CN113804122A - Method for detecting plane mirror shape containing defocusing aberration by using translation and rotation absolute detection method - Google Patents
Method for detecting plane mirror shape containing defocusing aberration by using translation and rotation absolute detection method Download PDFInfo
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Abstract
The invention discloses a method for detecting a plane mirror shape containing defocusing aberration by using a translation and rotation absolute detection method, belonging 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 realizes the removal of the inclination angle of the measured mirror by real-time adjustment. And then, substituting the detection data in the effective aperture of the measured mirror into an absolute detection algorithm, and finally achieving the purpose of accurately restoring the plane mirror shape containing the defocusing aberration. The method does not need any auxiliary device, and is simple, low in cost and few in error source.
Description
Technical Field
The invention belongs to the field of optical detection, and particularly relates to a method for detecting a plane mirror shape containing defocusing aberration by using a translation and rotation absolute detection method.
Background
The basic principle of interference detection is that a part of light emitted by a laser forms reference light after being reflected by a reference mirror with an ideal surface shape, the other part of light forms measured light after being reflected by a measured mirror, 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 the surface shape 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 the same, it is difficult to obtain the real surface type error of the measured mirror from the interference detection result, and the interference detection cannot be used for precise imaging and guidance processing.
The absolute detection technique is a method for separating a measured surface type error and a reference surface error from an interferometric measurement result, and is various, including a liquid level method for plane detection, a three-plate method, a double-plate method, a random sphere method for spherical detection, a three-position method, and their respective extension methods, and the like. The translational rotation method is the method which has the highest attention, is developed fastest in recent years, and is applied to many high-precision detection fields, and the method can be simultaneously applied to planes and spheres.
The basic principle of the translational rotation method is shown in fig. 1, in the interference detection process, the measured mirror is rotated in a translational manner relative to the reference mirror, and a plurality of groups of detection data after the rotational in the translational manner are obtained, as shown in formulas (1.1) to (1.8).
W0(x，y)＝S(x，y)+T(x，y) (1.1)
W1(x，y)＝S(x，y)+T(x+Δx，y) (1.2)
W2(x，y)＝S(x，y)+T(x-Δx，y) (1.3)
W3(x，y)＝S(x，y)+T(x，y+Δy) (1.4)
W4(x，y)＝S(x，y)+T(x，y-Δy) (1.5)
W5(r，θ)＝S(x，y)+T(r，θ+Δθ1) (1.6)
W6(r，θ)＝S(x，y)+T(r，θ+Δθ2) (1.7)
W7(r，θ)＝S(x，y)+T(r，θ+Δθ3) (1.8)
Subtracting the detection data after translation and rotation from the face data measured at the initial position, offsetting the face data S (x, y) of the reference face to obtain multiple groups of shearing data of the measured face, wherein the shearing data are substituted into a phase extraction algorithm as shown in formulas (2.1) -2.7, and thus, the face errors of the measured face and the reference face can be simultaneously obtained.
DW1(x，y)＝T(x+Δx，y)-T(x，y) (2.1)
DW2(x，y)＝T(x-Δx，y)-T(x，y) (2.2)
DW3(x，y)＝T(x，y+Δy)-T(x，y) (2.3)
DW4(x，y)＝T(x，y-Δy)-T(x，y) (2.4)
DW5(r，θ)＝T(r，θ+Δθ1)-T(x，y) (2.5)
DW6(r，θ)＝T(r，θ+Δθ2)-T(x，y) (2.6)
DW7(r，θ)＝T(r，θ+Δθ3)-T(x，y) (2.7)
However, in the process of translational rotation, the postures of the measured mirror and the reference mirror are difficult to be kept unchanged all the time, and an included angle between the measured mirror and the reference mirror may slightly change due to the influence of environmental vibration, mechanical motion and the like, and is expressed as a change of an inclination amount in a surface type detection result, as shown in formulas (3.1) to (3.7). These amounts of tilt will cause serious errors in the recovery results.
DW1(x，y)＝T(x+Δx，y)-T(x，y)+a1x+b1y (3.1)
DW2(x，y)＝T(x-Δx，y)-T(x，y)+a2x+b2y (3.2)
DW3(x，y)＝T(x，y+Δy)-T(x，y)+a3x+b3y (3.3)
DW4(x，y)＝T(x，y-Δy)-T(x，y)+a4x+b4y (3.4)
DW5(r，θ)＝T(r，θ+Δθ1)-T(x，y)+a5x+b5y (3.5)
DW6(r，θ)＝T(r，θ+Δθ2)-T(x，y)+a6x+b6y (3.6)
DW7(r，θ)＝T(r，θ+Δθ3)-T(x，y)+a7x+b7y (3.7)
In order to prevent the influence of the inclination on the measurement result, the traditional translation rotation method is used for adjusting the measured mirror in real time to adjust the inclination to zero 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 in the measurement result caused by the defocusing aberration in the measured mirror surface is also eliminated, and finally the defocusing of the measured mirror cannot be accurately restored. In order to solve the problem that the traditional translational rotation method can not recover the defocusing, researchers have made many efforts, and the common characteristic of the researchers is that only the defocusing of a system or a measured mirror is measured by means of another method.
