CN117490604B - Optical plane shape absolute detection method - Google Patents
Optical plane shape absolute detection method Download PDFInfo
- Publication number
- CN117490604B CN117490604B CN202410004055.3A CN202410004055A CN117490604B CN 117490604 B CN117490604 B CN 117490604B CN 202410004055 A CN202410004055 A CN 202410004055A CN 117490604 B CN117490604 B CN 117490604B
- Authority
- CN
- China
- Prior art keywords
- mirror
- plane
- auxiliary transmission
- surface shape
- transmission mirror
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 230000003287 optical effect Effects 0.000 title claims abstract description 42
- 238000001514 detection method Methods 0.000 title claims abstract description 40
- 230000005540 biological transmission Effects 0.000 claims abstract description 70
- 230000005484 gravity Effects 0.000 claims abstract description 29
- 238000000034 method Methods 0.000 claims abstract description 21
- 239000011159 matrix material Substances 0.000 claims abstract description 9
- 230000002452 interceptive effect Effects 0.000 claims abstract description 3
- 230000007246 mechanism Effects 0.000 claims description 18
- 238000004364 calculation method Methods 0.000 claims description 6
- 230000008030 elimination Effects 0.000 abstract description 3
- 238000003379 elimination reaction Methods 0.000 abstract description 3
- 238000005516 engineering process Methods 0.000 abstract description 3
- 230000008878 coupling Effects 0.000 abstract description 2
- 238000010168 coupling process Methods 0.000 abstract description 2
- 238000005859 coupling reaction Methods 0.000 abstract description 2
- 238000010586 diagram Methods 0.000 description 4
- 230000008859 change Effects 0.000 description 3
- 238000005259 measurement Methods 0.000 description 3
- 230000006870 function Effects 0.000 description 2
- 239000000463 material Substances 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N Silicium dioxide Chemical compound O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000008901 benefit Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 238000004441 surface measurement Methods 0.000 description 1
- 230000009897 systematic effect Effects 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
- 238000013519 translation Methods 0.000 description 1
- 230000007306 turnover Effects 0.000 description 1
Classifications
-
- 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
Abstract
The invention relates to the technical field of surface shape detection, in particular to an optical plane surface shape absolute detection method, which is used for sequentially interfering four planes of a reference mirror, an auxiliary transmission mirror and a to-be-detected mirror based on a four-plane method to obtain a group of underdetermined equation sets, and removing elements by adding and subtracting the equations to eliminate the influence of optical non-uniformity; rotating the auxiliary transmission mirror, and obtaining absolute surface shape data of the auxiliary transmission mirror under a cylindrical coordinate system by utilizing Moore-Penrose generalized inverse matrix, so as to obtain surface shape errors of all surfaces under the condition of gravity decoupling; and obtaining an interference result of the auxiliary transmission mirror and the to-be-inspected mirror by using a wavelength modulation interferometer, and calculating to obtain the gravity deformation of the TF mirror, thereby obtaining the absolute surface shape of the to-be-inspected mirror under the gravity-free coupling condition. The invention is based on the existing four-plane absolute detection technology, and performs calibration and elimination on the influence factors such as optical non-uniformity, gravity deformation and the like of the auxiliary transmission mirror, thereby greatly improving the precision of large-caliber optical plane surface shape detection.
Description
Technical Field
The invention relates to the technical field of surface shape detection, and particularly provides an optical plane surface shape absolute detection method based on a four-plane method.
Background
With the improvement of requirements in the fields of aerospace and the like, the large-caliber plane mirror can be used as a reference mirror of an interferometer reference, a foldback mirror in an optical system, a standard reflecting mirror used for auto-collimation detection of the optical system and the like, and has wider and wider application and higher precision requirements. However, high-precision surface shape detection of large-aperture optical planes still faces a number of problems. At present, high-precision detection of an optical plane is mainly finished based on interference detection, but the traditional interference detection is affected by the surface shape precision of a reference standard mirror of an interferometer, and the absolute surface shape of a mirror to be detected cannot be obtained. Therefore, a higher precision absolute detection technique is demanded.
Currently, fizeau interferometers are most commonly used for high-precision surface measurement, and some systematic errors can be counteracted due to the common-path characteristics of the Fizeau interferometers. However, fizeau interferometers detect based on the surface shape information of a reference plane, and a plane with higher accuracy is required as the reference plane, so that the absolute surface shape information of the measurement plane is still limited by the surface shape error of the reference plane.
