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Remote and high precision step height measurement with an optical fiber multiplexing interferometric system
Optics and Lasers in Engineering 66 (2015) 52–57
Contents lists available at ScienceDirect
Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Remote and high precision step height measurement with an optical fiber multiplexing interferometric system Yunzhi Wang, Fang Xie n, Sen Ma, Liang Chen Optical Science and Technology Laboratory, Department of Physics, School of Science, Beijing Jiaotong University, Beijing 100044, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 14 March 2014 Received in revised form 1 August 2014 Accepted 10 August 2014
An optical fiber multiplexing low coherence and high coherence interferometric system, which includes a Fizeau interferometer as the sensing element and a Michelson interferometer as the demodulating element, is designed for remote and high precision step height measurement. The Fizeau interferometer is placed in the remote field for sensing the measurand, while the Michelson interferometer which works in both modes of low coherence interferometry and high coherence interferometry is employed for demodulating the measurand. The range of the step height is determined by the low coherence interferometry and the value of it is measured precisely by the high coherence interferometry. High precision has been obtained by searching precisely the peak of the low coherence interferogram symmetrically from two sides of the low coherence interferogram and stabilizing the Michelson interferometer with a feedback loop. The maximum step height that could be measured is 6 mm while the measurement resolution is less than 1 nm. The standard deviation of 10 times measurement results of a step height of 1 mm configurated with two gauge blocks is 0.5 nm. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Optical fiber sensing Low coherence interferometry High coherence interferometry Step height measurement
1. Introduction In order to control the quality of the products in the fields of microelectronics, micro-electric-mechanical system, flat panel displays, and photovoltaic cells, etc. there is a great requirement for the measurement of step heights ranging from several micrometers to larger than 1 mm. As optical fiber measurement systems have the advantages of non-contact, compactness, light weight, immunity to electromagnetic interference, high resolution, low cost and without the need of adjusting optical elements, there is a great interest of developing optical fiber measurement systems [1–15]. As the measurement range of an optical fiber low-coherence interferometric measurement system (OFLCIS) which is illuminated with a broadband light source is not limited by the wavelength, OFLCIS has become an important technique for the absolute measurement of static and quasistatic parameters, such as displacement, temperature, pressure, strain, refractive index, and step height. In order to obtain high measurement precision, it is very important for OFLCIS to identify precisely the peak position of the low coherence interferogram (PPI) obtained during the period the optical path difference (OPD) of the interferometer is tuned linearly. But the top area of the low coherence interferogram is flatten and thus it is very difficult to address precisely the PPI. Rao [3] used two light sources
n
Corresponding author. Tel.: þ 86 10 51688333; fax: þ 86 10 51840433. E-mail address: [email protected] (F. Xie).
http://dx.doi.org/10.1016/j.optlaseng.2014.08.008 0143-8166/& 2014 Elsevier Ltd. All rights reserved.
with two different wavelengths to make the peak prominent, which needs two light sources and the system is expensive and complicated. The proposed optical fiber multiplexing interferometric system, which includes a Fizeau interferometer and a Michelson interferometer is suitable for remote and absolute measurement of step height with high precision. The Fizeau interferometer which is inserted in the remote sensing field is used for sensing the measurand, while the Michelson interferometer which is stabilized by a feedback loop works in both modes of low coherence interferometry and high coherence interferometry. The range of the measured step height is determined by the low coherence interferometry, while the resolution of the measurement is decided by the high coherence interferometry. High precision of addressing the PPI has been obtained by symmetrical peak-searching method. The maximum step height that can be measured is 6 mm while the measurement resolution is less than 1 nm. The standard deviation of 10 times measurement results of a step with the height of 1 mm which is configurated with two gauge blocks is 0.5 nm. 2. Principle of the optical fiber multiplexing interferometric measurement system 2.1. Optical fiber measurement system The proposed optical fiber measurement system is shown in Fig. 1. It includes a Fizeau interferometer and a Michelson interferometer.
Y. Wang et al. / Optics and Lasers in Engineering 66 (2015) 52–57
Gauge block B Gauge block A Broadband light source
1
ASE
FBG1
Isolator 1
M1
GRIN lens
3dB-coupler Mirror
Isolator 2
M2
2 GRIN lens
Signal generator PZT
Circulator Electronic feedback loop
FBG2 PD1
PD2 Electronic processor
A/D converter
Output
Fig. 1. The scheme of the principle of the measurement system.
A broadband light source of amplified spontaneous emission (ASE) with flatten spectrum of C-band is used in the system. The ASE gives an output power of about 200 mW with a spectral bandwidth 35.8 nm. The FBG1 and FBG2 are used as in-fiber reflective mirrors and have the same Bragg wavelength at 1557 nm with 3 dB bandwidth 0.2 nm. Light emitted from the light source ASE passes through the isolator 1, 3 dB-coupler 1 and reaches FBG1. The light of the wavelength 1557.00 nm is reflected by FBG1 while the light of the left wavelength passes FBG1 and reaches the GRIN lens. As the end face of the GRIN lens is not coated with any film, part power of the light is reflected because of the Fresnel reflection. The left power of light passes the GRIN lens and is collimated at the same time and then is incident perpendicularly on the surface of the gauge block mounted on an one-dimension translation stage (M1) and then is reflected into the system again by the surface of the gauge block. The end face of the GRIN lens and the surface of the gauge block configure the two reflective planes of a Fizeau interferometer. The light reflected by the two planes of the Fizeau interferometer passes FBG1 and is split into two beams by the 3 dB-coupler 1. The beam from one port of the 3 dB-coupler 1 cannot reach the light source because of isolator 1. The beam from the other port of the 3 dB-coupler 1 passes isolator 2 and reaches 3 dB-coupler 2 and then is split into two beams. The two beams reach two GRIN lenses and are collimated respectively. As the end faces of the two GRIN lenses are coated with highly transmissive film, there is no light reflected by the end faces of these two GRIN lenses. The collimated two beams are reflected back into the system again by two mirrors that are mounted respectively on an onedimension translation stage (M2) and a piezoelectric stretcher (PZT). The reflected beams are combined at the 3 dB-coupler 2 again. The combined light from one port of the 3 dB-coupler 2 cannot reach 3 dBcoupler 1 because of isolator 2, while the combined light from the other port of 3 dB-coupler 2 is guided by the circulator and passes FBG2 and is detected by a photo detector (PD1). The signal detected by PD1 can be expressed by Eq. (1) [9]. h i 1 I ¼ I 0 1 þ exp ð2ΔX=Lc Þ2 cos ðkΔXÞ ð1Þ 2 where I 0 is the total optical power arriving at PD1, ΔX ¼ ðX 1 X 2 Þ, X 1 ; X 2 are the OPDs of the Fizeau interferometer and the Michelson interferometer respectively, Lc is the coherence length of the ASE light
53
source, and k is the wave number. It can be known that any change in ΔX will induce change in both the fringe visibility and the phase of the signal. The signal will be the maximum when ΔX ¼ X 1 X 2 ¼ 0 and the PPI appears. The OPD of the Fizeau interferometer will vary proportionally with the variation of the measurand and the PPI will also shift correspondently. The key issue of OFLCIS is how to measure the shifting range of the PPI precisely. A Michelson interferometer which works in both modes of low-coherence interferometry and high-coherence interferometry is exploited as the demodulating interferometer to measure the shifting range of the PPI. The shifting range is determined by the low-coherence interferometry and the value of it is measured by the high-coherence interferometry. In order to reduce the influences resulted from the environmental disturbances, the length of the fiber in the two interfering arms of the Michelson interferometer is made to be as short as about 11 mm, just as shown in Fig. 2. Moreover, an electronic feedback loop is designed to compensate for the influences to the Michelson interferometer which is resulted from the environmental disturbances so as to stabilize the Michelson interferometer. The reflected light from FBG1 passes 3 dB-coupler 1 and isolator 2 and 3 dB-coupler 2 and then is split into two beams. The two beams are collimated by two GRIN lenses and are reflected respectively by two mirrors which are mounted respectively on the translation stage (M2) and the PZT. The two reflected beams are combined at 3 dB-coupler 2 and interfere with each other. The interferometric signal from one port of the 3 dB-coupler 2 cannot reach 3 dB-coupler 1 because of isolator 2. And the interferometric signal from the other port of 3 dB-coupler 2 is guided by the circulator and reaches FBG2 and is reflected by FBG2 and is guided by the circulator again and then is detected by a photo detector (PD2). The signals from PD1 and PD2 are processed by the electronic processor simultaneously while the signal from PD2 is also input into the electronic feedback loop to produce a correction signal which is applied on the PZT and drives the PZT to adjust the OPD of the Michelson interferometer in order to keep it in quadrature state (the phase between two interfering arms is π=2). The signal detected by PD1 will be the maximum when the OPDs of the Fizeau interferometer and the Michelson interferometer are equal, just as shown in Eq. (1). As the signal detected by PD2 is a high coherence interferometric signal with the Bragg wavelength of FBG, it will vary periodically with the cosine function law while translation stage M2 tunes linearly the OPD of the Michelson interferometer. The number of the interferometric fringes during the shifting range of the PPI of the low interferogram is proportional to the height of the step. The PPI is searched symmetrically from two sides of the low coherence interferogram, and the value of the step height is measured by the amount of fringes of the signal detected by PD2 during the shifting range of PPI. The measured step height can be calculated by the relationship shown in Eq. (2). Δh ¼
1557 n 2
ð2Þ
GRIN lens
3dB-coupler
Fig. 2. The optical fiber Michelson interferometer with short interfering arms.
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Y. Wang et al. / Optics and Lasers in Engineering 66 (2015) 52–57
Fig. 3. The scheme of the electronic feedback loop.
2.2. Compensating electronic feedback loop Besides being used for performing the measurement task, the high coherence interferometric signal detected by PD2 is also used to erase the influences to the Michelson interferometer that is resulted from the environmental disturbances. The schematic diagram of the circuit of electronic feedback loop is shown in Fig. 3. PD2 is connected to the current-to-voltage converter U1 which has low input impedances. The output voltage from U1 will have the form shown in Eq. (3) u1 ¼ u0 ½1 þ k cos ðϕd þ ϕs Þ
ð4Þ
where K is the conversion gain of the interferometric signal from U2. After passing through the electronic integrator U3, the output from U3 is the value shown in Eq. (5) u3 ¼ K 1 cos ðϕd þ ϕs Þ
After the feedback loop is turned on The signal detected by PD1
The signal detected by PD2
Time (*10ms) Fig. 4. The signals detected by PD1 and PD2 before and after the feedback loop is turned on.
ð3Þ
where u0 is related to the input optical power and the gain of U1, k is the interferometric fringe visibility, ϕd is the static differential phase between the two interfering arms, and ϕs is the differential phase induced by environmental disturbances. After passing through the electronic differentiator U2, the direct voltage part in u1 will be erased, and the output from U2 will be shown as Eq. (4) u2 ¼ K sin ðϕd þ ϕs Þ
Before the feedback loop is turned on Signal detected by PD1and PD2
where Δh is the measured step, n is the amount of fringes of the signal detected by PD2 during the shifting range of the PPI. The key issue is how to determine precisely the value of n.
ð5Þ
where K 1 is the conversion gain of U3. The function of the electronic differentiator U2 and the electronic integrator U3 is to erase the direct voltage part in u1 . The alternating parts shown in Eqs. (3) and (5) have the same function and are in phase with each other. The output of the electronic integrator U3 is put into another electronic integrator U4 after which the signal is applied on the PZT to drive it tuning the OPD of the Michelson interferometer to keep the Michelson interferometer in quadrature state. When the interferometer is in quadrature position, there will be ϕd þ ϕs ¼ ðπ=2Þ, it obtains that the signal applied on the PZT will be u4 ¼ 0, and in the vicinity of the quadrature position, the signal applied on the PZT will be u4 a 0 which drives PZT to tune the optical path of the reference arm and draw the interferometer back to the quadrature position again. By this means, the Michelson interferometer is always kept at the quadrature state and is stabilized. The feedback loop is a first order system with a frequency bandwidth ranging from 0 to 21.65 Hz which is verified by the experiments sufficient to erase the environmental disturbances.
