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Fiber optic heterodyne displacement detection in wide dynamic range
Volume 65, number 2
OPTICS C O M M U N I C A T I O N S
15 January 1988
FIBER OPTIC H E T E R O D Y N E D I S P L A C E M E N T DETECTION IN WIDE DYNAMIC RANGE Yoshiro SUEMOTO and Yasuyuki TAKEISHI Applied Science Course, Faculty of Engineering, Kagoshima University, 1-21-40Korimoto, Kagoshima, 890, Japan Received 25 August 1987
The dynamic range of displacement measurements was experimentally estimated for the case of laser heterodyne technique with fiber optics. Even using flexible fiber optics, a wide dynamic range of 105 order, i.e. from 100 lam to 10/k displacement, was obtained.
Heterodyne ~ tnterferometer
I. Introduction The non-contact optical profiler has been investigated using the laser heterodyne technique [ 1-3 ]. In this case, the laser scans the surface of the object. Therefore, the principle is the same as displacement detection over the surface or a vibration measurement. In all cases, a minute surface structure is of concern. For fairly rough surface measurements, the dynamic range of the displacement amplitude becomes important. The upper limit of the displacement amplitude has been shown to be limited by the bandwidth of the heterodyne signal amplifier [4]. But this was the case without using fiber optics. In recent years, fiber optics have made optical instruments flexible and versatile. This is also the case for instruments using the heterodyne technique [5]. In this paper, the attainable dynamic range is reported in the case of using flexible fiber optics in the system. The experimentally and theoretically verified results give a fundamental importance for the fabrication of a surface profiler.
2. Experimental procedure The principle of surface profile measurements is shown in fig. 1. The laser probe focused on the surface by a microscope objective fixed on a moving stage is flexibly connected with a heterodyne interferometer by an optical fiber. As the stage moves at
~MS
Optical -~Fiber
MS L a s e ~ .-~ M o v i n g D i r e c t i on Beam ~lSurface Profilef(x)
Focused
Fig. 1. Principle of surface profile measurement using fiber optic heterodyne detection. The end of an optical fiber and the microscope objective (MO) are fixed to the moving stage (MS).
a constant speed, the surface profile in the x direction f ( x ) is converted to a time function f(t). In order to avoid the influence of other factors such as the focused laser probe size, the stage scanning, and to measure only the dynamic range of the system, the profile measurement may as well be converted to the measurement of the displacement f(t), i.e. the vibration measurement. The experimental arrangement for the vibration measurement is shown in fig. 2. A 5 mW He-Ne laser beam was collimated by the lenses LI, L2 and frequency shifted by an acoustic diffraction cell driven by 10 MHz radio frequency. The + 1st order diffracted beam was launched into a graded-index optical fiber of 50 lam core diameter and about 1 meter long by a microscope objective MO~, and the diverging beam from the other end of the fiber was focused also by another microscope objective MO2 on a reflecting fleck adhered on the cone of a speaker. The light reflected by the fleck was transmitted backwards through the same optical fiber and collimated
0 030-4018/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
67
Volume 65, number 2
OPTICS COMMUNICATIONS
15 JanumT 1988
Diffraction I0©
+lsf -Ist Order
2
Order
E o
Photo
B S ~ Reference
Defector
I0
o
Mirror
"6 I
MO~
E
\
D
,, \\
MO~opti ~ c[i Fiber
OI
Fig. 2. Experimental arrangement for dynamic range measurement of fiber optic heterodyne vibration detection. L,, L~: lenses, BS: beam splitter, MO~, MO2: microscope objectives.
onto the photodetector through the beam splitter. The - 1st order diffracted light was used as a reference beam for the heterodyning. Therefore, the beat frequency became 20 MHz. The heterodyne signal I [4] is given by
I=I, sin[2K[,t+ (4~z/2)f(t)],
(1)
where f, is the carrier frequency (f, = 20 MHz), 2 the wavelength, f(t) the displacement of the fleck. The signal was amplified by an amplifier and demodulated by a demodulator to represent f(t) on an oscilloscope. The calibration for the absolute amplitude of the displacement was made by feeding a known phase modulated signal into the demodulator and making a calibration curve plotting the demodulator output versus amplitude. The calibration curve was linear and independent of the displacement speed or vibration frequency. The validity of the calibration was ascertained by a homodyne method [6].
