- Email: [email protected]
Real-time surface profile measurement using a feedback type of sinusoidal phase modulating interferometer
ARTICLE IN PRESS
Optik
Optics
Optik 120 (2009) 553–557 www.elsevier.de/ijleo
Real-time surface profile measurement using a feedback type of sinusoidal phase modulating interferometer He Guotiana,b,c,, Liao Changrongb, Jiang helund, Yuangang Lue, Huang Shanglianb a
Optical Engineering Key Laboratory, College of Physics and Information Technology, Chongqing Normal University, Chongqing 400047, China b Chongqing University, Chongqing 400030, China c Shanghai Institute of Optics and Fine Mechanics, The Chinese Academy of Sciences, Shanghai 201800, China d Chongqing Technology and Business University, Chongqing 400067, China e Institute of Optical Communication Engineering, School of Engineering and Management, Nanjing University, Nanjing 210093, China Received 6 July 2007; accepted 12 December 2007
Abstract In this paper, we propose a sinusoidal phase modulating (SPM) interferometer that is insensitive to external disturbances, and its measuring principle is analyzed theoretically. In the SPM interferometer, the interference signal is detected by a high-speed image sensor based on a low-speed CCD and a signal processing circuit is used to obtain the phase of each point on the surface. Therefore, the surface profile can be measured real-time. The experiments measuring the surface profile of a wedge-shaped optical flat show that the measurement time of the SPM interferometer is less than 10 ms, the repetitive measurement accuracy is 4.2 nm. The results show that the impacts of nonlinear distortion of the piezoelectric transducer (PZT) and part external disturbance are removed. r 2008 Published by Elsevier GmbH. Keywords: Feedback control; Real-time measurement; Surface profile; SPM interferometer
1. Introduction The measurement of surface profile is important in many applications. The surface profile measurement technique becomes a research hotspot in the field of measurement [1–6]. There exist two methods in the surface profile measurement. One is contact measurement, the other is non-contact. But there exist some problems in the contact measurement, such as low accuracy, damage to surface easily, etc. The non-contact Corresponding author at: Chongqing University, Chongqing 400030, China. Tel.: +86 2169918576; fax: +86 2365103126. E-mail address: [email protected] (H. Guotian).
0030-4026/$ - see front matter r 2008 Published by Elsevier GmbH. doi:10.1016/j.ijleo.2007.12.014
measurement includes the capacitance method, the optical interference method, the scanning electronic microscope method, etc. [7–9]. In these methods, the optical interference method is intensively researched for the merit of high accuracy, high sensitivity [10,11], and it has been widely used in the industry. The optical interferometry for the surface profile measurement is high accuracy, non-contact, and has a wide application in industry and scientific research. The high-accuracy surface profile interferometry measurements include the heterodyne interferometric method, the phase-shifting interferometric method, and sinusoidally phase modulating (SPM) interferometry. The heterodyne interferometry needs to shift the optical
ARTICLE IN PRESS 554
H. Guotian et al. / Optik 120 (2009) 553–557
frequency accurately, which is very difficult. The phaseshifting interferometry has some faults, such as inaccurate phase-shifting, strong noise, low resistance to environmental disturbance, complex structure, etc. While for the characteristics of the SPM interferometry are simple phase-shifting, high accuracy, excellent resistance to disturbance, etc., it becomes an important surface profile measurement technique [12–16]. However, presently the SPM interferometry also has some faults, such as bad performance in real-time, complex circuit, etc. [17]. In this paper, we propose a new method to realize the real-time surface profile measurement using the SPM interferometer, and analyze the measuring principle theoretically. In this SPM interferometer, a high-speed image sensor based on a low-speed CCD is used to detect interference signal, and a designed circuit is used to process the phase-demodulation of the interference signal to get the phase distribution of each point on the surface. According to the phase distribution, the surface profile can be obtained. And we utilize this SPM interferometer to measure the surface profile of a wedge-shaped optical flat. The experimental results confirm the validity of this SPM interferometer.
