JP5220345B2 - Diffraction grating design program - Google Patents

Description

  The present invention relates to a diffraction grating design program, and more particularly to improvement of a design method of a holographic diffraction grating.

  Conventionally, for example, a diffractive optical element has been used as a wavelength dispersion element of a spectroscope. As the diffractive optical element, for example, a diffraction grating manufactured by holography is used.

The holographic diffraction grating is manufactured as follows. That is, a photosensitive resin is applied to the surface of the base material constituting the diffraction grating. This element is irradiated with coherent light from two point light sources, the interference fringes are baked on the resin, the unexposed part is removed by development to form a lattice, and a reflective film such as aluminum is deposited thereon. To do.
FIG. 7 is a schematic diagram showing the exposure. The spherical waves from the point light sources S ₁ and S ₂ interfere with each other on the surface of the element G to generate interference fringes, which are printed on the photosensitive resin. In addition to this arrangement, there is also known a method called aspherical exposure in which light from point light sources S ₁ and S ₂ is once reflected by spherical mirrors M ₁ and M ₂ and applied to element G as shown in FIG. For example, see Patent Document 1).
JP 62-30201 A

  By the way, designing a diffraction grating determines the characteristics of the spectrometer to be made, that is, the optical arrangement (positional relationship between the diffraction grating and the entrance / exit slit), the wavelength dispersion ability, and the like. In other words, the exposure parameters such as the radius of curvature and the position of the point light source for exposure are determined. Conversely, there may be a case where the optimum value of the arrangement of the elements of the spectroscope incorporating the diffraction grating created based on a certain standard (relative position of the entrance / exit slit with respect to the diffraction grating) is obtained.

  In the exposure, what kind of interference fringes occur on the element surface is clear if the phase difference between the light reaching the element surface points from the two light sources is an integral multiple of the wavelength at each point on the element surface, If it is a half-integer multiple, it will be dark and very simple physical phenomena. Also, in a spectroscope incorporating a diffraction grating, how light from an incident light source (incidence slit) is split by the diffraction grating, gathers on the exit slit surface, and is extracted from the exit slit is also in accordance with well-known physical laws. Is based.

  However, the functional relationship that links the shape and radius of curvature of the diffraction grating, the exposure parameters, the arrangement of the spectrometer and the imaging state is an extremely simple system (the diffraction grating is a plane, and the gratings engraved there are linearly parallel and equally spaced, The positions of the entrance slit and the exit slit are extremely complicated except for infinity, that is, incident light and diffracted light are parallel light), and it is impossible to determine an optimum value as a mathematical solution therefrom.

  Conventionally, diffraction gratings have been designed by trial and error. That is, a diffraction grating was prototyped by exposure, and the diffraction grating was incorporated into a spectroscope to evaluate the state of diffraction and imaging. Then, the diffraction grating is designed by changing the exposure parameters and the like based on empirical rules by trial and error.

However, the design of a diffraction grating and a spectroscope using the diffraction grating requires deep experience and enormous amount of time, and there is no basis for its optimality. This problem becomes more serious in the conventional method, that is, a method of designing a diffraction grating by trial and error.
For this reason, in the design of holographic diffraction gratings, further improvement has been demanded in terms of speeding up and optimization, but conventionally, there has been no appropriate technology that can solve this. .
The present invention has been made in view of the above-described problems of the prior art, and an object thereof is to provide a diffraction grating design program capable of automatically and quickly designing an optimum diffraction grating.

As a result of studying the design of the holographic diffraction grating by the present inventor, attention was paid to the design by simulation.
Here, a prototype of a diffraction grating by exposure is simulated on a computer, the diffraction grating is brought into an appropriate ray tracing program, where the state of diffraction / imaging is simulated, and the result is evaluated (the imaging is good) It was fed back to the exposure parameters based on empirical rules, and the diffraction grating was designed by repeated trial and error. Time is needed and there is no reason for it to be optimal.
On the other hand, the present inventor found that it is extremely effective to automatically optimize the parameters as follows in order to quickly design the optimum diffraction grating, and completed the present invention. It came to do.

