Improvement and validity of shock measurements using heterodyne laser interferometer

Accepted Manuscript Improvement and validity of shock measurements using heterodyne laser interferometer H. Nozato, W. Kokuyama, A. Ota PII: DOI: Reference:

S0263-2241(15)00462-5 http://dx.doi.org/10.1016/j.measurement.2015.08.037 MEASUR 3551

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Measurement

Please cite this article as: H. Nozato, W. Kokuyama, A. Ota, Improvement and validity of shock measurements using heterodyne laser interferometer, Measurement (2015), doi: http://dx.doi.org/10.1016/j.measurement. 2015.08.037

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Improvement and validity of shock measurements using heterodyne laser interferometer

Improvement and validity of shock measurements using heterodyne laser interferometer H. Nozato1,2, W. Kokuyama1 and A. Ota1 1

National Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology,

Tsukuba, Ibaraki 305-8563, Japan 2

Corresponding Author: H. Nozato

E-mail: [email protected]

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Improvement and validity of shock measurements using heterodyne laser interferometer

Abstract The improvement and validity of shock measurements using only the laser head (heterodyne laser interferometer) of a commercial laser Doppler vibrometer was investigated by comparing acceleration waveforms measured by a homodyne laser interferometer with those measured by a heterodyne laser interferometer. The acceleration waveforms were generated from the displacement waveforms obtained with a reference quadrature homodyne laser interferometer by applying a numeric differentiation process twice. The differences between the two acceleration waveforms were found to be small with the measurement uncertainty in case of high acceleration level. In a further investigation, the accuracy of the shock measurements taken by the homodyne and heterodyne laser interferometers were compared in computational simulation. The results indicated that the accuracy of the heterodyne laser interferometer was superior to that of the homodyne laser interferometer.

Keywords: shock, acceleration measurement, homodyne laser interferometer, laser Doppler vibrometer, heterodyne laser interferometer

PACS Submitted to Measurement

1.

Introduction This paper reports an investigation of shock measurements performed using only the laser head of a Laser

Doppler Vibrometer (LDV). Recently, commercial LDVs with high sensitivity have appeared on the market and are being used to perform a variety of dynamic measurements. This is because, as a non-contact instrument, a LDV does not affect the object being measured. In general, LDVs have a compact laser head, a high frequency response, and a wide dynamic range for velocity measurement. These characteristics are also

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Improvement and validity of shock measurements using heterodyne laser interferometer

useful for measuring physical quantities such as displacement or acceleration. LDVs are heterodyne-type measurement instruments that comprise a compact laser head and a signal demodulator. The laser head has a heterodyne laser interferometer with a built-in acousto-optic modulator (AOM) to obtain a frequency offset in the optical domain. At the output of the photo detector, the same frequency as the carrier frequency of the heterodyne Doppler signal occurs. The signal demodulator outputs a voltage signal proportional to the velocity signal with a little time delay by calculating the Doppler signal. According to a previous research, three different commercial analogue signal demodulators showed a deviation of several percentages from nominal sensitivity each other, and the nominal sensitivity also included nonlinearity higher than 5 % in velocity range from 3 mm/s to 100 mm/s at 160 Hz. [1]. However, in some cases the laser head of a commercial LDV has various advantages as heterodyne laser interferometer over our homodyne laser interferometer. First, the heterodyne laser interferometer does not utilize reflective mirrors on the back-to-back transducer’s surface to obtain a sufficient intensity of interferometric signals; this is because the heterodyne laser interferometer equips optical lenses to efficiently collect scattered light in a larger area. However, our homodyne laser interferometer does not equip such optical lenses. Thus, the resonance frequency of the transducer does not shift in shock calibration. A second advantage, which relates specifically to compact laser heads, is the efficient and easy multi-point measurement. This allows various types of transducers to be calibrated. Based on these advantages, many users consider replacing homodyne laser interferometers with heterodyne laser interferometers of LDVs. Therefore, homodyne and heterodyne laser interferometers were compared with no time delay by recording both interferometric signals with digitizers and off-line processing. To confirm the reliability of shock measurements taken by the heterodyne laser interferometer, we evaluated the shock measurements with those taken by a homodyne laser interferometer. Both the homodyne and heterodyne laser interferometers’ measurements were taken in the shock calibration system [2] at National Metrology Institute of Japan (NMIJ), which was developed with a He–Ne homodyne quadrature laser interferometer in compliance with ISO 16063-13 [3].

