Data compression apparatus, exposure apparatus, and data compression method

Abstract

This technology provides a way to reduce the computational cost of curve approximation. [Solution] The data compression method includes the steps of: reading first data from a storage unit; inputting the first data into a trained model and obtaining the curve parameters output by the trained model; using the curve parameters output from the trained model as initial values, searching for curve parameters of an approximate curve that represents the figure represented by the first data; and generating second data that represents the point cloud represented by the first data using the curve parameters obtained by the search.

Description

TECHNICAL FIELD

[0001] The subject matter disclosed in the present specification relates to a data compression apparatus, an exposure apparatus, and a data compression method.

BACKGROUND ART

[0002] Conventionally, for manufacturing substrates such as semiconductor substrates and printed circuit boards, exposure apparatuses that directly expose a pattern onto the upper surface of a substrate are known. In this type of exposure apparatus, alignment marks formed on the substrate are detected, and exposure alignment on the substrate is performed based on the positions of the alignment marks. Specifically, exposure data represented by CAD data is corrected to match positional deviation of the alignment marks. Then, exposure is performed based on the corrected exposure data.

[0003] In general, in CAD data, curves are approximated by short vectors. Here, in order to improve the approximation accuracy, it is necessary to increase the number of divisions of the short vectors. As a result, there is a problem that the data size of the exposure data increases, and the calculation time required for correction becomes longer.

[0004] Data represented by short vectors can be reduced in data size by being approximated by a curve represented by predetermined parameters, so that speeding up of correction processing can be expected. For example, an nth-order Bezier curve is a curve obtained from (n+1) control points. The control points include a start point, an end point, and (n-1) direction points (internal control points). According to the Bezier curve, the shape of the curve can be uniquely drawn by adjusting the position of each control point. Therefore, data can be compressed by approximating a group of points arranged in a curve with a Bezier curve. A method for approximating CAD data is described in, for example, Patent Document 1.

PRIOR ART DOCUMENTS

PATENT DOCUMENTS

[0005]

PATENT DOCUMENT 1

[0006] To approximate data represented by short vectors using, for example, a Bézier curve, the position of control points needs to be adjusted, and this adjustment is performed using search (optimization) methods such as the least squares method. The higher the search accuracy, the smaller the distance error with the short vector point cloud that can be generated. Furthermore, increasing the number of times the control points are searched allows for more precise adjustment. However, if the initial placement of control points deviates significantly from the optimal solution, there is a challenge in that the computation time required to optimize the control points becomes long.

[0007] The object of the present invention is to provide a technique that can reduce the computational cost of curve approximation. [Means for solving the problem]

[0008] To solve the above problems, the first embodiment is a data compression device comprising a processor and a storage unit. The storage unit stores first data representing a figure as a point cloud, and a trained model that takes the first data as input and outputs curve parameters for approximating the point cloud represented by the first data as a curve. The processor performs the following processes: reading the first data from the storage unit; inputting the first data into the trained model and obtaining the curve parameters output by the trained model; using the curve parameters output from the trained model as initial values ​​and searching for curve parameters of an approximation curve that approximates the figure represented by the first data; and generating second data representing the point cloud represented by the first data using the curve parameters obtained by the search.

[0009] The second aspect is a data compression device according to the first aspect, wherein the approximation curve is a Bézier curve, and the curve parameters indicate the control points of the Bézier curve.

[0010] A third embodiment is a data compression device according to the first or second embodiment, wherein the processor performs a process that includes searching for the curve parameters using the least squares method in the search process.

[0011] The fourth embodiment is an exposure apparatus comprising: a substrate holding unit for holding a substrate; an exposure head for exposing the substrate held by the substrate holding unit; a data compression apparatus according to any one of claims 1 to 3; and a correction unit for correcting the second data generated by the data compression apparatus.