That is, to achieve the above object, a diffraction grating design program according to the present invention is a diffraction grating design program for causing a computer to execute a parameter setting procedure, an exposure simulation procedure, a ray tracing simulation procedure, and a parameter optimization procedure. There,
In the parameter setting procedure, an alignment parameter that defines the optical arrangement of the diffraction grating in the spectroscope, an exposure parameter that defines the exposure conditions for making the diffraction grating by the holographic exposure method, and the shape of the diffraction grating element are defined. Set each initial value of the shape parameter,
In the exposure simulation procedure, holographic diffraction grating data is simulated using curved surface shape data of the diffraction grating element defined by the shape parameter and exposure conditions defined by the exposure parameter,
In the ray tracing simulation procedure, the holographic diffraction grating data is arranged with respect to the entrance slit and the exit slit of the spectrometer in the optical arrangement defined by the alignment parameter, and diffraction image data on the exit slit surface Simulate the
In the parameter optimization procedure, using the simplex method for evaluating the spot shape data of the diffraction image data obtained in the ray tracing simulation procedure, the alignment parameter, so that the spot shape data is small, Optimize each setting value of the exposure parameter and the shape parameter,
The parameter optimization procedure includes a first-layer optimization procedure for each setting value of the alignment parameter and a second-layer optimization procedure for each setting value of the exposure parameter, characterized Rukoto hierarchically to perform the optimization of the second hierarchy to the computer based on the one level of optimization results.

In the present invention, the parameter optimization procedure further includes a third hierarchy optimization procedure for each set value of the shape parameter, and the computer is based on the optimization result of the second hierarchy. Rukoto hierarchically to perform the optimization of the third hierarchy is suitable.

In the present invention, in the parameter optimization procedure, a simplex having (N + 1) vertices is automatically set in the computer in an N-dimensional space with each of N set values to be optimized as one coordinate axis. by, the exposure simulation and ray tracing simulation using N setting values constituting one vertex coordinates of the simplex Te row Align automatic, (N + 1) pieces of the spot shape simulation results for all vertices data by shifting the simplex by Rukoto is replaced with its mirror image point vertices becomes maximum automatic, is Rukoto is changed automatically the N each setting value in a direction in which the spot shape data is reduced Particularly preferred.

An example of the spectrometer of the present invention includes an incident slit, a diffraction grating, and an exit slit. Examples of the alignment parameter of the present invention include a distance from the center of the diffraction grating to the entrance slit, a distance from the center of the diffraction grating to the exit slit, an angle between the entrance slit and the center of the diffraction grating, and the exit slit.
The exposure parameters of the present invention, for example, the position of the exposure light source S ₁ (distance and inclination angle from the diffraction grating element center), (distance and inclination angle from the diffraction grating element center) position of the exposure light source S _2, exposure curvature of the exposure reflector M ₁ for use light sources S ₁ radial position (distance and angle of inclination to the diffraction grating element center), the radius of curvature, the position of the exposure reflector M ₂ for the exposure light source S ₂ (Distance to the center of the diffraction grating element and tilt angle) and the like are examples.
An example of the shape parameter of the present invention is the radius of curvature of the diffraction grating element.

As used herein, the diffraction grating element refers to a substrate provided with a photosensitive resin.
Making a diffraction grating virtually here means, for example, providing a photosensitive resin on the surface of a diffraction grating element, irradiating it with coherent light from two points, generating interference fringes, and developing it. Further, it means that the formation of a diffraction grating by providing a reflective material thereon is performed on a computer.

  Simulation of diffraction and imaging of the diffraction grating here refers to simulating on the computer the imaging state of the diffraction image obtained on the exit slit surface when light from the entrance slit of the spectrometer enters the diffraction grating. That means.

According to the diffraction grating design program of the present invention, since the computer is caused to function as the parameter setting means, the simulation means, the evaluation means, and the parameter changing means, the optimum diffraction grating design can be performed automatically and quickly. Can be done.
In the present invention, the parameter changing means can quickly search for the optimum value by automatically changing the parameter to be optimized in the direction in which the diffraction image obtained by the simulation becomes smaller. The design of the diffraction grating can be performed more quickly.

Hereinafter, a preferred embodiment of the present invention will be described with reference to the drawings.
FIG. 1 shows a schematic configuration of a diffraction grating design apparatus according to an embodiment of the present invention.
The diffraction grating design apparatus 10 shown in FIG. 1 includes a computer, and includes a computer main body (computer) 12, an input device 14, and a display 16.