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Improvement and validity of shock measurements using heterodyne laser interferometer

The shock waveforms typically have half-sine shapes with peak accelerations of 50 m/s2 to 10,000 m/s2 and durations of 0.5 ms to 5.0 ms. Previous studies have evaluated the use of heterodyne laser interferometers to demodulate a Doppler signal from their laser head. NMIJ [1] and PTB [4,5] compared an in-house developed homodyne with heterodyne laser interferometers, respectively. However, since the acceleration measurements were performed using a vibration exciter, the sinusoidal velocity was limited to below a few hundredths of a meter per second. The Doppler signal frequency shifts in response to the velocity of the object being measured. For velocities lower than a few hundredths of a meter per second, the frequency shift is about 1 MHz. The velocity generated in shock calibration with a peak acceleration of 10,000 m/s2 approaches 3 m/s, in which case the frequency shift of the Doppler signal could be up to 30 MHz. However, no report exist evaluating performance of heterodyne laser interferometer with large frequency shifts. Thus, it is significant to investigate the reliability of shock measurements taken using heterodyne laser interferometers in the velocity range up to 3 m/s. This study reports an investigation of such performances.

2. Methods and experimental configuration of homodyne and heterodyne laser interferometers Figures 1 shows a set-up photograph of the homodyne and heterodyne laser interferometers installed in the shock calibration system. Figure 2 stands for a schematic block diagram of the set-up photograph. The homodyne and heterodyne laser interferometers measure the motion of the generated shock at the same position by means of a beam splitter. The homodyne laser interferometer is a modified Michelson type. It detects a pair of quadrature signals that have a phase difference of 90 degrees. The quadrature signals respond to the change in displacement [6] and are twice transformed into acceleration through double numerical differentiation. The heterodyne laser interferometer is the laser head of a commercial LV-1800 manufactured by Ono Sokki Co., Ltd. It has high sensitivity with a carrier frequency of 80 MHz by an AOM. The Doppler signal includes the information in displacement change, which is finally converted to acceleration.

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Improvement and validity of shock measurements using heterodyne laser interferometer

The output signals of the two measuring devices were connected to a PXI system to record the quadrature and Doppler signals respectively, as shown in Table 1. The PXI system consisted of two PXI 5152 digitizers with 8 bit resolution and maximum sampling frequency of 1 GHz. The system digitized both the quadrature and Doppler signals synchronously, even if their sampling frequencies would differ. A rubidium frequency standard provided the reference frequency of 10 MHz to the PXI system to improve the sampling accuracy from 10-5 to 10-12. The phase-jitter of the PXI system is up to 1 ps RMS because of the specification sheet, and locked to the clock generator with rubidium frequency standard.

Figure 1 Homodyne laser interferometer and laser head (heterodyne laser interferometer) of LDV in shock calibration system.

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Improvement and validity of shock measurements using heterodyne laser interferometer

PXI 5152 Heterodyne laser interferometer

Homodyne laser interferometer PD1

Charge amplifier

PD2

Personal computer

Clock generator

WP Shock exciter PP

BS

BS Hammer

Anvil Laser

QP

PP

transducer RMM

RM

PD: photo detector, WP: Wollaston prism, BS: beam splitter, PP: polarizing plate, QP: quarter wave plate, RM: reference mirror, RMM: reflective mirror to be measured Figure 2 Block diagram of two measuring devices in shock calibration system.

Table 1 Specification of two measuring devices.

Two measuring devices Interferometer type

Homodyne laser interferometer

Heterodyne laser interferometer

Manufacturer

AIST

Ono sokki co., ltd.

