of water molecules was obtained after obtaining the stable arrangement of plastics molecules, but step S12 of the diffusion constant acquisition process S10 (scattered object molecule arrangement calculation process) was omitted, In S13 (water molecule displacement calculation process), calculation for stabilizing the arrangement of the plastics molecules may be performed simultaneously.

  As described above, according to the present invention, the diffusion constant is accurately determined without being affected by variations in the measurement environment and the test piece, and the water absorption distribution required for determining the deformation of the optical system due to water absorption is accurately determined. Therefore, it becomes possible to accurately grasp the change in optical characteristics based on the influence of the deformation of the optical surface caused by water absorption.

  Further, it can be obtained earlier than actually measuring the diffusion constant of the plastic parts constituting the optical system. In particular, when the temperature dependence of the diffusion constant is not linear and the diffusion constant must be obtained under many temperature conditions, or when the number of parts constituting the optical system is large and the diffusion constant of these parts is unknown In this case, a larger period shortening effect can be obtained.

  Furthermore, since it is possible to determine an accurate diffusion constant that is not affected by the test environment and the variation of the test piece in the material test of the component materials constituting the optical system, the prediction accuracy of the optical characteristics is improved.

  Therefore, for example, it becomes possible to quickly and accurately grasp the optical characteristics considering the deformation of the component material constituting the optical system caused by water absorption in a high humidity environment and the refractive index change inside the component material, and a new material is used. Since it is possible to evaluate the optical system without making a prototype, it is possible to determine the optimum mechanical and optical design parameters of the optical system by comparing and examining the optical characteristics of many optical systems.

  In this embodiment, since the potential function is used for the potential energy calculation, the calculation time of the molecular dynamics calculation can be shortened, and the diffusion constant can be calculated in a short time.

  In the present embodiment described above, the water diffusion constant for each plastics material is calculated as the material characteristic of the optical system. However, for example, the elastic modulus and the density can be acquired by the same concept as the diffusion constant acquisition unit 1. Means may be further provided to calculate the elastic modulus and density, and the calculated elastic modulus and density may be used in the optical property calculating means 3.

It is a figure which shows the principle of the optical characteristic analysis system which concerns on a present Example. It is a flowchart which shows the process of the optical characteristic analysis system which concerns on a present Example. It is a figure which shows the example of the basic rectangular parallelepiped cell used in a present Example. It is a figure which shows the outline | summary of the algorithm of the periodic boundary condition used in a present Example. It is a figure which shows the structural example of the optical system which is the analysis object of the optical characteristic analysis system which concerns on a present Example. It is the figure which divided the optical system shown in FIG. 3 into meshes. It is a figure which shows the cross section of the optical surface shape of the optical system which concerns on a present Example. It is a figure which shows the optical characteristic acquired by the optical characteristic analysis system which concerns on a present Example.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Diffusion constant acquisition means 2 ... Optical system model production | generation means 3 ... Optical characteristic calculation means 4 ... Information storage means 5 ... 1st molecular arrangement | positioning calculation means 6 ... 2nd Molecular arrangement calculation means 7 ... Diffusion constant calculation means 8 ... Stable arrangement storage means 9 ... Diffusion constant storage means 10 ... Numerical analysis model storage means 11-13 ... Lens 14 ... Lens support Component 15 ... Node 16 ... Optical surface after correction (design surface)
17 ... Node 18 ... Optical surface 19 before correction 19 ... Local coordinates 20 ... Basic rectangular parallelepiped cell

Claims (4)

For a component material constituting an optical system whose diffusion constant is unknown, a stable arrangement in which the potential energy between atoms constituting the molecule of the component material and water molecules arranged in an arbitrary rectangular parallelepiped region is almost constant is stored. Diffusion constant storage means for calculating a diffusion constant from the amount of displacement of the water molecules obtained by reading stable arrangement data from the stable arrangement storage means and analyzing the movement of the water molecules for a predetermined time from the stable arrangement by a molecular dynamics method A diffusion constant acquisition means for storing
An optical system model generating means for dividing the optical system into meshes to generate a numerical analysis model necessary for numerical analysis by a finite element method, and storing the numerical analysis model in the numerical analysis model storage means;
A refractive index distribution obtained by calculating a water absorption distribution of the optical system under a predetermined humidity environment using the diffusion constant and the numerical analysis model, and a displacement amount of the optical system caused by the water absorption distribution are calculated. An optical property calculation means for calculating an optical property from the obtained optical surface shape after deformation;
An optical characteristic analysis system for an optical device comprising at least The diffusion constant acquisition means
A first molecular arrangement in which a first stable arrangement in which the potential energy between atoms constituting molecules of the component material arranged in the rectangular parallelepiped region is substantially constant is calculated by a molecular dynamics method and stored in a stable arrangement storage means. A calculation means;
A second stable configuration in which the potential energy between atoms constituting the water molecules arranged in the rectangular parallelepiped region in the first stable configuration is substantially constant is calculated by the molecular dynamics method and stored in the stable configuration storage means. A second molecular configuration calculating means;
The movement of the water molecule in a predetermined time from the second stable arrangement is analyzed by a molecular dynamics method to calculate the displacement amount of the water molecule, and the sum of squares of the displacement amount of the water molecule is divided by the predetermined time. A diffusion constant calculating means for calculating the diffusion constant and storing the diffusion constant in the diffusion constant storage means;
The optical characteristic analysis system for an optical instrument according to claim 1, comprising: For a component material constituting an optical system whose diffusion constant is unknown, a stable arrangement in which the potential energy between the atoms constituting the molecule of the component material and the water molecule arranged in an arbitrary rectangular parallelepiped region is almost constant is predetermined. A diffusion constant acquisition processing step of calculating a diffusion constant from a displacement amount of the water molecule obtained by tracking the movement of the water molecule over time by molecular dynamics analysis;
Optical system model generation processing step for generating a numerical analysis model necessary for numerical analysis by a finite element method by dividing the optical system into meshes;
Using the numerical analysis model and the diffusion constant, the refractive index distribution obtained by calculating the water absorption distribution of the optical system under a predetermined humidity environment and the amount of displacement of the optical system caused by the water absorption distribution are calculated. An optical characteristic calculation processing step for calculating optical characteristics from the deformed optical surface shape;
An optical characteristic analysis method for an optical device that causes at least an information processing apparatus to execute the above. The diffusion constant acquisition processing step includes
A first molecular arrangement calculation processing step of calculating a first stable arrangement by which a potential energy between atoms constituting the molecules of the component material arranged in the rectangular parallelepiped region is substantially constant by a molecular dynamics method;
A second molecular configuration calculation processing step of calculating a second stable configuration in which the potential energy between atoms constituting the water molecule arranged in the rectangular parallelepiped region in the first stable configuration is substantially constant by a molecular dynamics method. When,
The movement of the water molecule in a predetermined time from the second stable configuration is analyzed by a molecular dynamics method to calculate the displacement amount of the water molecule, and the sum of squares of the displacement amount of the water molecule is divided by the predetermined time. A diffusion constant calculation processing step for calculating a diffusion constant by
The method for analyzing an optical characteristic of an optical apparatus according to claim 3, comprising: