Laser-Doppler-Vibrometer calibration by laser stimulation ACTA IMEKO ISSN: 221-870X December 2020, Volume 9, Number 5, 357-360 Laser-Doppler-Vibrometer calibration by laser stimulation H. Volkers1 and Th. Bruns2 1Physikalisch-Technische Bundesanstalt, Braunschweig und Berlin, Germany, henrik.volkers@ptb.de 2Physikalisch-Technische Bundesanstalt, Braunschweig und Berlin, Germany, thomas.bruns@ptb.de Abstract A new set-up for primary laser vibrometer cali- bration was developed and tested at the acceleration laboratory of PTB. Contrary to existing set-ups, this configuration makes use of electro-optical excitation. While avoiding the limitations imposed by mechanical motion generators in classic set-ups, the new method still encompasses all components of commercial laser vibrometers in the calibration and thus goes beyond the current capabilities of the purely electrical excita- tion schemes. Keywords: primary calibration, laser doppler vi- brometer, LDV calibration 1 INTRODUCTION Laser Doppler vibrometers (LDV) are great tools for all kind of vibration measurements, especially for the use as a primary reference for calibration of ac- celerometers as described in the standards [1, 2]. IF PD x(t) y(t) Demodulator/ Controller u PD_raw (t) f AOM u x,v,a (t) LDV Figure 1: Schematic signal chain of a laser Doppler vibrom- eter Figure 1 shows a schematic diagram of the signal flow in an LDV. At the measurement point, the mo- tion quantity x(t) is measured via a laser beam that passes an interferometer (IF) including an acousto- optical modulator (AOM) and finally illuminates a photodetector (PD) with an intensity modulated by in- terference according to I(t) = I0 ·sin(2π fAOM ·t + 4π x(t) λ + τ0)+ b + enoise (1) with fAOM as the frequency of the AOM, λ the wave- length of the laser, τ0 a constant delay due to the time of flight of the laser light, a constant bias intensity b typical for interference and a noise component enoise, e.g. from stray ambient light. The voltage output uPDraw of the photo detector fol- lows the intensity with a certain additional delay and additional noise from embedded amplifiers and feeds into the demodulation stage of the LDV controller. The internal processing of a commercial LDV is gener- ally unknown to the user but probably follows an arct- angents demodulation scheme as described in [3]. The demodulated analog (voltage) output of the in- strument is then characterized by its complex transfer functions S in the frequency domain: Sux( f ) = Ux( f ) X( f ) (2) where the signal delay is characterized by the phase of this complex quantity. 2 EXISTING METHODS Existing calibration methods and set-ups either fol- low the classical approach of measuring a mechani- cal vibration [4, 5] or use an electrical excitation of the LDV controller and thus simulate the optical laser head. For the former set-up a typical primary accelerom- eter calibration system is utilized where a reference LDV measures the motion of a shaker’s armature to provide a reference acceleration signal. The mea- surement beam of the device under test (DUT) is co- aligned to the reference beam using a beam splitter and points at the same spot on the armature surface. In the optimized set-up [6] only a single laser beam needs to be adjusted, hence, inaccuracies of the co-alignment are avoided. This method provides a significant smaller uncer- tainty for LDV calibration than for the classical ac- celerometer calibration. However, it still suffers from the mechanical limitations of the utilized shaker sys- tem in terms of a limited frequency and amplitude range and non-ideal motion. The second method substitutes the laser head of the DUT with an electrical signal generator. The signal generator provides the frequency modulated input to ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 357 henrik.volkers@ptb.de thomas.bruns@ptb.de IF PD Pol λ/4 Demodulator/ Controller u PD_REF (t) f AOM u x,v,a (t) LD Signal generator PD ADC1 ADC2 u AM (t) LDV BS Figure 2: Schematic of a LDV calibration setup with amplitude-modulated laser diode stimulation the LDV controller of the DUT, simulating the photo diode output of the laser head. By providing a cor- responding FM signal, a very wide variety of virtual motion patterns can be simulated under almost ideal conditions. By simultaneous sampling of the genera- tor signal and the DUT output a precise determination of the complex transfer function of the DUT is possi- ble. This method, however, requires good knowledge of the working principle of the hardware in order to provide adequate signal levels and carrier frequencies to the controller. In addition, it is not able to ac- count for any signal preconditioning performed within the original laser head. On the other hand it suffers from far less limitations by avoiding any mechanical components[7]. 