Model

Self-made

LV-1800

Laser source

Stabilized He-Ne laser (632.8 nm)

Unstabilized He-Ne laser (632.8 nm)

Carrer frequency

-

80 MHz

Sampling frequency

50 MHz

500 MHz

Resolution

8 bits

8 bits

Input range

±1 V

±1 V

Figure 3 (a) presents typical quadrature (upper) and Doppler (bottom) signals of a shock with different sampling frequencies of 50 MHz and 500 MHz respectively. The quadrature signal can be expressed by the following equations

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Improvement and validity of shock measurements using heterodyne laser interferometer

 4   4  V1 (t )  V1 cos  L  s(t ) and V2 (t )  V2 sin  L  s(t ) ,      

(1)

where t denotes the time, V1 and V2 are the voltage amplitude of the quadrature signal,  is the He–Ne laser wavelength (632.8 nm), L is a constant that depends on the optical path difference between the measuring path and the reference path from the beam splitter (BS), and s(t) is the displacement from the initial position of the transducer. The quadrature signals are finally demodulated to the displacement [1] after correction [7], because V1 and V2 are not equal because of optical attenuation or differences in gain of the photo detectors. Moreover, the dc component of each quadrature signals should be compensated. The Doppler signal VDoppler is described by the following equation

4 s(t )   VDoppler (t )  V cos  t  ,   

(2)

where  is the carrier frequency (80 MHz). The quadrature signal exhibited no remarkable change in amplitude, whereas the Doppler signal showed a notable change in amplitude. However, since the heterodyne laser interferometer outputs the change of the carrier frequency in response to the displacement, the change in amplitude on the Doppler signal is expected to give little effect on the displacement measurement. Because the time width during the change in amplitude was approximately 0.5 ms from 3 ms, and the change in amplitude was considerably slow when compared with a period of the carrier frequency. [See figure 3 (b).] Figures 4 and 5 show the block diagram of the signal processing performed to calculate the acceleration from the quadrature and Doppler signals. Both calculation processes shown were used to obtain acceleration from displacement.

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Improvement and validity of shock measurements using heterodyne laser interferometer

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Improvement and validity of shock measurements using heterodyne laser interferometer

Figure 3 (a) Quadrature and Doppler signals measured by two measuring devices. (b) Expanded Doppler signal from figure 3 (a).

V1 (t ) [p wave]

Low-pass,

Arctan, Phase unwrapping

Low-pass, Reverse array

Differentiation

s (t )

Reverse array Differentiation

a (t )

v (t )

V2 (t ) [s wave] Figure 4 Signal processing for quadrature signal of homodyne laser interferometer.

Doppler signal Low-pass

Reverse array

Low-pass

Reverse array

arctan, Phase unwrapping

Same process with fig.4

80 MHz cos sin

Low-pass

Reverse array

Low-pass

Reverse array

Figure 5 Signal processing for Doppler signal of heterodyne laser interferometer.

3. Results of experimental comparison of homodyne and heterodyne laser interferometers Figure 6 shows typical waveforms of a shock measured by the homodyne (thick gray line) and heterodyne (thin black line) laser interferometers, and the difference between the two waveforms (dashed line). The

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Improvement and validity of shock measurements using heterodyne laser interferometer

shock was a pulse with peak acceleration of about 3,500 m/s2 and a duration of 0.5 ms. The duration is given as the time width between two points at 10% of the peak acceleration [8]. The difference between the waveforms was ±1 m/s2, and the deviation between the peak values of the waveforms was around 5 × 10−3 %. Figure 7 shows an expanded view of part of figure 6 to indicate the high accuracy of the shock measurement taken by the heterodyne laser interferometer. The experimental measurement error by the homodyne laser interferometer was within ±0.8 m/s2, but that by the heterodyne laser interferometer was lower, at around ±0.1 m/s2. Then, each system noise floor of the quadrature and Doppler signals was 5 mV peak-to-peak and 4 mV peak-to-peak, respectively. Moreover, the ground noise on a passive table was less than 10-3 m/s2 as the effective value. Table 2 presents a summary of deviations of the measured peak acceleration values between the two measuring devices, from around 70 m/s2 to 10,000 m/s2. The higher the peak shock values were, the smaller the deviation between the two measured peak acceleration values was.

Figure 6 Typical waveforms of shock measured by homodyne (thick gray line) and heterodyne (thin black line) laser interferometers, and difference (dashed line) between the two measured waveforms.

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Improvement and validity of shock measurements using heterodyne laser interferometer

Figure 7 Expanded view of shock from figure 6.

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Improvement and validity of shock measurements using heterodyne laser interferometer

Table 2 Summary of deviation between two peak values in shock measurements.