[0012] A fifth aspect is a data compression method comprising: reading first data from a storage unit; inputting the first data into a trained model and obtaining the curve parameters output by the trained model; using the curve parameters output from the trained model as initial values, searching for curve parameters of an approximation curve that represents the figure represented by the first data; and generating second data that represents the point cloud represented by the first data using the curve parameters obtained by the search. [Effects of the Invention]

[0013] According to the first to fifth embodiments, the curve parameters can be efficiently searched by using the curve parameters output by the trained model as initial values. This reduces the computational cost of curve approximation.

[0014] According to the data compression device of the second embodiment, in the case of a Bézier curve, the curve can be represented with fewer curve parameters. Therefore, the data compression ratio can be improved.

[0015] According to the exposure apparatus of the fifth embodiment, the computational cost can be reduced compared to correcting the first data by correcting the second data which represents the point cloud with an approximation curve. [Brief explanation of the drawing]

[0016] [Figure 1]It is a perspective view showing the overall configuration of the exposure apparatus according to the embodiment. [Figure 2A] It is a top view schematically showing a distortion-free substrate. [Figure 2B] It is a top view schematically showing a substrate with distortion. [Figure 3] It is a control block diagram of the exposure apparatus. [Figure 4] It is a diagram conceptually showing a learning dataset. [Figure 5] It is a flowchart showing the procedure of data compression processing executed by the control unit according to the embodiment. [Figure 6] It is a flowchart showing the procedure of exposure processing executed by the control unit. [Modes for Carrying Out the Invention]

[0017] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. Note that the constituent elements described in this embodiment are merely examples, and are not intended to limit the scope of the present invention to only those. In the drawings, for ease of understanding, the dimensions and numbers of each part may be exaggerated or simplified as necessary for illustration.

[0018] In Figure 1 and each subsequent figure, an XYZ orthogonal coordinate system is defined to explain the positional relationship of elements. Here, the X-axis direction and Y-axis direction are horizontal directions, and the Z-axis direction is a vertical direction. In the following description, in the Z-axis direction, the +Z direction is the vertically upward direction, and the -Z direction is the vertically downward direction.

[0019] <1. Embodiment> FIG. 1 is a perspective view showing the overall configuration of an exposure apparatus 1 according to an embodiment. The exposure apparatus 1 is a substrate processing apparatus that irradiates light onto the upper surface of a substrate W coated with a photosensitive material to expose a pattern on the upper surface of the substrate W. The substrate W is, for example, a printed wiring board or a semiconductor substrate. For example, in a manufacturing process of a printed wiring board, a step of forming a layer on the upper surface of the substrate W in another apparatus and a step of exposing a pattern on the upper surface of the substrate W in the exposure apparatus 1 are repeatedly performed. Thereby, a printed wiring board having a multilayer structure is manufactured.

[0020] The exposure apparatus 1 includes a base 10, a gantry 15, a first stage 21, a first moving mechanism 23, a second stage 25, a second moving mechanism 27, an exposure unit 40, an alignment camera 50, and a control unit 70.

[0021] The base 10 is a support table that supports each element of the exposure apparatus 1 such as the gantry 15 and the first stage 21. The base 10 has a flat plate-shaped outer shape extending along a horizontal plane. The base 10 is made of a stone material such as granite. The base 10 is fixed to the floor surface of a factory. The base 10 has a rectangular shape in top view. The long side of the base 10 is parallel to the Y-axis direction. The short side of the base 10 is parallel to the X-axis direction.

[0022] The gantry 15 is fixed to the upper surface of the base 10. The gantry 15 has a pair of leg portions 151 and a bridge portion 152. The pair of leg portions 151 are provided at intervals in the X-axis direction. Each leg portion 151 extends upward (+Z direction) from the upper surface of the base 10. The bridge portion 152 connects upper end portions of the leg portions 151 to each other in the X-axis direction. A through port 18 through which the substrate W can pass in the Y-axis direction is formed between the upper surface of the base 10 and the gantry 15.

[0023] The first stage 21 is movable along the Y-axis direction. The first stage 21 has a flat plate-shaped outer shape. The shape of the first stage 21 in top view is a rectangular shape smaller than the base 10. The first stage 21 is disposed above the base 10 in a substantially horizontal posture.