3. R e s u l t s a n d d i s c u s s i o n
As f(t) can be represented by a Fourier integral, i.e. by each frequency component, the upper limit of 68
I0
i
I
iI
l
I
O0
I
I
KI
l
1000 F F equency (Hz)
i
i
II
[
{0000
I
Fig. 3. Upper limit of vibration amplitude as a function of frequency. BW: bandwidth, - O - experimental values, - . . . . calculated values.
the vibration amplitude was measured using sinusoidal vibrations at some arbitrary frequencies. The upper limit was defined as the point where the loss oflinearity of the amplitude versus the speaker driving current occurred. Above this limit, the wave form on the oscilloscope suffered from distortion. The results obtained using amplifier bandwidths of 81 kHz and 7 kHz are shown in fig. 3. Only the data point at the frequency of 16.5 kHz was obtained by using a BaTiO3 vibrator (resonant frequency 16.5 kHz) instead of the speaker in fig. 2. As the result curve is linear and inclined 45 ° in a log-log plot, the upper limit is inversely proportional to the frequency and dependent on the amplifier bandwidth and an amplitude upto about 100 gm can be measured. From a theoretical point of view [7], the necessary bandwidth A f o f an amplifier is approximately given by Af = (4~z/2)Af
(2)
where A and f a r e the vibration amplitude and the vibration frequency, respectively. From eq. (2), the upper limit of vibration amplitude MaxA becomes Max A = (2/4n) Af/f.
(3)
Max A is proportional to Af and inversely propor-
Volume 65, number 2
OPTICS COMMUNICATIONS
tional to f a n d plotted by dotted lines in fig. 3. The experimental results coincide with the calculated values fairly well. The calculated value is somewhat lower in amplitude due to the approximation of eq. (2). For a large vibration amplitude, the heterodyne signal was strongly amplitude modulated due to the use of the fiber optic system including microscope objectives. This influence seems to have been well avoided by an amplitude limiter in front of the demodulator. As for the lower limit, a distinguishable amplitude was limited by the noise in the electronics and was about 10 A at a frequency of 16.5 kHz. This limit was also ascertained by the measurement of the deflection of a vibrating mirror [6]. For a comparison between the cases with and without the fiber optics, an experiment without the optical fiber was also made, removing the microscope objective MO~ and the optical fiber and setting the microscope objective MO2 and the speaker on a straight line of the + 1st order beam direction in fig. 2, and the same results as shown in fig. 3 were obtained. This shows that no difference exists between the cases with and without the fiber optics. The effect of movement of the fiber was observed during the measurement as an amplitude fluctuation of the heterodyne signal and was avoided by the amplitude limiter. As far as a surface profiler for small objects is concerned, i.e. a short moving range, the effect would be negligible. However, in the case of larger bending, torsion and vibration of the optical fiber, it would be necessary to examine the possibility of a phase fluctuation of the heterodyne signal, by constructing the moving stage and measuring an object having known surface profile, e.g. a sinusoidal grating.
4. Conclusion The upper limit of the vibration amplitude in the heterodyne technique using fiber optics was meas-
15 January 1988
ured and coincided well with the theoretical prediction. The maximum amplitude attained was up to about 100 ~tm. The distinguishable small amplitude was limited by the noise in the electronics and was about 10/k. Therefore, the dynamic range was of order 105 . The dependence of the amplitude upper limit on frequency concerns the frequency components off(t) converted from the surface profile fix). The spatial frequency components in fix) usually decrease monotonically with frequency, but this is not so for all the cases. Therefore, it is concluded that the fabrication of a non-contact surface profiler has to adapt to the surfaces to be measured, the speed of the moving stage and the amplifier bandwidth, together with the mechanism and the accuracy of the moving stage, focusing the laser probe.
Acknowledgement The authors acknowledge useful discussions with Professor S. Fujita of Osaka Industrial University and the support of Messrs, K. Obara, H. Idoji and T. Yoshimoto in the experiments.
References [ 1] G.E. Sommargren, Appl. Optics 24 (1985) 1553. [2] C.W. See, M. Vaez Iravani and H.K. Wickramasinghe, Appl. Optics 24 (1985) 2373. [3] H.K. Wickramasinghe, Opt. Eng, 24 (1985) 926. [4] F.J. Eberhardt and F.A, Andrew, J. Acoust. Soc. Am. 48 (1970) 603. [5] S. Ueha, N. Shibata and J. Tsujiuchi, Optics Comm. 23 (t977) 407. [6] Y. Suemoto, Rev. Laser Eng. 12 (1984) 636 (in Japanese). [7] K. Sam Shanmugam, Digital and analogue communiication systems (John Wiley, New York, 1979).