Homodyne

Heterodyne

Peak acceleration Duration Velocity Peak acceleration Duration Velocity 2

m/s 2639 3257 4014 4428 5228 5864 6574 8256 8892 9105 9420 9908 3279 3316 2491 826.4 1544 1418 982.8 702.8 221.4 102.0 72.19

ms 0.49 0.48 0.47 0.46 0.46 0.45 0.45 0.45 0.45 0.45 0.45 0.45 1.5 1.5 1.8 3.1 1.7 1.9 2.0 2.4 3.9 4.9 5.3

m/s 0.83 1.0 1.2 1.3 1.6 1.7 1.9 2.4 2.6 2.7 2.8 2.9 2.8 2.8 2.3 1.3 1.6 1.6 1.2 0.88 0.43 0.27 0.22

2

m/s 2639 3257 4014 4428 5228 5864 6574 8256 8892 9106 9421 9910 3279 3316 2491 826.2 1543 1418 982.9 703.7 220.7 101.4 72.09

ms 0.49 0.48 0.47 0.46 0.46 0.45 0.45 0.45 0.45 0.45 0.45 0.45 1.5 1.5 1.8 3.1 1.7 1.9 2.0 2.4 3.9 4.9 5.3

m/s 0.83 1.0 1.2 1.3 1.6 1.7 1.9 2.4 2.6 2.7 2.8 2.9 2.8 2.8 2.3 1.3 1.6 1.6 1.2 0.88 0.42 0.27 0.22

Deviation % -1.9E-03 -4.8E-03 -5.5E-03 -1.0E-02 -1.7E-04 -5.5E-03 -9.8E-03 4.7E-03 7.2E-03 4.7E-03 1.4E-02 1.4E-02 2.1E-02 1.8E-02 -1.3E-03 -2.6E-02 -5.9E-02 -4.1E-02 1.1E-02 1.4E-01 -3.1E-01 -5.2E-01 -1.4E-01

4. Results of computational simulation comparison of homodyne and heterodyne laser interferometers Figures 8 and 9 show the results of a computational simulation comparing the homodyne laser interferometer to the heterodyne laser interferometer in cases of a known shock with a peak value of 1,000 m/s2 and a duration of 1 ms. In the simulation, the theoretical quadrature and Doppler signals of the homodyne and heterodyne laser interferometers were created from equations (1) [2] and (2) [9] respectively on the basis of the displacement in response to the known shock (thick gray line), and were arrayed according as the sampling frequencies of 50 MHz and 500 MHz at a resolution of 8 bits on an input voltage of ±1 V. Then, white noise of 4 mV peak-to-peak as the electric noise of the photo detector was added to both the

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Improvement and validity of shock measurements using heterodyne laser interferometer

quadrature and Doppler signals with an amplitude of 0.2 V. After the above-mentioned demodulation and decimation of 1 MHz, the simulation results (solid line) were obtained. The differences between the known and simulated accelerations in case of the homodyne and heterodyne laser interferometers are depicted in figures 8 and 9. The results show the measurement accuracy expected by the homodyne and heterodyne laser interferometers. The pulses observed at the rising and falling edges at 1 ms and 2 ms are due to the effect of the Butterworth low-pass filter (with cut-off frequency of 10 kHz). Figure 10 illustrates the measurement accuracy dependence on noise by the homodyne and heterodyne laser interferometers with sampling conditions of 50 MHz, 500 MHz and 1 GHz. Consequently, the measurement accuracy (open squares) by the heterodyne laser interferometer was superior to that by the homodyne laser interferometer, despite the noise and the sampling frequency. This indicates that the measurement accuracy by the homodyne laser interferometer is more sensitive to the intensity of the quadrature signal.

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Improvement and validity of shock measurements using heterodyne laser interferometer

Figure 8 Known and simulated accelerations in case of homodyne laser interferometer, and difference between both the accelerations.

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Improvement and validity of shock measurements using heterodyne laser interferometer

Figure 9 Known and simulated accelerations in case of heterodyne laser interfeormeter, and difference between both the accelerations.

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Improvement and validity of shock measurements using heterodyne laser interferometer

Figure 10 Measurement accuracy dependence on noise in homodyne and heterodyne laser interferometers.

