JP5610800B2 - Optical element manufacturing method - Google Patents

Description

The present invention relates to a method for manufacturing an optical element for manufacturing an aspherical optical element, and in particular, an aspherical surface having a higher-order shape, a paraboloid, a hyperboloid, a spheroid, etc. The present invention relates to a method for manufacturing an optical element that polishes an optical element having a shape that is difficult to process with a full-surface polishing tool.

Although materials such as synthetic quartz glass, low thermal expansion glass, CVD-SiC, and CaF ₂ single crystal are expensive, they are used for lenses and mirrors for short wavelength light because of their excellent physicochemical properties. However, there have been many simple shapes such as a flat surface and a spherical surface. Recently, however, there is an increasing demand for high-order aspheric lenses and mirrors.

  The production of optical elements such as lenses and mirrors or optical element molding dies requires high shape accuracy, and the required accuracy has been satisfied by repeating measurement and processing. Here, it is possible to polish the shape finished by grinding to a smooth surface with a whole surface polishing tool as long as it is a simple shape such as a flat surface or a spherical surface. However, it is difficult to maintain the shape accuracy after grinding in complicated shapes such as aspherical surfaces and free-form surfaces having higher orders.

  In the processing of such a shape, particularly in the polishing process which is the final finish, in order to improve the shape followability of the polishing tool, shape correction processing is mainly performed by a local processing method using a small diameter tool smaller than the processing region. It is common. As typical examples of such local processing methods, methods disclosed in Patent Document 1 and Patent Document 2 have been devised.

  In the processing method disclosed in Patent Document 1, a unit removal shape that is a polishing removal shape per unit time of the polishing tool is acquired in advance prior to processing of a workpiece. Subsequently, based on the shape error data obtained from the unit removal shape and the measurement result of the surface to be processed, tool dwell time distribution data is obtained to perform shape correction polishing. This method obtains tool dwell time distribution data on the assumption that the unit removal shape acquired in advance is the same or constant over time in the entire machining region, and performs shape correction polishing by controlling the tool dwell time. Is.

  Further, in this type of partial polishing method, one of the processing conditions is how the polishing tool is moved on the processing surface. As a method for setting the trajectory, a method disclosed in Patent Document 3 is known. In this prior art, a polishing tool having a small contact area is raster-scanned on the surface to be processed, and polishing is performed by changing the direction of raster scanning and performing a plurality of polishing steps.

Japanese Patent No. 3304994 JP 2007-144568 A Japanese Patent Laid-Open No. 9-267244

By the way, the shape required as an optical element for a short wavelength is almost an axisymmetric aspherical surface, and high shape accuracy is required. In such a polishing method that polishes such an axially symmetric aspherical surface by sequentially changing the direction of a plurality of raster scans as in the prior art described above, there are the following problems.
(1) Usually, the pre-processing for creating an axisymmetric aspherical shape is a grinding process. In this grinding process, the workpiece is rotated around the symmetry axis (optical axis), and the grinding wheel is trajected on the radius. Grinding is controlled. Due to this shape creation principle, concentric error shapes centering around the symmetry axis (optical axis) often remain on the aspherical surface of the workpiece. Furthermore, in the Precision Engineering Society “2008 Spring Conference Academic Lecture Proceedings” (pages 1037-1038), etc., in addition to the concentric error shape as described above, periodic rotation unevenness of the grinding wheel or grinding wheel It has already been reported that minute waviness components remain due to shaft vibration. This is a periodic waviness component called nanotopography having a relatively high frequency and a small unevenness along the circumferential grinding wheel trajectory. Raster scanning is not appropriate as a tool scanning method for partial polishing (local polishing) to remove these concentric shape errors and nanotopography along the grinding wheel trajectory in the circumferential direction. (Processing residuals) are likely to occur.
(2) By evaluating the parameter indicating the isotropic and anisotropy of the tool passing direction on the work surface and the surface roughness, the deviation of the trajectory of the tool affects the surface roughness. It has been reported in the Japan Society for Precision Engineering “Proceedings of the Fall Meeting of the 1990 Fall Conference” (pp. 653-654). In partial polishing (local polishing), it is the degree of anisotropy of the polishing trajectory that affects the surface roughness under the motion conditions, and if the isotropic of the polishing trajectory is maintained, good surface roughness can be maintained. it can. However, the method of proceeding with the polishing process by sequentially changing the directions of a plurality of raster scans is, in principle, superposition of the straight scans of the polishing tool, and all the scans are straight. For this reason, the rectilinear scanning pattern itself remains on the surface to be processed, and a new grid-like undulation (a region where the spatial period of this undulation is longer than the surface roughness) occurs due to the superposition of changing the direction. Cheap.

