Chapter 4 FPGA Verification
4.3 Optical System and Function Generator Testing
The optical system setup is shown on the left side of Figure 4.8, the laser light
passes through a non-polarizing beam splitter and splits to two lights. The bended
light passes through the double passes plane mirror interferometer, which increase an
extra resolution in λ/4. The receiver which picks up the interference light outputs the
measurement signal.
The reference signal output from the laser head is shown on the right side of the
Figure 4.8. The picture shows the situation of the reference light when light mask of
the laser head is closed and open. The laser source and the reference signal here suffer
the influence by some indeterminable reasons. One of the suggestions may be the
reflection light of the receiver lens re-incident onto the laser head and cause the
Figure 4.8 The optical setup and the troubles in heterodyne laser source.
influence, but the situation needs to be clarified. Sometimes the laser source can work
properly which is not affected by the reflection light. Under this circumstance, the
Doppler frequency is taken by the digital interface. The measured Doppler frequency
is shown on Figure 4.9 when the stage is stopped. Figure 4.9 also shows that the
average of Doppler frequency in this experiment is not 0 exactly. The scope also
shows that the frequency comes from reference and measurement signal has a
difference about 1 kHz.
Then the piezo stage below the target mirror is fed on a sine wave with 25 Hz and
10v peak-to-peak signal. The Doppler frequency data is shown on Figure 4.10, it is
not sure the velocity information can be acquired by this implicit data directly. The
following experiment uses the function generator to pretend the reference and
0 0.5 1 1.5 2 2.5 3 3.5
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Time (s)
Doppler Frequency (MHz)
Measured Doppler Frequency when target is stopped.
Figure 4.9 The measured Doppler frequency when the target is stopped.
measurement signal to verify this interface deeply.
As shown in Figure 4.11, two function generators generate the signals as the pseudo
measurement and reference signal. The higher one is Model FG-513 13 MHz
Sweep/Function Generator manufactured by American Reliance Inc. This generator
provides the square wave in 4 MHz as the reference for the FPGA board. The lower is
33220A 20 MHz Function/Arbitrary Waveform Generator manufactured by Agilent
Technology. This one provides the square wave varies from 3.8 MHz to 4.0 MHz with
the sweep frequency and 11 different frequencies level testing. The Figure 4.12 shows
the frequency data captured by the digital interface. The available frequency range is
± 0.8 MHz, which is equivalent to ± 0.5 m/s target speed without the fold factor. The
0 0.5 1 1.5 2 2.5 3 3.5
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
0.5 The Doppler Frequency when the piezo target moves in 10v p-p sine input voltage
Time (s)
Doppler Frequency (MHz)
Figure 4.10 The Doppler frequency result in a moving stage
interface reacts generally like the setting in the function generator with a little
variance. The simulation in previous section is assume as the square wave, but the
signal is not perfect signal in MHz frequency, due to the discussion in section 3.5 , the
calculated results is not affected by the signal variance if the variance or the timing
jitter of the reference of measurement signal is under (reference period/512).
The level testing is shown in Figure 4.13 and Figure 4.14, the different frequencies
pretend as the Doppler frequency from the moving target mirror are applied on the
digital interface, the results shows the interface capture the frequency indeed but with
a big variance. The RMSE is shown in and reveals the resolution here is about 9 nm,
the reason that the resolution can’t achieve the sub-nanometer scale may come from:
(1) The glitches from the integral counter can’t be canceled clearly through this
method.
Figure 4.11 The diagram of the function generator testing.
(2) The clock transmission line is not protected well and causes the noise to affect the
frequency detection.
Although the testing results are not as expected, this digital interface can also
provide λ/64 resolution under this testing.
Doppler Frequency varies from 0.8 MHz to -0.8 MHz sweep in 1 sec.
Doppler Frequency varies from 0.8 MHz to -0.8 MHz sweep in 100 msec.
Doppler Frequency varies from 0.8 MHz to -0.8 MHz sweep in 10 msec.
Doppler Frequency varies from 0.8 MHz to -0.8 MHz sweep in 5 msec.
Figure 4.12 The captured Doppler frequency in the function generator sweep mode.