The computer main body 12 includes program storage means 18. Program storage means 18
The diffraction grating design program 20 is stored. The diffraction grating design program 20 causes the computer main body 12 to function as parameter setting means 22, simulation means 24, evaluation means 25, parameter change means 26, and comparison means 27.

The parameter setting unit 22 includes an alignment parameter setting unit 28, an exposure parameter setting unit 30, and a shape parameter setting unit 32.
The alignment parameter setting unit 28 sets an initial value of the alignment parameter. The alignment parameter defines the optical arrangement of the diffraction grating relative to the entrance and exit slits in the spectrometer.
The exposure parameter setting unit 30 sets an initial value of the exposure parameter. The exposure parameter defines an exposure condition for making a diffraction grating from a diffraction grating element by a holographic exposure method.
The shape parameter setting unit 32 sets initial values of shape parameters. The shape parameter defines the shape of the diffraction grating element, the radius of curvature, and the like.

The simulation means 24 virtually creates a diffraction grating under the diffraction grating element defined by the shape parameter and the exposure condition defined by the exposure parameter. A virtually created diffraction grating is virtually incorporated into a spectrometer with an optical arrangement defined by alignment parameters. The imaging state at the exit slit of the diffraction image of the diffraction grating virtually incorporated is simulated.
The evaluation means 25 evaluates the image formation state of the diffraction image obtained by the simulation means 24 at a higher evaluation point as the diffraction image at the exit slit becomes smaller.

The parameter changing unit 26 sequentially changes a parameter to be optimized among the alignment parameter, the exposure parameter, and the shape parameter.
In the present embodiment, the parameter changing unit 26 automatically changes the parameter to be optimized in the direction in which the evaluation point is high, that is, the direction in which the spot shape of the diffraction image on the exit slit by simulation is small. This is output to the simulation means 24.

The simulation unit 24 performs the simulation using the parameter values sent from the parameter change unit 26.
Evaluation points of the simulated parameters are compared by the evaluation unit 25. The evaluation unit 25 instructs the parameter change unit 26 to change the parameter so that the parameter is changed in the direction in which the evaluation score increases.

In this embodiment, the simulation by the simulation unit 24 with the parameters from the parameter change unit 26, the evaluation of the imaging state of the diffraction image by the evaluation unit 25, and the parameter change by the parameter change unit 26 are automatically repeated, and the simulation is performed. The optimum parameter value that minimizes the spot shape of the diffraction image at the exit slit is searched.
The comparison unit 27 compares the evaluation points, and outputs a parameter optimum value that maximizes the evaluation point, that is, a parameter optimum value that minimizes the spot size of the diffraction image at the exit slit.

The input device 14 includes, for example, a keyboard and a mouse, and inputs initial values of parameters.
The display 16 displays, for example, parameter setting values, simulation results, optimum parameter values, and the like.

The diffraction grating design apparatus 10 according to the present embodiment is configured as described above, and the operation thereof will be described below.
According to the diffraction grating design apparatus 10 according to the present embodiment, the computer main body 12 is caused to function as the parameter setting means 22, the simulation means 24, the evaluation means 25, the parameter change means 26, and the comparison means 27 by the diffraction grating design program 20. be able to.

That is, in the present embodiment, a diffraction grating is virtually created, light diffraction and imaging at the diffraction grating are simulated, and what kind of diffraction image can be obtained on the exit slit surface is displayed on the screen of the display 16. Can be displayed above.
In particular, in the present embodiment, the parameter can be automatically changed in the direction in which the diffraction image at the exit slit becomes smaller, so that the parameter can be optimized automatically. As a result, the present embodiment can automatically and quickly design an optimum diffraction grating as compared with the conventional method, that is, a method for obtaining parameters by trial and error.

Hereinafter, the operation will be specifically described with reference to FIG.
That is, in the exposure simulation as shown in FIG. 6A, two point light sources S ₁ are formed on the surface of a diffraction grating element (base material) G ′ having a curved surface shape (for example, a spherical surface, an ellipsoidal surface, a toroidal surface, etc.). , S ₂ and the coherent light 38 are irradiated via the spherical spheres M ₁ and M ₂ and interfered on the surface to form the holographic diffraction grating G ″.
In the ray tracing simulation as shown in FIG. 5B, the state of diffraction and imaging when the monochromatic light 42 is incident from the incident light source (or slit) 40 to the diffraction grating G ″ created by the exposure simulation. Can be simulated.

