PROCESSING APPARATUS AND OPTICAL MEMBER MANUFACTURING METHOD

Technical Field

[0001] The present invention relates to a processing apparatus and an optical member manufacturing method that can mainly provide high-precision processing.

[0002] The optical members include those that are shaped to be flat, spherical, or aspherical, and are sized to be one meter or more . The optical members also include a mold to shape optical members. Major materials of optical members to be processed include glass, ceramic, metal, and crystal.

Background Art

[0003] Lenses for semiconductor exposure apparatuses or mirrors for astronomical telescopes represent an optical member having high-precision aspherical surface. A widely known method of processing the surface of such optical members uses a tool whose diameter is smaller than a workpiece surface to be processed. For example, a tool whose diameter is smaller than 1/10 of the workpiece surface to be processed. The tool is scanned to polish the entire worked surface of the workpiece.

[0004] This polishing method is hereinafter referred to as a local polishing method . The local polishing method previously identifies the tool's removal shape and volume per unit time (hereinafter referred to as a unit removal shape) . Inthemethod, the unit removal shape is assumed to be invariable and constant during processing, and the entire worked surface of the workpiece is polished based on a specified removal quantity.

[0005] Usually, an aspherical workpiece includes locally different shapes at different positions on the workpiece. If a tool is scanned over the workpiece, local shapes on the workpiece vary depending on positions that contact the tool.

[0006] Usually, on the tool surface that is in contact with the workpiece, a polishing member such as polyurethane is attached. The tool surface shape and the thickness of the polishing member remains constant regardless of positions that contact the tool. As a result, the contact condition between the tool and the workpiece changes during scanning or processing due to the change of the workpiece surface in shape with which the tool surface is in contact. The unit removal shape also changes accordingly . Aprocessing method proposed to solve this problem uses a variable shape tool that can vary the tool surface shape during processing depending on workpiece shapes.

[0007] PTL 1 discusses the variable shape tool, for example. According to the conventional example, a tension band contained in a tool deforms the tool surface to control the radius of the tool in a cross-section thereof.

[0008] The tool surface is basically assumed to be spherical . According to the processing method using this tool, the radius of the tool surface varies with a local workpiece shape (local radius of the workpiece) at positions in contact with the tool

(see Fig. 9) .

[0009] This causes little changes in the contact condition between the tool and the workpiece during processing, and prevents the unit removal shape from changing. On condition that the unit removal shape is constant, the entire worked surface of the workpiece is polished with an approximately constant removal quantity to prevent the figure accuracy from degrading due to processing. Further, the contact condition between the tool and the workpiece during processing is not easily changed, whereby the waviness on the workpiece surface to be processed can be smoothened.

[0010] The "waviness" generally means a short-wavelength workpiece component with reference to the diameter of a small-diameter tool as described in the local polishing method.

On the other hand, the "figure accuracy" means the accuracy of a workpiece component having a wavelength longer than the tool diameter.

Citation List

Patent Literature

[0011] PTL 1: USP 7364493

Summary of Invention

Technical Problem

[0012] According to the conventional example, however, improving the waviness accuracy of a workpiece degrades the figure accuracy, which is problematic.

[0013] More specifically, in order to improve the workpiece waviness accuracy, the convention example needs to increase the tool diameter enough to smooth a waviness having a longer spatial wavelength (hereinafter simply a wavelength) .

[0014] However, the conventional example controls the tool surface based on the radius. Increasing the tool diameter also increases the controllable wavelength for a tool surface. Therefore, the tool cannot fit short-wavelength workpiece shapes In a case where the tool surface is controlled based on shapes, if the tool surface rigidity has distribution or changes, the contact condition between the tool surface and workpiece also changes .

[0015] The rigidity distribution or change more easily occurs as the tool diameter increases . Therefore, increasing the tool diameter easily varies the unit removal shape during processing and degrades the figure accuracy of the workpiece.

