CN105737763B - A kind of spherical mirror curvature radius measurement method based on Moire fringe - Google Patents
A kind of spherical mirror curvature radius measurement method based on Moire fringe Download PDFInfo
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Abstract
The invention discloses a kind of spherical mirror curvature radius measurement method based on Moire fringe, it is superimposed using sphere to be measured with interference fringe caused by reference planes interference with the sphere of the known curvature radius based on Computer Simulation with interference fringe caused by plane interference, pass through frequency domain low-pass ripple, the Moire fringe for carrying two width interference pattern difference frequency information is proposed that the Moire fringe for carrying difference frequency information can be considered interference pattern caused by the spherical interference of sphere to be measured and the known curvature radius of Computer Simulation.The radius of curvature of sphere to be measured is calculated by the radius of curvature of Moire fringe and Computer Simulation sphere.The present invention avoids the damage to spherical mirror surface using contactless measuring method, and the noninvasive measurement for larger radius of curvature sphere curvature radius provides feasible method.
Description
Technical field
The invention belongs to field of optical measuring technologies, the measurement of particularly a kind of sphere curvature radius based on Moire fringe
Method.
Background technology
Aspherical elements are a kind of optical elements common in optical system, there is important application in all kinds of optical systems.
For example, in photoetching projection objective lens system (Extreme Ultra-violet, abbreviation EUV), using transmission-type lithographic objective.Should
Multi-disc spherical mirror is included in system, the crudy of spheric reflection has the influence of key to the imaging effect of whole system.It is bent
Rate radius (radius of curvature, ROC) is the Important Parameters for characterizing optical spherical surface mirror optical characteristics.Spherical optics table
Curvature radius has very big influence to the image quality of optical system.It is accurate to survey in the process of spherical optics minute surface
The radius of curvature that sphere must be measured is the important process that optical workshop is examined.
Currently, the method for measuring spherical optics curvature radius has many kinds.Spherometer is measurement spherical optics element
Universal method, measurement range are generally 20~1200mm, and because test mode contacts sphere, measured piece surface is easily damaged.Knife
Mouthful instrument is one of method of measurement sphere curvature radius commonly used in optical workshop, and measurement range is up to hundreds of meters, metering system
To be contactless, but very high is required to test environment.The measurement range of laser interference length-measuring method is less than 2 meters, can be simultaneously
The local error of sphere is detected, but the required precision to instrument is very high.Auto-collimating microscope measurement radius-of-curvature method can measure
Less radius of curvature, metering system is contactless, but instrument adjustment is complicated, it is difficult to efficient operating.Auto-collimation is preposition
Mirror can measure larger radius of curvature, and metering system is contactless, but measurement accuracy is limited, it is difficult to promote the use of.
The content of the invention
It is an object of the invention to provide a kind of spherical mirror curvature radius measurement method based on Moire fringe, is ensureing to measure
On the basis of precision, non-contact measurement is realized to the radius of curvature of spherical mirror, avoids the damage to spherical mirror surface to be measured,
It can realize that larger radius of curvature sphere curvature radius quick high accuracy measures.
The technical solution for realizing the object of the invention is：A kind of spherical mirror radius of curvature measurement side based on Moire fringe
Method, measuring process are as follows：
Step 1), using Plane reference face and the spherical interference to be measured of interferometer obtain one group of actual measurement interference pattern, above-mentioned reality
Survey the light intensity I of interference pattern1For：
A in formula1To survey interference pattern background light intensity, b1To survey the visibility of interference fringe, w1For sphere to be measured and interference
Rise between instrument reference planes, λ are the operation wavelength of interferometer.
Step 2), the sphere and a plane for emulating a known curvature radius, utilize the interferometer in step 1, emulation
Obtain the sphere of known curvature radius and one group of emulation interference pattern of plane, the light intensity I of above-mentioned emulation interference pattern2For：
A in formula2To emulate interference pattern background light intensity, b2To emulate the visibility of interference fringe, w2For emulation sphere and plane
Between rise, λ be interferometer operation wavelength.
