JP6139950B2 - Measuring device, measuring method and original device - Google Patents

Description

  The present invention relates to a measuring apparatus, a measuring method, and a prototype for measuring the shape of a test surface including an aspherical surface.

  A light wave interferometer (interferometer) such as a Fizeau interferometer is known as a measuring device for measuring the shape of a lens or mirror (optical element) used in an optical system such as an exposure apparatus or an astronomical telescope (see Patent Document 1). ). In an interferometer that measures a spherical surface as a test surface, the test surface is irradiated with a spherical wave, and the reflected light (test light) from the test surface interferes with the reflected light from the Fizeau surface (reference surface). Then, the shape of the test surface is measured. The data obtained with such an interferometer is generally the deviation between the actual shape of the surface to be examined and the ideal shape. Hereinafter, “data in which the deviation between the actual shape and the ideal shape of the test surface is mapped to the one-dimensional or two-dimensional abscissa” is referred to as shape data.

  If the shape of the test surface is an ideal shape, the shape data obtained by the interferometer is zero (no deviation from the ideal shape). However, in practice, even if the shape of the test surface is an ideal shape, the shape data does not become zero due to the system error and reproducibility of the interferometer. Note that the influence of reproducibility can be sufficiently reduced by averaging a plurality of shape data. Therefore, here, the influence of reproducibility is assumed to be sufficiently small. Hereinafter, “shape data obtained by actually measuring an ideal shape with an interferometer” is referred to as a system error. A case where the ideal shape of the test surface is a spherical surface is referred to as spherical measurement, and an interferometer in which the light applied to the test surface becomes a spherical wave on the test surface is referred to as a spherical interferometer.

  In a spherical interferometer, the system error is generally reduced by bringing the reference surface closer to an ideal spherical surface. In addition, using a spherical prototype whose shape is guaranteed, the system error of the spherical interferometer is guaranteed, and the shape data obtained by measuring a spherical prototype with a shape close to the ideal spherical surface is sufficient. Guaranteed to be small. Further, the measurement value of the spherical prototype is used as the system error of the interferometer, and the system error is calibrated by subtracting this system error from the measurement value of the surface to be measured.

  In addition, when the ideal shape of the test surface is an aspherical surface, for example, an aspherical wave is irradiated onto the test surface using a null element to acquire shape data. Hereinafter, the case where the ideal shape of the test surface is an aspheric surface is referred to as aspheric measurement. Patent Document 1 discloses a technique for calibrating a system error using a master master having a separately calibrated master base having a shape substantially equal to the surface to be measured in aspherical measurement using a null element. Yes.

  On the other hand, even when the test surface is an aspheric surface, the aspherical surface measurement can be performed within a range where the interference fringes do not exceed the resolution of the interferometer.

  Data obtained directly from the spherical interferometer when measuring the test surface with the spherical interferometer is data representing a deviation from a spherical surface with a certain radius of curvature. Hereinafter, such data representing the deviation from the spherical surface is referred to as a direct output of the spherical interferometer.

  In aspherical measurement using a spherical interferometer, it is necessary to convert the direct output into shape data. For this purpose, for example, an operation may be performed using “data representing a deviation from an ideally shaped spherical surface” and a direct output. Hereinafter, “data representing the deviation of the ideal shape from the spherical surface” is referred to as an ideal measurement shape. By subtracting the ideal measurement shape from the direct output, it can be converted into shape data.

  Even in aspherical measurement using a spherical interferometer, it is necessary to calibrate the system error of the interferometer in order to measure the test surface with high accuracy. However, even with the same spherical interferometer, the system error of the interferometer in aspherical measurement is generally different from the system error of the interferometer in spherical measurement. This is because, as will be described later, the influence of the aberration in the optical system of the interferometer such as magnification error and distortion on the measurement can be ignored in the spherical measurement, but cannot be ignored in the aspherical measurement.

  In order to perform aspheric measurement using such a spherical interferometer with high accuracy, a system using a separately calibrated aspheric prototype having a shape substantially the same as the test surface as disclosed in Patent Document 1 is used. It is possible to calibrate the error.

Japanese Patent Laid-Open No. 10-22102

  However, when the test surface is an aspherical surface having an effective diameter exceeding 300 mm, calibrating the system error using the same aspherical surface of the same surface may cause a problem of deterioration in calibration accuracy or a cost / tact surface. There is a problem with, it is difficult. Further, when the test surface is an aspherical surface having an effective diameter of 1 mm or less, it is difficult to calibrate an aspherical original device of the same size with high accuracy.