Disclosure of Invention
The invention aims to detect the inclination of the measured mirror caused by external factors by monitoring the inclination amount of the full aperture according to the characteristic that the effective aperture of translational rotation is always smaller than the full aperture of the measured mirror, remove the inclination in real time, and finally realize the purpose of accurately restoring defocusing by detecting the inclination amount caused by defocusing through the effective aperture.
The invention adopts the technical scheme that a method for detecting a plane mirror shape containing defocusing aberration by using a translation and rotation absolute detection method comprises the following steps:
the method comprises the following steps: measuring inclination coefficients Z1 and Z2 along the X direction and the Y direction in the light transmission caliber of the measured mirror at the initial position of the measured mirror;
step two: at the initial position, measuring to obtain surface type data W in the effective caliber of the measured lens0；
Step three: the reference mirror is fixed, the measured mirror is rotated in a translation mode, and at each translation and rotation position of the measured mirror, the inclination coefficients Z1 'and Z2' of the measured mirror in the X direction and the Y direction in the light-transmitting caliber are measured and obtained, 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 to obtain surface type data W in the effective caliber at the positioniWherein i is 1-7; at this time, the detection data W is compared with the initial position0In contrast, WiThe tilt in (1) is entirely caused by defocus aberrations of the measured surface;
step five: wiIn order to obtain the return error and remove it, after the inclinations in the effective aperture are all zeroed at eight positions including the initial position and the translational and rotational positions, a set of surface profile data W is measuredi', where i is 0-7, in which case WiNeither tilt nor return error in';
step six: data WiMinus Wi', the difference is WiThe sum of the tilt and return error in the process, and then after the difference value is decomposed by Zernike, the de-tilt processing is carried out to obtain Wi", this is the return error of the measured mirror introduced by the inclination, where i is 0-7;
step seven: subtracting the return error from the surface type data in the effective caliber to obtain WRi＝Wi-Wi", where i is 0-7, WRiThe method has the advantages that useless inclination caused by external factors is avoided, useful inclination caused by defocusing aberration is reserved, and return errors caused by the inclination are eliminated;
step eight: w is to beRiAnd substituting an absolute detection algorithm to obtain a measured mirror surface type with defocusing, wherein i is 0-7.
In the second step, the effective aperture is the intersection part of the light-transmitting apertures at the eight positions and is always smaller than the light-transmitting aperture.
In the third step, after the translation rotation, the inclination angle of the measured mirror is adjusted in real time, so that the inclination coefficient in the light transmission aperture is consistent with the initial position, and the inclination change of the measured mirror caused by the translation rotation process can be avoided.
And step five, adjusting the inclination angle of the measured mirror, and zeroing all the inclinations in the effective caliber to obtain a group of measured mirror surface Wi' without inclination and return stroke errors.
And in the sixth step, subtracting Wi 'from the data Wi, decomposing the difference value through zernike, and then performing inclination removal processing to obtain Wi', namely the measured mirror return error introduced by inclination.
Compared with the prior art, the invention has the advantages that:
(1) no other devices are needed, the operation is simple and convenient, and the cost is low;
(2) the error that other detection device probably brought has been avoided, and the precision is higher.
Drawings
Fig. 1 is a schematic view of translation and rotation.
Fig. 2 is a schematic view of the total clear aperture and effective aperture.
FIG. 3 is a schematic view of the clear aperture and effective aperture in the initial position.
Fig. 4 is a schematic view of the clear aperture and the effective aperture of one of the translational and rotational positions.
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 measuring plane mirror shape containing defocusing aberration by using a translation and rotation absolute detection method, which is shown in figure 2 as a schematic diagram of the measuring method, wherein a thick dotted circle in the diagram represents a light-passing aperture of a measured mirror, and the light-passing aperture of the measured mirror is dislocated with an initial position along with translation and rotation in the translation and rotation process. After each translation rotation, only the inclination angle of the measured mirror needs to be adjusted, the inclination coefficient in the light transmission aperture is ensured to be consistent with the initial position all the time, and the change of the inclination of the measured mirror in the translation rotation process can be avoided. Finally, the effective aperture of the measured mirror is the intersection part of the light-transmitting 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, the inclination is reserved, and the measured mirror surface containing the defocusing aberration can be recovered by substituting the inclination into an absolute detection algorithm.
In a specific embodiment, the method comprises the steps of:
the method comprises the following steps: the relationship between the effective aperture and the clear aperture at the initial position of the test mirror is as shown in fig. 3, and the fringes within the clear aperture are processed to obtain tilt coefficients Z1, Z2 of the test mirror in the initial position clear aperture with respect to the reference mirror in the X direction and the Y direction.