Then, the alignment parameters (10x (horizontal width) + vertical width]) of the diffraction image 46 on the exit slit surface 44 as shown in FIG. distance from the center of the grating G'' a distance between the exit slit 44 to the entrance slit 40), the exposure parameters (position of the exposure light source S ₁ and the exposure light source S _2), the shape parameters (the diffraction grating element G' (Radius of curvature) can be automatically optimized.
Here, in this embodiment, the parameter changing unit automatically changes the parameter to be optimized in the direction of reducing the spot shape of the diffraction image 46 on the exit slit surface 44 using the simplex method. As a result, the optimum value can be searched automatically. For this reason, this embodiment can search for an optimal value rapidly compared with what changes a parameter by trial and error.

Hereinafter, the operation of the parameter changing means will be specifically described.
In the design of the present embodiment, for N parameters to be optimized, an N-dimensional space with each parameter as one coordinate axis is considered, and there are N + 1 vertices with appropriate side lengths. A simplex is set up.
Next, N + 1 tests are performed using the coordinate value of each vertex as a parameter value, and an evaluation score at each point is obtained.
The evaluation points thus obtained are arranged in order, and the vertex giving the worst evaluation point is moved to the opposite side with respect to the surface extending with the other N vertices. For the N + 1 points obtained by discarding the previous worst point and adding the points obtained by moving it to the opposite side, the operation of obtaining the worst value again and moving the point to the opposite side is repeated.
This operation eventually moves the simplex to the position containing the best point.
As a result, according to the present embodiment, the search for the optimum parameter value can be quickly performed as compared with a case where the search is performed by trial and error.

The operation will be described more specifically with reference to FIG.
In the figure, the case where the distance x ₁ of the entrance slit and the distance x _{2 of the} exit slit from the diffraction grating center are optimized as alignment parameters will be described.
In the initial value setting shown in FIG. 5A, a two-dimensional space having two coordinate parameters (x ₁ , x ₂ ) to be optimized as one coordinate axis is considered, and an appropriate side length is set there. A simplex having _three vertices P ₁ , P ₂ , and P ₃ is set.
Next, three kinds of simulations are performed using the coordinate values of the vertices P ₁ , P ₂ , and P ₃ as parameter values, and evaluation points at the vertices P ₁ , P ₂ , and P ₃ are obtained.
Among the evaluation points thus obtained, as shown in FIG. 4B, the vertex P ₁ that gives the worst evaluation point is the vertex opposite to the line extending with the other two vertices P ₂ and P _3. Move to P ₄ (mirror image point) (parameter change), and perform a simulation with the parameter value corresponding to the vertex P ₄ to obtain an evaluation point.
For the three vertices P ₂ , P ₃ , and P ₄ obtained by discarding the worst vertex P ₁ and adding the vertex P ₄ obtained by moving it to the opposite side (mirror image point), the worst value is obtained again. transfer the vertex P ₂ to the vertex P ₅ on the opposite side (Kagamizoten) (parameter change), repeated operation of. This operation eventually moves the simplex to the position containing the best vertex.
For this reason, if the vertex having the best evaluation point is obtained from the vertices of the final simplex, the corresponding parameter optimum value can be obtained from the vertex.

In the present embodiment, parameter optimization is performed hierarchically. The method will be described below.
As the first level, consider optimizing the optical arrangement (alignment parameters) of the spectrometer. Assume a diffraction grating formed by exposing a diffraction grating element having a shape defined by an initial value of a shape parameter under exposure conditions defined by an initial value of an exposure parameter. The optimum optical arrangement (alignment parameter) when this diffraction grating is used is optimized by the following procedure.
As alignment parameters to be optimized, the distance from the diffraction grating center to the entrance slit, the distance from the diffraction grating to the exit slit, and the angle between the entrance slit—the center of the diffraction grating—the exit slit are taken up.
Using these three alignment parameters as coordinate axes, a simplex consisting of four points fitted with appropriate values is constructed. Ray tracing is performed for the optical arrangement having the value of each vertex coordinate of the simplex, and an image of the entrance slit formed on the exit slit surface is calculated. The image is applied to an appropriate evaluation function, and an evaluation score is calculated. Optimization is carried out according to the procedure of the simplex method so that this evaluation point is the best, and the best point and its evaluation point are obtained. This best point is the best optical arrangement for the assumed diffraction grating.
For the three alignment parameters that determine the optical arrangement, for example, it is possible to impose appropriate restrictions such as fixing the angle constant or fixing the distance between the entrance slit and the exit slit constant.