[0016] The present invention has been made in consideration of the foregoing. The invention aims at providing a processing method that can improve the figure accuracy and the waviness accuracy and highly precisely polish the surface of a flat, a spherical, or an aspherical optical member, and the like. More particularly, the invention aims at providing a processing apparatus and an optical member manufacturing method that can allow a tool surface to fit a workpiece regardless of tool diameters and improve the workpiece figure accuracy at the same time .

Solution to Problem

[0017] According to an aspect of the present invention, a processing apparatus generates a pressure between a polishing member and a workpiece and relatively moves the polishing member and the workpiece to process a workpiece. The processing apparatus includes a support member that causes oscillating movement, and a processing portion that is rotatably attached to the support member. The processing portion includes one or more pressure generation units to generate different pressures between the polishing member and the workpiece.

[0018] According to another aspect of the present invention, an optical member manufacturing method generates a pressure between a polishing member and a workpiece and relatively moves the polishing member and the workpiece to process a workpiece. More than one pressure generation unit is provided to generate different pressures between the polishing member and the workpiece. A target removal quantity at each position on the workpiece is found from a workpiece shape before processing acquired by measuring the workpiece and a target shape of the workpiece. The workpiece is processed by varying a pressure generated between the polishing member and the workpiece according to a target removal quantity at each position on the workpiece .

Advantageous Effects of Invention

[0019] The invention can improve the figure accuracy and the waviness accuracy and highly precisely process the surface of a flat, a spherical, an aspherical optical element or the like.

[0020] Further features and aspects of the present invention will become apparent from the following detailed description of exemplaryembodiments with reference to the attached drawings . Brief Description of Drawings

[0021] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate exemplary embodiments, features, andaspects of the invention and, together with the description, serve to explain the principles of the invention .

[0022] Fig. 1 illustrates a first exemplary embodiment of the invention.

[0023] Figs. 2A and 2B illustrate a workpiece and a tool.

[0024] Figs. 3A and 3B illustrate positions of the workpiece and the tool.

[0025] Figs. 4A and 4B illustrate a second exemplary embodiment of the invention.

[0026] Figs. 5A, 5B, and 5C illustrate other exemplary embodiments of the invention.

[0027] Figs. 6A, 6B, and 6C illustrate examples of supporting members .

[0028] Fig. 7 illustrates an example of a simplified processing apparatus.

[0029] Fig. 8 illustrates an example of a processing flow.

[0030] Fig. 9 illustrates a conventional technology.

Description of Embodiments

[0031] Various exemplary embodiments, features, and aspects of the invention will be described in detail below with reference to the drawings .

[0032] The present invention is applicable to processing of an optical member such as a mirror or a lens that has a free-formed surface and requires a high figure accuracy. Optical elements related to the present invention include a flat, a spherical, an aspherical, or free-formed surface, and larger ones sized to be one meter or more. The optical elements also include a mold to mold optical elements. Major materials of optical elements to be processed include glass, ceramic, metal, and crystal .

Example 1

[0033] Fig.1 illustrates an example of a processing apparatus according to an exemplary embodiment of the present invention, which is applied to a horizontal swing polishing machine.

[0034] A processing portion 20 of the processing apparatus will be described first. The processing portion 20 includes one or more pressure generation units 2 two-dimensionally placed on a base 1. For the base 1, a high-rigidity and lightweight lattice type frame may preferably be used.

[0035] The pressure generation unit 2 includes an actuator and a detector that are placed in series. The actuator may be a piezoelectric element, an electrostrictive actuator, a voice coil motor, a pneumatic cylinder, or a hydraulic cylinder. The detector may be a pressure sensor or a load cell. The tip of the pressure generation unit 2 contacts a faceplate 3.

[0036] The faceplate 3 is connected to the outer periphery of the base 1. Materials for the faceplate include SUS316 stainless steel, for example. A polishing member 4 is attached to the faceplate 3. The polishing member surface works as a tool surface.