  The present invention has been made in view of such a problem of the prior art, and an object of the present invention is to provide a technique that is advantageous for measuring the shape of a test surface including an aspheric surface with high accuracy.

  In order to achieve the above object, a measuring apparatus according to one aspect of the present invention is a measuring apparatus for measuring the shape of a test surface including an aspheric surface, and includes a master including a reflecting surface having an aspheric shape, A first interference between the test light and the reference light, including an optical element that combines the test light reflected by the test surface or the reflected light reflected by the reflection surface and the reference light reflected by the reference surface; Light, an interference optical system that generates second interference light of the reflected light and the reference light, a first interference signal by detecting the first interference light, and a second interference light by detecting the second interference light. A detection unit that generates two interference signals, and a processing unit that obtains the shape of the test surface based on the first interference signal and the second interference signal. A coordinate point on a straight line connecting an arbitrary coordinate point on the surface representing the design shape of the surface and one reference point, Wherein the distance from the coordinate point at will is a shape defined by a set of coordinate points at a predetermined distance.

  Further objects and other aspects of the present invention will become apparent from the preferred embodiments described below with reference to the accompanying drawings.

  According to the present invention, for example, it is possible to provide a technique advantageous for measuring the shape of a test surface including an aspheric surface with high accuracy.

It is the schematic which shows the structure of the measuring device as 1 side surface of this invention. It is a figure for demonstrating the shape of the reflective surface of the aspherical surface prototype of the measuring device shown in FIG. It is a figure for demonstrating the shape of the reflective surface of the aspherical surface prototype of the measuring device shown in FIG. It is a flowchart for demonstrating the measurement process of the shape of the to-be-tested surface 17a in the measuring device shown in FIG. 6 is a detailed flowchart of a first calculation in S102 shown in FIG. 6 is a detailed flowchart of determination of the abscissa of measurement data in S202 shown in FIG. 6 is a detailed flowchart of a second calculation in S104 shown in FIG.

  DESCRIPTION OF EXEMPLARY EMBODIMENTS Hereinafter, preferred embodiments of the invention will be described with reference to the accompanying drawings. In addition, in each figure, the same reference number is attached | subjected about the same member and the overlapping description is abbreviate | omitted.

  FIG. 1 is a schematic diagram showing a configuration of a measuring apparatus 100 as one aspect of the present invention. The measuring device 100 is a measuring device that measures the shape of the test surface, particularly the shape of the test surface including an aspheric surface, and is suitable for measuring the surface shape of an optical element such as a lens or a mirror, for example. is there. In the present embodiment, the test surface has an effective diameter exceeding 300 mm. The measurement apparatus 100 includes an interference optical system 10, a light source 11, a fiber 12, an aspherical prototype 31, a prototype holding unit 32 that holds the aspherical prototype 31, and a subject holding that holds a subject 17. A unit 18 and a processing unit 22.

  In the measuring apparatus 100, the aspherical prototype 31 is configured to be detachable from the optical path between the Fizeau lens 15 of the interference optical system 10 and the test surface 17a. Specifically, the aspherical prototype 31 is detachably held by the prototype holder 32. In other words, the master holding unit 32 has a configuration in which the aspheric master 31 can be removed. In the measuring apparatus 100, the measurement of the aspherical prototype 31 and the measurement of the subject 17 can be repeated by removing the aspherical prototype 31.

  The light source 11 is composed of, for example, a helium neon laser (wavelength λ = 632.8 nm). The light L emitted from the light source 11 enters the interference optical system 10 held by an interferometer holding unit (not shown) via the fiber 12.

  The interference optical system 10 includes an optical element that combines test light reflected by the test surface 17a or reflected light reflected by the reflection surface 31a of the aspherical prototype 31 and reference light reflected by the reference surface. Interference light between the detection light and the reference light and interference light between the reflected light and the reference light are generated. In the present embodiment, the interference optical system 10 includes an optical system 13, a half mirror 14, a Fizeau lens 15, a ground glass 19, an optical system 20, and a detection unit 21.

  The light L incident on the interference optical system 10 becomes parallel light by the optical system 13, is reflected by the half mirror 14, and enters a Fizeau lens 15 having a spherical Fizeau surface (reference surface) 16. The Fizeau surface 16 divides the light L incident on the interference optical system 10 into a reference light LR and a transmitted light LT.