3. Experiments and experimental results 3.1. Experiments on validation of the electronic feedback loop With the two mirrors mounted respectively on the translation stage M2 and PZT in static state and the electronic feedback loop out of operation, the signals detected by PD1 and PD2 are shown during the first part of the recorded time in Fig. 4. In the present case, as the difference between the OPDs of the Fizeau interferometer and Michelson interferometer is larger than the coherent length of the light source, the signal detected by PD1 which is a low coherence interferometric signal is simply the intensity of the sum of the two combined beams. So this signal is a constant value during the recorded time, while the signal detected by PD2 which is a high coherence interferometric signal is fluctuating at all the time even though the two reflective mirrors of the Michelson interferometer are not moving. The variation in the high coherence interferometric signal is induced by various types of environmental disturbances. However, as soon as the feedback loop is turned on, the high coherence interferometric signal detected by PD2 is stabilized at a constant value, just as shown during the second part of the recorded time in Fig. 4. The feedback loop had been turned on continuously for several hours (more than 4 h) during the experiments, it was shown that the interferometric signal detected by PD2 had been always stabilized. This indicates that the influences to the Michelson interferometer that is resulted from environmental disturbances have been erased effectively.
Y. Wang et al. / Optics and Lasers in Engineering 66 (2015) 52–57
Gauge block A
55
Gauge block B
Point a
Point b
Fig. 5. The measured step height configurated with two gauge blocks.
8
Interferometric signal
The signal detected by PD1
6
4 The signal detected by PD2
Δ1 2 0
30
15
45
60
×10
5
Interferometric signal (V)
Point 1
8
The converted data serial number
7 6 5 4 3 0 9
4.5
13.5
22.5
18
×103
The converted data serial number 8 The signal detected by PD1
6
4 The signal detected by PD2
Δ2 2
0 15
30
45
60
×10
5
The converted data serial number
Fig. 6. The detected low coherence inteferometric signal and high coherence interferometric signal while tuning linearly the OPD of the Michelson interferometer, (a) With the measurement beam incident perpendicularly on point a, (b) With the measurement beam incident perpendicularly on point b.
Interferometric signal (V)
Interferometric signal
Point 1
Fig. 7. The zoom of the top area of low coherence interferogram.
7
The left side chosen fringe
6 5 4
Point 1 0
9
18
27
36
The converted data serial number Fig. 8. The fringes with the amplitude of about half of the maximum amplitude.
3.2. Experiments on the measurement of a step height 3.2.1. Measurement procedure A gauge block with the height of 1 mm (gauge block B) is contacted to another gauge block (gauge block A) to configurate a step with the height of 1 mm, just as shown in Fig. 5. Firstly, with the measurement beam incident perpendicularly on point a that is on the surface of gauge block A, the translation stage M2 tunes linearly the OPD of the Michelson interferometer during which PD1 and PD2 detect the corresponding signals that are shown in Fig. 6(a). The variation of OPD (Δ1 ) of the Michelson interferometer from the beginning of tuning to the PPI can be calculated by Eq. (2) where n is the number of the fringes of the high coherence interferometric signal between the beginning of tuning the OPD and the PPI, and n can be obtained by counting the fringes of the high coherence interferometric signal with software program. Secondly, the one-dimension translation stage M1 moves the gauge blocks horizontally until the measurement beam is incident perpendicularly on point b that is on the surface of gauge block B. Again, the translation stage M2 tunes linearly the OPD of the Michelson interferometer during which PD1 and PD2 detect the
corresponding signals that are shown in Fig. 6(b). The variation of OPD (Δ2 ) of the Michelson interferometer from the beginning of tuning to the PPI can be also calculated by Eq. (2) where n is the number of the fringes of the high coherence interferometric signal between the beginning of tuning the OPD and the PPI, and n can be obtained by counting the fringes of the high coherence interferometric signal with software program. The height of the step can be calculated with Eq. (6) Δh ¼ jΔ2 Δ1 j
ð6Þ
3.2.2. Addressing precisely the peak of the low coherence interferogram In order to obtain high measurement precision, it is very important to count precisely the number of the fringes of the high coherence interferometric signal between the beginning of tuning the OPD of the Michelson interferometer and the PPI. As the top area of the low coherence interferogram is flatten and there are usually several fringes with the same amplitude in the top area, it is very difficult to address the PPI precisely, just as
56
Y. Wang et al. / Optics and Lasers in Engineering 66 (2015) 52–57
Measurement serial number
1
2
3
4
5
Measurement results(nm)
99999.4
1000000.5
99999.7
99999.6
1000000.6
Measurement serial number
6
7
8
9
10
Measurement results(nm)
1000000.3
1000000.7
99999.5
1000000.4
99999.6
deviation (nm)
0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 1
2
3
4
5
6
7
8
9
10
measurement serial number Fig. 9. The measurement results and each deviation of the step height.
shown in Fig. 7. Fig. 7 is the zoom of top area of the low coherence interferogram that is shown in Fig. 6. When the OPD of the Michelson interferometer is tuned linearly, the detected low coherence interferogram is symmetrical about the peak point, which can be seen from the low coherence interferogram in Fig. 6. But in the vicinity of half of the maximum amplitude, it can be seen that the amplitude of the fringes varies apparently. During these varying amplitude fringes, we chose one fringe of which the amplitude does significantly not equal to its adjacent fringes, just as shown in Fig. 8. As the low coherence interferogram is symmetrical about its peak, it is able to choose another fringe with the same amplitude on the other side of the interferogram. As the two chosen fringes are symmetrical about the peak of the low coherence interferogram, if tracking from the two chosen fringes to the center where the position of the peak is, the peak could be identified precisely. The beginning tracking point on one of the fringes is chosen to be the point that with the average value and is on the side of the fringe nearer to the center of the interferogram (point 1, shown in Fig. 8). The other beginning tracking point on the other side is chosen with the same method. The peak of the interferogram is the center between these two points. The peak could be determined only by finding out the center between these two chosen points. This procedure could be done by a software program in a computer. As the signals detected by PD1 and PD2 are simultaneously processed by the electronic processor and converted to be digital data by an A/D converter, the amount of fringes of the high coherence interferometric signal between the beginning of tunning and PPI could be counted easily by the software program. As the high coherence interferometric signal is obtained by the reflection of the FBG, the measurement range which equals the coherence length of the reflective spectrum of FBG is 6 mm. The frequency of the detected signals from PD1 and PD2 is about 45 Hz which is higher than the cutoff frequency of the feedback loop, so the compensating action of the feedback loop will not influence the signals. As the converting speed of the A/D converter is 100 KS/s, there are 2222 data in one period of the high coherence interferometric signal. The corresponding resolution of the measurement is less than 1 nm. The
measurement of the step height configurated with the two gauge blocks have been performed 10 times repeatedly. Each measurement result and deviation is shown in Fig. 9(a) and (b), and the standard deviation of the 10 times measurement is 0.5 nm.