[0037] A pressure generated from the pressure generation unit presses the polishing member 4 against a workpiece to process it. That is, the workpiece and the processing portion are relatively moved to independently control the pressure generation unit of the processing portion. To process the workpiece, a pressure (suppress strength) against the workpiece is changed in the polishing member on the surface of the polishing member in contact with a worked surface of the workpiece. The distribution of the pressure on the surface (tool surface) of the polishing member is changed to process the workpiece. Materials for the polishing member include polyurethane, for example.

[0038] Fig.2A illustrates an example of the workpiece . Fig. 2B is an example of the processing portion 20 and illustrates relationship between the faceplate and 12 pressure generation units 2 (a through 1) . The effect of the invention is generated with more than one pressure generation unit 2. Increasing the number of pressure generation units 2 improves the processing accuracy. Due to physical restrictions, however, the processing portion preferably contains approximately several tens of actuators or fewer.

[0039] The processing portion 20 is rotatably supported while it is mounted through a globe 5 at the tip of support member (an oscillating rod (knockout bar)) 6 and the base (frame) 1. The processing portion 20 freely rotates in a rotation direction 7. A tool rotation angle sensor 8 detects a phase change in the processing portion 20, which is a rotation in the rotation direction 7 around the support member 6. Further, the processing portion 20 and the base 1 are attached to the support member 6 through the globe 5, whereby the processing portion 20 and the base 1 can also rotate according to an angle of inclination of the workpiece surface to be processed. The configuration of the apparatus that enables the rotation around the support member and the rotation according to the angle of inclination of the workpiece surface to be processed described above is not limited thereto. Fig. 10 illustrates an example in which a rotation/revolution support mechanism discussed in Japanese Patent 2938593 is applied to the present invention. The processing portion 20 is attached to a processing portion holding member 104 through a rotation support portion 105. The processing portion 20 is rotatable with the rotation support member 105. The processing portion holding member 104 includes a convex spherical portion 103 that functions as a bearing surface . An edge portion 100 of the support member 6 includes a concave spherical portion 101 that functions as a bearing surface, and configures a bearing portion at the end portion of the support member 6, which enables the rotation of the processing portion 20 via a spherical member 102 the convex spherical portion 101 and the convex spherical portion 103. With such a configuration, the rotation of the processing portion 20 and the rotation according to the angle of inclination of the workpiece surface to be processed becomes possible.

[0040] A guide 9 and an oscillating stage 10 move and oscillate the processing portion 20 in an oscillation direction 11. A tool oscillation position sensor 12 detects a positional change in the processing portion 20. As illustrated in Fig. IB, the support member 6 is desirably attached to an end portion of an arm 19 as illustrated in Fig. IB, and the arm 19 can desirably circle in the direction indicated by an arrow 23 with respect to the oscillating stage 10. With this configuration, if the processing portion 20 is moved on the workpiece 13, the support member 6 is moved up and down according to the height of the workpiece 13. Therefore, oscillating operation can be easily performed.

[0041] A table 14 holds the workpiece 13 as an optical element such as a mirror or a lens. A spindle 15rotates in a rotation direction 16, and rotates the table 14 to rotate the workpiece 13. A workpiece rotation angle sensor 17 detects a phase change in the workpiece 13 with reference to the rotation direction 16. A rotation speed preferably ranges from 0.01 rpm to 10 rpm.

[0042] Fig. 3A illustrates a relationship between the workpiece and the pressure generation units of the processing portion before processing. Fig. 3B illustrates a relationship between the workpiece and the pressure generation units of the processing portion immediately after processing. Referring to Figs. 3A and 3B, it can be seen that, before the processing (Fig. 3A) , the processing portion 20 is positioned to the left from the center of the workpiece 13. Immediately after the processing (Fig.3B) , the processing portion 20 oscillates and is positioned to the center of the workpiece.

[ 0043] The globe 5 at the tip of the knockout bar 6 rotatably supports the processing portion 20. The workpiece 13 rotates to slightly rotate the processing portion 20 from the position before the processing. The pressure generation unit accordingly changes its position.

[0044] The tool rotation angle sensor 8 , the tool oscillation position sensor 12, and the workpiece rotation angle sensor 17 detect positions and phases of the processing portion 20 and the workpiece 13 that move as described above. A calculation unit 18 acquires the detected positions and phases.

[ 0045] The calculation unit 18 controls the pressure generation unit 2. As an example, suppose that the pressure generation unit 2 represents a pneumatic cylinde . In this case, the calculation unit 18 determines the quantity of air supplied to and exhausted from the pneumatic cylinder so that a pressure sensor 22 provided between each pneumatic cylinder 21 and the faceplate 3 satisfies a specified value. As another example, suppose that the pressure generation unit 2 is a piezoelectric element. In this case, the calculation unit 18 determines the quantity of electric charge supplied to the piezoelectric element so that a pressure sensor provided between each piezoelectric element and the faceplate 3 satisfies a specified value.

[ 0046] The pressure generation units included in the tool control distribution of the pressure on the tool surface. The controllable distribution of a pressure depends on a distance between the mounted pressure generation units and an area where the tool surface contacts the workpiece surface to be processed, not on the tool diameter. The pressure distribution control keeps contact condition between the tool surface and the workpiece unchanged even if the tool surface rigidity has distributions or changes.

[0047] The tool surface can maintain the even contact condition with the entire workpiece surface regardless of tool diameters . This can restrain the workpiece figure accuracy from degrading due to increasing tool diameters. The present invention can provide tool diameters larger than conventional examples. Therefore, the invention can increase a workpiece area for the tool to be polishable at a time and greatly improve the removal rate.

[0048] Like the above-mentioned local polishing method, a small-diameter tool is generally used to process an aspherical surface. The invention allows the use of a large-diameter tool that is nearly as large as the worked surface of a workpiece and is used for a full-disk polishing method. The invention produces very effective results.

Example 2

[0049] Fig. 4 illustrates a second exemplary embodiment according to the present invention . Fig.4A illustrates a cross sectional view taken along the line LI in Fig. 4B. Fig. 4B is a conceptual diagram illustrating the processing apparatus viewed from the worked surface opposite the workpiece. The processing apparatus according to the present exemplary embodiment includes tool units A through G. The tool units form a processing portion. Fig. 4A illustrates only the tool units A, B, and C because the cross sectional view is taken along the line LI of Fig. 4B. The other tool units D, E, F, and G are similarly configured.

[0050] A supporting member 410 allows the processing apparatus to contact with a workpiece . According to the present exemplary embodiment, the supporting member 410 and polishing members 41a through 41c simultaneously contact the workpiece. The supporting member 410 is annularly provided around the polishing members to surround them.

[0051] Referring to Fig .4A, the polishing members 4 la through 41c use polyurethane or asphalt pitch and are attached to tool shanks 42a through 42c. According to the example in Figs. 4A and 4B, the polishing member is independently attached to each tool unit. The polishing member may be attached to more than one tool unit.

[0052] In Figs. 4A and 4B, the supporting member is continuously formed to be annular but may be separated into parts . The polishingmember surface works as a tool surface . Waterproof sheets 43a through 43c prevent polishing solution from penetrating housings 49a through 49c. Tool guide mechanisms 44a through 44c include a parallel spring mechanism or a slide unit .

[0053] Pressure sensors 45a through 45c work as detectors that detect pressure applied to the tool guide mechanisms 44a through 44c, respectively. Actuators 46a through 46c drive the tool guide mechanisms 44a through 44c. The tool guide mechanism, the pressure sensor, and the actuator configure a polishing member pressure generation unit.

[ 0054] The actuator may use a piezoelectric element, an electrostrictive actuator, a voice coil motor, a pneumatic cylinder, or a hydraulic cylinder. The detector may use a pressure sensor or a load cell. Amplifiers 47a through 47c operate the pressure sensors 45a through 45c and the actuators 46a through 46c.

[0055] CPUs 48a through 48c provide drive control over the amplifiers 47a through 47c, the pressure sensors 45a through 45c, and the actuators 46a through 46c, and output drive instruction values to the amplifiers 47a through 47c.

[0056] The tool shanks 42a through 42c are attached to the tool guide mechanisms 44a through 44c via the waterproof sheets 43a through 43c. The pressure sensors 45a through 45c are attached between the tool guide mechanism 44a through 44c and the housings 49a through 49c in series with the actuators 46a through 46c.

[0057 ] The CPUs 48a through 48c attached to the housings provide drive control over the amplifiers 47a through 47c, the pressure sensors 45a through 45c, and the actuators 46a through 46c, and output drive instruction values to the amplifiers 47a through 47c.

[0058 ] The tool unit having the above-mentioned configuration is contained in a frame 412. No actuator is provided for part of the surface of the frame 412 opposite a workpiece 415. The supporting member 410 is attached to this part of the surface through a supporting member mounting portion 411. The frame has a supporting member pressure generation unit (not illustrated) for the supporting member to apply pressure to the workpiece. The supporting member pressure generation unit may generate a pressure using the weight of the processing apparatus or using another pressure generation unit such as an additional actuator .

[0059] A rotation supporting portion 413 is provided on the top of the frame 412. A support member 414 has an approximately globular tip and is attached to the rotation supporting portion 413. The frame 412 oscillates in synchronization with the support member 414 that oscillates in the direction of the arrow in Fig. 4A. The tool unit and the supporting member 410 work as an integrated tool and simultaneously contact the workpiece 415 to process it.

[0060] Controlling the actuator of the tool unit distributes a pressure on the surface (tool surface) of the polishing member 41 opposite the workpiece. As a result, a large pressure and a small pressure are generated. The distribution of generated pressures causes a moment around the rotation supporting portion 413. To cancel the moment, the supporting member pressure generation unit applies a pressure to the surface of the supporting member 410 opposite the workpiece.

[0061] As a result, high-precision processing is available while maintaining the distribution of pressures generated on the surface of the polishing members 41a through 41c opposite the workpiece.

[0062 ] Next, a method of eliminating (compensating) an unbalanced moment is described with reference to Fig. 7.

[ 0063] Fig. 7 illustrates an example of a simplified processing apparatus. In Fig. 7, the processing apparatus includes tool units 7A and 7B, a supporting member 710, and polishing members 71a and 71b. For simplicity, Fig. 7 provides a model that applies a load to the center of each of the polishing members 71a and 71b. Loads 730a and 730b are applied to the polishing members 71a and 71b . There is a difference 732 between the loads 730a and 730b applied to the polishing members 71a and 71b. A difference between the loads unbalances the moment.

[0064] Distance L is provided from a rotation supporting portion 713 to each of the loads 730a and 730b applied to the polishing members. Distance 2L is provided from the rotation supporting portion 713 to the center of the supporting member in the radial direction.

[0065] The load 730a is assumed to have load value H set to 10. The load 730b is assumed to have load value 2H set to 20. The processing apparatus weight is assumed to be set to 60. Similar to Fig. 4B, the supporting member is assumed to be annularly shaped though the supporting member 710 seems to be separated as illustrated in the sectional view of Fig. 7. The supporting member has a given width. For simplicity, a load is assumed to act on the center of the annular shape in the radial direction .

[0066] The supporting member distributes to cancel

(compensate) a moment generated from the loads 730a and 730b applied to the tool units 7A and 7B that generate a pressure. A load applied to the entire supporting member is calculated as 30 by subtracting 10 as the load 730a and 20 as the load 730b from 60 as the processing apparatus weight.