  When the subject 17 is measured, the transmitted light LT is reflected by the subject surface 17a of the subject 17 held by the subject holding unit 18 and becomes the subject light LM1. Further, when measuring the aspherical prototype 31, the transmitted light LT is reflected by the reflection surface 31 a of the aspherical prototype 31 held by the prototype holding unit 32 and becomes reflected light LM 2. Here, when measuring the subject 17, the test surface 17 a is arranged with a Fizeau gap GW interval with respect to the Fizeau surface 16 of the Fizeau lens 15. Further, when measuring the aspherical prototype 31, the reflecting surface 31 a is arranged with an interval of the Fizeau gap GM.

  The subject 17 includes a test surface 17a including a concave aspheric surface. The subject 17 is an optical component in which the effective diameter of the test surface 17a is 1 m, the radius of curvature of the spherical surface that fits the test surface 17a is 2 m, and the center thickness is 0.5 m. The ideal shape (design shape) of the test surface 17a is, for example, the number of zags at which a plurality of interference fringes are generated even when the Fizeau gap GW is set so that the number of interference fringes in the effective region is minimized. It is an aspherical surface of μm. In the present embodiment, it is assumed that the ideal shape of the test surface 17a is represented by the following equation (1) in the distribution of deviation from a spherical surface having a curvature radius of 2 m.

However,
x, y: The coordinates (X, Y) of a point obtained by projecting an arbitrary point on the surface representing the ideal shape of the test surface 17a onto a certain plane is half of the effective diameter of the test surface 17a (in this embodiment, , 0.5 m) divided by FD (X, Y): The point on the surface representing the ideal shape of the surface to be measured 17a represented by the coordinates (x, y) from the spherical surface having a curvature radius of 2 m Deviations C1, C2, C3, C4, C5,...: Coefficient The subject 17 is held in the subject holding unit 18 in the measurement apparatus 100 in the same state as the actual use state. Specifically, the subject holding unit 18 that holds the subject 17 is designed so that a part thereof is the same as a part of the holding unit of the subject 17 in the actual use state within a predetermined tolerance range ( Manufactured). In addition, the subject 17 is held by the subject holding unit 18 so that the direction of the optical axis of the test surface 17a with respect to the gravity direction g is the same as the actual use state. For example, as shown in FIG. 1, the subject 17 is held by the subject holding unit 18 so that the optical axis of the test surface 17a is perpendicular to the gravity direction g. In this way, by measuring the shape of the test surface 17a while holding the subject 17 so as to be in the same state as the actual use state, the shape data of the test surface 17a including the deformation of the subject 17 by its own weight is obtained. Can be acquired. Further, using the shape data, the subject 17 can be manufactured so that the test surface 17a has an ideal shape in the actual use state.

  The aspherical prototype 31 includes a reflecting surface 31a having an aspherical shape. In the present embodiment, as will be described later, it is possible to configure (design) the reflecting surface 31a of the aspherical base 31 with a diameter of 1 mm to 300 mm. The aspherical prototype 31 is a concave spherical surface in which the effective diameter of the reflecting surface 31a is 0.1 m, the radius of curvature of the spherical surface that fits the reflecting surface 31a is 0.2 m, and the center thickness is 0.05 m.

  With reference to FIG. 2, the shape of the reflecting surface 31a of the aspherical prototype 31 will be described. As shown in FIG. 2, an optical axis Z is defined as one straight line that intersects the ideal shape 17 c of the test surface 17 a of the subject 17. FIG. 2 shows a cross section obtained by cutting the ideal shape 17 c of the test surface 17 a of the subject 17 by a plane passing through the optical axis Z. When the ideal shape 17c of the test surface 17a is a rotationally symmetric shape, the center of rotational symmetry may be the optical axis, but the present invention is not limited to this.

  In FIG. 2, a dotted line indicates a cross section of the spherical surface SW having a center on the optical axis Z and fitting the ideal shape 17c of the test surface 17a. A center point of the spherical surface SW is a point O, a radius is SR, and an arbitrary point on the surface representing the ideal shape 17c of the test surface 17a is a point P. The alternate long and short dash line indicates a straight line OP passing through the point O and the point P. The straight line OP is inclined with respect to the optical axis Z by an angle θ. Here, FIG. 2 shows a two-dimensional cross section, but actually, the point P is a coordinate in a three-dimensional space as shown in FIG. 3, and two angles θ and φ are used. The angle with respect to the optical axis Z can be expressed.