[0024] The first moving mechanism 23 is a mechanism for moving the first stage 21 in the Y-axis direction relative to the base 10 and the gantry 15. The first moving mechanism 23 is a linear motor mechanism having a pair of guide rails and a linear motor. The pair of guide rails are rails for guiding the first stage 21 in the Y-axis direction. The pair of guide rails are provided on the upper surface of the base 10 at intervals in the X-axis direction and extend linearly along the Y-axis direction. The linear motor has a stator provided on the upper surface of the base 10 and a mover fixed to the lower surface of the first stage 21. When a drive signal is supplied to the linear motor from the control unit 70, the mover moves along the stator in the Y-axis direction due to the magnetic attractive and repulsive forces generated between the stator and the mover. As a result, the first stage 21 moves in the Y-axis direction relative to the base 10. Note that the drive source of the first moving mechanism 23 is not limited to a linear motor. The first moving mechanism 23 may be, for example, a mechanism that converts the rotational motion of a servo motor into linear motion using a ball screw.

[0025] The second stage 25 is movable along the X-axis. The second stage 25 has a flat, plate-like shape. In a top view, the shape of the second stage 25 is a smaller rectangle than that of the first stage 21. The second stage 25 is positioned above the first stage 21 in a substantially horizontal position.

[0026] The second moving mechanism 27 is a mechanism for moving the second stage 25 in the X-axis direction relative to the first stage 21. The second moving mechanism 27 is a linear motor mechanism having a pair of guide rails and a linear motor. The pair of guide rails are arranged on the upper surface of the first stage 21 at intervals in the Y-axis direction. Each guide rail extends linearly along the X-axis direction. The pair of guide rails are rails for guiding the second stage 25 in the X-axis direction. The linear motor includes, for example, a stator provided on the upper surface of the first stage 21 and a mover fixed to the lower surface of the second stage 25. However, the second moving mechanism 27 is not limited to a linear motor mechanism, and may be, for example, a ball screw mechanism.

[0027] The substrate W is supported on the upper surface of the second stage 25 in a substantially horizontal position. The second stage 25 may have chuck pins for fixing the substrate W and a plurality of suction holes for adsorbing the substrate W. The exposure apparatus 1 moves the substrate W in the Y-axis direction (main scanning direction) and the X-axis direction (sub-scanning direction), respectively, by operating the first moving mechanism 23 and the second moving mechanism 27.

[0028] The exposure unit 40 is a unit that exposes the substrate W supported by the second stage 25. The exposure unit 40 has four exposure heads 41. The multiple exposure heads 41 are fixed to the bridging portion 152 of the gantry 15. The multiple exposure heads 41 are arranged at equal intervals along the X-axis. Each exposure head 41 has a spatial light modulation element to form a desired pattern on the substrate W. As the spatial light modulation element, for example, a GLV (Grating Light Valve) (registered trademark) or a DMD (Digital Micromirror Device) can be used. A GLV is a diffraction grating type spatial light modulator that uses a minute diffraction grating structure to control the diffraction of laser light, thereby adjusting the transmittance and reflectance of the light and forming a patterned light. A DMD uses a minute mirror array to change the direction of light reflection by tilting individual mirrors and forming a patterned light.

[0029] The exposure unit 40 spatially modulates the laser light supplied from the light source 43 to form patterned light, which is then irradiated onto the substrate W. The light source 43 can be, for example, a laser oscillator, an LED (Light Emitting Diode), or a mercury lamp. The laser light from the light source 43 is converted into linear laser light by the illumination optical system 45 and guided to the spatial light modulator of the exposure head 41. The illumination optical system 45 includes, for example, a collimator lens that converts the light from the light source 43 into parallel light, and a cylindrical lens that converts it into linear light.