[0067] Though the supporting member is annular, it is assumed to be linear from the rotation supporting portion 713 for ease of explanation. The distance 2L is assumed between the rotation supporting portion 713 and each of the centers 731a and 731b of the supportingmember in the radial direction . The supporting member distributes and supports loads using the entire linear area of 2 ^χ 2L. The loads are calculated as follows.

Force balance:

Since 730a = 10 and 730b = 20 a -x -i- b dx = 30

-2L

Moment balance:

Since 730a = 10 and 730b = 20

When L = 25

a = 15/8L ² b = 7.5/L b = 7.5/L 731a = 0.45 731b = 0.15 The left side of the supporting member 710 is supplied with load 731a calculated as 0.45. The right side thereof is supplied with load 731b calculated as 0.15. The distributed loads compensate the moment due to the loads 730a and 730b.

[0068] The load value for the supporting member 710 is 5% or less of the load values for the polishing members 71a and 71b as a result of comparison thereof. The supporting member 710 gives no effect on processing because its load value is sufficiently small, even if the supporting member 710 uses a polishing member equivalent to the polishing members 71a and 71b that form the pressure distribution.

[0069] As described above, the present exemplary embodiment of the present invention can compensate an unbalanced moment generated on the polishing member and enable processing while maintaining the pressure distribution within the tool surface if the processing forms the pressure distribution within the polishing member surface (tool surface) .

Example 3

[0070] Fig. 5A illustrates a processing apparatus according to a third exemplary embodiment of the present invention and provides a conceptual diagram viewed from the worked surface opposite the workpiece. The mutually corresponding parts in Figs.5A, 4A, and 4B are designated by the same reference numerals and a detailed description is omitted. The supporting member 410 is provided with respect to the polishing members 41a through 41g to surround the polishing members 41a through 41g. This configuration can also provide an effect similar to the second exemplary embodiment .

Example 4

[0071] Fig. 5B illustrates a processing apparatus according to a fourth exemplary embodiment of the present invention and provides a conceptual diagram viewed from the worked surface opposite the workpiece. The mutually corresponding parts in Figs. 5B and 4 are designated by the same reference numerals and a detailed description is omitted. The supporting member 410 is provided for each outer periphery of the polishing members 41a through 41g. This configuration can also provide an effect similar to the second exemplary embodiment.

Example 5

[0072] Fig. 5C illustrates a processing apparatus according to a fifth exemplary embodiment of the present invention and provides a conceptual diagram viewed from the worked surface opposite the workpiece. The mutually corresponding parts in Figs. 5C and 4 are designated by the same reference numerals and a detailed description is omitted. More than one supporting member 410 is provided between the respective polishing members 41a through 41g. This configuration can also provide an effect similar to the second exemplary embodiment.

[0073] Figs. 6A, 6B, and 6C illustrates example

configurations of the supporting member 410 in the polishing apparatus according to the present invention. The mutually corresponding parts in Figs. 6A, 6B, 6C, and 4 are designated by the same reference numerals and a detailed description is omitted for simplicity.

[0074] Fig. 6A illustrates an example of using a polishing pad as the supporting member 410. Fig.6B illustrates an example of using a low-friction material as the supporting member 410. Fig. 6C illustrates an example of using a hydrostatic bearing 420 as the supporting member.

[0075] A fluid supplied from a fluid supply pipe 422 forms an air film between the supporting member and the worked surface of the workpiece. The air film supports an applied load. This configuration supports the supporting member in a contactless manner and causes no friction between the supporting member and the workpiece , thereby enabling more high-precision processing .

[0076] A polishing method according to the present invention uses the above-mentioned polishing tool, and therefore can effectively reflect the pressure distribution within the tool surface on processing. The method can apply high-precision processing to workpieces.

[0077] While there have been described specific exemplary embodiments of the present invention, it is to be distinctly understood that the present invention is not limited thereto. Furthermore, the invention may be embodied in various modifications without departing from the spirit and scope of the invention.