An object of the present invention is to provide a method of manufacturing an optical element that can polish an axisymmetric aspherical shape such as an optical element made of a highly brittle material such as synthetic quartz glass with high reliability and high accuracy. It is what.

In the method of manufacturing an optical element according to the present invention, the surface of the optical element is scanned by relatively scanning a polishing tool along a spiral locus passing through the rotation axis of the optical element with respect to the rotating optical element. In the method of manufacturing an optical element that is polished into an aspherical shape, an error shape measurement step for measuring the surface shape of the optical element before processing and obtaining an error shape with respect to a target shape, and an error obtained in the error shape measurement step Extracting the first shape component of the shape that is axisymmetric with respect to the rotation axis, and taking the difference between the error shape and the first shape component, thereby providing non-axisymmetric with respect to the rotation axis Extracting the second shape component, determining the high frequency shape component of each of the first shape component and the second shape component, and polishing the first shape component from each of the high frequency shape components Remove A first polishing tool because the the steps of the second shape component selected a second polishing tool for polishing removal, wherein the first shape component first polishing tool of the error shape calculating a first residence time distribution required to polish removed using, the necessary said second shape component of the error shape to polish removed by the second polishing tool A step of calculating a residence time distribution of 2 and a first polishing performed by a first polishing tool along the spiral trajectory while controlling a scanning speed so as to realize the first residence time distribution. A polishing step, and a second polishing step of polishing with a second polishing tool along the spiral trajectory while controlling a scanning speed so as to realize the second residence time distribution. It is characterized by.

  The error shape remaining from the previous process is evaluated by separating it into an axially symmetric component and a non-axisymmetric component, and the dwell time distribution of the polishing tool is calculated to effectively remove each component. Do. As a result, the error shape remaining in the annular zone can be smoothed and removed with higher accuracy than the method of processing the residence time distribution of the polishing tool in one pass and the method of changing the direction when dividing them into multiple raster scans. Can do. Further, such two-component processing can be performed by one shape measurement before processing, and the efficiency of the entire polishing process can be improved.

  In addition to the concentric error shape remaining in the grinding process, it effectively removes periodic micro-waviness components called nanotopography of relatively high frequency remaining in the circumferential direction along the grinding wheel trajectory in the grinding process. Therefore, a highly accurate and smooth aspherical shape can be obtained. In addition, it is possible to process the ring-shaped swell shape, which is a relatively low frequency component, at a high removal rate, which can contribute to shortening the overall processing time.

It is a schematic block diagram which shows the grinding | polishing apparatus which concerns on one Example. It is a flowchart which shows the grinding | polishing processing method using the apparatus of FIG. It is a figure explaining spiral scanning of an abrasive tool.

  In FIG. 1, a y table 52 that is reciprocally movable in the y direction is mounted on a bed 50. An encoder 56 is attached to the y motor 54 for driving the y table 52, and the encoder 56 detects the amount of movement in the y direction of the y table 52. An x table 58 that is movable in the x direction is mounted on the y table 52. An encoder 62 is attached to the motor 60 for driving the x table 58, and the encoder 62 detects the amount of movement in the x direction of the x table 58.