The existing absolute detection method is mainly a three-plane method, and the surface morphology of the optical element can be obtained by adopting the three-plane method which can only measure the profile deviation of the section line in the axial direction in various ways. However, the three-plane method has no good treatment means for optical non-uniformity and gravity deformation of the plane mirror, and the effect of removing the reference plane error is poor. In order to separate the reference plane errors and obtain the absolute surface shape errors of the element to be measured, researchers propose a four-plane method absolute detection, and compared with a three-plane method, the four-plane method avoids complex assembly and disassembly steps of a large-caliber plane, simplifies the operation and improves the measurement precision. The four-plane method is to sequentially pass through a reference mirror and an auxiliary transmission mirror (TF mirror) to reach a to-be-inspected mirror, and calculate the absolute surface shape of each surface by using the operations such as rotation, turnover, translation and the like of the TF mirror.
The refractive index non-uniformity of Corning silica glass Grade 2F serving as a TF mirror body material is better than 5ppm, and even for the high-uniformity material, the generated additional optical path can still reach the wavelength level. Therefore, eliminating optical non-uniformity is one of the problems that absolute detection needs to solve. In addition, the existing four-plane absolute detection is processed in a Cartesian coordinate system, and the used data processing means such as a parity function method, an N-bit rotation method and the like often neglect the influence of gravity on the surface shape change before and after the TF mirror is overturned, so that the surface shape measurement is inaccurate, and the application of the four-plane absolute detection in the large-caliber optical plane surface shape detection is limited. Therefore, the invention provides an absolute detection method capable of eliminating errors of the reference mirror, calibrating optical non-uniformity and gravitational deformation at the same time.
Disclosure of Invention
The invention provides an optical plane shape absolute detection method for solving the problems that the existing four-plane absolute detection technology and device are complex in operation, optical non-uniformity and gravity cannot be calibrated simultaneously or are calibrated only by means of simulation.
The absolute detection method of the optical plane surface shape provided by the invention is defined as follows: the plane of the reference mirror is A, the planes of the two sides of the auxiliary transmission mirror are B and C, and the plane of the to-be-inspected mirror is D, and the method comprises the following steps:
s1: directly interfering the planes A and D by using a wavelength modulation interferometer;
the auxiliary transmission mirror is arranged between the reference mirror and the to-be-inspected mirror, and the plane A is interfered with B, C and D in sequence by utilizing the wavelength modulation interferometer;
the position of the auxiliary transmission mirror is switched between B and C, and the plane A is sequentially interfered with B, C and D by utilizing a wavelength modulation interferometer;
obtaining a system of underdetermined equations and decoupling the wavefront deviation of the auxiliary transmission mirror;
removing the term containing the wavefront deviation in the underdetermined equation set to obtain an interference result equation set;
s2: the auxiliary transmission mirror rotates along the axial direction by an angleThe interference of the plane A and the plane C is carried out by utilizing a wavelength modulation interferometer, and the surface shape variation quantity ++ ∈under the Cartesian coordinate system is calculated according to the interference result between the plane A and the plane C before and after rotation>；
Calculating absolute surface shape data of the auxiliary transmission mirror under a cylindrical coordinate system by using Moore-Penrose generalized inverse matrix, and calculating by combining an interference result equation set to obtain absolute surface shapes of all planes under gravity;
s3: utilizing a wavelength modulation interferometer to interfere the planes B and C, and combining the interference result equation set to calculate and obtain the gravity deformation of the auxiliary transmission mirror;
and obtaining the absolute surface shape of the to-be-inspected mirror without the influence of gravity based on the gravity deformation of the auxiliary transmission mirror and the absolute surface shape calculation under gravity decoupling.
Preferably, the wavelength modulation interferometer is arranged above the reference mirror, the auxiliary transmission mirror performs pose adjustment through the six-dimensional adjustment mechanism, before overturning, the plane B of the auxiliary transmission mirror faces the reference mirror, and the mirror to be inspected is arranged on the four-dimensional adjustment mechanism.
