CN114858091B - Method for calibrating return stroke error simultaneously suitable for plane and spherical surface - Google Patents
Method for calibrating return stroke error simultaneously suitable for plane and spherical surface Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/2441—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures using interferometry
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
- G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
- G01B21/042—Calibration or calibration artifacts
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Abstract
The invention discloses a method suitable for calibrating return stroke errors of a plane and a spherical surface at the same time, and belongs to the field of optical detection. The invention firstly measures and obtains the return error size caused by the inclination of the measured mirror relative to the reference mirror along the X direction, the inclination of the Y direction and the defocusing through an actual measurement mode, and performs Zernike polynomial decomposition on the return error one by one. And then establishing a three-dimensional coordinate system by using the inclination coefficient in the X direction, the inclination coefficient in the Y direction and the defocusing coefficient, and obtaining a functional relation between each zernike coefficient in the return error and a three-dimensional coordinate point through data fitting. When the interferometer is used for detecting any measured mirror, the inclination coefficient and the defocusing coefficient are substituted into the function relation obtained before, and the corresponding return error can be calculated and removed.
Description
Technical Field
The invention belongs to the field of optical detection, and particularly relates to a method suitable for calibrating return stroke errors of a plane and a spherical surface simultaneously.
Background
The basic principle of interference detection is that a part of light emitted by a laser is reflected by a reference mirror to form reference light, the other part of the light is reflected by a measured mirror and is called measured light, and the reference light and the measured light are transmitted through an optical system in the interferometer and then are coherently superposed at the position of an observation screen to form interference fringes and are received by a CCD. By processing the interference fringes collected by the camera, the phase information of the detected light relative to the reference light can be obtained.
When the measured light and the reference light transmit the same path in the interferometer, the phase difference between the measured light and the reference light is the surface shape difference between the measured mirror and the reference mirror, and the measured mirror and the reference light can be used for guiding the processing of the measured mirror. If the detected light and the reference light are transmitted in different paths inside the interferometer, additional aberration may be brought, as shown in formula (1), the detection result of the interferometer includes a "return error" trace in addition to the detected surface type T and the reference surface type R.
W＝T-R+retrace, (1)
In order to avoid the influence of the return error on the detection result of the interferometer, the measured mirror is usually adjusted to be in a state of sharing the optical path with the reference mirror as much as possible during detection. However, it is difficult to achieve an absolute common-path state in some cases, for example, when the curvature radius of the measurement lens is small, the non-confocal state of the measured light and the reference light in the micron order causes a non-negligible defocus aberration. While others intentionally require the measured light to deviate from the reference light, such as carrier phase shift, differential de-high order spherical aberration, and dual aperture POWER. In the plane detection, the adjustment error is the tilt in the X direction and the tilt in the Y direction, and in the sphere detection, the adjustment error includes not only the tilt error but also the shift in the Z direction, that is, the defocus error. Mathematically, the plane can be regarded as a spherical surface with infinite curvature radius, so that the invention only needs to consider calibrating the return stroke error by using a spherical model.
Disclosure of Invention
The invention aims to obtain a functional relation between adjustment error (X-direction inclination, Y-direction inclination and defocusing) coefficients and return error polynomial coefficients of various orders by a real measurement method. During actual measurement, the return error can be calculated only by substituting the adjustment error coefficient into the return error function.
The invention adopts the technical scheme that a method suitable for calibrating return errors of a plane and a spherical surface simultaneously comprises the following steps:
the method comprises the following steps: selecting a reflector with negligible surface shape error as the calibration return error of the measured mirror, adjusting the measured mirror and the reference mirror to a confocal position, namely a 'zero stripe' position, and measuring to obtain the surface shape data W 0 ；
Step two: adjusting the azimuth angle of the measured lens to obtain a new set of surface shapes W i Wherein i =1,2, … N represents the number of groups of measured data, N represents the total number of measurements, and the tilt coefficient in X direction, the tilt coefficient in Y direction and the defocus coefficient are respectively a1 , i ,a2 , i ,a3 , i ；
Step three: w i W after removal of tilt and defocus i ', corresponding return error is WR i ＝W i ’-W 0 Return error is decomposed into WR by zernike i ＝b 4,i *Z4+b 5,i *Z5+…+b 37,i *Z37；
Step four: fitting to obtain each zernike polynomial coefficient and a of return error WR 1 ,a 2 ,a 3 Is respectively expressed as b 4 ＝f 4 (a1,a2,a3)，b 5 ＝f 5 (a1,a2,a3)，…，b 37 ＝f 37 (a1,a2,a3)；
Step five: when tilt and defocus coefficients (i.e., a1, a2, a 3) are determined, the corresponding return error expression is WR = b 4 *Z4+b 5 *Z5+…b 37 * Z37; each time a new measured mirror shape is obtained by measurement, the tilt and defocus coefficients are substituted into the function f n The return error can be calculated.
The principle of the invention is as follows: the method is suitable for calibrating return stroke errors of a plane and a spherical surface at the same time, and the plane can be regarded as the spherical surface with infinite curvature radius in practice, so that the calibration of the return stroke errors can be realized by the spherical surface no matter plane detection or spherical surface detection is carried out. The method comprises the following steps: the method comprises the following steps: actually measuring N groups of surface types to obtain the return error surface types WR corresponding to the inclination in the X direction, the inclination in the Y direction and the defocusing in different sizes i (i =1,2, … N); step two: decomposing the return error surface type one by a Zernike polynomial to obtain various Zernike polynomial coefficients b n (n =4,5, …); step three: fitting the functional relationship f between each zernike polynomial coefficient and the inclination coefficient in the X direction, the inclination coefficient in the Y direction and the defocusing coefficient n (a 1, a2, a 3) (n =4,5, …), and the return stroke error expression is WR = f 4 Z4+f 5 Z5+…+f 37 Z37; step four: each time a new measured surface shape is obtained by measurement, the inclination and defocus coefficients are substituted into the function f n The return error can be calculated. Since the plane can be regarded as a spherical surface with an infinite radius of curvature in practice, it is possible to use the plane regardless of whether it is a spherical surface with an infinite radius of curvatureWhether plane detection or spherical detection is adopted, and the calibration of return errors can be realized by using a spherical surface.