3 STIMULATION BY AMPLITUDE MOD- ULATED LASER SOURCE The basic idea of the new set-up evolves from the Eq. (1) and Figure 1 and is shown in Figure 2. The photo diode, being the central sensing part of the LDV, cannot distinguish the cause of an intensity variation. Whether it is the result of optical interference or sim- ply is an intensity variation caused by a modulated ex- ternal light source makes no difference. If an appropri- ate light source with a suitable amplitude modulation following Eq. (1) is targeted at its sensing element, the LDV response will be identical to the respective inter- ference caused by real motion. This approach combines the benefits of those exist- ing set-ups described above, while avoiding the dis- advantages. While ommiting any mechanical moving components, that may limit the scope or accuracy, it still includes the potential preprocessing of the laser head in the calibration. All requested excitations for the calibration of LDVs can be provided by electro- optical means. In the new calibration set-up at PTB (c.f. Figure 2), the light source is a common 10 mW laser diode (LD) of a wavelength of 635 nm, well matching the LDV’s He-Ne wavelength. The bias current is adjusted such that the mean beam power entering the LDV is less than 1 mW, matching approximately the typical output power of the LDV’s laser. An non-polarising beam splitter (BS) separates about 50 % of the light which is directed to a reference photo diode (FEMTO HCA-S-400M) of a bandwidth of 400 MHz and a known time delay [8]. An RF gen- erator with phase modulation capability provides the modulation current for the laser diode. The modula- tion depth is adjusted in a range of 30% to 50% and monitored by the reference photo diode. A polarization filter (Pol) and a λ /4 plate between LD and LDV ensure that circular polarized laser light enters the interferometer. The majority of the emitted light from the LD is already linear polarized, however, for the first set-up, the orientation of the polarity is unknown, hence, a polarization filter eases the initial orientation of the λ /4 plate. Not shown in Figure 2 is the collimator lens of the laser diode and two aperture plates used to ease the alignment of the stimulating laser diode unit with the LDV’s beam line. 4 SIGNAL GENERATION AND PROCESS- ING The data acquisition system is based on a PXI sys- tem controlled by a LabVIEW program and provides two synchronized ADC channels for the acquisition of the reference signal and the DUT output. While the final stage of the set-up is supposed to include an arbi- trary waveform generator and the ability to phase lock the generator or the whole PXI system to the LDV car- rier frequency, the preliminary results given here were acquired by utilizing an RF generator (Type Agilent E4400B). The system is similar to the acquisition sys- tems already used and validated for the primary accel- eration calibration facilities at PTB. The synchronous data acquisition was performed at 200 MS/s to account for the high carrier frequency. The demodulation of the reference followed the vali- dated arctangents demodulation of PTB’s national pri- mary calibration standards. Finally, the evaluation of the simulated motion used the usual three-parameter sine-approximation. 4.1 Determination of time delays Figure 3 shows the involved time delays of the cal- ibration set-up depicted in Figure 2. All components except HLDV are assumed to have a true time delay, i.e. the time delay is constant within the frequency ranges observed. The time delay τcor = Φcor ω , with ω = 2π f (3) ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 358 LD PD τ r1 τ m1 LDV Head τ m2.1 τm2.2 LDV Controller τm2.3 HContr ADC2 ADC1 τm3 τ r2 τr3 ΔτADC HLDV Figure 3: Time delays of the signal chains to correct the measured transfer function Hmeas to get HLDV HLDV(ω) = |Hmeas(ω)|·e jω(Φmeas−Φcor) (4) is calculated as τcor = τr1 −τm1 + τr2 + τr3 −τm3 + ∆τADC (5) with the values: τr1 −τm1 = −545(5)mm·cair =−1.82(3)ns(6) cair = 2.9971×108 m/s being the difference of the laser beam lengths mea- sured from the reference surface of the LDV head stated in the manual. Its uncertainty covers the un- known delays of the λ /4 plate and the polarization fil- ter. The photo diode delay τr2 was measured in [8] as τr2 = 3.10(8)ns. (7) The time delay difference between the two simultane- ously sampled channels, each with an RG58 cable of 2 m length, representing the term τr3−τm3 + ∆τADC, is measured by feeding both cable ends with a common signal from the generator via a power splitter Mini- Circuits ZFSC-2-4. By doing multiple measurements with swapped cables at the power splitter and ADC in- puts we found τr3 −τm3 + ∆τADC = 0.15(5)ns (8) including variances due to remounting. Putting the re- sults into (5) gives τcor = 1.43(10)ns (9) The