speed CCD (including the special drive circuit and noiseremoval circuit of CCD). After phase-demodulated realtime by a signal processing circuit to the CCD output video signal, the phase distribution of the measured surface can be obtained. Therefore, we can obtain the surface profile. The processing circuit is shown in Fig. 2, which mainly consists of a real-time phase-demodulation processing circuit, and a time sequential circuit. The real-time phase-demodulation processing circuit is made up of a calculator, a filter, and an amplifier. Under the control of the time sequential circuit, the video signal is phase demodulated by the real-time phase-demodulation processing circuit, and the phase distribution can be obtained. According to the phase distribution of the surface, we can obtain the surface profile. The modulated voltage signal V(t) acting on the PZT is given by V ðtÞ ¼ A cosðoc t þ yÞ,
(1)
where A is the amplitude and oc the angular frequency. The interference signal accepted by CCD can be given by [18] sðx; y; tÞ ¼ s1 ðx; yÞ þ s0 ðx; yÞ cos½zðx; yÞ cos oc t þ a0 ðx; yÞ þ ar ðx; y; tÞ,
2. Principle of the real-time surface profile measurement Fig. 1 shows an SPM He–Ne laser interferometer, which consists of the optical and electrical systems. The reference wave is phase modulated with a sinusoidally vibrating mirror attached to a piezoelectric transducer (PZT). After collimated by lens L1 and split by beam splitter BS, a He–Ne laser is split into two interference beams. One beam is reflected by a mirror and served as the reference beam, the other is reflected by an object and served as the object beam. The two beams interfere to form the interference signal. And this signal is imaged onto a CCD image sensor. The interference signal is detected by a high-speed image sensor based on a low(t)
PZT
Acos(ωct+θ)
Mirror
(2)
where s1 is the dc component of the interference signal, s0 the amplitude of ac component, z ¼ 4pA/l, l the wavelength of the He–Ne laser, x and y coordinates of the measured surface. a0 is the phase change of the interference signal when the mirror is still and it is determined by the optical path difference between the two interference arms 2D0. It can be given by a0 ¼ ð4p=lÞD0 . ar(x, y, t) is the phase change of the interference signal arising from the measured surface profile. Expanding Eq. (2) and neglecting the dc component, we have [18] sðx; y; tÞ ¼ s0 fcos aðx; y; tÞ½J 0 ðzÞ 2J 2 ðzÞ cosð2oc t þ 2yÞ þ sin aðx; y; tÞ ½2J 1 ðzÞ cosðoc t þ yÞ 2J 3 ðzÞ cosð3oc t þ 3yÞ þ g,
(3)
Acos(ωct+θ) V(t)
Object BS
Acosωct
CCD image sensor
Amplifier2
Amplifier1
Feedback control
He-Ne
system L1 VPD(t)
PD Lens
Calculation
Signal processing
and
and A/D convertor CCD image sensor
Filter Computer
Fig. 1. A SPM He–Ne laser interferometer for real-time surface profile measurement.
Time sequence control
Fig. 2. The signal processing circuit.
P (x,y)
ARTICLE IN PRESS H. Guotian et al. / Optik 120 (2009) 553–557
where aðx; y; tÞ ¼ a0 þ ar ðx; y; tÞ, and Jn(z) is the nthorder Bessel function. The signal s(x, y, t) and modulation voltage signal A cos(oct+y) are amplified by amplifiers 1 and 2, respectively. The distortion sinusoidal phase-modulated signal VPD(t) is attained through filtering the PD-detected interference signal. The difference between the sinusoidal phase-modulated signal V(t) and VPD(t) is the feedback signal XV(t) DV ¼ V ðtÞ V PD ðtÞ.
(4)
The nonlinear distortion of the PZT and part external disturbance can be removed by adding the feedback signal DV(t) to the sinusoidal phase-modulated signal. The two amplified signals are phase demodulated and filtered, and we obtain the signal P(x, y) Pðx; yÞ ¼ K 1 K 2 K m K L s0 AJ 1 ðzÞ sin aðx; yÞ,
(5)
555
3. Experiments of the 3-D surface profile The experimental setup is shown in Fig. 1. The interferometer signal is detected with the home-made high-speed image sensor based on low-speed CCD. The frame rate is 800 frame/s and the resolution is 30 30 pixel. The light source is a He–Ne laser with the wavelength 632.8 nm and output power 10 mW. The measured object is a wedge-shaped optical flat, which can cancel the disturbance of the back reflection light. The light path difference 2D0 between the two interference arms is 6 cm. The gain K1 of amplifier 1 is 60.2, the gain K2 of amplifier 2 is 88.6, and the coefficient of multiplier Km is 5 105/mV. In this experiment, we choose a 4-level low-pass, low-energy filter with the cutoff frequency 100 Hz and the gain KL ¼ 100. The modulated voltage signal frequency acting on PZT is 398 Hz, and the modulation voltage is 500 mV. The sinusoidal phase modulation depth is 2.58. The measured ac component s0 is 1.452 mW. The system conversion coefficient K ¼ 2.351 103 mV/rad.
