CN102589472A - Method for highly precisely eliminating adjustment error in spherical surface shape interference detection - Google Patents
Method for highly precisely eliminating adjustment error in spherical surface shape interference detection Download PDFInfo
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Abstract
The invention discloses a method for highly precisely eliminating an adjustment error in spherical surface shape interference detection. In the method, adjustment error-containing wave surface data is obtained by an interferometer, the curvature radius and the caliber of a spherical surface to be measured are measured, and then data obtained by measurement serves as auxiliary data for eliminating the adjustment error, wherein the radius of the spherical surface to be measured is measured by a single-frequency laser interference method; the caliber is measured by using a vernier caliper; the adjustment error is moved by adopting an optimum fit ideal spherical model; the position and the radius of the ideal spherical surface are found by the model; and the wave surface measured by the interferometer is moved so that the center of the wave surface is overlapped with the sphere center of the ideal spherical surface. The invention provides a new method for eliminating the adjustment error in the spherical surface shape detection of an optical element by researching spherical interference detection; and the method has important application value on the detection and the machining of high-precision optical elements.
Description
Technical field
The present invention relates to the interference detection technique field of optical element, relate in particular to a kind of in sphere face shape interfere to be detected high precision eliminate the method for adjustment error.
Background technology
Along with the development of Optical manufacture technology, spherical surface shaped accuracy of detection demand is also increasingly high.Sphere interferes the detection technique can Rapid Realization spherical optics component side shape high-precision test, and the interference detection technique of sphere face shape is updated and is used widely for this reason.In the interference testing of reality, realize that through adjusting mechanism seized sphere sentences the position that zero-bit detects, make that always comprising defocus error and droop error etc. debugs error in the test result but actual mechanism is undesirable.People have proposed to remove corresponding constant term, the out of focus item in the face shape test result and the removal of item to realize debuging error of tilting for this reason.This traditional method is simple and convenient, can well satisfy people's demand under and the situation that accuracy requirement is not high big at seized F/#.But along with diminishing and the raising of accuracy requirement of seized F/#, the influence that traditional mode can not high-precision removal defocus error be brought.Still there is not at present the method that suitable high precision is gone out of focus.
Summary of the invention
The objective of the invention is the deficiency to said method, provide a kind of sphere face shape interfere detect in high precision eliminate the method for adjustment error.
The objective of the invention is to realize through following technical scheme: a kind of in sphere face shape interfere to be detected high precision eliminate the method for adjustment error, may further comprise the steps:
(1), adopt the single-frequency laser interference method to record the radius-of-curvature
of tested sphere;
(2), measure the bore D of tested sphere; Calculate the F number of tested sphere;
; Select with reference to spherical mirror according to tested sphere F number, make with reference to the F number of spherical mirror F number less than tested sphere;
(3), being installed on the interferometer with reference to spherical mirror, the light path of adjustment interferometer, measure have alignment error from tested corrugated that tested sphere returns
W, 
, wherein,
With
Be respectively the horizontal ordinate and the ordinate of pixel on the CCD phase machine side,
For
The optical path difference on the tested corrugated that corresponding pixel detects, the face shape of the tested sphere that it is corresponding does
(4), the face graphic data
of tested sphere is transformed to global coordinate system, obtain tested sphere:
；
Wherein,
is the radius with reference to spherical mirror;
is reference sphere ground roll radius;
;
is the lateral resolution of CCD; The coordinate figure of tested sphere measurement point in global coordinate system of correspondence that
is
; Global coordinate system be initial point in the reference sphere vertex of surface, the coordinate system of z axle and optical axis coincidence;
(5), set up the least square objective function:
?；
Wherein, Subscript i representes i measurement point;
;
is
projection on ideal spherical face; Ideal spherical face is the centre of sphere and overlap with reference to the sphere centre of sphere; Radius is the sphere of
; The unit normal vector of correspondence that
is
;
is the Euclid transformation matrix; Symbol
expression vector dot; Promptly represent the distance of point
to point
; N is a measure dot number; The quadratic sum of corresponding distance is had a few in
expression, is used for characterizing the deviation of tested sphere to ideal spherical face; So subscript k representes the parameter after the iteration the k time; The 0th iteration is that initial parameter is:
,
is unit matrix;
(6), with the Taylor expansion first progression linearization least square objective function, promptly:
Substitution least square objective function;
Wherein,
is the parameters optimization of Euclid conversion g,
be optimal reference spherical wave radius parameters optimization;
(7), set up least squares equation
according to the least square objective function after the linearization
Wherein:
；
(8), separate least squares equation; Obtain vectorial m, upgrade parameter
and
according to step 6 then;
(9), follow according to step 5 is calculated
; Be designated as
; if
; Then iterative process is accomplished; Get into next step, otherwise got into for the 7th step;
is fault-tolerant for design; Precision set that can be as requested generally can be made as
;
(10), this moment, the alignment error compensation was accomplished; Calculate
, this is the surface shape value of i measurement point of tested sphere.