Preferably, the set of under-determined equations is:
；
wherein,representing the direct interference result of planes A and D, < >>Indicating the interference result of the flip front planes a and B,indicating the interference result of the flip front planes a and C, respectively>Indicating the interference result of the flip front planes A and D, < >>Indicating the interference result of planes A and C after inversion, < >>Indicating the interference result of planes A and B after inversion, < >>The interference result of the planes A and D after the overturning is shown; />Representing plane A at->Shape error of position->Representing plane B at->Shape error of position->Representing plane B at->Shape error of position->Representing plane C atShape error of position->At->Shape error of position->The representation plane D is +.>Surface shape error of the position; />Representing the gravitational deformation of the auxiliary transmission mirror, +.>Representing the refractive index of the auxiliary transmission mirror, +.>Indicating the optical non-uniformity due to the optical non-uniformityCausing a wavefront deviation of the auxiliary transmission mirror.
Preferably, the wavefront deviation of the auxiliary transmission mirror is obtained by decoupling through addition, subtraction and elimination of different equations in the underdetermined equation set, as follows:
。
preferably, the interference result equation set is:
；
where H represents the interference result from removing the wavefront deviation.
Preferably, in S2, the auxiliary transmission mirror rotates by an angle in the axial directionInterference results H of planes A and C 8 The method comprises the following steps:
；
wherein,indicating the rotation angle of the auxiliary transmission mirror>Plane C is +.>Surface shape error of the position;
surface shape variation under Cartesian coordinate systemThe calculation formula of (2) is as follows:
。
preferably, planes B and D are dried using a wavelength-modulating interferometerInvolves obtaining interference result H 9 The method comprises the following steps:
。
compared with the prior art, the invention has the following beneficial effects:
the invention is based on the existing four-plane absolute detection technology, performs calibration and elimination on the influence factors such as optical non-uniformity and gravity deformation of the auxiliary transmission mirror (TF mirror), greatly improves the precision of large-caliber optical plane shape detection, avoids the problems of poor optical non-uniformity of the auxiliary transmission mirror, influence on deformation caused by gravity before and after the auxiliary transmission mirror is overturned, and truly realizes the absolute detection of the full-caliber plane shape by combining coordinate transformation and triangulation interpolation.
Drawings
FIG. 1 is a schematic diagram of an optical plane shape absolute detection device according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of seven interferometric detection provided in accordance with an embodiment of the present invention;
FIG. 3 is a computational flow diagram of an absolute detection of an optical planar surface shape provided in accordance with an embodiment of the present invention;
FIG. 4 is a schematic diagram of additional interference required for rejecting gravitational deformation provided in accordance with an embodiment of the present invention.
Wherein reference numerals include:
the device comprises a wavelength modulation interferometer 1, a reference mirror 2, an auxiliary transmission mirror 3, a six-dimensional adjusting mechanism 4, a to-be-inspected mirror 5, a supporting mechanism 6 and a four-dimensional adjusting mechanism 7.
Detailed Description
Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, like modules are denoted by like reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, a detailed description thereof will not be repeated.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not to be construed as limiting the invention.
The embodiment of the invention provides an optical plane surface shape absolute detection method, which is based on the existing four-plane absolute surface shape detection method and eliminates the influences of optical non-uniformity, gravity deformation and the like of an auxiliary transmission mirror (TF mirror), and specifically comprises the following steps of:
s1: as shown in fig. 1, the optical plane shape absolute detection device is first built, and the detection device mainly comprises a wavelength modulation interferometer 1, a reference mirror 2, an auxiliary transmission mirror 3 and a to-be-detected mirror 5, wherein the wavelength modulation interferometer 1 is arranged above the reference mirror 2 and is connected with the upper part of a supporting mechanism 6, the to-be-detected mirror 5 is arranged below the reference mirror 2 and is fixed on a four-dimensional adjusting mechanism 7, the pose of the to-be-detected mirror 5 can be adjusted through the four-dimensional adjusting mechanism 7, and the four-dimensional adjusting mechanism 7 is connected with the lower part of the supporting mechanism 6. The auxiliary transmission mirror 3 is arranged between the reference mirror 2 and the to-be-inspected mirror 5, the auxiliary transmission mirror 3 is arranged on the six-dimensional adjusting mechanism 4, the pose adjustment is carried out through the six-dimensional adjusting mechanism 4, and the six-dimensional adjusting mechanism 4 is connected with the middle part of the supporting mechanism 6.
Firstly, a four-plane absolute detection mathematical model needs to be constructed, and four interference surfaces of a reference mirror 2, an auxiliary transmission mirror 3 and a to-be-detected mirror 5 are defined, specifically, the following is defined: the downward plane of the reference mirror 2 is A, the two side planes of the auxiliary transmission mirror 3 are B and C respectively, and the upward plane of the to-be-inspected mirror 5 is D.