where K1 and K2 are the gains of the amplifier, corresponding to amplifiers 1 and 2, respectively. Km is the coefficient of calculation circuit, and KL is the gain of the filter. According to the above equation, and near the position ar ðx; yÞ ¼ 2np p=2ðn ¼ 0; 1; 2; . . .Þ, we can obtain aðx; yÞ Pðx; yÞ=K,
(6)
where the system conversion coefficient K ¼ K 1 K 2 K m K L s0 AJ 1 ðzÞ. Neglecting the dc component a0, we can obtain rðx; yÞ ¼ aðx; yÞl=ð4pÞ.
(7)
Near the position aðx; yÞ ¼ p=2, the signal P(x, y) is proportional to the surface profile r(x, y). According to Eq. (6), the span of the phase a(x, y) locates between p/2 and +p/2; therefore, the measured range of r(x, y) is l/4. Therefore, if we obtain the signal P(x, y), the surface profile can be obtained. According to the above description, the high-speed image sensor based on low-speed CCD can convert the interference signal into the original video signal by the special drive circuit. The noise of the original video signal can be eliminated, and we obtain the video signal. Under the control of the time sequential circuit, the realtime signal processing circuit will amplify, calculate, and filter the video signal. Therefore, we can obtain the signal P(x, y). According to Eq. (7), the surface profile can be obtained real-time, but we describe the method of feedback control of the injection voltage of the PZT to eliminate the phase fluctuations of the interference signal.
Fig. 3. (a) The measured surface profile of the wedge-shaped and (b) the measured surface profile after a time interval of a few minutes with (a).
ARTICLE IN PRESS 556
H. Guotian et al. / Optik 120 (2009) 553–557
repetitive measurement accuracy are 2.852 and 2.95 nm, respectively. The results show that we can measure the wedgeshaped optical flat surface profile, but some interferes still exist in the measurements.
4. Conclusions
Fig. 4. Surface profile of the wedge-shaped optical flat along the x-axis.
Fig. 5. Measured result after an interval of a few minutes.
According to the detective signal P(x, y), the displacement curve can be measured real-time. In order to enhance the measurement accuracy, we acquisite 8 maps sequentially, and calculate the mean value of each point. The measured surface profile is shown in Fig. 3(a) and (b), while the time interval is a few minutes between the two maps. x and y are the position axis in units of 5 mm, while z-axis is the roughness in the units of nanometer. The repetitive measurement accuracy of Fig. 3(a) is 4.2 nm. The related coefficient of Fig. 3(a) and (b) is 0.9826, and the maximum difference value is 3.6 nm. The read-out time of a pixel is 0.125 mm, and the retardation time of the circuits is less than 200 ns. The time for phase demodulation and calculation is less than 8 ms. Therefore the measurement time is less than 10 ms. In order to analyze the measurement accuracy clearly, we can select a row or column from Fig. 3(a) randomly to analyze the accuracy. Figs. 4 and 5 show the maps of the first row in the direction of the x-axis of Fig. 3(a) and (b), respectively. The repetitive measurement accuracy of Fig. 4 is 3.2 nm, while that of Fig. 5 is 2.93 nm. In the same way, we select the first column in the direction of the y-axis of Fig. 3(a) and (b), and their
Improvement of the measurement accuracy in optical interferometry is essential if it is to be used in the measurement of an optical surface profile. In the text, a sinusoidal phase modulating (SPM) interferometer to realize real-time surface profile measurement is proposed, and its measurement principle is analyzed theoretically. The interference signal is detected by a high-speed image sensor based on a low-speed CCD and a signal processing circuit is used to obtain the phase of each point on the surface. The impacts of nonlinear distortion of the PZT and part external disturbance are removed. Therefore, the surface profile can be measured real-time. The experiments measuring the surface profile of a wedge-shaped optical flat show that the measurement time of the SPM interferometer is less than 10 ms, the repetitive measurement accuracy is 4.2 nm. The experimental results confirm the validity of the SPM interferometer, and the merits of the interferometer are the simple structure and high measurement accuracy.
