CN113804122B - Method for measuring plane mirror surface type containing defocusing aberration by using translation rotation absolute detection method - Google Patents
Method for measuring plane mirror surface type containing defocusing aberration by using translation rotation absolute detection method Download PDFInfo
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- CN113804122B CN113804122B CN202111036664.XA CN202111036664A CN113804122B CN 113804122 B CN113804122 B CN 113804122B CN 202111036664 A CN202111036664 A CN 202111036664A CN 113804122 B CN113804122 B CN 113804122B
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- 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
Abstract
The invention discloses a method for measuring a plane mirror surface containing defocus aberration by using a translation and rotation absolute detection method, and belongs to the field of optical detection. According to the characteristic that the effective caliber of translational rotation is always smaller than the full caliber of the measured mirror, the invention provides the method for monitoring the inclination of the measured mirror caused by external factors by monitoring the inclination amount of the full caliber, and realizing the inclination angle removal of the measured mirror by real-time adjustment. And substituting the detection data in the effective caliber of the detected lens into an absolute detection algorithm, and finally, accurately recovering the plane mirror surface containing the defocus aberration. The invention has the advantages of no need of any auxiliary device, simple method, low cost and less error source.
Description
Technical Field
The invention belongs to the field of optical detection, and particularly relates to a method for measuring a plane mirror surface containing defocus aberration by using a translational rotation absolute detection method.
Background
The basic principle of interference detection is that a part of light emitted by a laser is reflected by an ideal plane type reference mirror to form reference light, the other part of light is reflected by a measured mirror to form measured light, the reference light and the measured light enter an imaging system together, interference fringes are formed by coherent superposition on an observation screen and are collected by a camera, and plane type information of the measured mirror relative to the reference mirror can be obtained by analyzing the interference fringes. The interference detection is a relative measurement, and if the reference mirror and the measured mirror have surface type errors at the same time, especially when the error magnitude is quite similar, the real surface type errors of the measured mirror are difficult to obtain from the interference detection result, and the real surface type errors cannot be used for accurate imaging and guiding processing.
The absolute detection technique is a method of separating the measured surface type error and the reference surface error from the interferometry results, and is a wide variety of, including a liquid level method for planar detection, a tri-plate method, a bi-planar method, and a random ball method for spherical detection, a tri-position method, and their respective expansion methods, and the like. Among them, the translational rotation method is a method which has been the highest in attention, the fastest in development and applied in many high-precision detection fields in recent years, and can be applied to both planar and spherical surfaces.
The basic principle of the translational rotation method is shown in fig. 1, in the interference detection process, the detected mirror performs translational rotation relative to the reference mirror, and a plurality of groups of detection data after translational rotation are obtained, wherein the detection data are shown in the formulas (1.1) to (1.8).
W 0 (x，y)＝S(x，y)+T(x，y) (1.1)
W 1 (x，y)＝S(x，y)+T(x+Δx，y) (1.2)
W 2 (x，y)＝S(x，y)+T(x-Δx，y) (1.3)
W 3 (x，y)＝S(x，y)+T(x，y+Δy) (1.4)
W 4 (x，y)＝S(x，y)+T(x，y-Δy) (1.5)
W 5 (r，θ)＝S(x，y)+T(r，θ+Δθ 1 ) (1.6)
W 6 (r，θ)＝S(x，y)+T(r，θ+Δθ 2 ) (1.7)
W 7 (r，θ)＝S(x，y)+T(r，θ+Δθ 3 ) (1.8)
The detection data after translation and rotation are subtracted from the surface type data measured at the initial position, the surface type data S (x, y) of the reference surface are counteracted, a plurality of groups of shearing data of the measured surface are obtained, as shown in the formulas (2.1) to (2.7), and the shearing data are substituted into a phase extraction algorithm, so that the measured surface type and the reference surface type error can be obtained simultaneously.