  The reflecting surface 31a of the aspherical prototype 31 is on the straight line OP, and the distance from the point P on the surface representing the ideal shape 17c of the surface 17a to be measured is a constant value M (in this embodiment, M = 1. 8m) having a surface shape (ideal shape) 31c defined by the point Q. In other words, the reflection surface 31a of the aspherical prototype 31 is a straight line connecting an arbitrary coordinate point (point P) on the surface representing the ideal shape 17c of the test surface 17a and one reference point (point O). And a shape defined by a set of coordinate points whose distance from an arbitrary coordinate point is a predetermined distance.

  The distance from the point O to the point P on the surface representing the ideal shape 17c of the test surface 17 in the (θ, φ) direction is OP (θ, φ), and the reflecting surface in the (θ, φ) direction from the point O The distance to the point Q on the surface representing the surface shape 31c of 31a is defined as OQ (θ, φ). In this case, the surface shape 31c of the reflecting surface 31a of the aspherical prototype 31 is expressed by the following equation (2).

However,
M: Constant Thereby, the effective diameter of the reflecting surface 31a of the aspherical prototype 31 is expressed by the following equation (3).

However,
x, y: The coordinates (X, Y) of a point obtained by projecting an arbitrary point on the surface representing the ideal shape 31c of the reflecting surface 31a of the aspherical prototype 31 onto a certain plane is half the effective diameter of the reflecting surface 31a. (In this embodiment, a value divided by 0.1 m) FM (x, y): On the surface representing the ideal shape 31 c of the reflecting surface 31 a of the aspherical prototype 31 represented by coordinates (x, y) Deviation of the point from the spherical surface having a radius of curvature of 0.2 m C1, C2, C3, C4, C5,...: A coefficient representing the ideal shape 17c of the test surface 17a defined by the equation (3). , FM (x, y) = FD (x, y) with respect to the coordinate (x, y) normalized with respect to the effective diameter.

  The reference light LR reflected by the Fizeau surface 16 of the Fizeau lens 15 and the test light LM1 reflected by the test surface 17a or the reflected light LM2 reflected by the reflection surface 31a of the aspherical prototype 31 are reflected in the interference optical system 10. Return the same optical path. Then, the reference light LR and the test light LM1 or the reflected light LM2 are transmitted through the half mirror 14 and on the ground glass 19, interference fringes (first interference light between the reference light LR and the test light LM1, or Second interference light of the reference light LR and the reflected light LM2).

  The interference fringes formed on the ground glass 19 form an image on the detection surface of the detection unit 21 via the optical system 20. The detection unit 21 is configured by an image sensor such as a CCD sensor or a CMOS sensor, for example, and detects an interference fringe imaged on the detection surface to generate an interference signal. In the present embodiment, the detection unit 21 corresponds to the first interference signal corresponding to the first interference light of the reference light LR and the test light LM1, and the second interference light of the reference light LR and the reflected light LM2. A second interference signal is generated.

  The processing unit 22 is configured by a computer including a CPU, a memory, and the like, and obtains the shape of the test surface 17a based on the interference signal generated by the detection unit 21. As will be described later, the processing unit 22 obtains a system error of the interference optical system 10 based on the second interference signal, and calibrates the shape of the test surface 17a obtained from the first interference signal using the system error. For example, the processing unit 22 obtains a first numerical value group from the first interference signal, obtains a second numerical value group from the second interference signal, and obtains a numerical value group of differences between the elements of the first numerical value group and the elements of the second numerical value group. Based on the above, the shape of the test surface 17a is obtained.

  In the present embodiment, known interference fringe analysis software is installed in the processing unit 22, and the phase difference between the wavefront of the reference light LR and the wavefront of the test light LM1 and the wavefront of the reference light LR and the reflected light LM2 are detected. Calculate the phase difference from the wavefront. The direct output from the spherical interferometer (deviation from the spherical surface with an arbitrary curvature radius) can be obtained by a known calculation using phase difference data expressed by the following equation (4).

However,
F: Direct output [nm]
λ: wavelength of the light L emitted from the light source 11 [nm]
φ: Phase difference data [rad]
With reference to FIG. 4, the measurement process of the shape of the test surface 17a in the measurement apparatus 100 (that is, the measurement method using the measurement apparatus 100) will be described.

  First, in S101, the aspherical prototype 31 is measured. Specifically, the first aspherical surface 31 is disposed on the optical path between the Fizeau lens 15 and the test surface 17a, and the first reflective surface 31a is measured by measuring the reflective surface 31a. Measurement data DA as a numerical value group is acquired.

  Next, in S102, a first calculation for acquiring the calibration data IC of the interference optical system 10 is executed. More specifically, the measurement data DA acquired in S101 and the aspherical surface data DB representing the shape of the reflecting surface 31a of the aspherical surface material 31 acquired in advance are used as inputs, and the calculation of the interference optical system 10 is performed. Obtain calibration data IC.

