CN108413894A - A kind of phase measurement deviation art method of shearing dislocation absolute measurement - Google Patents
A kind of phase measurement deviation art method of shearing dislocation absolute measurement Download PDFInfo
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- CN108413894A CN108413894A CN201810200780.2A CN201810200780A CN108413894A CN 108413894 A CN108413894 A CN 108413894A CN 201810200780 A CN201810200780 A CN 201810200780A CN 108413894 A CN108413894 A CN 108413894A
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- face shape
- under test
- element under
- pmd
- zernike
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/2441—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures using interferometry
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- General Physics & Mathematics (AREA)
- Length Measuring Devices By Optical Means (AREA)
Abstract
The present invention proposes a kind of phase measurement deviation art (PMD) method of shearing dislocation absolute measurement.This method needs to carry out four PMD measurements to element under test altogether, and other than needing traditional PMD primary to element surface to be measured progress to measure, other measure three times is measured again to its surface by element under test translation and after rotating to three particular states.Four measurement data can be obtained in this way, to which there are three overlapping regions.The face shape calculated separately on each overlapping region is poor, and the face shape being then fitted using Zernike multinomials difference on each overlapping region is poor.The polynomial coefficients of Zernike finally are found out using least-squares algorithm, and reconstruct element under test surface face shape.The method increase the measuring accuracies of PMD systems.
Description
Technical field
The present invention relates to a kind of phase measurement deviation arts of shearing dislocation absolute measurement to realize planar optical elements face
The method of the measurement of shape.
Background technology
For the surface testing of element, to popular detection method in the world at present：Static planar interferometer, dynamic
Polarization phase-shifting interferometer, three kinds of interferometric methods of polarization phase-shifting radial-shear interferometer, based on Fizeau type phase shift interferences
Splicing, Ritchey-Common detection methods scan pentaprism method, Hartmann's sub-aperture stitching technology, phase measurement deviation
Art is described.In these methods, interferometry has had super as a kind of non-contacting high-precision optical detection method
100 years history is crossed, however, interferometry dynamic range is small, it is more sensitive to environment, on the side that element slope variation is larger
Edge is difficult to obtain preferable data, its application is made to be restricted.And most of interferometer measuration systems require optical device
It processes and is calibrated to very high precision.This makes interferometry very inflexible and expensive.In addition to directly measuring light
The interferometry technology of path difference, people again may be by the deviation of measuring beam to realize that the high-precision surface shape of element measures.
Currently, the measurement method of popular light beam deviation amount be byEt al. and the phase that proposes of Peng Su et al. survey
Measure deviation art.
Realize that absolute measurement in application field is very crucial using PMD systems, in order to obtain member to be measured from phase
The slope distribution of part needs to demarcate measuring system, it includes three steps：The calibration of display, camera calibration and
The geometry of system is demarcated.However, the measuring accuracy of PMD systems is highly susceptible to the influence of system calibrating precision, three steps
Any calibrated error in rapid can all introduce systematic error in the measurements.In order to improve the measuring accuracy of phase measurement deviation art,
Can be suitable with interferometer measuring accuracy, a usual reference element is accurately adjusted on the position of detected element,
And it is measured using PMD tests system.By subtracted from the element under test face shape that PMD systems are measured reference element face shape come
Deduct systematic error.If the face shape error of uncompensation reference mirror itself, it is necessary to which the surface figure accuracy of reference mirror is very high, if mended
Repay the face shape error of reference mirror, it is necessary to be demarcated in advance using other methods to the face shape error of reference mirror.This method
Define the flexibility of PMD test systems itself.
Invention content
In view of the above problems, it is flat to realize to propose a kind of phase measurement deviation art of shearing dislocation absolute measurement by the present invention
The method of the measurement of face optical component surface shape.The method increase the measuring accuracy of PMD systems, it is as follows shown：
Step 1：Measure four superposition face shape distributions under specific position state
One arbitrary element under test surface is subjected to PMD measurements, obtains original superposition face shape.Then make member to be measured respectively
Part is first translated along three directions to be rotated again, and ensures the displacement of any two state obtained after translating and rotating through
Angle is equal to same angle, and the displacement on three moving directions is equal.And record the superposition face under three states
Shape is distributed.Four measurement data are shared at this time, so three overlapping regions can be obtained.
Step 2：The face shape for calculating separately each overlapping region is poor
On each overlapping region, the superposition face shape distribution of corresponding states is subtracted into original superposition face shape and is distributed.It is cut
Butt journey.
Step 3：Zernike multinomial coefficients are calculated, and rebuild element under test surface face shape.
The face shape difference that equation is sheared in step 2 is fitted with Zernike multinomials difference.Then with least square method meter
Zernike multinomial coefficients are calculated, element under test surface face shape is finally gone out according to calculated coefficient reconstruction.
Description of the drawings
Position view behind the home positions Fig. 1 and movement.
The structure chart of Fig. 2 present invention.
Specific implementation mode
Below in conjunction with the drawings and specific embodiments, a more detailed description of the present invention is to do.It is necessary to indicated herein
It is that following embodiment is served only for the present invention and is described further, and should not be understood as limiting the scope of the invention, the neck
Field technique skilled person makes some nonessential modifications and adaptations according to aforementioned present invention content to the present invention, still falls within this hair
Bright protection domain.