Further, said step 1 comprises following substep:
(1.1) observe the interference imaging of CCD camera, regulate five adjustment racks, make interference fringe image that the CCD camera become near zero striped, find the sphere center position of tested spherical mirror, this position is as the starting point of surveying long light path;
(1.2) observe the interference imaging of CCD camera once more, regulate five adjustment racks, make interference fringe image that the CCD camera become near zero striped, find the vertex position of tested sphere, this position is as the terminal point of surveying long light path;
(1.3) read the step-by-step counting n that surveys long light path; Calculate tested spherical radius
;
; Wherein,
is for surveying the used optical maser wavelength of long light path.
The invention has the beneficial effects as follows; The present invention detects through sphere is interfered; The research that particularly little F/# is seized, the new method that provides a kind of optical element sphere face shape to eliminate the adjustment error in detecting has important use value to the detection and the processing of high-precision optical element.
Description of drawings
Fig. 1 measures the device synoptic diagram of optics spherical radius for single-frequency laser interference method of the present invention;
Fig. 2 is CCD coordinate of the present invention and global coordinate transform synoptic diagram;
Fig. 3 moves the synoptic diagram that changes with desirable radius surface for corrugated of the present invention;
Fig. 4 detects bore φ=37mm radius of curvature R=25mm spherical mirror for the present invention is directed to, utilize this spherical mirror that the ZYGO interferometer records face shape section profile and remove the section profile figure after the out of focus with the inventive method;
Among the figure, laser instrument 1, collimating and beam expanding system 2, reference planes mirror 3, lens 4, five dimension adjustment racks 5, reference prism 6, first quarter-wave plate 7, first polarizer 8, laser instrument 9, imaging len 10, CCD camera 11, second quarter-wave plate 12, first Amici prism 13, second Amici prism 14, the 3rd Amici prism 15, second polarizer 16, the 3rd polarizer 17, the 4th polarization spectroscope 18, first light intensity detector 19, second light intensity detector 20, the 3rd light intensity detector 21 and PC22, catoptron 23, polarization splitting prism 24, Amici prism 25, face shape section profile 28, the inventive method of recording with reference to spherical mirror 26, tested spherical mirror 27, ZYGO interferometer are removed the face shape section profile 29 after the out of focus.
Embodiment
The present invention's high precision in the interference of sphere face shape detects is eliminated the method for adjustment error, may further comprise the steps:
1, adopt the single-frequency laser interference method to record the radius-of-curvature
of tested sphere.