[0078] Next, an optical membermanufacturingmethod according to the invention is described . The optical member manufacturing method according to the present invention determines targeted removal quantities at positions on the workpiece based on the workpiece shape measured before processing and a targeted workpiece shape.

[0079] The method processes the workpiece by varying a pressure generated from the pressure generation unit according to the targeted removal quantities at positions on the workpiece .

[0080] Next, an exemplary embodiment of the optical member manufacturing method according to the present invention is described.

[0081] Fig. 8 illustrates an example of a processing flow. The processing flow previously processes a workpiece by generating a constant pressure from each pressure generation unit for a specified time to determine the reference removal quantity of the workpiece.

[0082] The processing flow in Fig. 8 is divided into a first half and a latter half. The latter half (steps S6 through S9) actually polishes a workpiece to be processed. The first half (steps SI through S5) prepares for the processing in advance. First, the first half (steps SI through S5) for the preparation is described step by step. [0083] In step SI, the method specifies a targeted workpiece shape andminimum requisite removal quantity B for the workpiece . The targeted workpiece shape at each position on the workpiece needs to be converted into data such as D(x, y) in a workpiece coordinate system. The pair (x, y) represents workpiece coordinates as illustrated in Figs. 2A, 3A, and 3B. The x direction at the beginning of the processing preferably corresponds to the tool oscillating direction because the calculation can be simplified.

[0084] In step S2, the method measures the workpiece shape before processing. The workpiece shape before processing at each position on the workpiece also needs to have been converted into data such as M(x, y) in the workpiece coordinate system.

[0085] In step S3, the method calculates a removal quantity at each position on the workpiece in relation to the targeted workpiece using equation 1 below that contains D(x, y) specified in step SI and M (x, y) measured in step S2. The calculated removal quantity for the targeted workpiece needs to be converted into data such as Rt(x, y) in the workpiece coordinate system. Rt(x, y) = M(x, y) - D(x, y) + B ... equation 1

[0086] In step S4, the method previously processes a test piece for a specified time by generating a constant pressure from each pressure generation unit. The test piece equals the workpiecemeasured in step S2 in terms of the shape and thematerial . The specified time preferably may be one hour and longer and ten hours or shorter, for example.

[0087] The pressure generation units 2 may generate different pressures, some equal pressures, or all equal pressures. For example, the method previously processes the workpiece for the specified time while causing the pressure generation units 2 to generate pressures set to 100 Pa or more and 300 Pa or less. After the pre-processing, themethod defines the removal quantity at each position on the workpiece as the reference removal quantity of the workpiece.

[0088] The reference removal quantity of the workpiece also needs to have been converted into data such as Rs(x, y) in the workpiece coordinate system. The pressure generated from each pressure generation unit is converted into data as a reference tool surface pressure in a tool surface coordinate system. For example, the tool surface pressure is represented as Ps (v, w) . The pair (v, w) represents the tool surface coordinate system as illustrated in Figs .2Band3. The v direction at the beginning of the processing preferably corresponds to the tool oscillating direction because the calculation can be simplified.

[0089] In step S5, the method calculates a correction value C(x, y) for the tool surface pressure using equation 2 below using Rt (x, y) calculated in step S3 and Rs (x, y) specified in step S4.

C(x, y) = Rt(x, y) ÷ Rs (x, y) ... equation 2

The method calculates the correction value (pressure correction coefficient) that represents a ratio of the removal quantity for the targeted workpiece to the reference removal quantity for the workpiece at each position on the workpiece. The first half of the processing flow has been described. [0090] Next, the latter half (steps S6 through S9) that actually polishes a targeted workpiece is described . As a maj or feature of the latter half, the pressure generation unit provided at each position of the workpiece generates a pressure equivalent to the pressure generated for the pre-processing multiplied by the pressure correction coefficient found in the first half of the processing flow. The generated pressure is used to polish the workpiece for the time specified in the pre-processing.