Acknowledgments The authors are grateful to the National Natural Science Foundation of China under Grant no. 60607007,60674097, and the National 863 Plans Projects under Grant no. 2006AA03Z104 for supporting this work. The authors also wish to thank the reviewers for their helpful comments and suggestions.
References [1] O. Sasaki, H. Okazaki, Sinusoidal phase modulating interferometry for surface profile measurement, Appl. Opt. 25 (1986) 3137–3140. [2] C.J. Tay, C. Quan, Y. Fu, et al., Surface profile measurement of low-frequency vibrating objects using temporal analysis of fringe pattern, Opt. Laser Technol. 36 (2004) 471–476. [3] S. Takamasa, S. Osami, et al., Real time two dimensional surface profile measurement in a sinusoidal phase modulating laser diode interferometer, Opt. Eng. 38 (1994) 754–758. [4] R. Shinozaki, O. Sasaki, T. Suzuki, Fast scanning method for one-dimensional surface profile measurement by detecting angular of a laser beam, Appl. Opt. 43 (2004) 4157–4163.
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[5] S. Yin, J. Li, M. Song, Surface profile measurement using a unique microtube-based system, Opt. Commun. 168 (1999) 1–6. [6] S. Lu, Y. Gao, T. Xie, et al., A novel contact/non-contact hybrid measurement system for surface topography characterization, Int. J. Mach. Tools Manuf. 41 (2001) 2001–2009. [7] J.M. Bennett, J. Jahanmir, J.C. Podelesny, et al., Scanning force microscope as a tool for studying optical surface, Appl. Opt. 34 (1995) 213–230. [8] G. Binning, C.F. Quate, C. Gerber, Atomic force microscopy, Phys. Rev. Lett. 56 (1986) 930–933. [9] G. Binning, H. Rohrer, C. Gerber, et al., Surface studies by scanning tunneling microscope, Phys. Rev. Lett. 49 (1982) 57–61. [10] G.F. Jin, J.Z. Li, Laser Surveying, Science Publishing House, Beijing, 1998, pp. 5–300. [11] G. Yang, The Modern Optical Measurement Technology, Hangzhou Zhe Jiang University Press, 1997, pp. 9–118. [12] Z. Luan, L. Liu, D. Liu, S. Teng, Double shearing wavefront testing, Acta Opt. Sinica 24 (2004) 1417–1420.
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[13] O. Sasaki, T. Okamura, T. Nakamura, Sinusoidal phase modulating Fizeau interferometer, Appl. Opt. 29 (1990) 514–515. [14] S. Takamasa, S. Osami, T. Shuich, M. Takeo, Real time displacement measurement using synchronous detection a sinusoidal phase modulating interferometer, Opt. Eng. 32 (1993) 1033–1037. [15] D. Li, X.Z. Wang, Y.M. Liu, Fiver optic interferometer for real-time wide-range distance measurements with ANN, Acta Photon. Sinica 34 (2005) 865–868. [16] X.F. Wang, X.Z. Wang, D.Y. Yu, et al., Photothermal modulation laser diode interferometer insensitive to external disturbances, Acta Opt. Sinica 21 (2001) 1368–11371. [17] S. Takamasa, S. Osami, et al., Real time two dimensional surface profile measurement in a sinusoidal phase modulating laser diode interferometer, Opt. Eng. 38 (1994) 754–758. [18] S. Takamasa, S. Osami, M. Takeo, Phase locked laser diode interferometry for surface profile measurement, Appl. Opt. 28 (1989) 4407–4410.