This step realizes on single-frequency laser interference optical spherical surface radius measuring device; As shown in Figure 1, the device that the single-frequency laser interference method is measured the optics spherical radius comprises laser instrument 1, collimating and beam expanding system 2, reference planes mirror 3, lens 4, five dimension adjustment racks 5, reference prism 6, first quarter-wave plate 7, first polarizer 8, laser instrument 9, imaging len 10, CCD camera 11, second quarter-wave plate 12, first Amici prism 13, second Amici prism 14, the 3rd Amici prism 15, second polarizer 16, the 3rd polarizer 17, the 4th polarization spectroscope 18, first light intensity detector 19, second light intensity detector 20, the 3rd light intensity detector 21 and PC22, catoptron 23, polarization splitting prism 24, Amici prism 25; The support of said five dimensional scaffolds 5 for moving and rotate around X, Y axle by X, Y, Z axle.With five dimension adjustment racks 5 is that separation is divided into left and right sides two parts to whole device and describes light path.Left-hand component laser through collimating and beam expanding system 2 collimator and extenders, goes out to be divided into two parts at Amici prism 25 from laser instrument 1 outgoing then, and a part of light returns after getting on the reference planes mirror 3, and this part light is the sheet ground roll as a reference.Another part light returns through getting to behind the lens 4 on the spherical reflector that is installed on the five dimension adjustment racks 5, and this part light is as tested corrugated.Two parts light forms interference fringe through imaging len 10 backs on CCD camera 11.Right-hand component laser after laser instrument 9 outgoing successively through first polarization spectroscope 8, first quarter-wave plate 7; After through polarization splitting prism 24, be divided into two parts; Part light returns after through reference prism 6; Part light is got to be installed on the plane mirror of five dimensions on the adjustment racks 5 and is returned, and two parts light is all successively through catoptron 23, second quarter-wave plate 12, and last two parts light is in first Amici prism 13, second Amici prism 14, the beam split successively of the 3rd Amici prism 15 places; Be divided into three parts; This three parts light light path symmetry is an example with the light path at first Amici prism, 13 punishment light, and laser is got on first light intensity detector 19 through second polarization spectroscope 16.
This step comprises following substep:
1.1, observe the interference imaging of CCD camera 11, regulate five adjustment racks 5, make interference fringe image that CCD camera 11 become near zero striped, find the sphere center position of tested spherical mirror, this position is as the starting point of surveying long light path.
1.2, observe the interference imaging of CCD camera 11 once more, regulate five adjustment racks 5, make interference fringe image that CCD camera 11 become near zero striped, find the vertex position of tested sphere, this position is as the terminal point of surveying long light path.
1.3, read the step-by-step counting n that surveys long light path; Calculate tested spherical radius
;
; Wherein,
is for surveying the used optical maser wavelength of long light path.
2, measure the bore D of tested sphere; Calculate the F number of tested sphere;
; Select with reference to spherical mirror according to tested sphere F number, make with reference to the F number of spherical mirror F number less than tested sphere;
Measure the bore D of tested sphere with vernier caliper.
3, being installed on the interferometer with reference to spherical mirror, the light path of adjustment interferometer, measure have alignment error from tested corrugated that tested sphere returns
W, 
Wherein,
is respectively the CCD horizontal ordinate and the ordinate of pixel on the machine side mutually with
; The optical path difference on
tested corrugated that corresponding pixel detects for
, the face shape of the tested sphere that it is corresponding is
.
4, the face graphic data
with tested sphere transforms to global coordinate system, obtains tested sphere:
Wherein,
is the radius with reference to spherical mirror;
is reference sphere ground roll radius;
;
is the lateral resolution of CCD; The coordinate figure of tested sphere measurement point in global coordinate system of correspondence that
is
; Global coordinate system be initial point in the reference sphere vertex of surface, the coordinate system of z axle and optical axis coincidence;
5, set up the least square objective function:
Wherein, Subscript i representes i measurement point;
;
is
projection on ideal spherical face; Ideal spherical face is the centre of sphere and overlap with reference to the sphere centre of sphere; Radius is the sphere of
; The unit normal vector of correspondence that
is
;
is the Euclid transformation matrix; Symbol
expression vector dot; Promptly represent the distance of point
to point
; N is a measure dot number; The quadratic sum of corresponding distance is had a few in
expression, is used for characterizing the deviation of tested sphere to ideal spherical face.Because this method has adopted iteration, so subscript k representes the parameter after the iteration the k time.The 0th iteration is that initial parameter is:
;
is unit matrix, and other parameter can calculate according to these two parameter integrating steps 4 and 5.