Step 3), actual measurement interference light intensity I1With emulating interference light intensity I2Moiré topography S (x, y) is obtained after multiplication superposition：
Step 4) by frequency domain low-pass filter, extracts above-mentioned moiré topography S (x, y) containing sphere to be measured with imitating
The Moire fringe s (x, y) of proper sphere curvature radius information：
Step 5) is according to above-mentioned Moire fringe s (x, y), then the light and shade bar that sphere to be measured is formed with emulation sphere equal thickness interference
Line condition is：
2(e1+e2)=k λ, k=1,2,3 ... ... (bright fringes)
(dark fringe)
Obtain kth level light and shade radius of interference fringe rkFor：
Obtain the radius of curvature R of sphere to be measured1For：
Wherein e1It is sphere kth level light and shade striped to be measured relative to the rise of interferometer reference planes, e2For emulation sphere the
K level light and shade stripeds relative to emulation plane rise, k be light and shade striped level, R2To emulate the radius of curvature of sphere.
Above-mentioned steps 5) in, bright fringe is identical with dark fringe radius calculation formula, and the radius of curvature of sphere to be measured is identical.
Wherein light and shade striped represents bright fringe or dark fringe.
The present invention compared with prior art, its remarkable advantage：A kind of spherical mirror radius of curvature measurement based on Moire fringe
Method, on the basis of measurement accuracy is ensured, non-contact measurement is realized to the radius of curvature of spherical mirror, avoided to ball to be measured
The damage on face mirror surface, it is possible to achieve larger radius of curvature sphere curvature radius quick high accuracy measures.
The present invention is described in further detail below in conjunction with the accompanying drawings.
Brief description of the drawings
Fig. 1 is a kind of flow chart of spherical mirror curvature radius measurement method based on Moire fringe of the present invention.
Fig. 2 is a kind of equivalent two spherical interference of spherical mirror curvature radius measurement method based on Moire fringe of the present invention
Newton's ring schematic diagram.
Fig. 3 is that a kind of embodiment of spherical mirror curvature radius measurement method based on Moire fringe of the present invention is directed to curvature
Radius is the sphere of the interference pattern and emulation known curvature radius obtained by 41400mm sphere to be measured detects in interferometer with putting down
The interference pattern of face interference；Wherein (a) is the interference pattern obtained by sphere to be measured and plane interference that radius of curvature is 41400mm；(b)
It is the interference pattern for the sphere and plane interference for emulating known curvature radius.
Fig. 4 is to be directed to treat in a kind of embodiment of spherical mirror curvature radius measurement method based on Moire fringe of the present invention
Survey the Moire fringe that part is enough formed by actual measurement interference fringe and emulation interference fringe superposition.
Fig. 5 is used in a kind of embodiment of spherical mirror curvature radius measurement method based on Moire fringe of the present invention
Frequency low-pass schematic diagram.
Fig. 6 is that a kind of embodiment frequency domain of spherical mirror curvature radius measurement method based on Moire fringe of the present invention is low
The Moire fringe formed after pass filter.
Embodiment
With reference to Fig. 1, a kind of spherical mirror curvature radius measurement method based on Moire fringe, specific measuring process is as follows：
1) one group of actual measurement interference pattern, above-mentioned actual measurement interference are obtained using the Plane reference face and spherical interference to be measured of interferometer
The light intensity I of figure1For：
A in formula1To survey interference pattern background light intensity, b1To survey the visibility of interference fringe, w1For sphere to be measured and interference
Rise between instrument reference planes, λ are the operation wavelength of interferometer.
2) sphere and a plane of a known curvature radius are emulated, using the interferometer in step 1, emulation obtains
Know the sphere of radius of curvature and one group of emulation interference pattern of plane, the light intensity I of above-mentioned emulation interference pattern2For：
A in formula2To emulate interference pattern background light intensity, b2To emulate the visibility of interference fringe, w2For emulation sphere and plane
Between rise, λ be interferometer operation wavelength.