Optik
Optics
Optik 120 (2009) 553–557 www.elsevier.de/ijleo
Real-time surface profile measurement using a feedback type of sinusoidal phase modulating interferometer He Guotiana,b,c,, Liao Changrongb, Jiang helund, Yuangang Lue, Huang Shanglianb a
Optical Engineering Key Laboratory, College of Physics and Information Technology, Chongqing Normal University, Chongqing 400047, China b Chongqing University, Chongqing 400030, China c Shanghai Institute of Optics and Fine Mechanics, The Chinese Academy of Sciences, Shanghai 201800, China d Chongqing Technology and Business University, Chongqing 400067, China e Institute of Optical Communication Engineering, School of Engineering and Management, Nanjing University, Nanjing 210093, China Received 6 July 2007; accepted 12 December 2007
Abstract In this paper, we propose a sinusoidal phase modulating (SPM) interferometer that is insensitive to external disturbances, and its measuring principle is analyzed theoretically. In the SPM interferometer, the interference signal is detected by a high-speed image sensor based on a low-speed CCD and a signal processing circuit is used to obtain the phase of each point on the surface. Therefore, the surface profile can be measured real-time. The experiments measuring the surface profile of a wedge-shaped optical flat show that the measurement time of the SPM interferometer is less than 10 ms, the repetitive measurement accuracy is 4.2 nm. The results show that the impacts of nonlinear distortion of the piezoelectric transducer (PZT) and part external disturbance are removed. r 2008 Published by Elsevier GmbH. Keywords: Feedback control; Real-time measurement; Surface profile; SPM interferometer
1. Introduction The measurement of surface profile is important in many applications. The surface profile measurement technique becomes a research hotspot in the field of measurement [1–6]. There exist two methods in the surface profile measurement. One is contact measurement, the other is non-contact. But there exist some problems in the contact measurement, such as low accuracy, damage to surface easily, etc. The non-contact Corresponding author at: Chongqing University, Chongqing 400030, China. Tel.: +86 2169918576; fax: +86 2365103126. E-mail address: [email protected] (H. Guotian).
0030-4026/$ - see front matter r 2008 Published by Elsevier GmbH. doi:10.1016/j.ijleo.2007.12.014
measurement includes the capacitance method, the optical interference method, the scanning electronic microscope method, etc. [7–9]. In these methods, the optical interference method is intensively researched for the merit of high accuracy, high sensitivity [10,11], and it has been widely used in the industry. The optical interferometry for the surface profile measurement is high accuracy, non-contact, and has a wide application in industry and scientific research. The high-accuracy surface profile interferometry measurements include the heterodyne interferometric method, the phase-shifting interferometric method, and sinusoidally phase modulating (SPM) interferometry. The heterodyne interferometry needs to shift the optical
ARTICLE IN PRESS 554
H. Guotian et al. / Optik 120 (2009) 553–557
frequency accurately, which is very difficult. The phaseshifting interferometry has some faults, such as inaccurate phase-shifting, strong noise, low resistance to environmental disturbance, complex structure, etc. While for the characteristics of the SPM interferometry are simple phase-shifting, high accuracy, excellent resistance to disturbance, etc., it becomes an important surface profile measurement technique [12–16]. However, presently the SPM interferometry also has some faults, such as bad performance in real-time, complex circuit, etc. [17]. In this paper, we propose a new method to realize the real-time surface profile measurement using the SPM interferometer, and analyze the measuring principle theoretically. In this SPM interferometer, a high-speed image sensor based on a low-speed CCD is used to detect interference signal, and a designed circuit is used to process the phase-demodulation of the interference signal to get the phase distribution of each point on the surface. According to the phase distribution, the surface profile can be obtained. And we utilize this SPM interferometer to measure the surface profile of a wedge-shaped optical flat. The experimental results confirm the validity of this SPM interferometer.