[0091] The latter half is provided as a loop that starts from step S6 and terminates in step S9 or returns to step S6. To start the loop, the workpiece such as a mirror is mounted on the processing apparatus. The processing apparatus starts relative motion while placing the tool in contact with the workpiece. The loop starts at the same time. Terminating the loop terminates the processing.

[0092] In step S6, the method measures positions and phases of the workpiece and the tool surface using the detectors such as the tool rotation angle sensor 8, the tool oscillation position sensor 12, and the workpiece rotation angle sensor 17.

Specifically, the tool rotation angle sensor 8 measures phase

Θ t of the tool surface. The tool oscillation position sensor 12 measures position p t of the tool surface. The workpiece rotation angle sensor 17 measures phase Θ w of the workpiece. At the beginning of the processing, Θ t, pt, and 0w are all assumed to be Os.

[0093] In step S7, the method calculates a tool surface pressure correction value C (v, w) by converting coordinates C (x, y) calculated in step S5 into values in the tool surface coordinate system using Θ t, p t, and Θ w measured in step S6 and equations 3 and 4 below.

x = v x cos ( Θ t- Θ w) + w x sin ( Θ t- Θ w) + p t ^χ cos ( Θ w) ... equation 3

y = -v x sin ( Θ t- Θ w) + w cos ( Θ t- Θ w) + p t sin ( Θ w) ... equation 4

[0094] In step S8, the method calculates a pressure instruction value distribution Pt (v, w) on the tool surface using equation 5 below from Ps (v, w) used for the pre-processing in step S4 and C (v, w) calculated in step S6. The method uses the instruction value to control the pressure distribution on the tool surface.

Pt(v, w) = C(v, w) x Pt (v, w) ... equation 5

[0095] Finally, in step S9, the method compares elapsed time Tn from the beginning of the loop with processing time Tp for the pre-processing. If Tn ≥ Tp is satisfied, the method terminates the processing. Otherwise, the method returns to step S6 and repeats the loop until Tn ≥ Tp is satisfied.

[0096] The present exemplary embodiment uses the

pre-processing to calculate the reference removal quantity for the workpiece and determines the correction coefficient as a pressure correction value. The present exemplary embodiment thereby determines a pressure generated from the pressure generation unit according to the removal quantity at each position on the workpiece in relation to the targeted workpiece . However, the invention is not limited thereto. [0097] According to a possible method, for example, pressures generated from the pressure generation units may be determined corresponding to workpiece positions based on large or small removal quantities for the targeted workpiece. The pressure generation units may be controlled so that the pressure generation units can generate pressures according to the instruction value. A removal quantity may be estimated or measured according to a history of data about pressures and tool positions. The workpiece may be processed until a targeted accuracy is obtained.

[0098] The tool may be caused to perform raster scan to enable relative movement between the workpiece and the tool.

[0099] The invention can highly precisely process the surface of an aspherical optical member such as a mirror. The invention can complete the high-precision processing with high processing efficiency in a short period of time.

[0100] The invention performs aspherical surface processing just by adding position and angle sensors to an existing low-cost apparatus. The invention can provide an environment capable of manufacturing high-precision aspherical optical elements without introducing an expensive special-purpose apparatus.

[0101] In addition, the present invention can provide tool diameters larger than conventional examples. Therefore, the invention can increase a workpiece area for the tool to be polishable at a time, and greatly improve the processing efficiency. Like the above-mentioned local polishing method, a small-diameter tool is generally used to process an aspherical surface. The invention allows the use of a large-diameter tool that is nearly as large as the worked surface of a workpiece and is used for a full-diskpolishingmethod . Thus, the invention produces very effective results.

[0102] While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments . The scope of the following claims is to be accorded the broadest interpretation so as to encompass all modifications, equivalent structures, and functions.

[0103] This application claims priority from Japanese Patent Application No. 2011-192815 filed September 5, 2011, which is hereby incorporated by reference herein in its entirety.