4. Conclusion An optical fiber multipexing low coherence and high coherence interferometric system that includes a Fizeau interferometer as the sensing element and a Michelson interferometer as the demodulating element has been designed for remote and high precision step height measurement. The range of the step height is determined by the low coherence interferometry while the value of it is measured precisely by the high coherence interferometry. High precision has been obtained by the methods of peak-searching symmetrically and stabilizing the Michelson interferometer with a feedback loop. The maximum step height that can be measured is 6 mm while the measurement resolution is less than 1 nm. The standard deviation of 10 times measurement results of a step with the height of 1 mm configurated with two gauge blocks is 0.5 nm.
Acknowledgments The authors thank greatly the National Natural Science Foundation of China (50975022) and the Beijing Natural Science Foundation (3132033) for supporting this research. References [1] Farahi F, Newson TP, Jones JDC, Jackson DA. Coherence multiplexing of remote fibre Fabry–Perot sensing system. Opt Commun 1998;65:319–21. [2] Rao Yun-Jiang, Jackson David A. Recent progress in fibre opticlow-coherent interferometry. Meas Sci Technol 1996;7:981–99. [3] Rao YJ, Ning YN, Jackson DA. Synthesized source for white-light sensing systems. Opt Lett 1993;18:462–4. [4] Zhang XM, Liu Yuxiang, Bae H, Pang C, Yu M. Phase modulation with micromachined resonant mirrors for low-coherence fiber-tip pressure sensors. Opt Express 2009;26:23965–74.
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[5] Lazo M, Manojlovic A. Novel common path interferometric technique for vibration measurement based on two-fiber-optic couplers. IEEE Sens J 2011;7:1541–7. [6] Jiang Mingzheng, Gerhard Edmund. A simple strain sensor using a thin film as a low-finesse fiber-optic Fabry–Perot interferometer. Sens Actuators A 2001;88:41–6. [7] Nguyen Linh Viet, Hwang Dusun, Moon Sucbei, Moon Dae Seung, Chung Youngjoo. High temperature fiber sensor with high sensitivity based on core diameter mismatch. Opt Express 2008;16:11369–75. [8] Wang Wenhui, Wu Nan, Tian Ye, Niezrecki Christopher, Wang Xingwei. Miniature all-silica optical fiber pressure sensor with an ultrathin uniform diaphragm. Opt Express 2010;18:9006–14. [9] Lazo M, Manojlovic A. Novel common path interferometric technique for vibration measurement based on two-fiber-optic couplers. IEEE Sens J 2011;7:1541–7. [10] Hand DP, Carolan TA, Barton JS, Jones JDC. Profile measurement of optically rough surfaces by fiber-optic interferometry. Opt Lett 1993;18:1361–3. [11] Rao Yunjiang. Study on fiber-optic low-coherence interferometric and fiber Bragg grating. Sens Photonic Sens 2011;4:382–400. [12] Fang Xie, Li Min, Song Ding, Sun Jinling, Zhang Tao. Large range and high resolution on-line displacement measurement system by combing doubleinterferometries. Opt Express 2010;24:24961–8. [13] Hyun Sangwon, Choi Minah, Chun Byung Jae, Kim Seuugman, Kim SeuugWoo, Kim Yonng-Jin. Frequency-comb-referenced multi-wavelength profilometry for largely stepped surfaces. Opt Express 2013;21:9780–91. [14] Yuan Libo. Overview and forecast of fiber optic white-light interferometry. Acta Opt Sin 2011;9:09001371–13. [15] Yan Chengzhi, Li Shangyuan, Zheng Xiaoping. Time delay measurement of photonic crystal fiber by phase sensitive optical low-coherence reflectometry. J Optoelectron Laser 2010;12:1813–6.
Miss Yunzhi Wang is a candidate Ph.D. in Optical Science and Technology Laboratory, Department of Physics, School of Science, Beijing Jiaotong University, PR China. Yunzhi Wang was born in Anhui province, PR China in 1990. She received B.Sc. at the Beijing Jiaotong University, PR China in 2013.
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Prof. Fang Xie, received B.Sc. (Mechanical Engineering) at Chongqing University, PR China in 1987; received M. Sc. (Optics and Precision Instruments) at the Chongqing University, PR China in 1992; received Ph.D. (Optical Engineering) at the Tsinghua University, PR China in 2002. She worked as a visiting research fellow at the Aston University, UK in 2002–2003. She is now a professor in the physics department at the Beijing Jiaotong University, PR China. She has authored and co-authored more than sixty research papers published in journals and conferences. Her research interest is in the fields of optic fiber sensors, optical precision measurement and instruments.
Mr. Sen Ma is a candidate Ph.D. in Optical Science and Technology Laboratory, Department of Physics, School of Science, Beijing Jiaotong University, PR China. Sen Ma was born in Shandong province, PR China in 1988. He received B.Sc. at Qingdao University, PR China in 2009.
Mr. Liang Chen is a graduate student in Optical Science and Technology Laboratory, Department of Physics, School of Science, Beijing Jiaotong University, PR China. Liang Chen was born in Anhui province, PR China in 1988. He received B.Sc. at Beijing Jiaotong University, PR China in 2011.