[0030] When exposing a pattern onto a substrate W, the exposure apparatus 1 alternately performs a main scanning process and a sub-scanning process. In the main scanning process, the exposure apparatus 1 moves the substrate W in the Y-axis direction while multiple exposure heads 41 emit pattern light. In the main scanning process, the exposure apparatus 1 moves the substrate W relative to the multiple exposure heads 41 in the Y-axis direction. This draws a pattern in a striped area. In the sub-scanning process, the substrate W is moved a predetermined distance in the X-axis direction to position the substrate W at the starting position of the next exposure. The exposure apparatus 1 exposes the entire surface of the substrate W by repeating these main scanning and sub-scanning processes.

[0031] The alignment camera 50 captures the alignment marks M formed on the substrate W supported by the second stage 25 and acquires an image (alignment image FA1) including the alignment marks M. The alignment camera 50 is attached to the bridging portion 152 of the gantry 15. The alignment camera 50 performs imaging based on a drive signal from the control unit 70.

[0032] The alignment camera 50 has an image sensor. The image sensor is a semiconductor device having a plurality of photodetectors that convert light into electrical signals, and specifically includes an image sensor such as a CCD (Charge-Coupled Device) or CMOS (Complementary Metal-Oxide Semiconductor). The alignment camera 50 is a line sensor in which a plurality of photodetectors are arranged in the X-axis direction. However, the alignment camera 50 may be a two-dimensional image sensor.

[0033] Figure 2A is a schematic top view of a substrate W without distortion. Figure 2B is a schematic top view of a substrate W with distortion. In Figures 2A and 2B, the grid lines within the substrate W represent distortion (expansion, displacement, rotation, warping, undulation, etc.) within the substrate W. For example, in the example shown in Figure 2A, multiple alignment marks M are all in their standard positions. This indicates that there is almost no distortion within this substrate W. On the other hand, in the example shown in Figure 2B, some of the alignment marks M are shifted from their reference positions. This indicates that localized distortion is occurring within this substrate W. In this way, the distortion distribution within the substrate W can be quantitatively calculated by detecting the positions of multiple alignment marks M.

[0034] Figure 3 is a control block diagram of the exposure apparatus 1. The control unit 70 is a unit for controlling the operation of each part of the exposure apparatus 1. The control unit 70 includes a processor 71 and a storage unit 73. The storage unit 70 is electrically connected to the processor 71 via bus wiring (not shown). The control unit 70 is an example of a "data compression device".

[0035] The processor 71 includes a CPU (Central Processing Unit) or an MPU (Micro Processing Unit). The processor 71 may include a general-purpose arithmetic unit, a dedicated arithmetic unit, a GPU (Graphics Processing Unit), or an NPU (Neural Network Processing Unit). A dedicated arithmetic unit includes, for example, an ASIC (Application Specific Integrated Circuit).

[0036] The storage unit 73 includes main memory. Main memory is, for example, semiconductor memory such as RAM (Random-Access Memory). The storage unit 73 may also include non-volatile memory such as ROM (Read-Only Memory) for storing programs and data. Furthermore, the storage unit 73 may include auxiliary storage. Examples of auxiliary storage include solid-state drives (SSDs) and hard disk drives (HDDs). The storage unit 73 may also include removable media.

[0037] The storage unit 73 stores the computer program Pg1. The computer program Pg1 includes a program for controlling the operation of the exposure apparatus 1. The computer program Pg1 also includes a program for performing the data compression process and exposure process described later.

[0038] The control unit 70 is electrically connected to the input unit 75 and the output unit 77. The input unit 75 inputs instructions or data to the control unit 70 in response to the operator's actions. The input unit 75 includes, for example, a keyboard and a mouse. The input unit 75 may also include a reader for reading data from removable media. The output unit 77 includes a display for displaying various information. The display is, for example, a liquid crystal display. The input unit 75 may also include a touch panel located on the display surface of the display, thereby realizing a GUI (Graphical User Interface) via the touch panel. The output unit 77 may also include a speaker, a printer, or a lamp.