3) interference light intensity I is surveyed1With emulating interference light intensity I2Moiré topography S (x, y) is obtained after multiplication superposition：
4) above-mentioned moiré topography S (x, y) is extracted containing sphere to be measured and emulation ball by frequency domain low-pass filter
The Moire fringe s (x, y) of curvature radius information：
5) according to above-mentioned Moire fringe s (x, y), then the light and shade striped bar that sphere to be measured is formed with emulation sphere equal thickness interference
Part is：
2(e1+e2)=k λ, k=1,2,3 ... ... (bright fringes)
(dark fringe)
Obtain kth level light and shade radius of interference fringe rkFor：
Obtain the radius of curvature R of sphere to be measured1For：
Wherein e1It is sphere kth level light and shade striped to be measured relative to the rise of interferometer reference planes, e2For emulation sphere the
K level light and shade stripeds relative to emulation plane rise, k be light and shade striped level, R2To emulate the radius of curvature of sphere.
Above-mentioned steps 5) in, bright fringe is identical with dark fringe radius calculation formula, and the radius of curvature of sphere to be measured is identical.
The present invention is by a kind of sphere curvature radius measurement apparatus and method based on Moire fringe, using contactless survey
The mode of amount avoids the damage to spherical optics element surface to be measured under conditions of measurement accuracy is ensured.Based on More's bar
The characteristic of line, it is possible to achieve the high-acruracy survey of the aspherical elements radius of curvature of larger radius of curvature, be larger radius of curvature spherical mirror
The noninvasive measurement of radius of curvature provides feasible method.
Embodiment
The radius of curvature of one spherical reflector is detected using the method for the present invention in embodiment, this speculum
The initial value of radius of curvature is R1=41400mm, the radius of curvature of the sphere of computer simulation emulation is R2=44000mm.It is based on
The spherical mirror curvature radius measurement method of Moire fringe, its specific measuring process are as follows：
1) one group of interference pattern is obtained using the Plane reference face and spherical interference to be measured of Zygo GPI interferometers, wherein interfering
The a length of 632.8nm of light wave of instrument, peak valley (PV) value of surface testing precision are better than λ/10.The light intensity I of above-mentioned actual measurement interference pattern1
For：
A in formula1To survey interference pattern background light intensity, b1To survey the visibility of interference fringe, w1For sphere to be measured and interference
Rise between instrument reference planes, λ are the operation wavelength of interferometer；Shown in the interference pattern of gained such as Fig. 3 (a)；
2) it is R using one radius of curvature of Computer Simulation2=44000mm sphere obtains one group of interference with plane interference
Figure, the light intensity I of above-mentioned emulation interference pattern2For：
A in formula2To emulate interference pattern background light intensity, b2To emulate the visibility of interference fringe, w2For emulation sphere and plane
Between rise, λ be interferometer operation wavelength；Shown in the interference pattern of gained such as Fig. 3 (b)；
3) interference light intensity I is surveyed1With emulating interference light intensity I2Moiré topography S (x, y) is obtained after multiplication superposition：
The processing procedure can be equivalent to two spherical interferences and form Newton's ring, as shown in Figure 2；The moiré topography of gained is such as
Shown in Fig. 4；
4) above-mentioned moiré topography S (x, y) is extracted containing sphere to be measured and emulation ball by frequency domain low-pass filter
The Moire fringe s (x, y) of curvature radius information：
With reference to Fig. 5 and Fig. 6, it can be seen from the expression formula of Moire fringe the Moire fringe can be regarded as sphere to be measured with
The interference fringe that the emulation spherical interference of known curvature radius is formed；
5) according to above-mentioned Moire fringe s (x, y), then the light and shade striped bar that sphere to be measured is formed with emulation sphere equal thickness interference
Part is：
2(e1+e2)=k λ, k=1,2,3 ... ... (bright fringes)
(dark fringe)
Obtain kth level light and shade radius of interference fringe rkFor：
Obtain the radius of curvature R of sphere to be measured1For：
Wherein e1It is sphere kth level light and shade striped to be measured relative to the rise of interferometer reference planes, e2For emulation sphere the
K level light and shade stripeds relative to emulation plane rise, k be light and shade striped level, R2To emulate the radius of curvature of sphere.