Contents lists available at ScienceDirect
Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Remote and high precision step height measurement with an optical fiber multiplexing interferometric system Yunzhi Wang, Fang Xie n, Sen Ma, Liang Chen Optical Science and Technology Laboratory, Department of Physics, School of Science, Beijing Jiaotong University, Beijing 100044, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 14 March 2014 Received in revised form 1 August 2014 Accepted 10 August 2014
An optical fiber multiplexing low coherence and high coherence interferometric system, which includes a Fizeau interferometer as the sensing element and a Michelson interferometer as the demodulating element, is designed for remote and high precision step height measurement. The Fizeau interferometer is placed in the remote field for sensing the measurand, while the Michelson interferometer which works in both modes of low coherence interferometry and high coherence interferometry is employed for demodulating the measurand. The range of the step height is determined by the low coherence interferometry and the value of it is measured precisely by the high coherence interferometry. High precision has been obtained by searching precisely the peak of the low coherence interferogram symmetrically from two sides of the low coherence interferogram and stabilizing the Michelson interferometer with a feedback loop. The maximum step height that could be measured is 6 mm while the measurement resolution is less than 1 nm. The standard deviation of 10 times measurement results of a step height of 1 mm configurated with two gauge blocks is 0.5 nm. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Optical fiber sensing Low coherence interferometry High coherence interferometry Step height measurement
1. Introduction In order to control the quality of the products in the fields of microelectronics, micro-electric-mechanical system, flat panel displays, and photovoltaic cells, etc. there is a great requirement for the measurement of step heights ranging from several micrometers to larger than 1 mm. As optical fiber measurement systems have the advantages of non-contact, compactness, light weight, immunity to electromagnetic interference, high resolution, low cost and without the need of adjusting optical elements, there is a great interest of developing optical fiber measurement systems [1–15]. As the measurement range of an optical fiber low-coherence interferometric measurement system (OFLCIS) which is illuminated with a broadband light source is not limited by the wavelength, OFLCIS has become an important technique for the absolute measurement of static and quasistatic parameters, such as displacement, temperature, pressure, strain, refractive index, and step height. In order to obtain high measurement precision, it is very important for OFLCIS to identify precisely the peak position of the low coherence interferogram (PPI) obtained during the period the optical path difference (OPD) of the interferometer is tuned linearly. But the top area of the low coherence interferogram is flatten and thus it is very difficult to address precisely the PPI. Rao [3] used two light sources
n
Corresponding author. Tel.: þ 86 10 51688333; fax: þ 86 10 51840433. E-mail address: [email protected] (F. Xie).
http://dx.doi.org/10.1016/j.optlaseng.2014.08.008 0143-8166/& 2014 Elsevier Ltd. All rights reserved.
with two different wavelengths to make the peak prominent, which needs two light sources and the system is expensive and complicated. The proposed optical fiber multiplexing interferometric system, which includes a Fizeau interferometer and a Michelson interferometer is suitable for remote and absolute measurement of step height with high precision. The Fizeau interferometer which is inserted in the remote sensing field is used for sensing the measurand, while the Michelson interferometer which is stabilized by a feedback loop works in both modes of low coherence interferometry and high coherence interferometry. The range of the measured step height is determined by the low coherence interferometry, while the resolution of the measurement is decided by the high coherence interferometry. High precision of addressing the PPI has been obtained by symmetrical peak-searching method. The maximum step height that can be measured is 6 mm while the measurement resolution is less than 1 nm. The standard deviation of 10 times measurement results of a step with the height of 1 mm which is configurated with two gauge blocks is 0.5 nm. 2. Principle of the optical fiber multiplexing interferometric measurement system 2.1. Optical fiber measurement system The proposed optical fiber measurement system is shown in Fig. 1. It includes a Fizeau interferometer and a Michelson interferometer.
Y. Wang et al. / Optics and Lasers in Engineering 66 (2015) 52–57
Gauge block B Gauge block A Broadband light source
1
ASE
FBG1
Isolator 1
M1
GRIN lens
3dB-coupler Mirror
Isolator 2
M2
2 GRIN lens
Signal generator PZT
Circulator Electronic feedback loop
FBG2 PD1
PD2 Electronic processor
A/D converter
Output
Fig. 1. The scheme of the principle of the measurement system.