6, with the Taylor expansion first progression linearization least square objective function, promptly:
Substitution least square objective function.
Wherein,
is the parameters optimization of Euclid conversion g,
be optimal reference spherical wave radius parameters optimization.
7, set up least squares equation
according to the least square objective function after the linearization
Wherein:
；
；
8, separate least squares equation; Obtain vectorial m, upgrade parameter
and
according to step 6 then.
9, follow according to step 5 is calculated
; Be designated as
; if
; Then iterative process is accomplished; Get into next step, otherwise got into for the 7th step.
is fault-tolerant for design; Precision set that can be as requested generally can be made as
.
10, this moment, the alignment error compensation was accomplished; Calculate
, this is the surface shape value of i measurement point of tested sphere.
Detect the face shape of bore φ=37mm radius of curvature R=25mm spherical mirror, and the process of using the inventive method processing and detecting result to obtain final face shape is:
1) utilize the single-frequency laser interference method to record moving to the pulse number that the sphere vertex position produces from the sphere sphere center position is 317573 (used optical maser wavelength 632.8nm), so
.
2) utilize the GPI interferometer of Zygo company to record the face graphic data
of seized sphere, the used optical maser wavelength of interferometer
.
3) the face graphic data is transformed to global coordinate system, calculate pose transformation matrix
and desirable radius surface variation
with least square method.
4) calculate the surface shape value go after the out of focus according to step 10.
Claims (3)
1. the method for a high precision elimination adjustment error in the interference of sphere face shape detects is characterized in that, may further comprise the steps:
(1), adopt the single-frequency laser interference method to record the radius-of-curvature
of tested sphere;
(2), measure the bore D of tested sphere; Calculate the F number of tested sphere;
; Select with reference to spherical mirror according to tested sphere F number, make with reference to the F number of spherical mirror F number less than tested sphere;
(3), being installed on the interferometer with reference to spherical mirror, the light path of adjustment interferometer, measure have alignment error from tested corrugated that tested sphere returns
W, 
, wherein,
With
Be respectively the horizontal ordinate and the ordinate of pixel on the CCD phase machine side,
For
The optical path difference on the tested corrugated that corresponding pixel detects, the face shape of the tested sphere that it is corresponding does
(4), the face graphic data
of tested sphere is transformed to global coordinate system, obtain tested sphere:
Wherein,
is the radius with reference to spherical mirror;
is reference sphere ground roll radius;
;
is the lateral resolution of CCD; The coordinate figure of tested sphere measurement point in global coordinate system of correspondence that
is
; Global coordinate system be initial point in the reference sphere vertex of surface, the coordinate system of z axle and optical axis coincidence;
(5), set up the least square objective function:
Wherein, Subscript i representes i measurement point;
;
is
projection on ideal spherical face; Ideal spherical face is the centre of sphere and overlap with reference to the sphere centre of sphere; Radius is the sphere of
; The unit normal vector of correspondence that
is
;
is the Euclid transformation matrix; Symbol
expression vector dot; Promptly represent the distance of point
to point
; N is a measure dot number; The quadratic sum of corresponding distance is had a few in
expression, is used for characterizing the deviation of tested sphere to ideal spherical face; So subscript k representes the parameter after the iteration the k time; The 0th iteration is that initial parameter is:
,
is unit matrix;
(6), with the Taylor expansion first progression linearization least square objective function, promptly:
Substitution least square objective function;
Wherein,
is the parameters optimization of Euclid conversion g,
be optimal reference spherical wave radius parameters optimization;
，
，
；
(7), set up least squares equation
according to the least square objective function after the linearization
Wherein:
(8), separate least squares equation; Obtain vectorial m, upgrade parameter
and
according to step 6 then;
(9), follow according to step 5 is calculated
; Be designated as
; if
; Then iterative process is accomplished; Get into next step, otherwise got into for the 7th step;
is fault-tolerant for design; Precision set that can be as requested generally can be made as
;
(10), this moment, the alignment error compensation was accomplished; Calculate
, this is the surface shape value of i measurement point of tested sphere.