69
OPTICS C O M M U N I C A T I O N S
15 January 1988
FIBER OPTIC H E T E R O D Y N E D I S P L A C E M E N T DETECTION IN WIDE DYNAMIC RANGE Yoshiro SUEMOTO and Yasuyuki TAKEISHI Applied Science Course, Faculty of Engineering, Kagoshima University, 1-21-40Korimoto, Kagoshima, 890, Japan Received 25 August 1987
The dynamic range of displacement measurements was experimentally estimated for the case of laser heterodyne technique with fiber optics. Even using flexible fiber optics, a wide dynamic range of 105 order, i.e. from 100 lam to 10/k displacement, was obtained.
Heterodyne ~ tnterferometer
I. Introduction The non-contact optical profiler has been investigated using the laser heterodyne technique [ 1-3 ]. In this case, the laser scans the surface of the object. Therefore, the principle is the same as displacement detection over the surface or a vibration measurement. In all cases, a minute surface structure is of concern. For fairly rough surface measurements, the dynamic range of the displacement amplitude becomes important. The upper limit of the displacement amplitude has been shown to be limited by the bandwidth of the heterodyne signal amplifier [4]. But this was the case without using fiber optics. In recent years, fiber optics have made optical instruments flexible and versatile. This is also the case for instruments using the heterodyne technique [5]. In this paper, the attainable dynamic range is reported in the case of using flexible fiber optics in the system. The experimentally and theoretically verified results give a fundamental importance for the fabrication of a surface profiler.
2. Experimental procedure The principle of surface profile measurements is shown in fig. 1. The laser probe focused on the surface by a microscope objective fixed on a moving stage is flexibly connected with a heterodyne interferometer by an optical fiber. As the stage moves at
~MS
Optical -~Fiber
MS L a s e ~ .-~ M o v i n g D i r e c t i on Beam ~lSurface Profilef(x)
Focused
Fig. 1. Principle of surface profile measurement using fiber optic heterodyne detection. The end of an optical fiber and the microscope objective (MO) are fixed to the moving stage (MS).
a constant speed, the surface profile in the x direction f ( x ) is converted to a time function f(t). In order to avoid the influence of other factors such as the focused laser probe size, the stage scanning, and to measure only the dynamic range of the system, the profile measurement may as well be converted to the measurement of the displacement f(t), i.e. the vibration measurement. The experimental arrangement for the vibration measurement is shown in fig. 2. A 5 mW He-Ne laser beam was collimated by the lenses LI, L2 and frequency shifted by an acoustic diffraction cell driven by 10 MHz radio frequency. The + 1st order diffracted beam was launched into a graded-index optical fiber of 50 lam core diameter and about 1 meter long by a microscope objective MO~, and the diverging beam from the other end of the fiber was focused also by another microscope objective MO2 on a reflecting fleck adhered on the cone of a speaker. The light reflected by the fleck was transmitted backwards through the same optical fiber and collimated
0 030-4018/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
67
Volume 65, number 2
OPTICS COMMUNICATIONS
15 JanumT 1988
Diffraction I0©
+lsf -Ist Order
2
Order
E o
Photo
B S ~ Reference
Defector
I0
o
Mirror
"6 I
MO~
E
\
D
,, \\
MO~opti ~ c[i Fiber
OI
Fig. 2. Experimental arrangement for dynamic range measurement of fiber optic heterodyne vibration detection. L,, L~: lenses, BS: beam splitter, MO~, MO2: microscope objectives.
onto the photodetector through the beam splitter. The - 1st order diffracted light was used as a reference beam for the heterodyning. Therefore, the beat frequency became 20 MHz. The heterodyne signal I [4] is given by
I=I, sin[2K[,t+ (4~z/2)f(t)],
(1)
where f, is the carrier frequency (f, = 20 MHz), 2 the wavelength, f(t) the displacement of the fleck. The signal was amplified by an amplifier and demodulated by a demodulator to represent f(t) on an oscilloscope. The calibration for the absolute amplitude of the displacement was made by feeding a known phase modulated signal into the demodulator and making a calibration curve plotting the demodulator output versus amplitude. The calibration curve was linear and independent of the displacement speed or vibration frequency. The validity of the calibration was ascertained by a homodyne method [6].