A broadband light source of amplified spontaneous emission (ASE) with flatten spectrum of C-band is used in the system. The ASE gives an output power of about 200 mW with a spectral bandwidth 35.8 nm. The FBG1 and FBG2 are used as in-fiber reflective mirrors and have the same Bragg wavelength at 1557 nm with 3 dB bandwidth 0.2 nm. Light emitted from the light source ASE passes through the isolator 1, 3 dB-coupler 1 and reaches FBG1. The light of the wavelength 1557.00 nm is reflected by FBG1 while the light of the left wavelength passes FBG1 and reaches the GRIN lens. As the end face of the GRIN lens is not coated with any film, part power of the light is reflected because of the Fresnel reflection. The left power of light passes the GRIN lens and is collimated at the same time and then is incident perpendicularly on the surface of the gauge block mounted on an one-dimension translation stage (M1) and then is reflected into the system again by the surface of the gauge block. The end face of the GRIN lens and the surface of the gauge block configure the two reflective planes of a Fizeau interferometer. The light reflected by the two planes of the Fizeau interferometer passes FBG1 and is split into two beams by the 3 dB-coupler 1. The beam from one port of the 3 dB-coupler 1 cannot reach the light source because of isolator 1. The beam from the other port of the 3 dB-coupler 1 passes isolator 2 and reaches 3 dB-coupler 2 and then is split into two beams. The two beams reach two GRIN lenses and are collimated respectively. As the end faces of the two GRIN lenses are coated with highly transmissive film, there is no light reflected by the end faces of these two GRIN lenses. The collimated two beams are reflected back into the system again by two mirrors that are mounted respectively on an onedimension translation stage (M2) and a piezoelectric stretcher (PZT). The reflected beams are combined at the 3 dB-coupler 2 again. The combined light from one port of the 3 dB-coupler 2 cannot reach 3 dBcoupler 1 because of isolator 2, while the combined light from the other port of 3 dB-coupler 2 is guided by the circulator and passes FBG2 and is detected by a photo detector (PD1). The signal detected by PD1 can be expressed by Eq. (1) [9]. h i 1 I ¼ I 0 1 þ exp ð2ΔX=Lc Þ2 cos ðkΔXÞ ð1Þ 2 where I 0 is the total optical power arriving at PD1, ΔX ¼ ðX 1 X 2 Þ, X 1 ; X 2 are the OPDs of the Fizeau interferometer and the Michelson interferometer respectively, Lc is the coherence length of the ASE light
53
source, and k is the wave number. It can be known that any change in ΔX will induce change in both the fringe visibility and the phase of the signal. The signal will be the maximum when ΔX ¼ X 1 X 2 ¼ 0 and the PPI appears. The OPD of the Fizeau interferometer will vary proportionally with the variation of the measurand and the PPI will also shift correspondently. The key issue of OFLCIS is how to measure the shifting range of the PPI precisely. A Michelson interferometer which works in both modes of low-coherence interferometry and high-coherence interferometry is exploited as the demodulating interferometer to measure the shifting range of the PPI. The shifting range is determined by the low-coherence interferometry and the value of it is measured by the high-coherence interferometry. In order to reduce the influences resulted from the environmental disturbances, the length of the fiber in the two interfering arms of the Michelson interferometer is made to be as short as about 11 mm, just as shown in Fig. 2. Moreover, an electronic feedback loop is designed to compensate for the influences to the Michelson interferometer which is resulted from the environmental disturbances so as to stabilize the Michelson interferometer. The reflected light from FBG1 passes 3 dB-coupler 1 and isolator 2 and 3 dB-coupler 2 and then is split into two beams. The two beams are collimated by two GRIN lenses and are reflected respectively by two mirrors which are mounted respectively on the translation stage (M2) and the PZT. The two reflected beams are combined at 3 dB-coupler 2 and interfere with each other. The interferometric signal from one port of the 3 dB-coupler 2 cannot reach 3 dB-coupler 1 because of isolator 2. And the interferometric signal from the other port of 3 dB-coupler 2 is guided by the circulator and reaches FBG2 and is reflected by FBG2 and is guided by the circulator again and then is detected by a photo detector (PD2). The signals from PD1 and PD2 are processed by the electronic processor simultaneously while the signal from PD2 is also input into the electronic feedback loop to produce a correction signal which is applied on the PZT and drives the PZT to adjust the OPD of the Michelson interferometer in order to keep it in quadrature state (the phase between two interfering arms is π=2). The signal detected by PD1 will be the maximum when the OPDs of the Fizeau interferometer and the Michelson interferometer are equal, just as shown in Eq. (1). As the signal detected by PD2 is a high coherence interferometric signal with the Bragg wavelength of FBG, it will vary periodically with the cosine function law while translation stage M2 tunes linearly the OPD of the Michelson interferometer. The number of the interferometric fringes during the shifting range of the PPI of the low interferogram is proportional to the height of the step. The PPI is searched symmetrically from two sides of the low coherence interferogram, and the value of the step height is measured by the amount of fringes of the signal detected by PD2 during the shifting range of PPI. The measured step height can be calculated by the relationship shown in Eq. (2). Δh ¼
1557 n 2
ð2Þ
GRIN lens
3dB-coupler
Fig. 2. The optical fiber Michelson interferometer with short interfering arms.
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Y. Wang et al. / Optics and Lasers in Engineering 66 (2015) 52–57
Fig. 3. The scheme of the electronic feedback loop.
2.2. Compensating electronic feedback loop Besides being used for performing the measurement task, the high coherence interferometric signal detected by PD2 is also used to erase the influences to the Michelson interferometer that is resulted from the environmental disturbances. The schematic diagram of the circuit of electronic feedback loop is shown in Fig. 3. PD2 is connected to the current-to-voltage converter U1 which has low input impedances. The output voltage from U1 will have the form shown in Eq. (3) u1 ¼ u0 ½1 þ k cos ðϕd þ ϕs Þ
ð4Þ
where K is the conversion gain of the interferometric signal from U2. After passing through the electronic integrator U3, the output from U3 is the value shown in Eq. (5) u3 ¼ K 1 cos ðϕd þ ϕs Þ
After the feedback loop is turned on The signal detected by PD1
The signal detected by PD2
Time (*10ms) Fig. 4. The signals detected by PD1 and PD2 before and after the feedback loop is turned on.
ð3Þ
where u0 is related to the input optical power and the gain of U1, k is the interferometric fringe visibility, ϕd is the static differential phase between the two interfering arms, and ϕs is the differential phase induced by environmental disturbances. After passing through the electronic differentiator U2, the direct voltage part in u1 will be erased, and the output from U2 will be shown as Eq. (4) u2 ¼ K sin ðϕd þ ϕs Þ
Before the feedback loop is turned on Signal detected by PD1and PD2
where Δh is the measured step, n is the amount of fringes of the signal detected by PD2 during the shifting range of the PPI. The key issue is how to determine precisely the value of n.
ð5Þ
where K 1 is the conversion gain of U3. The function of the electronic differentiator U2 and the electronic integrator U3 is to erase the direct voltage part in u1 . The alternating parts shown in Eqs. (3) and (5) have the same function and are in phase with each other. The output of the electronic integrator U3 is put into another electronic integrator U4 after which the signal is applied on the PZT to drive it tuning the OPD of the Michelson interferometer to keep the Michelson interferometer in quadrature state. When the interferometer is in quadrature position, there will be ϕd þ ϕs ¼ ðπ=2Þ, it obtains that the signal applied on the PZT will be u4 ¼ 0, and in the vicinity of the quadrature position, the signal applied on the PZT will be u4 a 0 which drives PZT to tune the optical path of the reference arm and draw the interferometer back to the quadrature position again. By this means, the Michelson interferometer is always kept at the quadrature state and is stabilized. The feedback loop is a first order system with a frequency bandwidth ranging from 0 to 21.65 Hz which is verified by the experiments sufficient to erase the environmental disturbances.