Backward velocity 0.253 m/s, Doppler frequency 0.8 MHz Backward velocity 0.202 m/s, Doppler frequency 0.64 MHz
Backward velocity 0.152 m/s, Doppler frequency 0.48 MHz Backward velocity 0.101 m/s, Doppler frequency 0.32 MHz
0 0.5 1 1.5 2 2.5 3 3.5
Backward velocity 0.051 m/s, Doppler frequency 0.16 MHz Target Mirror stops, Doppler frequency around 0 Hz
0 0.5 1 1.5 2 2.5 3 3.5
Forward velocity 0.051 m/s, Doppler frequency -0.16 MHz Forward velocity 0.101 m/s, Doppler frequency -0.32 MHz
0 0.5 1 1.5 2 2.5 3 3.5
Figure 4.13 The function generator testing from -0.32 MHz to 0.8 MHz
Forward velocity 0.152 m/s, Doppler frequency -0.48 MHz Forward velocity 0.202 m/s, Doppler frequency -0.64 MHz
Forward velocity 0.253 m/s, Doppler frequency -0.8 MHz
0 0.5 1 1.5 2 2.5 3 3.5
Figure 4.14The function generator testing from -0.8 MHz to -0.48 MHz
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Figure 4.15 The function generator testing RMSE in 11 different Doppler frequencies.
Chapter 5 Conclusion and Future work
In this research, a digital interface designed for heterodyne interferometers is
developed. This design implementation passes gate-level simulation and on-chip
testing. It provides a good displacement resolution with sufficient measurement
velocity. An innovative octonary phase interpolator for Agilent laser interferometer is
proposed. In function generator testing, the octonary phase interpolator doesn’t react
as expectation, but the interface also performs the resolution in λ/64 due to the 64
times faster clock speed than the reference signal.
The optical trouble affects the signal purity and makes it hard to detect the stage
motion; this trouble may be caused by the reflected light of the receivers lens and
induces the resonation in laser source. However, this trouble needs more verification
in future works and applied to this interface.
References
[1] Physik Instrumente (PI), GmbH & Co., ”Tutorial: Piezoelectrics in
Nanopositioning, Designing with Piezoelectric Actuators”, 2008.
[2] W. R. Steel, “Interferometry, 2nd ed.”, (Cambridge studies in modern optics),
Cambridge University Press, 1985.
[3] Eugene Hecht , “Optics ,4th edition” , Pearson Education, 2002.
[4] Wu, Wen-Jong; Lee, Chih-Kung; Hsieh, Chi-Tang, “Signal Processing
Algorithms for Doppler Effect Based Nanometer Positioning Systems”, Japanese
Journal of Applied Physics, Volume 38, Issue 3B, pp. 1725, 1999.
[5] Bernhard Günther Zagar, “Laser Interferometer Displacement Sensors ”,(The
Measurement, Instrumentation and Sensors Handbook Section 6.5 ),CRC Press,
2000.
[6] K. Oka, M. Tsukada, and Y. Ohtsuka, “Real-time phase demodulator for
optical heterodyne detection processes”, Meas. Sci. Technol., 2, 106-110, 1991.
[7] J. Waller, X. H. Shi, N. C. Altoveros, J. Howard, B. D. Blackwell, and G. B.
Warr, “Digital interface for quadrature demodulation of interferometer signals”,
Rev. Sci. Instrum., 66, 1171-1174, 1995.
[8] J. A. Smith and C. P. Burger, “Digital phase demodulation in heterodyne
sensors”, Opt. Eng., 34,2793-2801, 1995.
[9] A. E. Siegman, “Lasers”, Mill Valley, CA: University Science Books, 1986.
[10] W. R. C. Rowley, “The performance of a longitudinal Zeeman-stabilized He–Ne
laser (633 nm) with thermal modulation and control”, Meas. Sci. Technol., 1,
348-351, 1990.
[11] Mark Chapman, “Heterodyne and homodyne interferometry”, Renishaw
Corporation, 2006.
[12] Zygo Corporation, ”A Primer on Displacement Measuring Interferometers”,
Zygo Corporation, 1999.
[13] Agilent Technologies, “Chapter 14, Principles of Operation, Laser and Optics
User’s Manual”, 2002.
[14] Min-Seok Kim and Seung-Woo Kim,” Two-way frequency-conversion phase
measurement for high-speed and high-resolution heterodyne interferometry”,
Meas. Sci. Technol. Vol. 15 (2004) 2341–2348, 2004.
[15] Frank C Demarest, “High-resolution, high-speed, low data age uncertainty,
Heterodyne displacement measuring interferometer”, Meas. Sci. Technol. Vol. 9
(1998) 1024-1030, 1998.
[16] Zygo Corporation, “ZMI 1000 PC Software for Windows 3.11 Application
Manual OMP-0395”, 1997.
[17] H.P. Lio and M.S. Young ,”New digital phase meter concept and its application”
Rev. Sci. Instrum., Vol.68, No.4, American Institute of Physics, 1997.
[18] V.I. Teleshevskii and S.G. Grishin, “A HETERODYNE LASER
INTERFEROMETER WITH DIGITAL PHASE CONVERSION”, Measurement
Techniques, Vol. 49, No. 6, 2006.
[19] Altera Corporation, “Quartus II version 7.2 Handbook, Volume 3: Verification,