DW 1 (x，y)＝T(x+Δx，y)-T(x，y) (2.1)
DW 2 (x，y)＝T(x-Δx，y)-T(x，y) (2.2)
DW 3 (x，y)＝T(x，y+Δy)-T(x，y) (2.3)
DW 4 (x，y)＝T(x，y-Δy)-T(x，y) (2.4)
DW 5 (r，θ)＝T(r，θ+Δθ 1 )-T(x，y) (2.5)
DW 6 (r，θ)＝T(r，θ+Δθ 2 )-T(x，y) (2.6)
DW 7 (r，θ)＝T(r，θ+Δθ 3 )-T(x，y) (2.7)
However, in the translational rotation process, the postures of the measured mirror and the reference mirror are difficult to be kept unchanged all the time, and the included angle between the measured mirror and the reference mirror may slightly change due to the influence of environmental vibration, mechanical motion and other factors, and the change of the inclination amount is shown in the surface type detection result, as shown in formulas (3.1) to (3.7). These amounts of tilt will cause serious errors in the restoration results.
DW 1 (x，y)＝T(x+Δx，y)-T(x，y)+a 1 x+b 1 y (3.1)
DW 2 (x，y)＝T(x-Δx，y)-T(x，y)+a 2 x+b 2 y (3.2)
DW 3 (x，y)＝T(x，y+Δy)-T(x，y)+a 3 x+b 3 y (3.3)
DW 4 (x，y)＝T(x，y-Δy)-T(x，y)+a 4 x+b 4 y (3.4)
DW 5 (r，θ)＝T(r，θ+Δθ 1 )-T(x，y)+a 5 x+b 5 y (3.5)
DW 6 (r，θ)＝T(r，θ+Δθ 2 )-T(x，y)+a 6 x+b 6 y (3.6)
DW 7 (r，θ)＝T(r，θ+Δθ 3 )-T(x，y)+a 7 x+b 7 y (3.7)
In order to prevent the influence of the inclination on the measurement result, the conventional translational rotation method adjusts the inclination of the measured mirror to zero in real time in the measurement process, so that the inclination of the measured mirror relative to the reference mirror caused by environmental factors can be eliminated, but the inclination amount in the measurement result caused by the defocus aberration in the measured mirror surface is also eliminated, and finally, the defocus of the measured mirror cannot be accurately restored. In order to solve the problem that the conventional translational rotation method cannot restore defocus, researchers have made many efforts, and have the common characteristic of measuring defocus of a system or a measured mirror exclusively by means of another means.
Disclosure of Invention
According to the characteristic that the effective caliber of translational rotation is always smaller than the full caliber of the measured mirror, the inclination of the measured mirror caused by external factors is detected by monitoring the inclination amount of the full caliber and removed in real time, and the inclination amount caused by defocusing is detected by the effective caliber, so that the purpose of accurate recovery of defocusing is finally realized.
The technical scheme adopted by the invention is that the method for measuring the plane mirror surface type containing the defocus aberration by using a translational rotation absolute detection method comprises the following steps:
step one: measuring and obtaining inclination coefficients Z1 and Z2 along the X direction and the Y direction in the light-transmitting aperture of the measured mirror at the initial position of the measured mirror;
step two: at the initial position, measuring to obtain the surface data W in the effective caliber of the measured mirror 0 ；
Step three: the reference mirror is fixed, the measured mirror carries out translational rotation, the inclination coefficients Z1', Z2' of the measured mirror along the X direction and the Y direction in the light-passing aperture are measured at each translational rotation position of the measured mirror, and the included angle of the measured mirror relative to the reference mirror, namely the inclination angle of the measured mirror, is adjusted in real time until Z1 '=Z1, Z2' =Z2,;
step four: detecting and obtaining the surface data W in the effective caliber of the position i Where i=1 to 7; at this time, detection data W corresponding to the initial position 0 In comparison with W i The inclination in (2) is entirely caused by defocus aberration of the measured surface;
step five: w (W) i In (2) will cause return error, and in order to obtain return error for removal, a set of face data W is measured after all the tilts in the effective aperture are zeroed at eight positions including the initial position and the translational rotation position i ' where i=0 to 7, where W i ' neither tilt nor return error;
step six: data W i Subtracting W i ' the difference is W i The sum of the tilt and return error of the above-mentioned two-dimensional error-correction method, then making the difference undergo the process of zernike decomposition, then making de-tilt treatment so as to obtain W i "this is the return error of the measured mirror introduced by tilting, where i=0 to 7;
step seven: subtracting the return error from the surface data in the effective caliber to obtain W Ri ＝W i -W i "where i=0 to 7, W at this time Ri The lens has no useless inclination caused by external factors, retains useful inclination caused by defocusing aberration, and removes return error caused by inclination;
step eight: will W Ri Substituting the measured mirror surface with defocus into an absolute detection algorithm to obtain the measured mirror surface type with defocus, where i=0 to 7.