  Next, in S103, the subject 17 is measured. Specifically, the aspherical prototype 31 is taken out from the optical path between the Fizeau lens 15 and the test surface 17a, and the measurement as the second numerical value group representing the shape of the test surface 17a by measuring the test surface 17a. Data DD is acquired.

  Next, in S104, a second calculation for acquiring shape data DG representing the shape of the test surface 17a is executed. Specifically, the calculation is executed with the calibration data IC acquired in S102 and the measurement data DD acquired in S103 as inputs, and the shape data DG representing the shape of the test surface 17a is acquired.

  Details of the first calculation for acquiring the calibration data IC of the interference optical system 10 will be described with reference to FIG. First, in S201, the measurement data DA acquired in S101 and the aspherical original data DB acquired in advance are acquired. Next, in S202, the abscissa of the measurement data DA is determined by comparing the measurement data DA with the aspherical original data DB. For example, as the abscissa, the numerical values of the pixel scale p and the reference coordinates (xc, yc) on the detection surface of the detection unit 21 are determined. In S202, the rotation angle φ of the measurement data DA may be further determined.

  Next, in S203, based on the pixel scale p and the reference coordinates (xc, yc) on the detection surface of the detection unit 21, the aspherical original data DB is remeshed to generate remesh data DBB. Next, in S204, difference data SE representing the difference between the measurement data DA and the remesh data DBB is acquired. Next, in S205, the abscissa determined in S202 and the difference data SE acquired in S204 are output as calibration data IC of the interference optical system 10. However, the abscissa output in S205 is a part or all of the numerical value determined in S202.

  Details of determination of the abscissa of the measurement data DA will be described with reference to FIG. First, in S301, the abscissa (value) of the measurement data DA is provisionally determined. Next, in S302, based on the abscissa of the measurement data DA temporarily determined in S301, the aspherical original data DB is remeshed to generate remesh data DBB '. Next, in S303, difference data DC representing the difference between the measurement data DA and the remesh data DBB 'is acquired. Next, in S304, the statistic of the difference data DC is calculated. The processing from S301 to S304 is repeated a predetermined number of times while changing the value of the abscissa of the measurement data DA temporarily determined in S301. Next, in S305, the abscissa of the measurement data DA is determined based on the statistic of the difference data DC calculated in S304 (that is, the abscissa of the measurement data DA that minimizes the statistic of the difference data DC is determined). ).

  Here, in S304, the statistic of the difference data DC is calculated using, for example, an RMS value of a predetermined component included in the difference data DC. The predetermined component is, for example, a spatially high-frequency component that is characteristic of the processing error shape of the reflecting surface 31a of the aspherical prototype 31. Thereby, the influence of the shape of the reference surface can be made sufficiently small, and the abscissa of the measurement data DA can be matched with the abscissa of the aspherical original data DB. Further, the processing from S301 to S305 may be further repeated according to the required accuracy.

  With reference to FIG. 7, the detail of the 2nd calculation for acquiring the shape data DG showing the shape of the to-be-tested surface 17a is demonstrated. First, in S401, measurement data DD representing the shape of the test surface 17a acquired in S103 and calibration data IC of the interference optical system 10 acquired in S102 are acquired. Next, in S402, the abscissa of the measurement data DD is determined.

  Next, in S403, based on the abscissa of the measurement data DD determined in S402, ideal shape data DE using a function representing the ideal shape of the test surface 17a acquired in advance is generated. In step S404, the ideal shape data DE is subtracted from the measurement data DD to obtain first subtraction data DF. Next, in S405, the second subtraction data DF 'is obtained by subtracting the difference data SE included in the calibration data IC from the first subtraction data DF. Next, in S406, the abscissa determined in S402 and the second subtraction data DF 'acquired in S405 are output as shape data DG representing the shape of the test surface 17a.

  An example of determination of the abscissa of the measurement data DD in S402 will be described. As the abscissa of the measurement data DD, the pixel scale pw and the reference coordinates (xcw, ycw) are determined. The pixel scale pw is determined using, for example, the following formula (5). Here, p represents the pixel scale of the aspherical prototype 31 included in the calibration data IC, RM represents the radius of curvature of the spherical surface that fits the three-dimensional measurement data of the reflecting surface 31a of the aspherical prototype 31, and RWD Indicates the radius of curvature of the spherical surface that fits the ideal shape of the test surface 17a.

  With respect to the reference coordinates (xcw, ycw) on the detection surface of the detection unit 21, for example, the center coordinates of the test surface 17a on the detection surface are obtained using intensity data measured by providing a light shielding mask on the subject 17. The center coordinates may be obtained as reference coordinates (xcw, ycw). Further, for example, when it can be ensured that the optical axis direction of the reflecting surface 31a of the aspherical prototype 31 and the optical axis direction of the test surface 17a coincide with each other with sufficient accuracy, it is determined in the first calculation. The reference coordinates (xc, yc) may be set as the reference coordinates (xcw, ycw).

  As a function representing the ideal shape of the test surface 17a used in S403, for example, a polynomial whose parameter is the distance from the coordinates on the detection surface of the detection unit 21 corresponding to the center of the test surface 17a can be used.

  Further, the abscissa output in S406 does not necessarily have to be the same as the abscissa of the measurement data DD determined in S402. For example, the pixel scale pw ′ may be determined using the following equation (6). However, RM indicates the radius of curvature of the spherical surface that fits the three-dimensional measurement data of the reflecting surface 31a of the aspherical prototype 31, and RMM indicates the radius of curvature of the spherical surface that fits the three-dimensional measurement data of the test surface 17a. . Here, the three-dimensional measurement data of the test surface 17a is obtained by separately three-dimensionally measuring a plurality of points on the test surface 17a, for example, four points.

  Hereinafter, in the measurement process of this embodiment, the principle that can calibrate a system error caused by the aberration of the optical system (interference optical system 10) constituting the measurement apparatus 100 will be described. Here, it is assumed that the interference optical system 10 includes a magnification error and distortion as aberrations.

  The measurement data DA acquired in S201 uses a direct output from the spherical interferometer. When an ideal interferometer (that is, no aberration) is used as the interference optical system 10, the direct output MM (x ', y') is expressed by the following equation (7). Here, (x ′, y ′) is the coordinates on the detection surface of the detection unit of the ideal interferometer, corresponding to the coordinates (x, y) defined in Expression (3). In the following formula, the description of (x ′, y ′) is omitted.

However,
FM: Deviation from the spherical surface of the ideal shape 31c of the reflecting surface 31a of the aspherical prototype 31 expressed by equation (3) FME: Deviation from the ideal shape 31c of the reflecting surface 31 of the aspherical prototype 31 Equation (7 2) FM indicates data obtained by mapping the deviation of the reflection surface 31 a of the aspherical original device 31 from the spherical surface of the ideal shape 31 c on the detection surface of the detection unit 21. Further, FM = FD from the equations (2) and (3). Therefore, FM is equal to the ideal measurement shape of the test surface 17a of the subject 17. Hereinafter, the ideal measurement shape of the test surface 17a is assumed to be FD.

  However, when an interferometer including a magnification error and distortion is used as the interference optical system 10, (x + Δx, y + Δy) is a coordinate (x on the detection surface of the detection unit 21) with respect to the coordinates defined by Equation (3). ', Y'). Here, (Δx, Δy) is an abscissa error caused by the aberration of the interference optical system 10. Therefore, the measurement data DA is shape data represented by the following equation (8).

  Referring to Expression (8), the third and fourth terms are shapes resulting from the aberration of the interference optical system 10.

  In the present embodiment, the abscissa of the measurement data DA is determined using the three-dimensional coordinate data of the reflecting surface 31a of the aspherical prototype 31 in S202. Therefore, (Δx, Δy) corresponds to the error of the abscissa determined in S202.

  In the equation (8), other system error factors such as the shape of the Fizeau surface (reference surface) 16 of the Fizeau lens 15 and the influence of the reference light and the test light on the wavefront due to multiple reflection in the interference optical system 10 The shape is ignored. However, even if other system error factors are taken into consideration, the gist of the present invention is not affected.

  Further, the aspherical prototype data DB acquired in S201 is data calculated using the three-dimensional coordinate data of the reflecting surface 31a of the aspherical prototype 31 measured by a highly accurate three-dimensional measuring device. Specifically, the radius of the spherical surface fitted with the spherical surface and the deviation from the spherical surface are obtained using the center coordinates and the radius as parameters, and the deviation data from the spherical surface is defined as the aspherical original data DB. Since the aspherical original data DB is obtained from three-dimensional coordinate data, the abscissa is also obtained with high accuracy. The aspherical original data DB coincides with the shape data represented by Expression (7) on the assumption that the measurement error of the three-dimensional measuring apparatus is sufficiently small.

  The difference data SE acquired in S204 is data of the difference between the measurement data DA and the aspherical prototype data DB after the abscissa of the measurement data DA is determined based on the abscissa of the aspherical prototype data DB. Is represented by the following formula (9).

  Here, when FME << FD, the following equation (10) holds. Therefore, the difference data SE is expressed by the following equation (11).

  Whereas FD has a sag amount of several μm, if FME is made to have a shape of several nanometers, equation (11) is established with sufficient accuracy.

  In this embodiment, the measurement data DD acquired in S401 uses a direct output from the spherical interferometer. When an ideal interferometer (that is, no aberration) is used as the interference optical system 10, the direct output MW (x ', y') is expressed by the following equation (12). Here, (x ′, y ′) is a coordinate on the detection surface of the detection unit of the ideal interferometer corresponding to the coordinate (x, y) defined by the equation (1). In the following formula, the description of (x ′, y ′) is omitted.

However,
FD: Deviation from the spherical surface of the ideal shape 17c of the test surface 17a represented by Formula (1) FWE: Deviation from the ideal shape 17c of the test surface 17a In Formula (12), FD is the test surface 17a. The data which mapped the deviation from the spherical surface of the ideal shape 17c on the detection surface of the detection part 21 are shown. Therefore, the FD is equal to the ideal measurement shape of the test surface 17a of the subject 17.

  However, when an interferometer including a magnification error and distortion is used as the interference optical system 10, (x + Δx ″, y + Δy ″) is on the detection surface of the detection unit 21 with respect to the coordinates defined by Equation (1). Correspond to the coordinates (x ′, y ′). Here, (Δx ″, Δy ″) is an abscissa error caused by the aberration of the interference optical system 10. Therefore, the measurement data DD is shape data represented by the following equation (13).

  Referring to Equation (13), the second and third terms are shapes resulting from the aberration of the interference optical system 10.

  In general, the difference between the aberration when measuring the reflecting surface 31a of the aspherical prototype 31 and the aberration when measuring the test surface 17a of the subject 17 is small. Accordingly, the abscissa error (Δx, Δy) when measuring the reflecting surface 31a of the aspherical prototype 31 and the abscissa error (Δx ″, Δy ″ when measuring the test surface 17a of the subject 17). ) Can be considered equal.

  Further, when FWE << FD, the following formula (14) is established. Therefore, the direct output MW is expressed by the following equation (15).

  Whereas FD has a sag amount of several μm, if FWE is made to have a shape of several nanometers, equation (15) holds with sufficient accuracy.

  The second subtraction data DF ′ acquired in S405 is data obtained by subtracting the ideal shape data DE and the difference data SE from the measurement data DD. The ideal shape data DE is data obtained using the equation (1) representing the ideal shape 17c of the test surface 17a, and is equal to the ideal measurement shape FD. Further, the difference data SE is expressed by Expression 13. Therefore, the second subtraction data DF ′ is data obtained by subtracting the equation (11) and the ideal measurement shape FD from the equation (15), and is represented by the following equation (16).

  As described above, the second subtraction data DF ′ obtained in the measurement apparatus 100 of the present embodiment is deviation data from the ideal measurement shape in which the system error of the interference optical system 10 is calibrated. Therefore, the measuring apparatus 100 can measure the shape of the test surface 17a with high accuracy even if the test surface 17a of the test subject 17 has an aspherical shape.

  As described above, the principle that the system error caused by the aberration of the optical system (interference optical system 10) constituting the measurement apparatus 100 can be calibrated in the measurement process of the present embodiment has been described.

  In the calibration of the system error of the interference optical system 10, if there is a fixed temperature unevenness in the optical path (space) between the reflection surface 31 a of the aspherical original device 31 and the test surface 17 a of the subject 17, the calibration error is generated. Occur. However, such calibration errors can be made sufficiently small using various space temperature control techniques well known in the art.

  The reflection surface 31a of the aspherical prototype 31 used in the measuring apparatus 100 has a diameter of about 1/10 of the test surface 17a. Therefore, the measurement by the three-dimensional measuring device for guaranteeing the shape of the reflecting surface 31a of the aspherical prototype 31 is shorter than the case of measuring the master prototype surface having a shape substantially equal to the test surface 17a. Can be performed with high accuracy. In addition, a large three-dimensional measuring apparatus and jigs for measuring the subject 17 are not required.

  In the measuring apparatus 100, it is not necessary to rotate or tilt the test surface 17a or the interference optical system 10 in order to calibrate the system error. In particular, when trying to rotate the test surface 17a having a large effective diameter, a tact for suppressing the influence of disturbance such as air temperature fluctuations generated by the rotation is generated. Such a tact does not occur.

  Further, since the measuring apparatus 100 can reduce the self-weight deformation of the reflecting surface 31a of the aspherical original device 31, the system error can be calibrated with high accuracy without being affected by the self-weight deformation. Specifically, the self-weight deformation amount of a cylindrical object is proportional to the fourth power of the diameter of the object and inversely proportional to the square of the thickness based on the material dynamics theorem. Therefore, in general, an object having a small diameter is advantageous in suppressing the self-weight deformation. In the present embodiment, the diameter of the reflecting surface 31a of the aspherical prototype 31 is designed so that the value obtained by dividing the fourth power value of the diameter by the second power value of the thickness is about 0.005 times the surface 17a to be measured. Therefore, the amount of deformation of the reflecting surface 31a by its own weight is made sufficiently small.

  In addition, for example, even if an external force acts on the interference optical system 10 to cause a large aberration in the interference optical system 10 and a measurement error that cannot be ignored due to the aberration, the aspherical original 31 Anomalies can be detected by periodically measuring.

  As mentioned above, although preferable embodiment of this invention was described, it cannot be overemphasized that this invention is not limited to these embodiment, A various deformation | transformation and change are possible within the range of the summary.

Claims (8)

A measuring device for measuring the shape of a test surface including an aspheric surface,
A prototype including a reflective surface having an aspheric shape;
A first interference between the test light and the reference light, including an optical element that combines the test light reflected by the test surface or the reflected light reflected by the reflection surface and the reference light reflected by the reference surface; An interference optical system that generates light and second interference light of the reflected light and the reference light;
A detection unit that detects the first interference light to generate a first interference signal, detects the second interference light, and generates a second interference signal;
A processing unit that obtains the shape of the test surface based on the first interference signal and the second interference signal;
The aspherical shape is a coordinate point on a straight line connecting an arbitrary coordinate point on the surface representing the design shape of the test surface and one reference point, and the distance from the arbitrary coordinate point is a predetermined distance. A measuring apparatus having a shape defined by a set of coordinate points.   The measuring apparatus according to claim 1, wherein the reflecting surface has a diameter of 1 mm to 300 mm.   The measuring apparatus according to claim 1, wherein the original device is configured to be inserted into and removed from an optical path between the optical element and the test surface.   4. The apparatus according to claim 1, further comprising a holding unit that is disposed in an optical path between the optical element and the test surface and holds the original device in a detachable manner. 5. Measuring device.   The processing unit obtains a system error of the interference optical system based on the second interference signal, and calibrates the shape of the test surface obtained from the first interference signal using the system error. The measuring device according to any one of claims 1 to 4.   The processing unit obtains a first numerical value group from the first interference signal, obtains a second numerical value group from the second interference signal, and calculates a difference between an element of the first numerical value group and an element of the second numerical value group. The measuring apparatus according to claim 1, wherein the shape of the test surface is obtained based on a numerical value group. A measurement method for measuring the shape of a test surface including an aspheric surface using a measurement device,
The measuring device is
A prototype including a reflective surface having an aspheric shape;
A first interference between the test light and the reference light, including an optical element that combines the test light reflected by the test surface or the reflected light reflected by the reflection surface and the reference light reflected by the reference surface; An interference optical system that generates light and second interference light of the reflected light and the reference light;
Have
The aspherical shape is a coordinate point on a straight line connecting an arbitrary coordinate point on the surface representing the design shape of the test surface and one reference point, and the distance from the arbitrary coordinate point is a predetermined distance. A shape defined by a set of coordinate points
The measurement method is:
Detecting the first interference light to generate a first interference signal;
Disposing the original device in an optical path between the optical element and the test surface, detecting the second interference light, and generating a second interference signal;
Obtaining a first numerical value group from the first interference signal;
Obtaining a second group of numerical values from the second interference signal;
Obtaining a numerical group of differences between the elements of the first numerical group and the elements of the second numerical group;
Obtaining the shape of the test surface based on the numerical value group of the difference;
A measurement method characterized by comprising: Used in a measuring device for measuring the shape of a test surface including an aspheric surface, and is a prototype including a reflecting surface having an aspheric shape,
The aspherical shape is a coordinate point on a straight line connecting an arbitrary coordinate point on the surface representing the design shape of the test surface and one reference point, and the distance from the arbitrary coordinate point is a predetermined distance. A prototype characterized by a shape defined by a set of coordinate points.

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