Step two: processing the stripes in the effective caliber at the initial position to obtain surface type data W in the effective caliber0；。
Step three: the reference mirror is fixed, the measured mirror is subjected to translation or rotation operation, the position relation between the light transmission aperture and the effective aperture is shown in fig. 4, the position of the effective aperture is unchanged, and the light transmission aperture and the initial position are dislocated. At this time, the tilt coefficients Z1 ', Z2' of the inner profile of the light transmission aperture may be changed from the initial position due to the influence of factors such as mechanical movement of the measurement mirror, environmental vibration, and defocus aberration of the measurement mirror. And adjusting the inclination angle of the measured mirror in real time and measuring the inclination coefficient of the measured mirror in the clear aperture until the inclination coefficient of the measured mirror is consistent with the initial position, namely Z1 ═ Z1 and Z2 ═ Z2, and removing the whole inclination of the measured mirror caused by external factors.
Step four: measuring to obtain surface type data W in the effective caliber of the positioni(i 1-7), and at this time, the initial position detection data W0In contrast, WiThe tilt in (1) is entirely caused by defocus aberrations of the measured surface;
step five: wiIn order to obtain the return error and remove the return error, after the inclination in the effective caliber is completely zeroed, a group of surface type data W is measuredi', where i is 0-7, in which case WiNeither tilt nor return error in';
step six: data WiMinus Wi', the difference is WiThe sum of the tilt and return error in the process, and then after the difference value is decomposed by Zernike, the de-tilt processing is carried out to obtain Wi", this is the return error of the measured mirror introduced by the inclination, where i is 0-7;
step seven: subtracting the return error from the surface type data in the effective caliber to obtain WRi＝Wi-Wi", where i is 0-7, WRiThe method has the advantages that useless inclination caused by external factors is avoided, useful inclination caused by defocusing aberration is reserved, and return errors caused by the inclination are eliminated;
step eight: w is to beRiAnd (i is 0-7) substituting the absolute detection algorithm to obtain the measured mirror surface with defocusing.
By combining the above embodiments, it can be understood that the present invention proposes to detect the tilt caused by the external factor by monitoring the tilt amount of the full aperture according to the characteristic that the effective aperture of the translational rotation is always smaller than the full aperture of the measured mirror, and remove the tilt in real time, and finally achieve the purpose of accurately restoring the defocus by detecting the tilt amount caused by the defocus through the effective aperture. The method does not need any auxiliary device, and is simple, low in cost and few in error source.
The above description is only for the specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto, and these examples are only for illustrative purpose 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 devised by those skilled in the art without departing from the scope of the invention, and these alternatives and modifications are intended to fall within the scope of the invention.
Claims (2)
1. A method for detecting a plane mirror containing defocus aberration by using a translational-rotational absolute detection method, comprising:
the method comprises the following steps: measuring inclination coefficients Z1 and Z2 along the X direction and the Y direction in the light transmission caliber of the measured mirror at the initial position of the measured mirror;
step two: at the initial position, measuring to obtain surface type data W in the effective caliber of the measured lens0；
Step three: the reference mirror is fixed, the measured mirror is translated or rotated, and at each translation and rotation position, the tilt coefficients Z1 ', Z2' of the measured mirror in the light transmission aperture are measured and obtained, and the tilt angle of the measured mirror is adjusted in real time until Z1 ═ Z1, Z2 ═ Z2,;
step four: detecting the effectiveness of each translational and rotational positionSurface profile data W in caliberiWherein i is 1-7;
step five: adjusting the inclination angle of the measured mirror at eight positions including the initial position and the translational and rotational positions, zeroing the inclination in the effective aperture, and measuring a group of surface data Wi', where i is 0-7;
step six: data WiMinus Wi' and then subjecting the difference to zernike decomposition and then to a deskew process to obtain Wi", this is the return error of the measured mirror introduced by the inclination, where i is 0-7;
step seven: subtracting the return error from the surface type data in the effective caliber to obtain WRi＝Wi-Wi", where i is 0-7, WRiThe method has the advantages that useless inclination caused by external factors is avoided, useful inclination caused by defocusing aberration is reserved, and return errors caused by the inclination are eliminated;
step eight: w is to beRiAnd substituting an absolute detection algorithm to obtain a measured mirror surface type containing defocusing aberration, wherein i is 0-7.
2. The method according to claim 1, wherein the planar mirror type including defocus aberration is detected by the absolute translational rotation detection method,
in the second step, the effective aperture is the intersection part of the light-transmitting apertures at the eight positions and is always smaller than the light-transmitting aperture.
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| CN114858091A (en) * | 2022-04-27 | 2022-08-05 | 中国科学院光电技术研究所 | Method simultaneously suitable for calibrating return error of plane and spherical surface |
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