3. Experiments and experimental results 3.1. Experiments on validation of the electronic feedback loop With the two mirrors mounted respectively on the translation stage M2 and PZT in static state and the electronic feedback loop out of operation, the signals detected by PD1 and PD2 are shown during the first part of the recorded time in Fig. 4. In the present case, as the difference between the OPDs of the Fizeau interferometer and Michelson interferometer is larger than the coherent length of the light source, the signal detected by PD1 which is a low coherence interferometric signal is simply the intensity of the sum of the two combined beams. So this signal is a constant value during the recorded time, while the signal detected by PD2 which is a high coherence interferometric signal is fluctuating at all the time even though the two reflective mirrors of the Michelson interferometer are not moving. The variation in the high coherence interferometric signal is induced by various types of environmental disturbances. However, as soon as the feedback loop is turned on, the high coherence interferometric signal detected by PD2 is stabilized at a constant value, just as shown during the second part of the recorded time in Fig. 4. The feedback loop had been turned on continuously for several hours (more than 4 h) during the experiments, it was shown that the interferometric signal detected by PD2 had been always stabilized. This indicates that the influences to the Michelson interferometer that is resulted from environmental disturbances have been erased effectively.
Y. Wang et al. / Optics and Lasers in Engineering 66 (2015) 52–57
Gauge block A
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Gauge block B
Point a
Point b
Fig. 5. The measured step height configurated with two gauge blocks.
8
Interferometric signal
The signal detected by PD1
6
4 The signal detected by PD2
Δ1 2 0
30
15
45
60
×10
5
Interferometric signal (V)
Point 1
8
The converted data serial number
7 6 5 4 3 0 9
4.5
13.5
22.5
18
×103
The converted data serial number 8 The signal detected by PD1
6
4 The signal detected by PD2
Δ2 2
0 15
30
45
60
×10
5
The converted data serial number
Fig. 6. The detected low coherence inteferometric signal and high coherence interferometric signal while tuning linearly the OPD of the Michelson interferometer, (a) With the measurement beam incident perpendicularly on point a, (b) With the measurement beam incident perpendicularly on point b.
Interferometric signal (V)
Interferometric signal
Point 1
Fig. 7. The zoom of the top area of low coherence interferogram.
7
The left side chosen fringe
6 5 4
Point 1 0
9
18
27
36
The converted data serial number Fig. 8. The fringes with the amplitude of about half of the maximum amplitude.
3.2. Experiments on the measurement of a step height 3.2.1. Measurement procedure A gauge block with the height of 1 mm (gauge block B) is contacted to another gauge block (gauge block A) to configurate a step with the height of 1 mm, just as shown in Fig. 5. Firstly, with the measurement beam incident perpendicularly on point a that is on the surface of gauge block A, the translation stage M2 tunes linearly the OPD of the Michelson interferometer during which PD1 and PD2 detect the corresponding signals that are shown in Fig. 6(a). The variation of OPD (Δ1 ) of the Michelson interferometer from the beginning of tuning to the PPI can be calculated by Eq. (2) where n is the number of the fringes of the high coherence interferometric signal between the beginning of tuning the OPD and the PPI, and n can be obtained by counting the fringes of the high coherence interferometric signal with software program. Secondly, the one-dimension translation stage M1 moves the gauge blocks horizontally until the measurement beam is incident perpendicularly on point b that is on the surface of gauge block B. Again, the translation stage M2 tunes linearly the OPD of the Michelson interferometer during which PD1 and PD2 detect the
corresponding signals that are shown in Fig. 6(b). The variation of OPD (Δ2 ) of the Michelson interferometer from the beginning of tuning to the PPI can be also calculated by Eq. (2) where n is the number of the fringes of the high coherence interferometric signal between the beginning of tuning the OPD and the PPI, and n can be obtained by counting the fringes of the high coherence interferometric signal with software program. The height of the step can be calculated with Eq. (6) Δh ¼ jΔ2 Δ1 j
ð6Þ
3.2.2. Addressing precisely the peak of the low coherence interferogram In order to obtain high measurement precision, it is very important to count precisely the number of the fringes of the high coherence interferometric signal between the beginning of tuning the OPD of the Michelson interferometer and the PPI. As the top area of the low coherence interferogram is flatten and there are usually several fringes with the same amplitude in the top area, it is very difficult to address the PPI precisely, just as
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Y. Wang et al. / Optics and Lasers in Engineering 66 (2015) 52–57
Measurement serial number
1
2
3
4
5
Measurement results(nm)
99999.4
1000000.5
99999.7
99999.6
1000000.6
Measurement serial number
6
7
8
9
10
Measurement results(nm)
1000000.3
1000000.7
99999.5
1000000.4
99999.6
deviation (nm)
0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 1
2
3
4
5
6
7
8
9
10
measurement serial number Fig. 9. The measurement results and each deviation of the step height.
shown in Fig. 7. Fig. 7 is the zoom of top area of the low coherence interferogram that is shown in Fig. 6. When the OPD of the Michelson interferometer is tuned linearly, the detected low coherence interferogram is symmetrical about the peak point, which can be seen from the low coherence interferogram in Fig. 6. But in the vicinity of half of the maximum amplitude, it can be seen that the amplitude of the fringes varies apparently. During these varying amplitude fringes, we chose one fringe of which the amplitude does significantly not equal to its adjacent fringes, just as shown in Fig. 8. As the low coherence interferogram is symmetrical about its peak, it is able to choose another fringe with the same amplitude on the other side of the interferogram. As the two chosen fringes are symmetrical about the peak of the low coherence interferogram, if tracking from the two chosen fringes to the center where the position of the peak is, the peak could be identified precisely. The beginning tracking point on one of the fringes is chosen to be the point that with the average value and is on the side of the fringe nearer to the center of the interferogram (point 1, shown in Fig. 8). The other beginning tracking point on the other side is chosen with the same method. The peak of the interferogram is the center between these two points. The peak could be determined only by finding out the center between these two chosen points. This procedure could be done by a software program in a computer. As the signals detected by PD1 and PD2 are simultaneously processed by the electronic processor and converted to be digital data by an A/D converter, the amount of fringes of the high coherence interferometric signal between the beginning of tunning and PPI could be counted easily by the software program. As the high coherence interferometric signal is obtained by the reflection of the FBG, the measurement range which equals the coherence length of the reflective spectrum of FBG is 6 mm. The frequency of the detected signals from PD1 and PD2 is about 45 Hz which is higher than the cutoff frequency of the feedback loop, so the compensating action of the feedback loop will not influence the signals. As the converting speed of the A/D converter is 100 KS/s, there are 2222 data in one period of the high coherence interferometric signal. The corresponding resolution of the measurement is less than 1 nm. The
measurement of the step height configurated with the two gauge blocks have been performed 10 times repeatedly. Each measurement result and deviation is shown in Fig. 9(a) and (b), and the standard deviation of the 10 times measurement is 0.5 nm.