As shown in fig. 2, the auxiliary transmission mirror 3 is not arranged between the reference mirror 2 and the to-be-inspected mirror 5, and the wavelength modulation interferometer 1 is utilized to directly interfere the planes a and D once, arrows in the figure are used for indicating the interference direction, and the interference result is expressed as follows by using a hypofunction equation:
；
wherein,representing the direct interference result of planes A and D, < >>Representing plane A at->Shape error of position->The representation plane D is +.>Surface shape error of the position.
The auxiliary transmission mirror 3 is arranged between the reference mirror 2 and the to-be-inspected mirror 5, and in the initial state of the device (before the auxiliary transmission mirror 3 is turned over), the plane B of the auxiliary transmission mirror 3 faces the plane a of the reference mirror 2, and the plane C of the auxiliary transmission mirror 3 faces the plane D of the to-be-inspected mirror 5. At this time, the plane a is sequentially interfered with B, C and D by the wavelength modulation interferometer 1, and the interference results are expressed as:
；
；
；
wherein,indicating the interference result of the flip front planes A and B, < >>Indicating the interference result of the flip front planes a and C, respectively>Representing the interference result of the planes A and D before turning; />Representing plane B at->The shape error of the surface of the position,at->Shape error of position->The representation plane D is +.>Surface shape error of the position;representing the gravitational deformation of the auxiliary transmission mirror 3 +.>Representing the refractive index of the auxiliary transmission mirror 3 +.>The wavefront deviation of the auxiliary transmission mirror 3 due to optical non-uniformity is shown.
In order to eliminate the influence of optical non-uniformity of the auxiliary transmission mirror 3, the auxiliary transmission mirror 3 is turned 180 degrees by the six-dimensional adjusting mechanism 4, the spatial positions of planes B and C are exchanged, the plane A is sequentially interfered with B, C and D by the wavelength modulation interferometer 1, and the interference results are expressed as follows by using the underdetermined equation:
；
；
；
wherein,indicating the interference result of planes A and C after inversion, < >>Indicating the interference result of planes A and B after inversion, < >>The interference result of the planes A and D after the overturning is shown; />Representing plane B at->The shape error of the surface of the position,representing plane C at->Surface shape error of the position.
The above 7 interference results are combined to obtain the following underdetermined equation set:
。
adding, subtracting and eliminating elements by utilizing each equation in the underdetermined equation set, and decoupling the influence of the optical non-uniformity of the auxiliary transmission mirror 3 on the shape solving, wherein the wavefront deviation is expressed as follows:
。
eliminating errors in interference results, which are introduced by the influence of the optical non-uniformity of the auxiliary transmission mirror 3, and expressing the interference results by H after eliminating the influence of the optical non-uniformity, so as to obtain an interference result equation set as follows:
；
wherein H represents the interference result of removing the wave front deviation, and the angle marks of H correspond to M in the underdetermined equation set one by one.
S2: as shown in fig. 3, the absolute surface shape of the auxiliary transmission mirror 3 is calculated based on the cylindrical coordinate system to obtain absolute surface shape data under gravity decoupling, specifically, firstly, the six-dimensional adjustment mechanism 4 is used to adjust the pose of the auxiliary transmission mirror 3, and the auxiliary transmission mirror 3 is rotated counterclockwise along the Z axis by an angleRotation angle->Not equal to 360 ° or integer multiples of 360 °.
The rotated planes A and C are interfered with each other by a wavelength modulation interferometer 1, and the interference result H 8 The expression is as follows:
；
wherein,indicating the rotation angle of the auxiliary transmission mirror>Plane C is +.>Surface shape error of the position.
According to the interference result H between the planes A and C before and after rotation 5 And H 8 Calculating to obtain the surface shape change quantity under the Cartesian coordinate systemThe following are provided:
；
surface shape change quantity based on Cartesian coordinate systemThe interference result is rewritten under the cylindrical coordinate system by triangulation interpolation, and the radial coordinate ρ is 0 and the maximum ρ thereof max The polar angle theta is uniformly sampled between-180 DEG and 180 DEG, and the equation can be expressed in a matrix form as follows:
；
；
；
；
wherein,representing the coordinate position in the cylindrical coordinate system, the corner mark P representing the quantity under the cylindrical coordinate system; m represents a uniformly sampled value, M represents a uniformly sampled maximum value; />I is an identity matrix, R is a rotation matrix, and the form of R is expressed as follows:
；
where rows represents a column.