[0039] The memory unit 73 stores the first exposure data D1, the second exposure data D2, the corrected exposure data D3, and the learned model 81. The first exposure data D1 is information that defines the fine structure, such as a circuit pattern, to be formed on the substrate W. The first exposure data D1 is data that represents figures such as points, lines, or polygons as a point cloud, and includes information indicating the position (coordinates) of the point cloud. The first exposure data D1 is CAD data and is short vector data. In short vector data, curves included in the figure are described using short vectors (line segments). That is, in short vector data, curves are represented as a set of short straight lines. The first exposure data D1 is an example of "first data".

[0040] The second exposure data D2 is data generated by the control unit 70, and represents the point cloud of the figure represented by the first exposure data D1 using the curve parameters of an approximation curve. Here, a Bézier curve is used as the approximation curve. An nth-order Bézier curve is a curve represented by (n+1) control points, including the start point, end point, and (n-1) direction points (internal control points). When the line segment of the short vector has (n+2) or more point clouds, the number of point clouds can be reduced by approximating it with an nth-order Bézier curve, thereby reducing the data size. Here, a cubic Bézier curve is used as the approximation curve. The second exposure data D2 is an example of "second data".

[0041] Corrected exposure data D3 is data obtained by the control unit 70 correcting the second exposure data D2 in order to reduce exposure errors. As will be described later, the control unit 70 corrects the second exposure data D2 according to the distortion of the substrate W measured based on the alignment mark M of the substrate W. The control unit 70 is an example of a "correction unit". That is, the control unit 70 in this embodiment serves as both a "data compression device" and a "correction unit". The "correction unit" may be implemented by a device other than the control unit 70.

[0042] The trained model 81 generates curve parameters for the corresponding approximation curve based on the input point cloud. The trained model 81 is designed to output control points (start point, end point, and two direction points) of a cubic Bézier curve approximated by the point cloud. The training dataset 91 used to obtain the trained model 81 is described below.

[0043] Figure 4 is a conceptual diagram of the training dataset 91. The training dataset 91 consists of pairs of point cloud data 93 and corresponding control point data 95. The point cloud data 93 is data that shows the positions (coordinates) of multiple points. The control point data 95 is data that shows the positions (coordinates) of control points (start point P1, end point P2, direction points P3, P4) obtained when the point cloud shown by the point cloud data 93 is approximated by a Bézier curve.

[0044] The control point data 95 is obtained by curve approximation, which searches for control points on the Bézier curve. In curve approximation, initial control points are first set. Then, the control points that minimize the error (squared error) between the point cloud and the corresponding points on the curve are searched using the least squares method with matrix operations. By repeating this control point search sufficiently, the optimized control point data 95 is obtained.

[0045] The trained model 81 is obtained by training the machine learning model 810 on the training dataset 91. The machine learning model 810 can be a linear regression model, a neural network, or the like. The training of the machine learning model 810 may be performed by the control unit 70, or by a device other than the control unit 70.

[0046] <Data compression processing> Figure 5 is a flowchart showing the steps of the data compression process performed by the control unit 70 according to the embodiment. Each step shown in Figure 5 is a process performed by the processor 71 of the control unit 70 in accordance with the computer program Pg1. The order of each step shown in the flowchart can be changed as appropriate depending on the purpose. In addition, some steps can be omitted or other steps can be added as needed.

[0047] The control unit 70 starts data compression processing based on instructions from the operator. Once the data compression processing has started, the control unit 70 reads the first exposure data D1 stored in the storage unit 73 in the reading step S1. Next, in the list acquisition step S2, the control unit 70 obtains a list of multiple figures from the read first exposure data D1. After the list acquisition step S2, the control unit 70 determines in the determination step S3 whether or not there are unprocessed figures in the list. If it is determined that there are unprocessed figures (Yes), the control unit 70 proceeds to the selection step S4. In the selection step S4, the control unit 70 selects an unprocessed figure from the list. Hereinafter, the figure selected in the selection step S4 will be referred to as the "target figure".

[0048] After the selection step S4, the control unit 70 inputs the point cloud data of the target figure into the trained model 81 in the control point acquisition step S5 and acquires the control points (curve parameters) output by the trained model 81.