  A polishing rod 64 is fixed on the x table 58. A support 66 is fixed in the polishing rod 64, and a holding body 70 is attached to the support 66 by a shaft 68. A rotary table 71 is installed on the holding body 70, and a rotational drive and a rotational position are detected by a table rotational motor and an encoder (not shown) (hereinafter, this rotational axis is referred to as "A axis" as appropriate). ). Moreover, the axis | shaft 68 has faced the x direction, and the holding body 70 can be rotated around the axis | shaft along an x-axis. A motor 72 is attached to the support 66, and its drive rotation shaft is coupled to a shaft 68, and rotation driving and detection of the rotation position are performed by an encoder (not shown) (hereinafter, this rotation shaft is appropriately set). , Referred to as “B-axis”).

  On the other hand, a column 74 is fixed to the bed 50. The column 74 is formed with a guide 76 in the vertical direction, that is, in the z direction, and an inclination positioning mechanism for the holding body 78 is attached so as to reciprocate in the vertical direction along the guide 76. The holding body 78 supports a polishing head 80 capable of rotating. A first polishing tool T1 or a second polishing tool T2, which will be described later, is attached to the lower end of the rotating shaft 82 of the polishing head 80. A motor 86 is attached to the holding body 78, and its drive rotation shaft is connected to the polishing head 80, and can drive the tilt positioning mechanism of the polishing head 80. The tip of the rod 90 of the air cylinder 88 that is a driving means for moving the holding body 78 in the vertical direction along the guide 76 is connected to the holding body 78. The control device 92 receives the y table movement amount, the x table movement amount, and the rotation table movement amount from the encoders 56 and 62 and the like. Further, motors 54, 60, 72, 86, a polishing head drive motor (not shown) in the polishing head 80, and an air cylinder 88 or a motor that replaces the movement thereof are driven by commands from the control device 92.

When polishing is performed using the polishing apparatus configured as described above, the workpiece 100 that has been finished with a predetermined surface roughness and a predetermined shape accuracy by appropriate pre-processing (grinding) is held. It is loaded and fixed on the rotary table 71 on the body 70. In the present embodiment, the workpiece (optical element) 100 is an axisymmetric aspherical lens made of synthetic quartz glass having a diameter of 200 mm, and the light beam effective portion has a central diameter of 180 mm. The synthetic quartz glass material as the workpiece 100 is subjected to high-precision aspherical grinding by rotating the workpiece 100 around the symmetry axis (optical axis) as a pre-processing, and has a predetermined surface roughness and a predetermined surface roughness. It is finished with the shape accuracy. An appropriate amount of polishing liquid 102 is injected into the polishing bowl 64. In this example, cerium oxide abrasive grains were used as the abrasive grains in the polishing liquid.

  While the polishing tool of the polishing head 80 is pressed and rotated by the tool rotating shaft 82, the linear motion of the y table 52, the rotational motion of the A axis, and the B axis on the surface of the workpiece 100 having an aspherical shape. By rotating the direction, scanning is relatively performed along a spiral trajectory. In this way, local polishing by spiral scanning is advanced.

  Next, the procedure of the polishing method according to this embodiment will be described with reference to the flowchart of FIG. First, a pre-processed shape that is a surface shape before processing of a workpiece is measured, and an error shape with respect to a target shape (designed shape) of the pre-processed shape is obtained (step S1).

  Next, an axially symmetric component D1, which is a first shape component that is axially symmetric with respect to the rotation axis (optical axis) of the workpiece, is extracted from the error shape obtained by the error shape measuring step in step S1 (step S1). S2). As a method of extracting the axially symmetric component D1, each minute step (for example, every sampling pitch of a measurement shape that is an array of discrete coordinate values) from the center of the error shape in the radial direction is performed on each circumference. A general method for extracting the average value of the shape values is used. When this average value is plotted over the entire surface to be processed as the same value on each circumference in the radial direction, surface data representing concentric contour lines is obtained. At this time, the above-mentioned average value may be calculated after removing abnormal values protruding on one circle as appropriate.