Moore-Penrose generalized inverse matrix of FThe expression is as follows:
；
wherein,g is the inverse pseudo-matrix of F, +.>Is thatIs a subset of (a); />Is n times unit root, if and only if +.>When the characteristic value of F is zero.
Generalized inverse matrix according to Moore-PenroseAbsolute surface shape data of the auxiliary transmission mirror 3 under the cylindrical coordinate system is calculated, and the expression of the calculation process is as follows:
；
；
；
wherein,is a general solution of the above formula, is not uniquely determinable, and +.>Is the minimum F range of the aboveThe solution is unique.
Assume thatThe following two cases can be satisfied:
1) Angle of rotation of plane C，/>。
For example, whenDegree sum->When we get->。Is->，/>Is an arbitrary constant. At this time, a->Is a rotation invariant.
2）But->Does not have the right rotation angle of the component itself>Or frequency components that remain constant when the frequency components are symmetrical about the y-axis.
For example, whenDegree and->When (I)>Equal to 18.gcd () represents the maximum common factor of two numbers in parentheses. />The number of the general solution of (C) is 18, which means that the angular period of the undetectable component of C isWherein u is a positive integer from 1 to M and can ensure +.>Also positive integers. In general, the high frequency component of the optical plane is very small and the rotation invariant component is symmetrical about the y-axis. In this case, therefore, the base station, in this case,can meet the requirement.
The absolute shape of the calculation plane B under gravity decoupling is as follows:
；
reuse ofThe absolute shape of the plane C under gravity decoupling can be calculated and interpolated into a cartesian coordinate system.
S3: in order to eliminate the influence of gravity on the surface shape of the auxiliary transmission mirror 3, decoupling of gravity deformation and the surface shape of the auxiliary transmission mirror 3 is realized by using the wavelength modulation interferometer 1. As shown in fig. 3, the interference of planes B and C is directly performed by the wavelength modulation interferometer 1 to obtain an interference result H 9 The expression is as follows:
。
since the absolute surface shapes of the planes B and C of the auxiliary transmission mirror 3 under the gravity decoupling have been calculated in S2, the gravity deformation of the auxiliary transmission mirror 3 can be obtained. Based on the gravity deformation of the auxiliary transmission mirror 3 and the absolute surface shape under gravity decoupling, the absolute surface shapes of the reference mirror 2 and the to-be-detected mirror 5 under the influence of gravity coupling can be calculated and obtained.
While embodiments of the present invention have been illustrated and described above, it will be appreciated that the above described embodiments are illustrative and should not be construed as limiting the invention. Variations, modifications, alternatives and variations of the above-described embodiments may be made by those of ordinary skill in the art within the scope of the present invention.
The above embodiments of the present invention do not limit the scope of the present invention. Any other corresponding changes and modifications made in accordance with the technical idea of the present invention shall be included in the scope of the claims of the present invention.
Claims (7)
1. An absolute detection method of optical plane surface shape is defined: the plane of the reference mirror is A, the planes of the two sides of the auxiliary transmission mirror are B and C, and the plane of the mirror to be inspected is D, and the method is characterized by comprising the following steps:
s1: directly interfering the planes A and D by using a wavelength modulation interferometer;
the auxiliary transmission mirror is arranged between the reference mirror and the to-be-inspected mirror, and the plane A is interfered with B, C and D in sequence by utilizing the wavelength modulation interferometer;
the position of the auxiliary transmission mirror is switched between B and C, and the plane A is sequentially interfered with B, C and D by utilizing a wavelength modulation interferometer;
obtaining a system of underdetermined equations and decoupling the wavefront deviation of the auxiliary transmission mirror;
removing the term containing the wavefront deviation in the underdetermined equation set to obtain an interference result equation set;
s2: the auxiliary transmission mirror is arranged along the axisAngle of rotation toThe interference of the plane A and the plane C is carried out by utilizing a wavelength modulation interferometer, and the surface shape variation quantity ++ ∈under the Cartesian coordinate system is calculated according to the interference result between the plane A and the plane C before and after rotation>；
Calculating absolute surface shape data of the auxiliary transmission mirror under a cylindrical coordinate system by utilizing Moore-Penrose generalized inverse matrix, and calculating by combining an interference result equation set to obtain absolute surface shapes of planes under gravity decoupling;
s3: utilizing a wavelength modulation interferometer to interfere the planes B and C, and combining the interference result equation set to calculate and obtain the gravity deformation of the auxiliary transmission mirror;
and obtaining the absolute surface shape of the to-be-inspected mirror without the influence of gravity based on the gravity deformation of the auxiliary transmission mirror and the absolute surface shape calculation under gravity decoupling.