According to claim 1 said in sphere face shape interfere to be detected high precision eliminate the method for adjustment error, it is characterized in that said step 1 comprises following substep:
(1.1) observe the interference imaging of CCD camera, regulate five adjustment racks, make interference fringe image that the CCD camera become near zero striped, find the sphere center position of tested spherical mirror, this position is as the starting point of surveying long light path;
(1.2) observe the interference imaging of CCD camera once more, regulate five adjustment racks, make interference fringe image that the CCD camera become near zero striped, find the vertex position of tested sphere, this position is as the terminal point of surveying long light path;
(1.3) read the step-by-step counting n that surveys long light path; Calculate tested spherical radius
;
; Wherein,
is for surveying the used optical maser wavelength of long light path.
According to claim 1 said in sphere face shape interfere to be detected high precision eliminate the method for adjustment error, it is characterized in that, in the said step 2, measure the bore D of tested sphere with vernier caliper.
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|---|---|---|---|---|
| CN103207532A (en) * | 2013-04-21 | 2013-07-17 | 中国科学院光电技术研究所 | Coaxial focus detection measurement system and measurement method thereof |
| CN103292738A (en) * | 2013-06-26 | 2013-09-11 | 中国科学院光电技术研究所 | Spherical surface shape error absolute detection method |
| CN103335609A (en) * | 2013-07-05 | 2013-10-02 | 中国科学院光电技术研究所 | Method for determining rotation center, rotation angle and translation amount of optical surface shape data |
| CN111351425A (en) * | 2020-03-10 | 2020-06-30 | 南通大学 | Method for determining dynamic range of interferometer during spherical defocus detection |
| CN117346687A (en) * | 2023-12-04 | 2024-01-05 | 中国科学院长春光学精密机械与物理研究所 | Method and system for correcting specular error data points of interferometry reflecting mirror |
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Cited By (10)
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| CN103207532A (en) * | 2013-04-21 | 2013-07-17 | 中国科学院光电技术研究所 | Coaxial focus detection measurement system and measurement method thereof |
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| CN103292738A (en) * | 2013-06-26 | 2013-09-11 | 中国科学院光电技术研究所 | Spherical surface shape error absolute detection method |
| CN103292738B (en) * | 2013-06-26 | 2015-12-09 | 中国科学院光电技术研究所 | Spherical surface shape error absolute detection method |
| CN103335609A (en) * | 2013-07-05 | 2013-10-02 | 中国科学院光电技术研究所 | Method for determining rotation center, rotation angle and translation amount of optical surface shape data |
| CN103335609B (en) * | 2013-07-05 | 2016-01-20 | 中国科学院光电技术研究所 | Method for determining rotation center, rotation angle and translation amount of optical surface shape data |
| CN111351425A (en) * | 2020-03-10 | 2020-06-30 | 南通大学 | Method for determining dynamic range of interferometer during spherical defocus detection |
| CN111351425B (en) * | 2020-03-10 | 2022-06-03 | 南通大学 | Method for determining dynamic range of interferometer during spherical defocus detection |
| CN117346687A (en) * | 2023-12-04 | 2024-01-05 | 中国科学院长春光学精密机械与物理研究所 | Method and system for correcting specular error data points of interferometry reflecting mirror |
| CN117346687B (en) * | 2023-12-04 | 2024-02-13 | 中国科学院长春光学精密机械与物理研究所 | Method and system for correcting specular error data points of interferometry reflecting mirror |
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