CN1280293A - Method for measuring nanometer precision of object displacement - Google Patents
Method for measuring nanometer precision of object displacement Download PDFInfo
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- CN1280293A CN1280293A CN 00119556 CN00119556A CN1280293A CN 1280293 A CN1280293 A CN 1280293A CN 00119556 CN00119556 CN 00119556 CN 00119556 A CN00119556 A CN 00119556A CN 1280293 A CN1280293 A CN 1280293A
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- 238000006073 displacement reaction Methods 0.000 title claims abstract description 47
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- 238000002715 modification method Methods 0.000 claims description 2
- 238000012937 correction Methods 0.000 abstract description 4
- 238000000691 measurement method Methods 0.000 abstract description 3
- 230000009466 transformation Effects 0.000 abstract description 3
- 238000005070 sampling Methods 0.000 abstract 1
- 238000005259 measurement Methods 0.000 description 15
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Abstract
A method for measuring the nano-precision of object displacement is an interference measurement method by modulating the wavelength of a laser beam by using photo-thermal sinusoidal phase. The laser beam with wavelength modulated by photo-thermal sine phase is input into a computer for Fourier transformation through an interference signal generated by a Michelson interferometer, the sine phase modulation depth and the phase alpha of the interference signal of a measured object at the time t are obtained, a correction method that the absolute value of the phase difference between two adjacent sampling points is smaller than pi is adopted to obtain the correction value alpha of the phase, and the displacement of the measured object is obtained through the correction value alpha of the phase. The measuring range of the displacement is expanded to the centimeter magnitude.
Description
The present invention relates to the measuring method of the nano-precision of ohject displacement, the variation range that mainly is applicable to ohject displacement is in decimetre.
In laser interference measuring method, the sinusoidal phase modulation interferometry is a kind of high precision interferometric method, and the introducing of semiconductor laser makes the sinusoidal phase modulation interferometer structure compact more simple.On this basis, for reducing measuring error, improve measuring accuracy, inventors such as Wang Xiangchao have proposed the method that optical frequency photo-thermal Modulating Diode Laser wavelength is used for the sinusoidal phase modulation interferometer (technology [1] formerly, Wang XF, Wang XZ, Qian F, Chen G, Chen G, Fang Z, " Photothermal modulation oflaser diode wavelength:application to sinusoidal phase-modulating interferometer for displacementmeasurements, " Optics ﹠amp; Laser Technology, Vol.31, No.8, pp.559-564,2000).
In technology [1] formerly, obtain interference signal with photodetector earlier:
S (t)=S
0Cos[zcos (ω
cT)+α
0+ α (t)], in (1) formula
z=2πβα[ι+2r(t)]／λ
0 2，????(2)
α (t)=4 π r (t)/λ
0, (3) S
0Be the vibration amplitude of interference signal alternating component, ω
cBe the frequency of sinusoidal phase modulation, t is the time, α
0Phase place for testee interference signal when static, α (t) is the t phase place of interference signal constantly, z is the depth of modulation of sinusoidal phase modulation, β is the index of modulation of wavelength, α is the amplitude of semiconductor laser sinusoidal drive electric current, ι is the optical path difference of testee interferometer two arms when static, and r (t) is the displacement of testee, λ
0Be centre wavelength as the semiconductor laser of light source.
The displacement r (t) of testee is according to behind interference signal formula (1) Fourier transformation, obtains the z value earlier, utilizes arctan function to obtain then to obtain behind its phase place α (t).
The shortcoming of technology [1] formerly: because the codomain of α (t) be [π, π], so for the displacement of any size, according to formula (3), its value of obtaining is all at scope [λ
0/ 4, λ
0/ 4] in, this just can not surpass [λ by correct measurement
0/ 4, λ
0/ 4] displacement of scope.
As a kind of high-precision displacement measurement method, a kind of displacement measurement method that makes usage-Fabry-Parot interferent instrument (technology [2] formerly, the nano-grade displacement generator of calibration that inventors such as Li Zhu provide or calibrating usefulness, notification number: CN2097392Y,) be suggested, though it can be with the nanometer accuracy measurement displacement, measurement range is less than 2 microns, and can only be used to measure the quasistatic displacement, the adjustment of instrument requires very high.
Purpose of the present invention is exactly in order to overcome the deficiency in the above-mentioned technology formerly, a kind of measuring method of nano-precision of ohject displacement to be provided, and the measurement range of displacement is in decimetre.
The measuring method of the nano-precision of ohject displacement of the present invention is the interferometric method that adopts photo-thermal sinusoidal phase modulation laser beam wavelength, and the step of its measurement is:
1. get wavelength X
0By the laser beam of photo-thermal sinusoidal phase modulation.
2. above-mentioned laser beam is imported Michelson interferometer, make it produce interference, convert interference light signal to electric signal with photodetector, in data collecting card is input to computing machine through testee reflected probe light beam and reference beam.
3. the interference signal of gathering is carried out Fourier transform, obtains the sinusoidal phase modulation depth z, obtain the t phase place α ' sine function sin[α (t) (t) of interference signal constantly] and cosine function cos[α (t)].