Subsequently, the difference between the above-described error shape and the axially symmetric component D1 is taken, and the non-axisymmetric component D2, which is the second shape component that is non-axisymmetric with respect to the rotation axis, is extracted (step S3). Then, each of the axially symmetric component D1 and the non-axisymmetric component D2 in the error shape is subjected to a fast Fourier transform process to perform spatial frequency analysis. The result is represented in a chart with the horizontal axis representing the spatial frequency and the vertical axis representing the spectral intensity, and the shape component having the dominant spatial frequency at the higher frequency side is discriminated as the “high frequency shape component” (step S4). . In this embodiment, the dominant spatial frequency of the axially symmetric component D1 is 0.10 mm ⁻¹ (10 mm in spatial wavelength), and the dominant spatial frequency of the non-axisymmetric component D2 is 0.33 mm ⁻¹ (3 mm in spatial wavelength). Met. Here, the dominant spatial frequency of the axially symmetric component D1 is, for example, an accuracy error of a grinding apparatus feed shaft when a grinding wheel is fed in a radial direction while rotating a workpiece in the grinding process which is a previous process, or It is a relatively low-frequency concentric shape component due to thermal displacement or the like. On the other hand, the dominant spatial frequency of the non-axisymmetric component D2 is, for example, a nano frequency with a relatively high frequency and a small unevenness along the grinding wheel trajectory in the circumferential direction caused by periodic rotation unevenness or grinding wheel vibration of the grinding wheel. It is a periodic swell component called topography.

Next, two polishing tools having different unit removal shape sizes corresponding to the axially symmetric component D1 and the non-axisymmetric component D2 are selected (step S5). In the present embodiment, the dominant spatial frequency of the axially symmetric component D1 is 0.10 mm ⁻¹ , so the size of the first polishing tool T1 is about φ8 mm. The unit removal amount of the tool at this time is 1.5 mm ³ / h. On the other hand, since the dominant spatial frequency of the non-axisymmetric component D2 is 0.33 mm ⁻¹ , the size of the second polishing tool T2 is about φ2 mm. The unit removal amount of the tool at this time is 0.5 mm ³ / h. That is, a polishing tool having processing sensitivity up to a spatial frequency higher than the dominant spatial frequency of each of the axially symmetric component D1 and the non-axisymmetric component D2 is selected.

  Subsequently, dwell time distributions D3 and D4 on the work surface of the polishing tool necessary for polishing and removing each of the axially symmetric component D1 and the non-axisymmetric component D2 of the error shape are calculated (step S6). ). The residence time distribution is calculated in advance by a unit having a polishing removal shape per unit time for each of the first polishing tool T1 for the axially symmetric component D1 and the second polishing tool T2 for the non-axisymmetric component D2. Obtain the removal shape.

  Then, deconvolution calculation is performed from the acquired unit removal shape and the error shape (axisymmetric component D1 and non-axisymmetric component D2) to be removed, and a first residence time distribution D3 (corresponding to the axially symmetric component D1). And a second residence time distribution D4 (corresponding to the non-axisymmetric component D2).

  This calculation is described in detail in the document “Journal of the Japan Society for Precision Engineering: 62 (1996) 408”. The obtained residence time distributions D3 and D4 represent residence times of the polishing tool T1 and the polishing tool T2 (performing a regular and constant polishing motion) on the surface to be processed. If the scanning speed of the polishing tool is controlled so as to realize this residence time distribution, the error shape, that is, the waviness shape remaining in the previous step can be removed smoothly.

  In the axisymmetric component D1 and the non-axisymmetric component D2 of the error shape, a spatial frequency higher than each dominant spatial frequency is usually smoothed in the polishing process and may not be included in the error shape. Further, the shape measurement itself is an array of discrete coordinate values, and high spatial frequencies may be filtered out according to this sampling pitch. The sampling pitch is preferably 1 mm or less in terms of shape description.