In the second step, the effective aperture is the intersection part of the light-transmitting apertures of the eight positions and is always smaller than the light-transmitting aperture.
In the third step, after translation and rotation, the inclination angle of the measured mirror is adjusted in real time, so that the inclination coefficient in the light-transmitting aperture is consistent with the initial position, and the inclination change of the measured mirror caused by the translation and rotation process can be avoided.
In the fifth step, the inclination angle of the measured mirror is adjusted, the inclination in the effective caliber is all zeroed, and a group of measured mirror surfaces Wi' without inclination and return errors is obtained.
In the sixth step, wi' is subtracted from the data Wi, and then the difference is decomposed by zernike, and then declination processing is performed to obtain Wi ", which is the return error of the measured mirror introduced by tilting.
Compared with the prior art, the invention has the advantages that:
(1) The operation is simple and convenient without any other device, and the cost is low;
(2) The error possibly brought by other detection devices is avoided, and the precision is higher.
Drawings
Fig. 1 is a translational rotation schematic diagram.
Fig. 2 is a schematic diagram of the total light transmission aperture and the effective aperture.
FIG. 3 is a schematic diagram of the light passing aperture and the effective aperture in the initial position.
FIG. 4 is a schematic view of the light passing aperture and the effective aperture in one of the translational and rotational positions.
Detailed Description
The invention will be described in detail with reference to the drawings and detailed description.
The invention relates to a method for measuring plane mirror surfaces containing defocus aberration by using a translational rotation absolute detection method, which is shown in fig. 2 as a schematic diagram of the testing method of the invention, wherein a thick dotted circle in the diagram represents the light-passing caliber of a measured mirror, and the light-passing caliber is dislocated with an initial position along with translational rotation action in the translational rotation process of the measured mirror. After each translational rotation, only the inclination angle of the measured mirror needs to be adjusted, so that the inclination coefficient in the light-transmitting aperture is always consistent with the initial position, and the inclination change of the measured mirror in the translational rotation process can be avoided. Finally, the effective aperture of the measured mirror is the intersection part of the light transmission apertures at eight positions, as shown by a thin dotted circle in fig. 2, the inclination in the effective aperture is caused by the defocusing aberration in the measured mirror surface type, the inclination is reserved, and the absolute detection algorithm is substituted to recover the measured mirror surface type containing the defocusing aberration.
In a specific embodiment, the method comprises the steps of:
step one: in the initial position of the measured mirror, the relation between the effective aperture and the light-transmitting aperture is shown in fig. 3, and the fringes in the light-transmitting aperture are processed to obtain tilt coefficients Z1 and Z2 of the measured mirror in the initial position relative to the reference mirror along the X direction and the Y direction.
Step two: the stripes in the effective caliber of the initial position are processed to obtain the surface data W in the effective caliber 0 ；。
Step three: the reference mirror is fixed, the measured mirror is subjected to translation or rotation operation, the position relation between the light transmission caliber and the effective caliber is shown in fig. 4, the position of the effective caliber is unchanged, and the light transmission caliber is misplaced with the initial position. At this time, the tilt coefficients Z1', Z2' of the light-transmitting aperture inner profile may change from the initial position due to the influence of factors such as mechanical movement of the objective lens, environmental vibration, defocus aberration of the objective lens, and the like. And adjusting the inclination angle of the measured mirror in real time and measuring the inclination coefficient of the measured mirror in the light-transmitting aperture until the inclination coefficient of the measured mirror is consistent with the initial position, namely Z1 '=Z1, Z2' =Z2, and the whole inclination of the measured mirror caused by external factors is removed.