5. Conclusion To indicate the validity of shock measurements taken using only the laser head of a commercial LDV as heterodyne laser interferometer, a comparison between homodyne and heterodyne laser interferometers was performed in the shock measurement range from several tens of m/s2 to 10,000 m/s2. The experiments confirmed that the difference between acceleration waveforms obtained by the two laser interferometers was within ±1 m/s2. Also, the deviation in peak acceleration between the two laser interferometers was found to be sufficiently small in cases of shocks with peak accelerations higher than 1,000 m/s2. The accuracies of the shock measurements taken with the homodyne and heterodyne laser interferometers were computer simulated using a known acceleration pulse. This simulation also indicated the advantage of the heterodyne laser interferometer in taking shock measurements, as compared to the homodyne laser interferometer.

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Improvement and validity of shock measurements using heterodyne laser interferometer

References [1] A. Oota, H. Nozato, W. Kokuyama, Y. Kobayashi, O. Takano and N. Kasai, Digital demodulator unit of laser vibrometer standard for insitu measurement, IMEKO, 2, No. 2 (2013) 61–66. [2] H. Nozato, T. Usuda, A. Oota and T. Ishigami, Calibration of vibration pick-ups with laser interferometry: part IV. Development of a shock acceleration exciter and calibration system, Meas. Sci. Technol. 21 (2010) 065107. [3] ISO 16063-13 Methods for the calibration of vibration and shock transducers: part 13. Primary shock calibration using laser interferometry (2001). [4] T. Bruns, Frank Blume and A. Täubner, Laser vibrometer calibration at high frequencies using conventional calibration equipment, Proceedings of XIX IMEKO World Congress, Lisbon, Portugal (2009). [5] L. Zhang and R. Kumme, Investigation of a homodyne and a heterodyne laser interferometer for dynamic force measurefment, Proceedings of SPIE Vol. 5503 Sixth international conference on vibration measurements by laser techniques: Advances and applications (2004) 608–615. [6] M. Dobosz, T. Usuda and T. Kurosawa, Methods for the calibration of vibration pick-ups by laser interferometry: I. Theoretical analysis, Meas. Sci. Tech. 9 (1998) 232–239. [7] L. M. Heydemann, Determination and correction of quadrature fringe measurement errors in interferometers, Appl. Opt. 20, No. 19 (1981) 3382–3384. [8] ISO 16063-22 Methods for the calibration of vibration and shock transducers: part 22. Shock calibration by comparison to a reference transducer (2005). [9] Li Zhang and Jun Peng, Primary acceleration calibration by heterodyne laser interferometer and PXI instrument, Proceedings of SPIE 5503 Sixth international conference on vibration measurements by laser techniques: Advances and applications (2004) 588-597.

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Improvement and validity of shock measurements using heterodyne laser interferometer

Figure Captions Figure 1 Homodyne laser interferometer and laser head (heterodyne laser interferometer) of LDV in shock calibration system. Figure 2 Block diagram of two measuring devices in shock calibration system. Figure 3 (a) Quadrature and Doppler signals measured by two measuring devices. (b) Expanded Doppler signal from figure 3 (a). Figure 4 Signal processing for quadrature signal of homodyne laser interferometer. Figure 5 Signal processing for Doppler signal of heterodyne laser interferometer. Figure 6 Typical waveforms of shock measured by homodyne (thick gray line) and heterodyne (thin black line) laser interferometers, and difference (dashed line) between the two measured waveforms. Figure 7 Expanded view of shock from figure 6. Figure 8 Known and simulated accelerations in case of homodyne laser interferometer, and difference between both the accelerations. Figure 9 Known and simulated accelerations in case of heterodyne laser interfeormeter, and difference between both the accelerations. Figure 10 Measurement accuracy dependence on noise in homodyne and heterodyne laser interferometers.

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Improvement and validity of shock measurements using heterodyne laser interferometer

Highlights

1.

We compared homodyne with heterodyne laser interferometers in shock measurements.

2.

In experiment, heterodyne had higher measurement accuracy than homodyne.

3.

In simulation, heterodyne was superior to homodyne as to measurement accuracy.

4.

Measurement accuracy of heterodyne was simulated about noise and sampling

frequency.

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