2. The absolute detection method of optical plane surface shape according to claim 1, wherein the wavelength modulation interferometer is arranged above the reference mirror, the auxiliary transmission mirror performs pose adjustment through the six-dimensional adjustment mechanism, the plane B of the auxiliary transmission mirror faces the reference mirror before turning over, and the mirror to be inspected is arranged on the four-dimensional adjustment mechanism.
3. The method of claim 2, wherein the set of underdetermined equations is:
；
wherein,representing the direct interference result of planes A and D, < >>Indicating the interference result of the flip front planes A and B, < >>Indicating the interference result of the flip front planes a and C, respectively>Indicating the interference result of the flip front planes A and D, < >>Indicating the interference result of planes A and C after inversion, < >>Indicating the interference result of planes A and B after inversion, < >>The interference result of the planes A and D after the overturning is shown; />Representing plane A at->Shape error of position->Representing plane B at->Shape error of position->Representing plane B at->Shape error of position->Representing plane C at->Shape error of position->At->Shape error of position->The representation plane D is +.>Surface shape error of the position; />Representing the gravitational deformation of the auxiliary transmission mirror, +.>Representing the refractive index of the auxiliary transmission mirror, +.>Representing the wavefront deviation of the auxiliary transmission mirror due to optical non-uniformity.
4. The method for absolute detection of an optical plane surface shape according to claim 3, wherein the wavefront deviation of the auxiliary transmission mirror is obtained by decoupling by adding, subtracting and eliminating elements of different equations in the underdetermined equation set, as follows:
。
5. the method of claim 4, wherein the set of interference result equations is:
；
where H represents the interference result from removing the wavefront deviation.
6. The absolute detection method of optical plane surface shape according to claim 5, wherein in S2, the auxiliary transmission mirror rotates along the axial direction by an angleInterference results H of planes A and C 8 The method comprises the following steps:
；
wherein,indicating the rotation angle of the auxiliary transmission mirror>Plane C is +.>Surface shape error of the position;
surface shape variation under Cartesian coordinate systemThe calculation formula of (2) is as follows:
。
7. the absolute detection method of optical plane surface shape according to claim 6, wherein the interference of the planes B and D is performed by a wavelength modulation interferometer to obtain the interference result H 9 The method comprises the following steps:
。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202410004055.3A CN117490604B (en) | 2024-01-03 | 2024-01-03 | Optical plane shape absolute detection method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202410004055.3A CN117490604B (en) | 2024-01-03 | 2024-01-03 | Optical plane shape absolute detection method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN117490604A CN117490604A (en) | 2024-02-02 |
| CN117490604B true CN117490604B (en) | 2024-03-19 |
Family
ID=89683402
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202410004055.3A Active CN117490604B (en) | 2024-01-03 | 2024-01-03 | Optical plane shape absolute detection method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN117490604B (en) |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101799279A (en) * | 2010-04-16 | 2010-08-11 | 北京理工大学 | Optical fiber point diffraction phase shift interferometry method of surface shape of large relative aperture sphere |
| CN102155926A (en) * | 2011-03-09 | 2011-08-17 | 浙江大学 | Aspherical mirror vertex curvature radius measurement system and method |
| CN105627944A (en) * | 2015-12-21 | 2016-06-01 | 中国科学院长春光学精密机械与物理研究所 | Method of detecting surface figure of aspheric mirror based on null compensation optical system |
| CN106446460A (en) * | 2016-10-26 | 2017-02-22 | 北京宇航系统工程研究所 | Lightweight method of super-large three-dimensional model of carrier rocket |
| CN115164775A (en) * | 2022-08-24 | 2022-10-11 | 中国科学院长春光学精密机械与物理研究所 | Large-caliber convex aspheric reflector surface shape detection device and detection method thereof |