The exposure parameter is taken up as the second layer.
Exposure parameters in the case of spherical exposure position coordinates of the exposure light source S ₁ (distance and inclination angle from the center of the diffraction grating) and the position coordinates of the exposure light source S ₂ (distance and inclination angle from the center of the diffraction grating) It becomes four.
When considering aspherical exposure, the radius of curvature of the exposure mirror (using a spherical mirror) M ₁ for the exposure light source S ₁ , the position where it is placed (distance from the diffraction grating element to the mirror), and the angle at which the mirror is tilted Or three of the reflecting mirrors M ₂ for the exposure light source S ₂ or 6 of both are added to 7, 7, and 10 respectively (therefore, 4 and 7). , 7 and 10).
For each of these four cases, consider a four-dimensional, seven-dimensional, seven-dimensional, and ten-dimensional coordinate system, which has five, eight, eight, and eleven vertices and an appropriate side length. Think simplex.
An exposure simulation is performed according to a parameter (exposure parameter) corresponding to each vertex coordinate of the simplex to create a diffraction grating. The evaluation point of the created diffraction grating is optimized for the first layer, and is used as the evaluation point for the optimal optical arrangement (alignment parameter) of the spectrometer. The optimization of exposure parameters by the simplex method is advanced so that this evaluation point becomes the best, and the best point and its evaluation point are obtained. This best point is the best exposure parameter for the assumed shape of the element. At the same time, the best optical arrangement (alignment parameter) is obtained.
In the optimization of the second layer, the optical arrangement (alignment parameter) of the spectroscope is fixed and the optimization is not performed, and the result of one ray tracing may be used as the evaluation point.

As the third layer, the shape (shape parameter) of the diffraction grating element is taken up.
When considering a spherical diffraction grating, the radius of curvature (one piece), when considering a toroidal element, there are two curvature radii that define it, and in the case of an ellipsoidal element, there are generally three pieces. 2 are the parameters to be optimized.
Similarly in the case of this hierarchy, a one-dimensional, two-dimensional, and two-dimensional coordinate system is considered, and simplexes having two, three, and three vertices and appropriate side lengths are formed. For the elements with the shape corresponding to the coordinates of each vertex, the exposure parameter at the second level is optimized, and the evaluation point is set as the evaluation point of the shape parameter. Advance optimization and find the best points and their evaluation points.
This best point becomes the best shape of the diffraction grating element, and at the same time, the best exposure parameter and optical arrangement (alignment parameter) are obtained.

  As described above, according to the present embodiment, the parameter changing means determines the parameter changing direction to be optimized using the simplex method, and searches for the optimum value while changing the parameter in this direction, whereby the optimum diffraction is performed. The grid design can be done more quickly.

  The evaluation function for obtaining the evaluation points includes the width in the wavelength direction of the slit image (diffracted image on the exit slit), the standard deviation value in the wavelength direction, the spread of the image in the direction perpendicular to the wavelength, and the direction perpendicular to the wavelength. It is appropriate to use a standard deviation corresponding to the spread of the image, an average with an appropriate weight, etc.

  In addition to optimizing the optical arrangement of the first layer for one selected wavelength, it is also performed for a plurality of appropriately selected wavelengths, and the sum of evaluation points calculated from the image for each wavelength according to the evaluation function An average value considering the weight can also be used as the overall evaluation score. Since the best diffraction grating and arrangement for light of one wavelength is not necessarily the best for light of another wavelength, it is more practical to optimize with multiple wavelengths of light.

  An example of optimization achieved by the optimization method of this embodiment is shown below. FIG. 4 shows the state and image of diffraction of 850 nm light before performing optimization. FIG. 5 shows the diffraction pattern and image of light at 850 nm after optimization. Table 1 shows before and after optimization of each parameter.

(Table 1)

Parameter Before optimization After optimization

Radius of curvature of spherical diffraction grating (nm) 139 142.356


Exposure wavelength (nm) 441.67 441.67

Distance of light source 1 (mm) 148 139.973
Angle (°) −8 −45.262

Distance of light source 2 (mm) 154 145.017
Angle (°) 40 4.857


Entrance slit-diffraction grating distance (mm) 150 150

Output slit-diffraction grating distance (mm) 130 130

Opening angle (°) 30 30


Width of slit image in wavelength direction (nm) 1.12.