speed CCD (including the special drive circuit and noiseremoval circuit of CCD). After phase-demodulated realtime by a signal processing circuit to the CCD output video signal, the phase distribution of the measured surface can be obtained. Therefore, we can obtain the surface profile. The processing circuit is shown in Fig. 2, which mainly consists of a real-time phase-demodulation processing circuit, and a time sequential circuit. The real-time phase-demodulation processing circuit is made up of a calculator, a filter, and an amplifier. Under the control of the time sequential circuit, the video signal is phase demodulated by the real-time phase-demodulation processing circuit, and the phase distribution can be obtained. According to the phase distribution of the surface, we can obtain the surface profile. The modulated voltage signal V(t) acting on the PZT is given by V ðtÞ ¼ A cosðoc t þ yÞ,
(1)
where A is the amplitude and oc the angular frequency. The interference signal accepted by CCD can be given by [18] sðx; y; tÞ ¼ s1 ðx; yÞ þ s0 ðx; yÞ cos½zðx; yÞ cos oc t þ a0 ðx; yÞ þ ar ðx; y; tÞ,
2. Principle of the real-time surface profile measurement Fig. 1 shows an SPM He–Ne laser interferometer, which consists of the optical and electrical systems. The reference wave is phase modulated with a sinusoidally vibrating mirror attached to a piezoelectric transducer (PZT). After collimated by lens L1 and split by beam splitter BS, a He–Ne laser is split into two interference beams. One beam is reflected by a mirror and served as the reference beam, the other is reflected by an object and served as the object beam. The two beams interfere to form the interference signal. And this signal is imaged onto a CCD image sensor. The interference signal is detected by a high-speed image sensor based on a low(t)
PZT
Acos(ωct+θ)
Mirror
(2)
where s1 is the dc component of the interference signal, s0 the amplitude of ac component, z ¼ 4pA/l, l the wavelength of the He–Ne laser, x and y coordinates of the measured surface. a0 is the phase change of the interference signal when the mirror is still and it is determined by the optical path difference between the two interference arms 2D0. It can be given by a0 ¼ ð4p=lÞD0 . ar(x, y, t) is the phase change of the interference signal arising from the measured surface profile. Expanding Eq. (2) and neglecting the dc component, we have [18] sðx; y; tÞ ¼ s0 fcos aðx; y; tÞ½J 0 ðzÞ 2J 2 ðzÞ cosð2oc t þ 2yÞ þ sin aðx; y; tÞ ½2J 1 ðzÞ cosðoc t þ yÞ 2J 3 ðzÞ cosð3oc t þ 3yÞ þ g,
(3)
Acos(ωct+θ) V(t)
Object BS
Acosωct
CCD image sensor
Amplifier2
Amplifier1
Feedback control
He-Ne
system L1 VPD(t)
PD Lens
Calculation
Signal processing
and
and A/D convertor CCD image sensor
Filter Computer
Fig. 1. A SPM He–Ne laser interferometer for real-time surface profile measurement.
Time sequence control
Fig. 2. The signal processing circuit.
P (x,y)
ARTICLE IN PRESS H. Guotian et al. / Optik 120 (2009) 553–557
where aðx; y; tÞ ¼ a0 þ ar ðx; y; tÞ, and Jn(z) is the nthorder Bessel function. The signal s(x, y, t) and modulation voltage signal A cos(oct+y) are amplified by amplifiers 1 and 2, respectively. The distortion sinusoidal phase-modulated signal VPD(t) is attained through filtering the PD-detected interference signal. The difference between the sinusoidal phase-modulated signal V(t) and VPD(t) is the feedback signal XV(t) DV ¼ V ðtÞ V PD ðtÞ.
(4)
The nonlinear distortion of the PZT and part external disturbance can be removed by adding the feedback signal DV(t) to the sinusoidal phase-modulated signal. The two amplified signals are phase demodulated and filtered, and we obtain the signal P(x, y) Pðx; yÞ ¼ K 1 K 2 K m K L s0 AJ 1 ðzÞ sin aðx; yÞ,
(5)
555
3. Experiments of the 3-D surface profile The experimental setup is shown in Fig. 1. The interferometer signal is detected with the home-made high-speed image sensor based on low-speed CCD. The frame rate is 800 frame/s and the resolution is 30 30 pixel. The light source is a He–Ne laser with the wavelength 632.8 nm and output power 10 mW. The measured object is a wedge-shaped optical flat, which can cancel the disturbance of the back reflection light. The light path difference 2D0 between the two interference arms is 6 cm. The gain K1 of amplifier 1 is 60.2, the gain K2 of amplifier 2 is 88.6, and the coefficient of multiplier Km is 5 105/mV. In this experiment, we choose a 4-level low-pass, low-energy filter with the cutoff frequency 100 Hz and the gain KL ¼ 100. The modulated voltage signal frequency acting on PZT is 398 Hz, and the modulation voltage is 500 mV. The sinusoidal phase modulation depth is 2.58. The measured ac component s0 is 1.452 mW. The system conversion coefficient K ¼ 2.351 103 mV/rad.
where K1 and K2 are the gains of the amplifier, corresponding to amplifiers 1 and 2, respectively. Km is the coefficient of calculation circuit, and KL is the gain of the filter. According to the above equation, and near the position ar ðx; yÞ ¼ 2np p=2ðn ¼ 0; 1; 2; . . .Þ, we can obtain aðx; yÞ Pðx; yÞ=K,
(6)
where the system conversion coefficient K ¼ K 1 K 2 K m K L s0 AJ 1 ðzÞ. Neglecting the dc component a0, we can obtain rðx; yÞ ¼ aðx; yÞl=ð4pÞ.