The home position of measurement optical surface is indicated in attached drawing 1 with solid line circle, measuring will carry out for the first time in this position.Flute
Karr coordinate establishes the center of the circle indicated in solid line, and circle of dotted line indicates the position being subjected to displacement.The center of measurement surface
It is firstly moved to center cd, the displacement in x-axis and y-axis is Δ x, Δ y respectively, and then surface to be measured is around new center rotation
GyrationAttached drawing 2 show the structure chart of the present invention, and the round of Intermediate grey indicates that home position, the other three are surround in figure
Its circle to indicate that the position that displacement three times is formed by three measurement surfaces, the displacement angle between any two state occurs
It is equal to 120 °.In order to keep the symmetry of system, displacement and rotation angle on each shear direction are equal.
Step 1：Measure four superposition face shape distributions under specific position state
The use of the superposition face shape distribution measured on four positions of PMD systems in fig 2 is respectively W0,W1,W2,
W3.Wherein W0For home position element under test face shape, W1、W2And W3Respectively with W0It partly overlaps, obtains three overlapping regions.
Step 2：The face shape for calculating separately three overlapping regions is poor
Original superposition face shape on each overlapping region is expressed as W0,i, it is assumed that T0,iAnd E0,iIt is original to be measured respectively
True element under test face shape on the overlapping region of position and systematic error, TiAnd EiRespectively i+1 time measures obtained surface
Face shape and systematic error, i=1,2,3.
Use superposition face shape W1,W2And W3Original superposition face shape is subtracted on overlapping region respectively, obtains shearing equation such as
Under：
ΔWi=Wi-W0,i=Ti+Ei-T0,i-E0,i (2)
Since systematic error is the function of coordinate distribution, will not change before and after element under test rotation and translation, i.e.,
Ei=E0,i, formula (2) is rewritten as：
ΔWi=Ti-T0,i (3)
Step 3：Zernike multinomial coefficients are calculated, and rebuild the face shape distribution on element under test surface
The face shape being fitted in (3) formula using Zernike multinomial differences is poor, and matrix expression is：
ΔWi=Δ Zia (4)
A={ a in formula1,a2,…aJ}TIt is the J item Zernike multinomial coefficients on true element under test surface, Δ WiWith Δ Zi
Matrix size is respectively N × 1 and N × J, be illustrated respectively in face shape difference in N number of data point on i-th of overlapping region and
Zernike multinomials are poor, Δ W=[Δ W1；ΔW2；ΔW3], Δ Z=[Δ Z1；ΔZ2；ΔZ3]。
Pass through least-squares algorithm design factor a：A=Δs Z+Δ W, it is finally polynomial according to calculated Zernike
Coefficient reconstruction element under test surface face shape.
Claims (2)
1. a kind of phase measurement deviation art method of shearing dislocation absolute measurement, it is characterised in that：It needs altogether to element under test
It carries out four PMD to measure, the face shape obtained on three overlapping regions is poor, uses Zernike multinomials and least square method counterweight
Folded region is fitted and iterates to calculate, and reconstructs the shape distribution of detected element surface face；Shown in being as follows：
Step 1：Measure four superposition face shape distributions under specific position state
The superposition face shape distribution measured on four specific positions using PMD systems is respectively W0,W1,W2,W3, at this time altogether
There are four measurement data, wherein W0For the face shape of the element under test in home position, W1、W2And W3Respectively with W0It partly overlaps, obtains
Three overlapping regions；
Step 2：The face shape for calculating separately three overlapping regions is poor
Original superposition face shape on each overlapping region is expressed as W0,i, it is assumed that T0,iAnd E0,iIt is in original position to be measured respectively
True element under test face shape on overlapping region and systematic error, TiAnd EiRespectively i+1 time measures obtained surface face shape
And systematic error, i=1,2,3：
Use superposition face shape W1,W2And W3Original superposition face shape is subtracted on overlapping region respectively, it is as follows to obtain shearing equation：
ΔWi=Wi-W0,i=Ti+Ei-T0,i-E0,i (2)
Since systematic error is the function of coordinate distribution, will not change before and after element under test rotation and translation, i.e. Ei=
E0,i, formula (2) is rewritten as：
ΔWi=Ti-T0,i (3)
Step 3：Zernike multinomial coefficients are calculated, and rebuild the face shape distribution on element under test surface
The face shape being fitted in (3) formula using Zernike multinomial differences is poor, and matrix expression is：
ΔWi=Δ Zia (4)
A={ a in formula1,a2,…aJ}TIt is the J item Zernike multinomial coefficients on true element under test surface, Δ WiWith Δ ZiMatrix
Size is respectively N × 1 and N × J, face shape difference and the Zernike being illustrated respectively in N number of data point on i-th of overlapping region
Multinomial is poor, Δ W=[Δ W1；ΔW2；ΔW3], Δ Z=[Δ Z1；ΔZ2；ΔZ3]；
Pass through least-squares algorithm design factor a：A=Δs Z+Δ W, finally according to the polynomial coefficient weights of calculated Zernike
Build element under test surface face shape.
2. a kind of phase measurement deviation art method of shearing dislocation absolute measurement according to claim 1, it is characterised in that：
To element surface to be measured carry out four measurements carry out in a particular state, be first element surface to be measured is done it is traditional
PMD is measured, and so that element under test is first translated along three directions respectively and is rotated again, and is ensured after translating and rotating through
The rotation angle of obtained any two state is identical, and the displacement on each moving direction is equal.
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| CN103487441A (en) * | 2013-09-24 | 2014-01-01 | 电子科技大学 | Method for defect detection and surface measurement of silicon wafer |
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| CN106546192A (en) * | 2016-10-12 | 2017-03-29 | 上海大学 | A kind of high reflection Free-Form Surface and system |
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Application publication date: 20180817 |