  Subsequently, a motion control program for scanning the polishing tool over the entire surface to be processed while controlling the scanning speed so as to realize the above residence time distribution is calculated (step S9). Prior to this, the scanning parameters of the polishing tool relating to the high-accuracy dwell time control and the machining time reduction of the above-described “high-frequency shape component” are set as follows. A motion control program (also referred to as an NC program for polishing or a polishing program) drives a polishing tool to rotate at a constant rotation speed, and scans the processing surface according to a certain scanning pattern to stay on the processing surface. It is a machining program for realizing time.

  In the polishing process by spiral scanning of the polishing tool, the residence time distribution described above is residence for each discrete cell in the r-θ coordinate system represented by two axes of the radial direction r and the circumferential direction θ of the work surface. Coordinates have been converted to time distribution. Accordingly, the difference in the residence time of the polishing tool between the cells is expressed by the sum of the scanning speed differences of the polishing tool separated into the speed difference components of the scanning speeds Vr and Vθ of each axis of the r-θ coordinate system.

  First, at the time of spiral scanning of the “high-frequency shape component”, the rotation speed of the rotary table that holds the workpiece is controlled by a table rotation motor (so that the dwell time is controlled in the spiral rotation direction (circumferential direction of the workpiece surface). (Not shown) to change the speed.

In particular, in the “high-frequency shape component” polishing process, the resolution of the acceleration / deceleration command is increased so that the residence time difference in the scanning axis direction along the target removal shape can be realized more accurately. The command resolution of the scanning speed difference representing the residence time difference between the unit cells is determined by a polishing tool having a distance corresponding to the spatial wavelength λ corresponding to the above-described dominant spatial frequency (hereinafter referred to as “excellent spatial wavelength λ” as appropriate). It is represented by the number N of acceleration / deceleration commands within the passing time. Then, a minimum scanning speed V2min (referred to by adding “2” to the parameter related to the non-axisymmetric component) for increasing the acceleration / deceleration command number N to increase the resolution is set (step S7). Specifically, the residence time difference necessary for polishing removal of the non-axisymmetric component D2 as the “high-frequency shape component” is represented by the difference in scanning speed in the circumferential direction, that is, the rotation axis (A axis) of the workpiece. The acceleration / deceleration command count N2θ in this case is the acceleration and deceleration of the velocity V2θ at which the polishing tool T2 passes the distance corresponding to the dominant space wavelength λ2 of the non-axisymmetric component D2 in the circumferential direction on the outermost periphery of the processing surface. The total number of commands N2θ. Here, the acceleration / deceleration command number N2θ is expressed by the following equation (1) using the minimum scanning speed V2θmin at the outermost periphery of the workpiece, the dominant space wavelength λ2, and the command time interval ΔT of the acceleration / deceleration command issued from the control device 92. Represented.
N2θ = λ2 / (V2θmin × ΔT) (1)

  Therefore, by decreasing the minimum scanning speed V2θmin and the command time interval ΔT, the acceleration / deceleration command count N2θ can be set large, and the residence time difference can be controlled with higher resolution.

  The number of acceleration / deceleration commands N2θ is an acceleration command and a deceleration command that are output at least five times within the time required for the polishing tool T2 to pass the distance corresponding to the dominant space wavelength λ2 (one period of waviness) on the outermost periphery of the work surface. Therefore, as many as possible are set within the control range of the polishing apparatus. Thus, by setting the acceleration / deceleration command number N2θ to be large, it is possible to perform the dwell time control that more accurately reproduces the non-axisymmetric component that is the “high-frequency shape component”, that is, the circumferential target removal shape.

  Next, the minimum feed pitch P1min in machining the axially symmetric component D1 in the error shape is set (step S8). Here, since the axially symmetric component D1 is a shape component that does not have irregularities in the rotation direction of the workpiece, that is, in the circumferential direction, the rotary table is rotated at a constant speed in the processing of the axially symmetric component D1. A y motor that drives the y table and a rotary motor that drives the rotary table that tilts the workpiece so that the dwell time is controlled in the spiral feed direction (machined surface radial direction) (not shown). To control.

  At this time, in order to polish and remove the axially symmetric component D1, which is a concentric error shape, the spiral feed pitch shown in FIG. In the recess, the feeding speed is increased to increase the spiral feeding pitch. Further, in order to correct the change in the removal amount in the vicinity of the outer peripheral portion and the central portion, a correction value is applied to the residence time distribution in the radial direction. This correction value is obtained by performing verification processing or the like in advance from the rotation speed of the rotary table holding the workpiece.

  The axisymmetric component D1, which is a removal target, is a shape component having a relatively low frequency and a shape having a relatively large unevenness. For this reason, ensuring the tool scanning resolution necessary for removing the waviness of the dominant spatial frequency λ1 (hereinafter referred to as “1” as appropriate for the parameter related to the axial symmetry component) by the following tool scanning parameter setting method; At the same time, the machining time can be shortened.

First, when removing the waviness shape component in the radial direction of the surface to be processed, machining is performed with a residence time difference, that is, a speed difference in the tool feed direction. That is, a relatively long tool residence time is taken in the undulation-shaped convex portion, while a relatively short tool residence time is obtained in the undulation-shaped concave portion, but the lowest portion of the entire surface to be machined has the tool. It becomes a point that passes quickly. Since the tool speed at this lowest point cannot be made infinite, it is defined by the maximum speed specifications of the rotary motor of the rotary table and the y motor in the feed direction, and is the minimum uniform over the entire work surface. A removal depth d1min is generated (hereinafter referred to as “uniform removal depth” as appropriate). Accordingly, the processing time can be shortened by reducing the uniform removal depth d1min by the following method. First, the relationship between the uniform removal depth d1min, the unit removal rate R1, the maximum scanning speed V1θmax in the rotation direction, and the feed pitch P1 is expressed by the following equation (2).
d1min = R1 / (V1θmax × P1) (2)

  Here, since the unit removal rate R1 is determined by the polishing tool T1, and the maximum scanning speed V1θmax is defined by the maximum rotation speed (device specification) of the y table 52, it is assumed here to be constant. Therefore, in order to shorten the processing time by reducing the left side of the above equation, there is a demand to set the feed pitch P1 as large as possible as one parameter of the denominator of the right side.

On the other hand, the acceleration / deceleration command number N1 of the scanning speed in the feed direction that represents the resolution of the dwell time control of the axisymmetric component D1 is the minimum feed pitch P1 within the time during which the polishing tool passes the distance corresponding to the above-described dominant space wavelength λ1. Is represented by the following formula (3).
N1 = λ1 / P1 (3)

  In order to ensure the resolution of the dwell time control even in the axially symmetric component D1, the acceleration / deceleration command number N1 is set to 5 or more accelerations and 5 times within the time when the polishing tool T1 passes the distance corresponding to the dominant space wavelength λ1. The maximum feed pitch P1max that satisfies the total number of times of deceleration more than is set. In the following tool movement control program calculation, a feed pitch as large as possible is calculated within this condition range, and machining in a relatively short time is possible.

  As described above, based on the polishing tool scanning condition and the unit removal shape of the polishing tool, the dwell time distributions D3 and D4 of the axisymmetric component D1 and the non-axisymmetric component D2 on the work surface of the polishing tool are realized. A motion control program is calculated (step S9).