(7)
Near the position aðx; yÞ ¼ p=2, the signal P(x, y) is proportional to the surface profile r(x, y). According to Eq. (6), the span of the phase a(x, y) locates between p/2 and +p/2; therefore, the measured range of r(x, y) is l/4. Therefore, if we obtain the signal P(x, y), the surface profile can be obtained. According to the above description, the high-speed image sensor based on low-speed CCD can convert the interference signal into the original video signal by the special drive circuit. The noise of the original video signal can be eliminated, and we obtain the video signal. Under the control of the time sequential circuit, the realtime signal processing circuit will amplify, calculate, and filter the video signal. Therefore, we can obtain the signal P(x, y). According to Eq. (7), the surface profile can be obtained real-time, but we describe the method of feedback control of the injection voltage of the PZT to eliminate the phase fluctuations of the interference signal.
Fig. 3. (a) The measured surface profile of the wedge-shaped and (b) the measured surface profile after a time interval of a few minutes with (a).
ARTICLE IN PRESS 556
H. Guotian et al. / Optik 120 (2009) 553–557
repetitive measurement accuracy are 2.852 and 2.95 nm, respectively. The results show that we can measure the wedgeshaped optical flat surface profile, but some interferes still exist in the measurements.
4. Conclusions
Fig. 4. Surface profile of the wedge-shaped optical flat along the x-axis.
Fig. 5. Measured result after an interval of a few minutes.
According to the detective signal P(x, y), the displacement curve can be measured real-time. In order to enhance the measurement accuracy, we acquisite 8 maps sequentially, and calculate the mean value of each point. The measured surface profile is shown in Fig. 3(a) and (b), while the time interval is a few minutes between the two maps. x and y are the position axis in units of 5 mm, while z-axis is the roughness in the units of nanometer. The repetitive measurement accuracy of Fig. 3(a) is 4.2 nm. The related coefficient of Fig. 3(a) and (b) is 0.9826, and the maximum difference value is 3.6 nm. The read-out time of a pixel is 0.125 mm, and the retardation time of the circuits is less than 200 ns. The time for phase demodulation and calculation is less than 8 ms. Therefore the measurement time is less than 10 ms. In order to analyze the measurement accuracy clearly, we can select a row or column from Fig. 3(a) randomly to analyze the accuracy. Figs. 4 and 5 show the maps of the first row in the direction of the x-axis of Fig. 3(a) and (b), respectively. The repetitive measurement accuracy of Fig. 4 is 3.2 nm, while that of Fig. 5 is 2.93 nm. In the same way, we select the first column in the direction of the y-axis of Fig. 3(a) and (b), and their
Improvement of the measurement accuracy in optical interferometry is essential if it is to be used in the measurement of an optical surface profile. In the text, a sinusoidal phase modulating (SPM) interferometer to realize real-time surface profile measurement is proposed, and its measurement principle is analyzed theoretically. The interference signal is detected by a high-speed image sensor based on a low-speed CCD and a signal processing circuit is used to obtain the phase of each point on the surface. The impacts of nonlinear distortion of the PZT and part external disturbance are removed. Therefore, the surface profile can be measured real-time. The experiments measuring the surface profile of a wedge-shaped optical flat show that the measurement time of the SPM interferometer is less than 10 ms, the repetitive measurement accuracy is 4.2 nm. The experimental results confirm the validity of the SPM interferometer, and the merits of the interferometer are the simple structure and high measurement accuracy.
Acknowledgments The authors are grateful to the National Natural Science Foundation of China under Grant no. 60607007,60674097, and the National 863 Plans Projects under Grant no. 2006AA03Z104 for supporting this work. The authors also wish to thank the reviewers for their helpful comments and suggestions.
References [1] O. Sasaki, H. Okazaki, Sinusoidal phase modulating interferometry for surface profile measurement, Appl. Opt. 25 (1986) 3137–3140. [2] C.J. Tay, C. Quan, Y. Fu, et al., Surface profile measurement of low-frequency vibrating objects using temporal analysis of fringe pattern, Opt. Laser Technol. 36 (2004) 471–476. [3] S. Takamasa, S. Osami, et al., Real time two dimensional surface profile measurement in a sinusoidal phase modulating laser diode interferometer, Opt. Eng. 38 (1994) 754–758. [4] R. Shinozaki, O. Sasaki, T. Suzuki, Fast scanning method for one-dimensional surface profile measurement by detecting angular of a laser beam, Appl. Opt. 43 (2004) 4157–4163.
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