Step four: measuring to obtain the surface data W in the effective caliber of the position i (i=1 to 7), and at this time, the detection data W corresponding to the initial position 0 In comparison with W i The inclination in (2) is entirely caused by defocus aberration of the measured surface;
step five: w (W) i The inclination in (a) causes return error, and a group of face data W is measured after the inclination in the effective caliber is fully zeroed in order to obtain the return error so as to remove the return error i ' where i=0 to 7, where W i ' neither tilt nor return error;
step six: data W i Subtracting W i ' the difference is W i The sum of the tilt and return error of the above-mentioned two-dimensional error-correction method, then making the difference undergo the process of zernike decomposition, then making de-tilt treatment so as to obtain W i "this is the return error of the measured mirror introduced by tilting, where i=0 to 7;
step seven: subtracting the return error from the surface data in the effective caliber to obtain W Ri ＝W i -W i "where i=0 to 7, W at this time Ri The lens has no useless inclination caused by external factors, retains useful inclination caused by defocusing aberration, and removes return error caused by inclination;
step eight: will W Ri (i=0 to 7) is substituted into an absolute detection algorithm to obtain the mirror surface type to be detected with defocus.
With the above embodiments, it can be understood that according to the characteristic that the effective caliber of translational rotation is always smaller than the full caliber of the measured lens, the invention proposes to detect the inclination caused by external factors by monitoring the inclination amount of the full caliber, remove the inclination in real time, and finally realize the purpose of accurate recovery of defocus by detecting the inclination amount caused by defocus through the effective caliber. The invention has the advantages of no need of any auxiliary device, simple method, low cost and less error source.
The foregoing is merely a specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims and equivalents thereof. Various alternatives and modifications can be made by those skilled in the art without departing from the scope of the invention, and such alternatives and modifications are intended to fall within the scope of the invention.
Claims (2)
1. A method for measuring a planar specular pattern including defocus by using translational absolute detection, comprising:
step one: measuring and obtaining inclination coefficients Z1 and Z2 along the X direction and the Y direction in the light-transmitting aperture of the measured mirror at the initial position of the measured mirror;
step two: at the initial position, measuring to obtain the surface data W in the effective caliber of the measured mirror 0 ；
Step three: the reference mirror is fixed, the measured mirror translates or rotates, the inclination coefficient Z1', Z2' of the measured mirror in the light-transmitting aperture is measured at each translation and rotation position, and the inclination angle of the measured mirror is adjusted in real time until Z1 '=Z1, Z2' =Z2;
step four: detecting the surface data W in the effective caliber at each translational rotation position i Where i=1 to 7;
step five: the inclination angle of the measured mirror is adjusted at eight positions including the initial position and the translational rotation position, and a group of surface type data W is measured after the inclination in the effective caliber is all zeroed i ' where i=0 to 7;
step six: data W i Subtracting W i ' after the difference is decomposed by zernike, the de-tilting treatment is carried out to obtain W i "this is the return error of the measured mirror introduced by tilting, where i=0 to 7;
step seven: subtracting the return error from the surface data in the effective caliber to obtain W Ri ＝W i -W i "where i=0 to 7, W at this time Ri The lens has no useless inclination caused by external factors, retains useful inclination caused by defocusing aberration, and removes return error caused by inclination;
step eight: will W Ri Substituting the measured mirror surface type containing defocus aberration into an absolute detection algorithm, wherein i=0 to 7.
2. A method for measuring a planar mirror surface containing defocus as set forth in claim 1, wherein,
in the second step, the effective aperture is the intersection part of the light-transmitting apertures of the eight positions and is always smaller than the light-transmitting aperture.
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| CN110017776A (en) * | 2019-05-17 | 2019-07-16 | 山东大学 | Digital holographic microscope aberration absolute Calibrating Method and system based on sequential shifts and chebyshev approximating polynomial |
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| US6049373A (en) * | 1997-02-28 | 2000-04-11 | Sumitomo Heavy Industries, Ltd. | Position detection technique applied to proximity exposure |
| US6233043B1 (en) * | 1997-02-28 | 2001-05-15 | Sumitomo Heavy Industries, Ltd. | Position detection technique applied to proximity exposure |
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