The test result of the sphere curvature radius to be measured of gained is as shown in the table：
| Dark line level | Dark line radius (mm) | Result of calculation (mm) | Error (%) |
| 1 | 15.6690 | 41639 | 0.6 |
| 2 | 25.2830 | 41302 | 0.2 |
| 3 | 32.6762 | 41307 | 0.2 |
When the dark line level taken is 1, the radius of curvature of the sphere to be measured of gained is 41639mm, and measurement accuracy is
0.6%；When the dark line level taken is 2, the radius of curvature of the sphere to be measured of gained is 41302mm, and measurement accuracy is
0.2%；When the dark line level taken is 3, the radius of curvature of the sphere to be measured of gained is 41307mm, and measurement accuracy is
0.2%.
A kind of spherical mirror curvature radius measurement method based on Moire fringe, on the basis of measurement accuracy is ensured, to ball
The radius of curvature of face mirror realizes non-contact measurement, avoids the damage to spherical mirror surface to be measured, it is possible to achieve deep camber half
Footpath sphere curvature radius quick high accuracy measurement.
Above-mentioned steps 5) in, it can also be calculated by bright ring, the same Crape ring of method and step.
Claims (2)
1. a kind of spherical mirror curvature radius measurement method based on Moire fringe, it is characterised in that measuring process is as follows：
Step 1), using Plane reference face and the spherical interference to be measured of interferometer one group of actual measurement interference pattern is obtained, above-mentioned actual measurement is done
Relate to the light intensity I of figure1For：
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A in formula1To survey interference pattern background light intensity, b1To survey the visibility of interference fringe, w1Join for sphere to be measured and interferometer
The rise between plane is examined, λ is the operation wavelength of interferometer；
Step 2), the sphere and a plane for emulating a known curvature radius, using the interferometer in step 1, emulation obtains
The sphere of known curvature radius and the one of plane group of emulation interference pattern, the light intensity I of above-mentioned emulation interference pattern2For：
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A in formula2To emulate interference pattern background light intensity, b2To emulate the visibility of interference fringe, w2Between emulation sphere and plane
Rise, λ be interferometer operation wavelength；
Step 3), actual measurement interference light intensity I1With emulating interference light intensity I2Moiré topography S (x, y) is obtained after multiplication superposition：
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Step 4) by frequency domain low-pass filter, extracts above-mentioned moiré topography S (x, y) containing sphere to be measured and emulation ball
The Moire fringe s (x, y) of curvature radius information：
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Step 5) according to above-mentioned Moire fringe s (x, y), then sphere to be measured and the bright fringe that emulation sphere equal thickness interference is formed with it is dark
The condition of striped is respectively：
2(e1+e2)=k λ, k=1,2,3, bright fringe
Obtain kth level light and shade radius of interference fringe rkFor：
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Obtain the radius of curvature R of sphere to be measured1For：
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Wherein e1It is sphere kth level dark fringe to be measured relative to the rise of interferometer reference planes, e2It is bright for emulation sphere kth level
Dark fringe relative to emulation plane rise, k be light and shade striped level, R2To emulate the radius of curvature of sphere.
2. the spherical mirror curvature radius measurement method according to claim 1 based on Moire fringe, it is characterised in that：It is above-mentioned
In step 5), bright fringe is identical with dark fringe radius calculation formula, and the radius of curvature of sphere to be measured is identical.
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| CN102128600A (en) * | 2010-12-10 | 2011-07-20 | 西安科技大学 | Method and device for measuring curvature radius of lens by use of laser |
| CN103063415A (en) * | 2013-01-05 | 2013-04-24 | 浙江大学 | Long-focus lens focus distance measuring method based on moire fringe matching |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH06174451A (en) * | 1992-12-04 | 1994-06-24 | Nikon Corp | Measuring method by newton gauge |
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|---|---|---|---|---|
| CN1438468A (en) * | 2003-01-05 | 2003-08-27 | 浙江大学 | Equal-rise coefficient-comparison digital damage-free detection system for detecting large curvature radius |
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