Deviation standard (nm) 0.18

When a diffraction grating is created under the conditions shown in Table 1 before optimization and the state of diffraction is traced with a fixed arrangement, the diffraction image 46 at the exit slit 44 is not condensed at all as shown in FIG. In the state, the spectrometer is not used.
In contrast, when the radius of curvature and the exposure parameters are optimized by the optimization method of the present embodiment, after the optimization in Table 1, ray tracing of the state of diffraction at that time is as shown in FIG. As a result, the slit image (diffracted image 46 at the exit slit 44) is very well condensed, and its peak width is 1.12 nm in the wavelength direction and 0.18 nm in standard deviation.
The upper left figure in both figures shows the spot where each light beam is condensed on the exit slit surface.

  As described above, according to the diffraction grating design apparatus according to the present embodiment, the optimization of the present embodiment makes it possible to optimize the design of the diffraction grating compared to the case where the optimization of the present embodiment is not considered. And can be done quickly.

By the way, in the present embodiment, in order to further speed up the design of the diffraction grating, it is also very preferable to perform the following display display.
<Display screen>
FIG. 6 shows an example of a display screen of the display of the diffraction grating design apparatus 10 according to the present embodiment.
In the figure, the screen 50 includes a selection area 52, a setting area 54, an execution instruction area 56, and a display area 58. Then, the user moves the mouse cursor (not shown) to the area to be set, and selects, sets, and instructs.
Hereinafter, the selection area 52, the setting area 54, the execution instruction area 56, and the display area 58 will be described in detail.

<Selection area>
The selection area 52 includes a shape selection area 60, a direction selection area 62, an exposure light source 1 selection area 64, an exposure light source 2 selection area 66, and a simulation selection area 68.

In the shape selection area 60, the shape of the diffraction grating element is selected from spherical, elliptical, and toroidal.
Here, the spherical surface was a spherical surface having a curvature radius Rz.
The ellipse is a curved surface that can be expressed by the following formula f (x, y, z) = x ² / Rx ² + y ² / Ry ² + (z−Rz) ² / Rz ² −1 = 0.
Toroidal X-> Y is a curved surface formed by rotating a circle having a radius Rx (contacting the origin) with a radius Ry around a rotation axis parallel to the X axis on the XZ plane of Y = 0.
Toroidal Y-> X is a curved surface formed by rotating a circle having a radius Ry (contacting the origin) with a radius Ry around a rotation axis parallel to the Y axis on the YZ plane where X = 0.

In the direction selection area 62, it is selected whether to use the produced diffraction grating as it is (reverse in the figure) or to use it upside down (positive in the figure).
The exposure light source 1 selection area 64, the diffraction grating element light from the exposure light source S _1, or irradiation through a spherical mirror M _1, choose to irradiate directly without going through the spherical mirror M _1.
In the exposure light source 2 selection area 66, the diffraction grating element light from the exposure light source S _2, or irradiation through a spherical mirror M _2, choose to irradiate directly without going through the spherical mirror M _2.
In the simulation selection area 68, when simulating diffraction, the state of light incident on one point on the diffraction grating from one point of the light source (one point / one point) is observed, or one point of the light source is seen on the diffraction grating. Select whether to see the state of light incident on all points (1 point / Full) or to view the state of light incident on all points on the diffraction grating from all points of the entrance slit (Full / Full) .

<Setting area>
The setting area 54 includes a size setting area 70, an Rxyz setting area 72, an exposure wavelength setting area 74, a center engraving number area 76, an L, θ, Y setting area 78 of the light source 1, and a radius of the reference spherical surface. Center XYZ setting area 80, L, θ, Y setting area 82 of light source 2, radius and center XYZ setting area 84 of reference spherical surface, wavelength setting area 86, angle setting area 88, diffraction Order setting area 90, entrance slit L, α, Y setting area 92, slit W, H, pitch setting area 94, exit slit L, β setting area 96, diffraction point XY setting area 98 Diameter and pitch setting area 100.
And the setting area 54 shows the content of the parameter to set.

In the size setting area 70, the size (X × Y) of the diffraction grating element is set. Div sets the size of the pitch for calculating the exposure state. (X or Y) / Div is set to be 200 or less.
In the Rxyz setting area 72, the radius of curvature (in mm) of the diffraction grating element is set. Rz is used for a spherical surface, and Rx and Ry are used for a toroid.
In the exposure wavelength setting area 74, the wavelength of coherent light used for exposure is set.
In the center engraving number area 76, the number of engravings at the center (average) of the diffraction grating elements is set.
In the L, θ, Y setting area 78 of the light source ₁ , the exposure light source S ₁ is set by the distance (mm) from the diffraction grating element center and the inclination from the normal line. The value of Y (floating from the surface) can also be set.
In the reference spherical surface radius and center of the XYZ setting area 80, setting the radius of curvature and the installation position reflector M _1.
In the L, θ, Y setting area 82 of the light source ₂ , the exposure light source S2 is set by the distance (mm) from the center of the diffraction grating element and the inclination from the normal line. The value of Y (floating from the surface) can also be set.
In the reference spherical surface radius and center of the XYZ setting area 84, setting the radius of curvature and the installation position reflector M _2.
In the wavelength setting area 86 and the angle setting area 88, the wavelength of monochromatic light that simulates diffraction and the rotation angle of the diffraction grating at that time are set.
In the diffraction order setting area 90, a diffraction order for simulating diffraction is set.
In the L, α, Y setting area 92 of the entrance slit, the center position of the entrance slit is set by the distance from the center of the diffraction grating and the inclination from the normal line.
In the slit W, H and pitch setting area 94, the pitch of the incident slit size when scanning is set.
In the L and β setting area 96 of the exit slit, the center position of the exit slit is set by the distance from the center of the diffraction grating and the inclination from the normal line.
In the XY setting area 98 of the diffraction point, the coordinates of the point on the diffraction grating when simulating the diffraction direction of the light ray incident on one point on the diffraction grating from the incident slit (one point) is set.
In the diameter and pitch setting area 100, the step of the diffraction grating surface when simulating the diffraction state over the entire surface of the diffraction grating is set.

<Execution instruction area>
The execution instruction area 56 includes an exposure simulation button 102, a diffraction simulation button 104, an alignment optimization button 106, an exposure + alignment optimization button 108, a shape + exposure + alignment optimization button 110, and an exposure condition optimization button. 112 and a shape + exposure optimization button 114.

When the exposure simulation button 102 is clicked, the exposure by the simulation means is simulated.
When the diffraction simulation button 104 is clicked, the diffraction at the diffraction grating created by the exposure by the simulation means is simulated.
Clicking on the alignment optimization button 106 simulates diffraction with the diffraction grating and optimizes the alignment parameters such as the entrance slit position (distance only) and exit slit (distance only) so that the diffraction image is minimized. To do.
Clicking the exposure + alignment optimization button 108 simulates diffraction while changing the exposure conditions (exposure parameters), and exposure conditions (exposure parameters) and the entrance slit (only the distance) so that the diffraction image is minimized. And optimize the exit slit (only the distance).
Clicking the shape + exposure + alignment optimization button 110 changes the radius of curvature of the diffraction grating (shape parameter) and the exposure conditions (exposure parameters) while simulating diffraction so that the diffraction image is minimized. (Shape parameter), exposure conditions (exposure parameter), and alignment parameters, an entrance slit (only distance) and an exit slit (only distance) are optimized.
When the exposure condition optimization button 112 is clicked, the diffraction is simulated while changing the exposure condition (exposure parameter), and only the exposure condition (exposure parameter) is optimized so that the diffraction image is minimized.
Clicking the shape + exposure optimization button 114 simulates diffraction while changing the exposure conditions (exposure parameters), and sets the radius of curvature (shape parameters) and exposure conditions (exposure parameters) so that the diffraction image is minimized. Optimize.

<Display area>
In the display area 58, the center of the incident light source (or incident slit) 40, the diffraction grating G ″, the exit slit 44, the normal line of the diffraction grating G ″, the diffraction image 46 on the exit slit 44 surface, the result of simulation, and the like. Can be displayed.

  As described above, according to the diffraction grating design apparatus according to the present embodiment, it is possible to perform simulation and search while displaying an extremely large number of parameters and results on the screen on the screen. Can be easily set and confirmed. For this reason, the optimal diffraction grating design can be performed more quickly.