4. Conclusion An optical fiber multipexing low coherence and high coherence interferometric system that includes a Fizeau interferometer as the sensing element and a Michelson interferometer as the demodulating element has been designed for remote and high precision step height measurement. The range of the step height is determined by the low coherence interferometry while the value of it is measured precisely by the high coherence interferometry. High precision has been obtained by the methods of peak-searching symmetrically and stabilizing the Michelson interferometer with a feedback loop. The maximum step height that can be measured is 6 mm while the measurement resolution is less than 1 nm. The standard deviation of 10 times measurement results of a step with the height of 1 mm configurated with two gauge blocks is 0.5 nm.
Acknowledgments The authors thank greatly the National Natural Science Foundation of China (50975022) and the Beijing Natural Science Foundation (3132033) for supporting this research. References [1] Farahi F, Newson TP, Jones JDC, Jackson DA. Coherence multiplexing of remote fibre Fabry–Perot sensing system. Opt Commun 1998;65:319–21. [2] Rao Yun-Jiang, Jackson David A. Recent progress in fibre opticlow-coherent interferometry. Meas Sci Technol 1996;7:981–99. [3] Rao YJ, Ning YN, Jackson DA. Synthesized source for white-light sensing systems. Opt Lett 1993;18:462–4. [4] Zhang XM, Liu Yuxiang, Bae H, Pang C, Yu M. Phase modulation with micromachined resonant mirrors for low-coherence fiber-tip pressure sensors. Opt Express 2009;26:23965–74.
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[5] Lazo M, Manojlovic A. Novel common path interferometric technique for vibration measurement based on two-fiber-optic couplers. IEEE Sens J 2011;7:1541–7. [6] Jiang Mingzheng, Gerhard Edmund. A simple strain sensor using a thin film as a low-finesse fiber-optic Fabry–Perot interferometer. Sens Actuators A 2001;88:41–6. [7] Nguyen Linh Viet, Hwang Dusun, Moon Sucbei, Moon Dae Seung, Chung Youngjoo. High temperature fiber sensor with high sensitivity based on core diameter mismatch. Opt Express 2008;16:11369–75. [8] Wang Wenhui, Wu Nan, Tian Ye, Niezrecki Christopher, Wang Xingwei. Miniature all-silica optical fiber pressure sensor with an ultrathin uniform diaphragm. Opt Express 2010;18:9006–14. [9] Lazo M, Manojlovic A. Novel common path interferometric technique for vibration measurement based on two-fiber-optic couplers. IEEE Sens J 2011;7:1541–7. [10] Hand DP, Carolan TA, Barton JS, Jones JDC. Profile measurement of optically rough surfaces by fiber-optic interferometry. Opt Lett 1993;18:1361–3. [11] Rao Yunjiang. Study on fiber-optic low-coherence interferometric and fiber Bragg grating. Sens Photonic Sens 2011;4:382–400. [12] Fang Xie, Li Min, Song Ding, Sun Jinling, Zhang Tao. Large range and high resolution on-line displacement measurement system by combing doubleinterferometries. Opt Express 2010;24:24961–8. [13] Hyun Sangwon, Choi Minah, Chun Byung Jae, Kim Seuugman, Kim SeuugWoo, Kim Yonng-Jin. Frequency-comb-referenced multi-wavelength profilometry for largely stepped surfaces. Opt Express 2013;21:9780–91. [14] Yuan Libo. Overview and forecast of fiber optic white-light interferometry. Acta Opt Sin 2011;9:09001371–13. [15] Yan Chengzhi, Li Shangyuan, Zheng Xiaoping. Time delay measurement of photonic crystal fiber by phase sensitive optical low-coherence reflectometry. J Optoelectron Laser 2010;12:1813–6.
Miss Yunzhi Wang is a candidate Ph.D. in Optical Science and Technology Laboratory, Department of Physics, School of Science, Beijing Jiaotong University, PR China. Yunzhi Wang was born in Anhui province, PR China in 1990. She received B.Sc. at the Beijing Jiaotong University, PR China in 2013.
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Prof. Fang Xie, received B.Sc. (Mechanical Engineering) at Chongqing University, PR China in 1987; received M. Sc. (Optics and Precision Instruments) at the Chongqing University, PR China in 1992; received Ph.D. (Optical Engineering) at the Tsinghua University, PR China in 2002. She worked as a visiting research fellow at the Aston University, UK in 2002–2003. She is now a professor in the physics department at the Beijing Jiaotong University, PR China. She has authored and co-authored more than sixty research papers published in journals and conferences. Her research interest is in the fields of optic fiber sensors, optical precision measurement and instruments.
Mr. Sen Ma is a candidate Ph.D. in Optical Science and Technology Laboratory, Department of Physics, School of Science, Beijing Jiaotong University, PR China. Sen Ma was born in Shandong province, PR China in 1988. He received B.Sc. at Qingdao University, PR China in 2009.
Mr. Liang Chen is a graduate student in Optical Science and Technology Laboratory, Department of Physics, School of Science, Beijing Jiaotong University, PR China. Liang Chen was born in Anhui province, PR China in 1988. He received B.Sc. at Beijing Jiaotong University, PR China in 2011.