| CN116625269A (en) * | 2023-04-21 | 2023-08-22 | 成都太科光电技术有限责任公司 | Absolute detection method for plane surface shape of large-caliber optical element |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE102017217251A1 (en) * | 2017-09-27 | 2019-03-28 | Carl Zeiss Smt Gmbh | Method and device for analyzing the wavefront effect of an optical system |
-
2024
- 2024-01-03 CN CN202410004055.3A patent/CN117490604B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101799279A (en) * | 2010-04-16 | 2010-08-11 | 北京理工大学 | Optical fiber point diffraction phase shift interferometry method of surface shape of large relative aperture sphere |
| CN102155926A (en) * | 2011-03-09 | 2011-08-17 | 浙江大学 | Aspherical mirror vertex curvature radius measurement system and method |
| CN105627944A (en) * | 2015-12-21 | 2016-06-01 | 中国科学院长春光学精密机械与物理研究所 | Method of detecting surface figure of aspheric mirror based on null compensation optical system |
| CN106446460A (en) * | 2016-10-26 | 2017-02-22 | 北京宇航系统工程研究所 | Lightweight method of super-large three-dimensional model of carrier rocket |
| CN115164775A (en) * | 2022-08-24 | 2022-10-11 | 中国科学院长春光学精密机械与物理研究所 | Large-caliber convex aspheric reflector surface shape detection device and detection method thereof |
| CN116625269A (en) * | 2023-04-21 | 2023-08-22 | 成都太科光电技术有限责任公司 | Absolute detection method for plane surface shape of large-caliber optical element |
Non-Patent Citations (3)
| Title |
|---|
| Zhang, LJ.An Image Mosaic Algorithm Taking Into Account Speed and Robustness.《 MANUFACTURING SYSTEMS AND INDUSTRY APPLICATIONS》.2020,全文. * |
| 有界约束半光滑欠定方程组的非单调投影梯度信赖域方法;应晶晶;《中国运筹学会第十届学术交流会论文集》;20101016;全文 * |
| 环形子孔径拼接检测的中心偏移误差补偿;李兵;《光子学报》;20160816;全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN117490604A (en) | 2024-02-02 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110524309B (en) | Geometric error measuring method of numerical control turntable based on four-base-station laser tracking system | |
| Takatsuji et al. | The first measurement of a three-dimensional coordinate by use of a laser tracking interferometer system based on trilateration | |
| CN110375694B (en) | Self-calibration method for circular grating angle measurement error based on portable articulated coordinate measuring machine | |
| CN109655079B (en) | Method for measuring coordinate system from star sensor to prism coordinate system | |
| CN110030953B (en) | Circular grating angle measurement error compensation method | |
| CN105571527B (en) | A kind of turntable pivot angle precision measurement method | |
| CN102243068B (en) | Method for correcting system error during splicing sub-aperture | |
| CN109031659A (en) | A kind of Computer Aided Assembly Process Planning method of coaxial optical system | |
| CN103134660A (en) | Method acquiring telescope primary and secondary mirror alignment error based on astigmatism decomposition | |
| CN109737892A (en) | Surface shape measurement method is interfered in digital Moire phase shift based on zone location fitting algorithm | |
| CN110966957A (en) | Absolute inspection method for synchronous measurement of multiple spherical standard lenses | |
| CN103439085B (en) | A kind of method of contact type measurement curved surface prism parameter and device | |
| RU2561018C1 (en) | Interferometric method of adjusting two-mirror lens with aspherical elements | |
| Selberg | Interferometer accuracy and precision | |
| CN117490604B (en) | Optical plane shape absolute detection method | |
| CN106598084B (en) | The assembly method and device of tested aspherical mirror based on zero compensation system | |
| CN101566466A (en) | Profile analysis system and method | |
| US20060285123A1 (en) | Method and apparatus for tilt corrected lateral shear in a lateral shear plus rotational shear absolute flat test | |
| Li et al. | Research on high-precision error measurement system of angular displacements based on reciprocal roll angles | |
| CN108917662B (en) | Optimization method for reference surface flatness inspection | |
| CN110108271B (en) | Star deflection compensation method caused by pneumatic optical effect | |
| CN104315972A (en) | Interferometer outgoing wavefront detecting method based on rotating translation absolute detection | |
| CN110955013B (en) | Primary mirror position control method and device, large-caliber telescope and readable storage medium | |
| CN107883865B (en) | Zernike aberration unit for Rui Qikangmang detection motivates influence matrix calculation method | |
| CN104819703B (en) | A kind of angle of inclination parameter fitness method that fulcrum is sensed for inclination angle |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |