JP2000097663A - Interferometer - Google Patents

Abstract

PROBLEM TO BE SOLVED: To measure the distortion of a measuring optical system with high accuracy by giving an alignment deviation from a reference surface to a test surface by an already known amount and correcting the alignment error of the differential data of interference measuring data obtained before and after the deviation is given by using the data obtained by calibrating the distortion of the optical system at the time of correcting the alignment error. SOLUTION: The planar wave 2 from an interferometer 1 is reflected by a Fizeau surface 3a formed on a Fizeau flat plate 3 and, at the same time, a measuring wavefront 4a which is obtained by transforming the planar wave 2 into a designed aspherical shape at the reference position of measurement by means of a null element 4 is also reflected by the test surface 5a of a specimen 5 set to the reference position and forms interference fringes in the interferometer 1 together with the planar wave 2 reflected from the Fizeau surface 3a. The interference fringes are detected by means of a detector and analyzed by means of an information processing system. The attitude of a tilt is monitored from the rear surface of the specimen 5 by means of an interference optical system and the shifting amount of the tilt is controlled by means of a shifting amount detecting means.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an interferometer for measuring the distortion of a measuring optical system of an interferometer with high accuracy and ease.

[0002]

2. Description of the Related Art Conventionally, interferometric measurement data using a spherical measurement wavefront has a rotationally symmetric abscissa distortion (distortion) due to an unsatisfactory sine condition of a measurement optical system. It was pointed out. As shown in FIG. 1, for example, in the case of interferometric measurement using a Fizeau lens, the sine condition is such that grid points of equal pitch on the XY projection coordinates on the incident side of the Fizeau surface are on the XY projection coordinates of the test surface. Is a strain that does not satisfy the equal pitch property.

[0003] Japanese Patent Laid-Open No. 4-48201 is known as an interference measuring device for measuring this distortion. This device aligns the test surface with the measurement wavefront so that the fringe is as close to one color as possible, gives the test surface a tilt misalignment, and corrects the bends of these interference fringes, which are essentially parallel straight lines, Is calculated as a corresponding phase shift for each pixel of the CCD which is the detector of the above.

It is also disclosed that, in order to increase the calculation accuracy of the distortion, the section for obtaining the distortion is finely rotated around the measurement optical axis.

[0005]

However, in the above-mentioned conventional example, when the measured wavefront has a large wavefront aberration, the interference fringes can be formed using an ideal test surface (regardless of plane, spherical surface or aspherical surface). Even if it is observed, large residual interference fringes are generated, and it is inevitable that the calculated distortion has an error.

[0006] Conversely, even if the measured wavefront is an ideal wavefront having no wavefront aberration, if the surface accuracy error of the surface to be measured used for measurement is large, a large residual interference fringe similarly occurs, and the calculation is performed. It is inevitable that the distortion that is performed will have an error. In addition, since the measurement is based on the distortion of the cross section, there is a problem that the measurement of the distortion around the rotationally symmetric distortion axis defined by the effective diameter for measurement is complicated.

The present invention has been made in view of the above-mentioned drawbacks of the prior art, and has as its object to measure the distortion of a measurement optical system of an interferometer with high accuracy and ease.

[0008]

According to the present invention, in order to achieve the above object, the surface accuracy of a test surface (residual shape after fitting with a functional expression representing a design geometric shape) is measured. In the interferometer, a known amount is given to the surface to be inspected, and an alignment deviation with respect to the reference surface of the measuring optical system is given.
An interferometer that corrects the distortion of the measurement optical system of the interferometer and corrects the surface accuracy based on the obtained calibration data when performing the alignment error correction on the difference data of the interference measurement data before and after giving the alignment deviation. It was decided to use it. This makes it possible to easily calibrate the distortion that can be defined by the measurement effective diameter of the measurement wavefront even under conditions where the surface accuracy of the test surface and the measurement wavefront is poor.

Although the drawings of the embodiments of the present invention are used to make the present invention easy to understand, the present invention is not limited to the embodiments.

[0010]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The distortion calibration calculation of the present invention will be described below with reference to FIG. In the figure, F represents a Fizeau surface of the Fizeau lens, and W represents a test surface. First, the equation for giving the sine condition distortion is expressed as follows: R = C1 ・ r + C3 ・ r ** 3 + C5 ・ r ** 5 + C7 ・ r ** 7 (1) with respect to the axis of symmetry giving the rotationally symmetric distortion. This equation indicates that a point located on the incident side of Fizeau at a position of r units with respect to one unit of the abscissa is distorted to a position of R units with respect to one unit of the abscissa on the test surface. I have. An even term may be included to increase the accuracy.

At this time, the center is set to 0 on the incident side of the Fizeau, a break of sg (= 51) is provided at the outermost periphery, and the radius obtained by correcting a half pixel corresponding to the sampling point of the CCD is hw.
Assuming d, the following expression sc [C1, C3, C5, C7, p] which is a function of the expression (1)） C1 · p + C3 · p ** 3 + C5 · p ** 5 + C7 · p ** 7 (2) The following equation defined using g [pp] ｓｃ (sc [C1, C3, C5, C7, pp] / pp) / (sc [C1, C3, C5, C7, sg] / sg) (3) It is a normalized distortion function based on the outer diameter of the interference fringes. Therefore, if the address of the pixel data of the interference measurement data is [i, j] and the magnification of the interferometer is bun [mm / pixel], for example, the difference data when a known tilt alignment deviation Tx is given in the X-axis direction. Is given by the following equation: Z = Tx · g [{(i · bun) ** 2+ (j · bun) ** 2} ** 0.5 / hwd · sg] · i · bun (4) The notation of a ** b represents a raised to the power of b.). The piston component is omitted. The difference data obtained by multiplying the difference data by the alignment error correction and removing the error aberration determined by the tilt amount Fx optimally fitted becomes ΔZ = Z−Fx · i · bun (5). A similar error results.

The coefficient Ci is obtained by optimally fitting the difference data after the alignment error correction to the actual measurement data data [i, j]. Specifically, for SUM = Σi _{, j} (ΔZ-data [i, j]) ** 2 (6), the simultaneous equations represented by ∂SUM / ∂Ci = 0 (7) may be solved.

However, since the coefficient Ci exists as an unknown number in the denominator of the equation (4) due to the normalization of the equation (3), a temporary value such as “C1 = 1, C3 to 7 = 0” is obtained. It is necessary to insert the value of and fit. A design value may be used as the temporary value. In this case, the coefficient C
An error mixed into Ci calculated because the true value of i is not used is an offset error, and a property that does not become an error of the final sine condition distortion curve by normalizing Expression (3) is used.

In actual measurement data, it is conceivable that the sine condition (rotationally symmetric distortion) axis does not coincide with the calculation origin of the optimal fitting including the alignment error correction. This axis deviation also
The eccentricities Sx and Sy are introduced as variables in the equation (4), and the eccentricity is optimally fitted by a simultaneous equation expressed by ∂SUM / ∂Sx, y = 0 (8). Can be used to determine the coefficient Ci.

For the sake of simplicity, an equation assuming only a value in the X-axis direction is used as a component of the alignment (tilt) deviation, but a tilt component in the Y-axis direction may be used. Further, even when there is no monitor for the tilt component, an error may occur, but an alignment error correction value obtained by actual measurement may be used as the tilt component. At this time, the error may be corrected by changing the level of the amount of tilt to be given. Further, it has been confirmed by simulation calculation that the accuracy can be improved by applying a convergence calculation for feeding back a fitting value in the calculation of Sx and Ci.

[0016]

[Embodiment 1] In a unidirectional tilt stripe as in the conventional example,
It is clear that distortion that is not rotationally symmetric and occurs in the stripe direction cannot be evaluated. The idea is that the distortion can be defined by the distortion of the lattice-like pattern, and therefore, in the present embodiment, the tilt is misaligned twice in the orthogonal direction. Although the displacement of the lattice point can be easily obtained as an intersection of orthogonal interference fringes by image processing, the calculation of Ci can be performed with higher accuracy by the above-described calculation method. That is, if the sum of squares in the Y direction orthogonal to equation (6) is also added,
A similar procedure can be employed.

After correcting the obtained rotationally symmetric distortion determined by Sx, y and Ci, the aberration remaining in the data after the error correction is a non-rotationally symmetric distortion. The distortion component can be calculated. For example, in the case of the measurement by the Fizeau interferometer, in order to divide the error factor which gives this non-rotationally symmetric distortion into the Fizeau lens and the optical system of the interferometer main body including the CCD, the interferometer main body is rotated by the rotational symmetry. By rotating the lens about the distortion axis and performing the same calibration, the cause of the error is specified. FIG. 2 shows a measurement arrangement when performing Fizeau interference measurement on a plane.

[0018]

[Second Embodiment] The description has been given of the case where the alignment deviation described above is limited to the tilt deviation. However, it is conceivable to use the shift deviation except for insensitive defocusing. This is not a good idea for a plane, but for an aspheric surface,
The function formula that gives the tilt deviation based on the vertex becomes complicated,
This is because the function of (4) is difficult to realize, whereas the shift is possible. In this case, it is necessary to keep the shift amount as small as possible so that the aperture does not change. This is automatically satisfied when the amount of aspherical surface is large.

FIG. 3 is a layout diagram of a distortion measurement of a null wavefront using a null lens, and uses a prototype having a highly accurate flat surface on the back surface. That is, the plane wave 2 emitted from the interferometer 1 is reflected from a high-precision Fizeau surface 3a formed on the Fizeau plane plate 3, and the plane wave is converted by the null element 4 into a desired aspherical surface at a reference position for measurement. The measurement wavefront 4a converted into the shape is also reflected from the test surface 5a of the test object 5 set at the reference position, and each reflected light forms a single-color interference fringe inside the interferometer 1. Then, the interference fringes are detected by a detector such as a CCD (not shown), and the obtained signal is analyzed by an information processing system that processes information of an interferometer. Similar measurements are possible using a Twyman-Green interferometer.

The tilt posture is monitored from the back side by an interference optical system, and the shift amount is separately controlled by a shift amount detecting means (not shown). Further, by providing the interference optical system from the back surface as a null optical system for generating a spherical wave and providing a spherical surface portion on the back surface of the prototype, it is possible to perform attitude control using peripheral plane waves.

[0021]

As described above, if the interferometer according to the present invention is employed, it is possible to measure the distortion of the measuring optical system of the interferometer with high accuracy and simply.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating the principle of an interferometer according to the present invention.

FIG. 2 is an explanatory diagram of a first embodiment of the interferometer according to the present invention.

FIG. 3 is an explanatory diagram of a second embodiment of the interferometer according to the present invention.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Interferometer 2 Plane wave 3 Fizeau plane plate 3a Fizeau surface 4 Null element 4a Measurement wavefront 5 Test object 5a Test surface

Continued on the front page F term (reference) 2F064 AA09 BB03 DD09 EE02 EE05 HH03 HH08 2F065 AA45 BB05 CC21 CC22 EE00 FF01 FF04 FF51 JJ03 JJ26 MM06 QQ01 QQ13 QQ27 QQ42 SS02 SS12

Claims (4)

[Claims] An interferometer for measuring surface accuracy of a surface to be inspected (residual shape after fitting with a functional expression representing a design geometric shape), wherein the measurement is performed by an amount known to the surface to be inspected. When an alignment error with respect to the reference surface of the optical system is given and the difference data of the interference measurement data before and after the alignment error is given is corrected for the alignment error, the distortion of the measuring optical system of the interferometer is calibrated, and the obtained calibration is performed. An interferometer, wherein the surface accuracy is corrected by data. 2. The method according to claim 1, wherein the distortion is calibrated from two difference data obtained by giving the misalignment in two directions orthogonal to each other with the optical axis of the measuring optical system as a center. The interferometer according to claim 1. 3. A rotationally symmetric axis that defines a rotationally symmetric component of the distortion is detected from the difference data, and “a rotationally symmetric distortion and a non-rotationally symmetric distortion as a residual” based on the rotationally symmetric axis are detected. 3. The interferometer according to claim 1, wherein the interferometer is calibrated. 4. A relative displacement about the rotational symmetry axis is relatively given to the main body of the interferometer while maintaining the interference state between the reference surface and the test surface, and difference data before and after the rotational displacement is given. 4. The interferometer according to claim 3, wherein the non-rotationally symmetric distortion is separated into a component caused by the measurement optical system and a component caused by the main body of the interferometer.