Compared with the prior art, the invention has the advantages that:
(1) The invention calibrates the return error by an actual measurement mode, and avoids the condition that the calculated return error of the simulation software does not accord with the actual return error.
(2) The invention measures return errors of three dimensions of inclination and defocusing, and can be simultaneously used for plane detection and spherical detection.
Drawings
Fig. 1 shows that a coordinate point in a three-dimensional coordinate system corresponds to only one two-dimensional return stroke error surface type.
Fig. 2 is a theoretical ratio and actual ratio curve of spherical aberration coefficient and defocusing coefficient in a differential surface type when defocusing errors exist in large NA spherical surface detection.
FIG. 3 is a curve showing the ratio of spherical aberration coefficient to defocus coefficient in the difference surface after the return error is eliminated by the method of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and the detailed description.
The invention relates to a method for calibrating return stroke errors simultaneously suitable for planes and spheres, and a schematic diagram of the principle of the invention is shown in figure 1. The three coordinate axes on the left side of the graph represent an X-direction inclination coefficient, a Y-direction inclination coefficient and a defocus coefficient respectively, and the combination of the three coefficient values corresponds to a unique coordinate point in the space, and the coordinate point corresponds to a unique surface type of return error as shown on the right side of the graph 1. Since in real time, the measured tilt coefficient cannot traverse every point in space, a polynomial fitting is needed to approximate the functional relationship between the return error and the tilt and defocus coefficients. The more data measured, the higher the accuracy of the fit.
The method comprises the following steps: choosing a surface type error that is negligible (RMS)<0.5 nm) small NA spherical mirror (NA)<0.15 ) the reflector is used as a measured mirror to calibrate the return stroke error, the measured mirror and the reference mirror are adjusted to a confocal position, namely a 'zero stripe' position, and the surface type data W at the moment is measured 0 ；
Step two: adjusting the azimuth angle of the measured lens to obtain a new set of surface shapes W i Wherein i =1,2, … N represents the number of groups of measured data, N represents the total number of groups measured, and the tilt coefficient in X direction, the tilt coefficient in Y direction and the defocus coefficient are a1 respectively , i ,a2 , i ,a3 , i 。
Step three: w i W after tilting and defocusing i ', corresponding return error is WR i ＝W i ’-W 0 The return error is decomposed into WR by zernike i ＝b 4,i *Z4+b 5,i *Z5+…+b 37,i *Z37；
Step four: fitting to obtain each zernike polynomial coefficient and a of return error WR 1 ,a 2 ,a 3 Is respectively expressed as b 4 ＝f 4 (a1,a2,a3)，b 5 ＝f 5 (a1,a2,a3)，…，b 37 ＝f 37 (a1,a2,a3)。
Step five: when the tilt and defocus coefficients, i.e., a1, a2, a3, are determined, the corresponding return error expression is WR = b 4 *Z4+b 5 *Z5+…b 37 *Z37。
When the large NA spherical reflector is detected, the slight defocusing of the detected mirror can cause a serious non-common optical path of the detected light and the reference light, thereby causing return stroke errors. According to theoretical derivation, the ratio of the spherical difference coefficient to the defocusing coefficient in the differential surface type of the two defocusing surface types of the measured mirror should be always constant, however, in practice, it is found that the ratio of the spherical difference coefficient to the defocusing coefficient in the differential surface type is no longer constant due to the return error caused by defocusing, as shown in fig. 2, and the ratio increases as the defocusing amount increases. After the return error is removed by the method of the invention, as shown in fig. 3, the ratio of the spherical aberration coefficient to the defocusing coefficient is closer to the theoretical value.
Claims (1)
1. A method for calibrating return stroke errors simultaneously suitable for a plane and a spherical surface is characterized by comprising the following steps:
the method comprises the following steps: select oneThe reflector with negligible individual profile error is used as the measured mirror to calibrate the return stroke error, the measured mirror and the reference mirror are adjusted to the confocal position, namely the zero stripe position, and the profile data W at the moment is measured and obtained 0 ；
Step two: adjusting the azimuth angle of the measured lens to obtain a new set of surface shapes W i Wherein i =1,2, … N represents the number of groups of measured data, N represents the total number of measurements, and the tilt coefficient in X direction, the tilt coefficient in Y direction and the defocus coefficient are respectively a 1,i ,a 2,i ,a 3,i ；
Step three: w i W after tilting and defocusing i ', corresponding return error is WR i ＝W i ’-W 0 The return error is decomposed into WR by zernike i ＝b 4,i *Z4+b 5,i *Z5+…+b 37,i *Z37；
Step four: fitting to obtain each zernike polynomial coefficient and a of return error WR 1 ,a 2 ,a 3 Is respectively expressed as b 4 ＝f 4 (a 1 ,a 2 ,a 3 )，b 5 ＝f 5 (a 1 ,a 2 ,a 3 )，…，b 37 ＝f 37 (a 1 ,a 2 ,a 3 )；
Step five: when the tilt and defocus coefficients are a 1 ,a 2 ,a 3 When determined, the corresponding backhaul error expression is WR = b 4 *Z4+b 5 *Z5+…b 37 * Z37; each time a new measured mirror shape is obtained by measurement, the tilt and defocus coefficients are substituted into the function f n The return error can be calculated.
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