3. R e s u l t s a n d d i s c u s s i o n
As f(t) can be represented by a Fourier integral, i.e. by each frequency component, the upper limit of 68
I0
i
I
iI
l
I
O0
I
I
KI
l
1000 F F equency (Hz)
i
i
II
[
{0000
I
Fig. 3. Upper limit of vibration amplitude as a function of frequency. BW: bandwidth, - O - experimental values, - . . . . calculated values.
the vibration amplitude was measured using sinusoidal vibrations at some arbitrary frequencies. The upper limit was defined as the point where the loss oflinearity of the amplitude versus the speaker driving current occurred. Above this limit, the wave form on the oscilloscope suffered from distortion. The results obtained using amplifier bandwidths of 81 kHz and 7 kHz are shown in fig. 3. Only the data point at the frequency of 16.5 kHz was obtained by using a BaTiO3 vibrator (resonant frequency 16.5 kHz) instead of the speaker in fig. 2. As the result curve is linear and inclined 45 ° in a log-log plot, the upper limit is inversely proportional to the frequency and dependent on the amplifier bandwidth and an amplitude upto about 100 gm can be measured. From a theoretical point of view [7], the necessary bandwidth A f o f an amplifier is approximately given by Af = (4~z/2)Af
(2)
where A and f a r e the vibration amplitude and the vibration frequency, respectively. From eq. (2), the upper limit of vibration amplitude MaxA becomes Max A = (2/4n) Af/f.
(3)
Max A is proportional to Af and inversely propor-
Volume 65, number 2
OPTICS COMMUNICATIONS
tional to f a n d plotted by dotted lines in fig. 3. The experimental results coincide with the calculated values fairly well. The calculated value is somewhat lower in amplitude due to the approximation of eq. (2). For a large vibration amplitude, the heterodyne signal was strongly amplitude modulated due to the use of the fiber optic system including microscope objectives. This influence seems to have been well avoided by an amplitude limiter in front of the demodulator. As for the lower limit, a distinguishable amplitude was limited by the noise in the electronics and was about 10 A at a frequency of 16.5 kHz. This limit was also ascertained by the measurement of the deflection of a vibrating mirror [6]. For a comparison between the cases with and without the fiber optics, an experiment without the optical fiber was also made, removing the microscope objective MO~ and the optical fiber and setting the microscope objective MO2 and the speaker on a straight line of the + 1st order beam direction in fig. 2, and the same results as shown in fig. 3 were obtained. This shows that no difference exists between the cases with and without the fiber optics. The effect of movement of the fiber was observed during the measurement as an amplitude fluctuation of the heterodyne signal and was avoided by the amplitude limiter. As far as a surface profiler for small objects is concerned, i.e. a short moving range, the effect would be negligible. However, in the case of larger bending, torsion and vibration of the optical fiber, it would be necessary to examine the possibility of a phase fluctuation of the heterodyne signal, by constructing the moving stage and measuring an object having known surface profile, e.g. a sinusoidal grating.
4. Conclusion The upper limit of the vibration amplitude in the heterodyne technique using fiber optics was meas-
15 January 1988
ured and coincided well with the theoretical prediction. The maximum amplitude attained was up to about 100 ~tm. The distinguishable small amplitude was limited by the noise in the electronics and was about 10/k. Therefore, the dynamic range was of order 105 . The dependence of the amplitude upper limit on frequency concerns the frequency components off(t) converted from the surface profile fix). The spatial frequency components in fix) usually decrease monotonically with frequency, but this is not so for all the cases. Therefore, it is concluded that the fabrication of a non-contact surface profiler has to adapt to the surfaces to be measured, the speed of the moving stage and the amplifier bandwidth, together with the mechanism and the accuracy of the moving stage, focusing the laser probe.
Acknowledgement The authors acknowledge useful discussions with Professor S. Fujita of Osaka Industrial University and the support of Messrs, K. Obara, H. Idoji and T. Yoshimoto in the experiments.
References [ 1] G.E. Sommargren, Appl. Optics 24 (1985) 1553. [2] C.W. See, M. Vaez Iravani and H.K. Wickramasinghe, Appl. Optics 24 (1985) 2373. [3] H.K. Wickramasinghe, Opt. Eng, 24 (1985) 926. [4] F.J. Eberhardt and F.A, Andrew, J. Acoust. Soc. Am. 48 (1970) 603. [5] S. Ueha, N. Shibata and J. Tsujiuchi, Optics Comm. 23 (t977) 407. [6] Y. Suemoto, Rev. Laser Eng. 12 (1984) 636 (in Japanese). [7] K. Sam Shanmugam, Digital and analogue communiication systems (John Wiley, New York, 1979).
69