[0049] The control unit 70 may approximate the target figure using a cubic Bézier curve, and may divide the point cloud of the target figure into sets of point clouds corresponding to U-shaped or S-shaped shapes based on its local shape. Such division of the point cloud can be performed, for example, by classifying the point cloud based on the curvature at each point. The curvature can be calculated, for example, by calculating tangent vectors using neighboring points of each point. The control unit 70 may input the point clouds of each set obtained by the division into the trained model 81 and acquire the control points output from the trained model 81.

[0050] After the control point acquisition step S5, the control unit 70 searches for the optimal curve parameters in the search step S6. Specifically, the optimal control points are obtained by repeating the control point search at least once a specified number of times using a method such as the least squares method using matrix operations.

[0051] After the search step S6, the control unit 70, in the storage step S7, stores the optimal control points obtained in the search step S6 as second exposure data D2 in the storage unit 73. This generates second exposure data D2, in which the point cloud of the target figure in the first exposure data D1 is represented by a curve of control points (curve parameters).

[0052] After the storage process S7, the control unit 70 returns the process to the determination process S3 to determine whether or not there are any unprocessed figures. If the determination process S3 determines that there are no unprocessed figures (No), the control unit 70 terminates the compression process. Through the above data compression process, the second exposure data D2 is generated from the first exposure data D1. Next, the exposure process using the second exposure data D2 will be described.

[0053] <Exposure process> Figure 6 is a flowchart showing the exposure process performed by the control unit 70. The control unit 70 starts the exposure process based on instructions from the operator. The substrate W is assumed to be held in the second stage 25 beforehand. Once the exposure process starts, the control unit 70 uses the alignment camera 50 to image multiple alignment marks formed on the upper surface of the substrate W in the alignment process S11. The control unit 70 then measures the positional displacement of each alignment mark based on the obtained image. This measures the distortion of the substrate W.

[0054] In the correction step S12, the control unit 70 corrects the second exposure data D2 based on the measured distortion of the substrate W. This correction includes, at a minimum, a process of geometrically changing the point cloud of the figure represented by the second exposure data D2. Geometric changes include translation, rotation, scaling, and shearing. For example, if localized expansion occurs in the substrate W, the control unit 70 enlarges the figure of the second exposure data D2 corresponding to that location. The control unit 70 stores the corrected exposure data D3 obtained by the correction in the storage unit 73.

[0055] Furthermore, the second exposure data D2 may be corrected according to exposure error factors other than the distortion within the substrate W. Other exposure error factors include optical system errors (aberrations, uneven illumination, etc.) of the exposure head 41, light source 43, and illumination optical system 45, transport system errors (positioning errors, positional shifts due to vibrations during transport, etc.) of the first transport mechanism 23 and second transport mechanism 27, and process-related errors (variations in resist film thickness, variations in sensitivity due to uneven coating, etc.).

[0056] After the correction process S12, the control unit 70 converts the corrected exposure data into raster data such as a bitmap in the rasterization process S13, and stores the rasterized corrected exposure data D3 in the storage unit 73.

[0057] After the rasterization process S13, the control unit 70 executes the exposure process S14. In the exposure process S14, as described above, the control unit 70 repeatedly and alternately executes the main scanning process and the sub-scanning process. In the main scanning process, a spatially modulated beam based on the corrected exposure data D3 is irradiated onto the substrate W from the exposure head 41. This draws a pattern on the substrate W at the corrected position.

[0058] As described above, the control unit 70 (data compression device) of this embodiment can efficiently search for the optimal control point using the control point output by the trained model 81 as the initial value. Therefore, it is possible to reduce the computational cost of approximation calculations while avoiding a decrease in approximation accuracy.

[0059] Furthermore, the number of points in the second exposure data D2 obtained by curve approximation is less than the number of points in the first exposure data D1, which is short vector data. Therefore, correcting the second exposure data D2 reduces the computation time required for correction compared to correcting the first exposure data D1. In other words, the computation cost in the correction process can be reduced.

[0060] <2. Variant Example> Although embodiments have been described above, the present invention is not limited to those described above, and various modifications are possible.