In the above-described configuration, the example in which the parameter optimization of the present invention is performed hierarchically has been described. However, it is also preferable to perform as follows.
The parameter setting means sets an appropriate radius of curvature (shape parameter) of the diffraction grating element, exposure parameter, and slit position coordinates (alignment parameter) in the spectroscope as initial values. The total number is N, and all these are collectively called a set of parameters. Appropriate changes are appropriately added to the N set of parameters to create N (N + 1) set of parameters.
The simulation means subsequently exposes each parameter group using the parameters to create a diffraction grating, and incorporates it to perform ray tracing of the spectrometer, and the evaluation means calculates a diffraction image formed on the exit slit surface. For example, the horizontal width (wavelength dispersion width) is obtained, and the smaller one is set as a good evaluation point.
Then, this series of operations is repeated as a test of the simplex method according to the procedure of the simplex method.
Even when the parameter optimization of the present invention is performed in this way, the parameter to be optimized can be automatically changed and the optimum value can be automatically searched, so that the optimum diffraction grating can be designed more quickly. be able to.

It is explanatory drawing which shows schematic structure of the diffraction grating design apparatus concerning one Embodiment of this invention. It is explanatory drawing of an effect | action of the diffraction grating design apparatus concerning one Embodiment of this invention. It is explanatory drawing which shows the effect | action of the parameter change means of the diffraction grating design apparatus concerning one Embodiment of this invention. It is an example of the state of diffraction of light and an image before performing optimization of this embodiment. It is an example of the diffraction state and image of light after performing the optimization of this embodiment. It is explanatory drawing of the display display screen of the diffraction grating design apparatus concerning one Embodiment of this invention. It is a schematic diagram of a general exposure method. It is a schematic diagram of the aspheric exposure method.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Diffraction grating design apparatus 12 Computer main body 14 Input device 16 Display 20 Diffraction grating design program 22 Parameter setting means 24 Simulation means 25 Evaluation means 26 Parameter change means 27 Comparison means

Claims (3)

A diffraction grating design program for causing a computer to execute a parameter setting procedure, an exposure simulation procedure, a ray tracing simulation procedure, and a parameter optimization procedure,
In the parameter setting procedure, an alignment parameter that defines the optical arrangement of the diffraction grating in the spectroscope, an exposure parameter that defines the exposure conditions for making the diffraction grating by the holographic exposure method, and the shape of the diffraction grating element are defined. Set each initial value of the shape parameter,
In the exposure simulation procedure, holographic diffraction grating data is simulated using curved surface shape data of the diffraction grating element defined by the shape parameter and exposure conditions defined by the exposure parameter,
In the ray tracing simulation procedure, the holographic diffraction grating data is arranged with respect to the entrance slit and the exit slit of the spectrometer in the optical arrangement defined by the alignment parameter, and diffraction image data on the exit slit surface Simulate the
In the parameter optimization procedure, using the simplex method for evaluating the spot shape data of the diffraction image data obtained in the ray tracing simulation procedure, the alignment parameter, so that the spot shape data is small, Optimize each setting value of the exposure parameter and the shape parameter,
The parameter optimization procedure includes a first-layer optimization procedure for each setting value of the alignment parameter and a second-layer optimization procedure for each setting value of the exposure parameter, grating design program characterized Rukoto hierarchically to perform the optimization of the second hierarchy to the computer based on the one level of optimization results. The diffraction grating design program according to claim 1,
The parameter optimization procedure further includes a third hierarchy optimization procedure for each set value of the shape parameter, and the computer optimizes the third hierarchy based on the optimization result of the second hierarchy. hierarchically to execute the diffraction grating design program characterized Rukoto. In the diffraction grating design program according to claim 1 or 2,
Wherein in the parameter optimization procedure, the computer, the N-dimensional space and optimizing want the N setting value with each one of the coordinate axes, by setting the automatic simplex with (N + 1) number of vertices, the simplex Te line Align automatic the exposure simulation and ray tracing simulation using N setting values constituting one vertex coordinates, a (N + 1) pieces of the spot shape data up from the simulation results for all vertices vertex thereof by is replaced Rukoto mirror images point by shifting the simplex to automatic, diffraction grating, characterized in Rukoto is changed automatically the N each setting value in a direction in which the spot shape data is reduced Design program.

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