Next, a scan for removing the non-axisymmetric component D2 obtained by the calculation of the polishing program as described above (second polishing step), and a scan for removing the axially symmetric component D1 (first Each polishing step) is sequentially executed as shape correction polishing (step S10).
All of the above-described programs for the axisymmetric component and the non-axisymmetric component polishing are executed, and the polishing is completed. Thereafter, the shape of the workpiece after polishing is measured (step S11), an error shape with respect to the current target shape (design shape) of the work surface is obtained, and whether the error shape amount is within the design tolerance. Determination is made (step S12). If it is within the tolerance, the polishing process is terminated and the workpiece is sent to the next process (step S13). On the other hand, if the error shape has not yet reached the tolerance, the steps after step S2 are repeated.

  As described above, the error shape remaining from the previous process is evaluated by separating it into an axisymmetric component and a non-axisymmetric component, and the residence time distribution of the polishing tool that effectively removes each component is divided into two. The polishing is performed with different scanning methods. Compared to the method of processing the dwell time distribution of the polishing tool in one pass and the method of changing the direction when dividing them into multiple raster scans, in this embodiment, the error shape remaining in the annular zone is smoothed with high accuracy. Can be removed. Further, such two-component processing can be performed by one shape measurement before processing, and the efficiency of the entire polishing process can be improved. In particular, in addition to the concentric error shape remaining in the grinding process, periodic micro-waviness components called nanotopography of relatively high frequency remaining in the circumferential direction along the grinding wheel trajectory in the grinding process are processed. Can be effectively removed by high-resolution rotation control. Thereby, a highly accurate and smooth axisymmetric aspherical shape can be obtained. In addition, in the processing of the separated axisymmetric component, it is possible to cope with the removal of the ring-shaped swell shape, which is a relatively low frequency component, and it is possible to perform processing at a relatively high removal rate. Thereby, the whole processing time can be shortened.

50 bed 52 y table 58 x table 80 polishing head 100 optical element ( workpiece )

Claims (5)

An optical element that polishes the surface of the optical element into an aspherical shape by scanning the polishing tool relative to the rotating optical element along a spiral trajectory passing through the rotation axis of the optical element. In the manufacturing method,
An error shape measuring step of measuring a surface shape of the optical element before processing and obtaining an error shape with respect to a target shape;
Extracting a first shape component that is axisymmetric with respect to the rotational axis of the error shape obtained in the error shape measurement step;
Extracting a second shape component that is non-axisymmetric with respect to the rotation axis by taking a difference between the error shape and the first shape component;
A first polishing tool for discriminating a high-frequency shape component of each of the first shape component and the second shape component, and polishing and removing the first shape component from the respective high-frequency shape components; Selecting a second polishing tool for polishing away the second shape component;
Calculating a first residence time distribution necessary for polishing and removing the first shape component of the error shape using the first polishing tool ;
Calculating a second residence time distribution required to polish and remove the second shape component of the error shape using the second polishing tool ;
A first polishing step of performing polishing with a first polishing tool along the spiral trajectory while controlling a scanning speed so as to realize the first residence time distribution;
A second polishing step of performing polishing with a second polishing tool along the spiral trajectory while controlling a scanning speed so as to realize the second residence time distribution. A method for manufacturing an optical element.   The method of manufacturing an optical element according to claim 1, wherein the first and second polishing tools have different unit removal shapes. The high-frequency shape component of each of the first shape component and the second shape component is discriminated by performing a spatial frequency analysis by performing a fast Fourier transform process on the first shape component and the second shape component , respectively, axis spatial frequency and the vertical axis in charts and spectral intensity table eagle, the optical element according to claim 2, wherein the determine specific to Rukoto as a high-frequency shaped component having a dominant spatial frequencies in the frequency of the higher frequency side Production method.   4. The optical system according to claim 3, wherein an acceleration command and a deceleration command are each output five times or more within a time period in which one wave wave having a spatial wavelength corresponding to the dominant spatial frequency of the high-frequency shape component passes. Device manufacturing method.   The optical element manufactured by the manufacturing method of the optical element as described in any one of Claims 1 thru | or 4.

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