4. earlier according to sin[α (t)] and cos[α (t)] obtain α ' (t), adopt the phase differential absolute value of adjacent two sampled points α ' (t) to be revised then less than the modification method of π, try to achieve modified value α (t).
5. according to above-mentioned formula (3) α (t)=4 π r (t)/λ
0The modified value α (t) that obtains with above-mentioned steps obtains the displacement r (t) of testee.λ wherein
0For by the centre wavelength of photo-thermal sinusoidal phase modulation
Above-mentioned steps is shown in the process flow diagram of Fig. 1.
Above-mentioned the 4th step is as follows to α ' correction principle (t):
Surpass [λ in order to measure
0/ 4, λ
0/ 4] displacement, wherein λ
0For by the centre wavelength of photo-thermal sinusoidal phase modulation, at first consider object t at a time
1Displacement:
α (t wherein
1)=2n π+α
T1, (5)
In the following formula, n is an integer ,-π≤α
T1≤ π.For α (t
1)＞π or α (t
1The π of)＜-, if can determine the numerical value of n, then the displacement of object just can correctly be obtained.Since α (t) according to the interference signal Fourier transformation after pointwise obtain, therefore can pointwise consider.At first consider greater than with less than π (or-π) two some A and B, as Fig. 3, their phase place is respectively α
AAnd α
B, suppose 3.1＜α
A＜π, π＜α
B＜3.2, the phase value α ＇ that obtains according to arctan function then
A=α
A, and α ＇
B=α
B-2 π.If the absolute value of adjacent 2 phase differential is less than π, on the border of [π, π], we can surpass adjacent 2 phase differential π as judging that phase place surmounts the foundation of [π, π].For adjacent A, B 2 points, because α ＇
B-α
A＜-π, so α ＇
BThe phase value α of corresponding reality
BExceed [π, π] this scope, after it is revised, obtained α
B=α ＇
B+ 2 π.In like manner, for C, D 2 points, α
C=α ＇
C+ 2 π, α
D=α ＇
D+ 2 π.For F point and G point, α ＇
G-α
F＜-3 π, corresponding amendment type is α
G=α ＇
G+ 4 π.More generally, for 2 adjacent α
T1And α
T2If α ＇ is arranged
T2-α
T1＜-n π (n is an odd number), then α
T2=α
T1+ (n+1) π.On the contrary, if α ＇ is arranged
T2-α
T1＞n π, then α
T2=α
T1-(n+1) π.
According to above derivation, as long as the sinusoidal phase modulation frequencies omega
cThe phase differential absolute value that satisfies adjacent two sampled points with the sample frequency of data acquisition is less than π, and the n in the formula (5) just can correctly obtain, and ohject displacement just can be obtained according to formula (3).
The measuring method of the nano-precision of ohject displacement of the present invention, its measurement range only are subjected to data acquisition rate and computing machine can the deal with data quantitative limitation.If the maximum slope of the displacement time curve of object is a, then data acquisition rate is that f need satisfy
f≥4α／λ
0。(6) maximum displacement of object
r
Mzx=ft λ
0/ 4, (7) wherein the product of data acquisition rate f and time t are data volume, are made as 500k, optical source wavelength λ
0Be 785nm, then the maximum displacement that can survey is 9.8cm.
The said photo-thermal sinusoidal phase modulation laser beam wavelength λ that obtains
0The used device of interference signal, used device contains two light sources in the measuring method just of the present invention, one is the primary source 8 that only has dc driver 9, and another is except that having direct supply 1, also has the modulated light source 4 of sinusoidal signal generator 2 and driver 3.The light intensity of modulated light source 4 is by sinusoidal signal generator 2 and driver 3 control sinusoidal variations.The laser beam of modulated light source 4 output intensity sinusoidal variations is through first lens 5, the polarization beam apparatus 6 and second lens 7 are added on the primary source 8, utilizes photo-thermal effect that the output wavelength of primary source 8 is carried out sinusoidal phase modulation.The wavelength of primary source 8 output by behind the polarization beam apparatus 6, enters the Michelson interferometer that is made of beam splitter 10, reference mirror 11 and testee 12 to photodetector 13 through the laser beam of photo-thermal sinusoidal phase modulation.The interference light signal that photodetector 13 receives is exported after converting electric signal to, is input in the computing machine 15 through data collecting card 14 again.As shown in Figure 2.
Advantage of the present invention is:
The measurement range that has overcome displacement in the technology formerly is not more than the defective of half wavelength, expands the measurement range of displacement to a centimetre magnitude, and just in decimetre, simultaneously, measuring accuracy keeps nanometer scale.
The measuring method of the nano-precision of ohject displacement of the present invention can the slow in time or vertiginous displacement of Measuring Object.
Description of drawings:
Fig. 1 is the process flow diagram of measuring method of the nano-precision of ohject displacement of the present invention.
Fig. 2 is the used measurement mechanism synoptic diagram of measuring method of the nano-precision of ohject displacement of the present invention.
Fig. 3 is the synoptic diagram that the displacement of measuring method of the nano-precision of ohject displacement of the present invention enlarges principle.
Embodiment:
This measuring method adopts device as shown in Figure 2, the wavelength X 0 that is used as the semiconductor laser of primary source 8 is 785nm, the wavelength of primary source 8 (semiconductor laser) is to be added on the primary source 8 by sinusoidal signal generator 2 and driver 3 control modulated light sources 4 output intensity sinusoidal variations, utilizes photo-thermal effect to carry out sinusoidal phase modulation.Wavelength X
0Through behind the polarization beam apparatus 6, enter the Michelson interferometer that constituted by beam splitter 10, reference mirror 11 and testee 12 through the output beam of the primary source 8 of photo-thermal sinusoidal phase modulation to photodetector 13.Photodetector 13 receives by testee 12 reflected probe light beams with by the reference beam that reference mirror 11 reflects and converts electric signal to through the interference light signal that beam splitter 6 produces, and carries out data processing in the computing machine 15 through being input to behind the data collecting card 14.Measuring process is shown in the process flow diagram of Fig. 1.Earlier the data that collect are carried out Fourier transform, obtain sinusoidal phase modulation depth z=2.35rad.Obtain sin[α (t) again] be ... 0.4434,0.0894 ,-0.0275 ,-0.6029 ... corresponding cos[α (t)] be ..., 0.8244,0.9187,0.8761,0.7067 ..., the α ' that obtains correspondence (t) is ..., 2.6574,3.0467 ,-2.8412 ,-2.4463 ... α ' (t) is modified to α (t), equals ..., 2.6574,3.0467,3.4419,3.8369 ..., according to above-mentioned formula (3) r (t)=α (t) λ
0/ 4 π obtain ohject displacement r (t) ..., 166.0043nm, 190.3194nm, 215.0111nm, 239.6810nm ..., the maximal value of r (t) is 1dm, the root-mean-square error of displacement measurement is 0.98nm.As only adopting the measuring method in the technology formerly, though be all nano-precision, only the energy measurement maximal value is no more than the displacement of 392.5nm.Measuring method of the present invention has enlarged the measurement range of displacement r (t) greatly under the prerequisite that keeps nano-precision.
The measurement range of the measurement result of present embodiment and technology formerly more as shown in table 1.But the maximal value that location of the present invention moves is that formerly but the technology location moves peaked 255100 times.
But the peaked comparison that the maximum displacement that table 1, the embodiment of the invention can be surveyed and technology location formerly move.
| Optical source wavelength λ 0 | The depth of modulation Z of sinusoidal phase modulation | Displacement r (t) maximal value that can measure of technology formerly | The present invention records r (t) maximal value of displacement | The root-mean-square error of displacement measurement of the present invention |
| 785nm | ???～2．35rad | ????392．5nm | ????1dm | ????0．98nm |
Claims (2)
1. the measuring method of the nano-precision of an ohject displacement is the interferometric method that adopts photo-thermal sinusoidal phase modulation laser beam wavelength, and concrete steps are:
＜1〉gets wavelength X
0By the laser beam of photo-thermal sinusoidal phase modulation;
＜2〉above-mentioned laser beam is imported Michelson interferometer, produce interference signal, convert interference light signal to electric signal with photodetector, in data collecting card is input to computing machine through testee reflected probe light beam and reference beam;
＜3〉interference signal of gathering is carried out Fourier transform, obtains sinusoidal phase modulation degree of depth Z, obtain phase place α ' (t) the sine function sin[a (t) of testee at t moment interference signal] and cosine function cos[a (t)]; It is characterized in that
＜4〉according to the sin[a (t) of above-mentioned steps] and cos[a (t) obtain α ' (t) after, adopt the phase differential absolute value of adjacent two sampled points α ' (t) to be revised less than the modification method of π, obtain modified value α (t);
＜5〉according to the above-mentioned modified value α that tries to achieve (t) and formula α (t)=4 π r (t)/λ
0Obtain the displacement r (t) of testee, wherein λ
0For by the centre wavelength of photo-thermal sinusoidal phase modulation.
2. the measuring method of the nano-precision of ohject displacement according to claim 1 is characterized in that the said photo-thermal sinusoidal phase modulation laser beam wavelength λ that obtains
0The used device of interference signal mainly contain two light sources, one is primary source (8), another is that the light intensity of being controlled by sinusoidal signal generator (2) and driver (3) is the modulated light source (4) of sinusoidal variations, modulated light source (4) utilizes photo-thermal effect that the wavelength of primary source (8) output is carried out Sine Modulated, the laser beam of primary source (8) output sinusoidal phase modulation wavelength is by behind the polarization beam apparatus (6), enter by beam splitter (10), the Michelson interferometer that reference mirror (11) and testee (12) constitute is to photodetector (13), and the output of photodetector (13) is in data collecting card (14) is input to computing machine (15).
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|---|---|---|---|
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| CN100538260C (en) * | 2007-02-07 | 2009-09-09 | 中国科学院上海光学精密机械研究所 | Micro-displacement high-precision real-time interferometer |
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