[0061] In the above embodiment, the trained model 81, in the control point acquisition step S5, acquires all four control points (start point, end point, and two direction points) of the cubic Bézier curve approximated by the input point cloud. Although the control points are included in the learning process, only some of the four control points may be included in the learning process. For example, the trained model 81 may exclude the start and end points from the learning process and only search for the two direction points. In this case, the start and end points output by the trained model 81 will remain unchanged, for example, at the same positions as the two points located at both ends of the point cloud. This reduces the computational cost of initial values ​​for the control points used in the control point search.

[0062] In the above embodiment, the control unit 70 searches for all four control points (start point, end point, and two direction points) of the cubic Bézier curve in the search step S6. However, it is also possible to search for only some of the four control points. For example, the start point and end point may be excluded from the search, and only the two direction points may be searched. In this case, the start point and end point after the search remain in the same positions as the start point and end point output by the trained model 81 in the control point acquisition step S5. This reduces the computational cost of the control points of the Bézier curve that approximates the input point cloud.

[0063] In the above embodiment, a cubic Bézier curve is used as the approximation curve, but it is also possible to use a quadratic Bézier curve or a Bézier curve of a higher order than cubic. Furthermore, approximation may be performed using Bézier curves of different orders depending on the shape of the point cloud array. In this case, pre-trained models for each order may be used. For example, when approximating with a cubic, quartic, or quintic Bézier curve, control points may be generated by inputting them into pre-trained models for cubic, quartic, and quintic curves, respectively.

[0064] Furthermore, while a Bézier curve is used as the approximation curve in the above embodiment, other approximation curves may be used. Other approximation curves include spline curves, B-spline curves, and polynomial regression curves. Even with other approximation curves, data compression can be achieved using the same method described in the above embodiment. Note that Bézier curves can represent the curve with fewer curve parameters than other curves. Therefore, the data compression ratio can be improved.

[0065] Although this invention has been described in detail, the above description is illustrative in all respects, and the invention is not limited thereto. It is understood that countless variations not illustrated can be conceived without falling outside the scope of this invention. The components described in each of the above embodiments and variations can be combined or omitted as appropriate, as long as they do not contradict each other. [Explanation of Symbols]

[0066] 1: Exposure device 41: Exposure head 70: Control Unit (Data Compression Device) 71: Processor 73: Storage section 81: Pre-trained model W: Circuit board D1; First exposure data (first data) D2: Second exposure data (second data)

Claims

1. A data compression device, Processor and Memory unit and, Equipped with, The aforementioned storage unit is The first data represents the shape as a point cloud, A trained model that takes the first data as input and outputs curve parameters for approximating the point cloud represented by the first data as a curve, Remember this, The aforementioned processor, A process of reading the first data from the storage unit, The process involves inputting the first data into the trained model and obtaining the curve parameters output by the trained model, A process to search for curve parameters of an approximate curve that approximates the figure represented by the first data, using the curve parameters output from the trained model as initial values, A process to generate second data that represents the point cloud represented by the first data using curve parameters obtained by the search, A data compression device that performs this operation.

2. A data compression device according to claim 1, A data compression device in which the approximation curve is a Bézier curve, and the curve parameters indicate the control points of the Bézier curve.

3. A data compression device according to claim 1, The processor is a data compression device that, in the search process, performs a process that includes searching for the curve parameters using the least squares method.

4. An exposure apparatus, A substrate holding section that holds the substrate, An exposure head for exposing the substrate held in the substrate holding portion, A data compression device according to any one of claims 1 to 3, A correction unit that corrects the second data generated by the data compression device, An exposure apparatus equipped with the following features.

5. A data compression method, The process of reading the first data from the memory unit, The process involves inputting the first data into the trained model and obtaining the curve parameters output by the trained model, A step of searching for curve parameters of an approximate curve that represents the figure represented by the first data, using the curve parameters output from the trained model as initial values, The process involves generating second data that represents the point cloud represented by the first data using curve parameters obtained through the search, A data compression method that includes this.

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