measurement of a time delay was performed in a two-step process. In the first step, a signal with a car- rier frequency of 40 MHz and an FM sine modulation of 500 Hz and a modulation depth of 3.15 MHz was applied and a coarse time delay was determined by the maxima of a computed cross correlation, see Figure 4. In the final step the modulation was turned off and the phase difference of the 40 MHz carrier signal was measured by applying a three parameter sine approxi- mation. This process was chosen to be able to measure time delays of heterodyne signal outputs of LDV con- trollers with a time delay greater than one period of the carrier signal (25 ns in this case) due to internal signal processing like amplitude stabilisation or filter. 800 -800 0 A m p li tu d e 800 -800 0 A m p li tu d e 800 -800 0 A m p li tu d e 0 0 80n 120n 160n40n0-40n-80n -10µ -8µ -6µ -4µ -2µ 2µ 4µ 6µ 8µ 10µ -0.2m-0.4m-0.6m-0.8m-1m 0.2m 0.4m 0.6m 0.8m 1m Time in s Figure 4: Cross correlation of the two ADC channels at a sample rate of 200 MHz, both fed with a 40 MHz FM sig- nal modulated with a 500 Hz sine of 3.15 MHz modulation depth, on different time scales, with one of the two connec- tion cables being about 8 m longer, resulting in a delay of 41.90(5)ns. 5 RESULTS First tests with a LDV controller Polytec OFV- 5000-KU and a laser head OFV 353, connected via a 5 m cable, were performed and figure 5 shows a mea- sured frequency response obtained with the new set- up. The LDV is based on a carrier frequency fAOM of 40 MHz. The LDV controller settings were: • Velocity decoder: VD-01 • Range: 1 m/s/V • Max. frequency: 50 kHz • Tracking filter: off • Low pass filter: 100 kHz • High pass filter: off The frequency range in terms of the simulated vibra- tion was 100 Hz to 30 kHz and an amplitude of 1 m/s leading to a modulation depth of 3.159 MHz. The plots show the relative deviation in magnitude and the ab- solute phase of the analog velocity output in relation to the demodulated intensity stimulus on a linear fre- quency scale. The nearly linear phase corresponds to a delay of about 7.52 µ s. 6 OUTLOOK Instead of a photo diode with known delay, a known laser source would obviate the beam splitter and photo ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 359 0 5000 10000 15000 20000 25000 30000 -4.0% -3.5% -3.0% -2.5% -2.0% -1.5% -1.0% -0.5% 0.0% 0.5% -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Magnitude Phase Frequency in Hz re l. d ev ia ti o n m ag n it u d e P h as e in 1 ° Figure 5: Transfer function of a LDV analog velocity output at 1 V/(m/s) diode, simplifying the set-up. It is a classical chicken- or-egg dilemma; in our case we had the known PD first to relate an optical signal to an electrical signal. The measurement uncertainty budget is still under investigation, the absence of mechanical excitation are expected to significantly reduce the uncertainties, leaving the absolute AC voltage measurement as the main contributor for magnitude uncertainty, while the phase uncertainties are expected to be better than 0.01° for frequencies up to 100 kHz. ACKNOWLEDGMENT The authors like to thank Dr. Siegmund of Polytec for some inspiring walks and talks. 7 References [1] ISO 16063-11:1999 Methods for the calibration of vibration and shock transducers — Part 11: Pri- mary vibration calibration by laser interferometry, ISO, Geneva, Switzerland, 1999 [2] ISO 16063-13:2001 Methods for the calibration of vibration and shock transducers — Part 13: Pri- mary shock calibration using laser interferometry [3] ISO 16063-41:2011 Methods for the calibration of vibration and shock transducers — Part 41: Cali- bration of laser vibrometers [4] U Buehn et al., "Calibration of Laser Vi- brometer Standards According to ISO 16063-41", XVIII IMEKO World Congress 2006, Rio de Janeiro, Brazil, September, 2006 https://www.imeko.org/publications/wc- 2006/PWC-2006-TC22-007u.pdf. [5] Th. Bruns, F. Blume, A. Täubner, "Laser Vibrometer Calibration at High Frequen- cies using Conventional Calibration Equip- ment", XIX IMEKO World Congress, September 6-11, 2009, Lisbon, Portugal http://www.imeko2009.it.pt/Papers/FP_495.pdf [6] F. Blume, A. Täubner, U. Göbel, Th. Bruns, "Pri- mary phase calibration of laser-vibrometers with a single laser source", Metrologia, 2009, Vol. 46, N. 5, https://dx.doi.org/10.1088/0026-1394/46/5/013 [7] M. Winter, H. Füser, M. Bieler, G. Sieg- mund, C. Rembe, "The problem of calibrating Laser-Doppler Vibrometers at high frequencies", AIP Conference Proceedings 1457, 165 (2012) https://doi.org/10.1063/1.4730555 [8] Th. Bruns, F. Blume, K.Baaske, M. Bieler, H. Volkers "Optoelectronic Phase Delay Mea- surement for a Modified Michelson Inter- ferometer", Measurement, 2013, Vol.46, N. 5, https://doi.org/10.1016/j.measurement.2012.11.044 ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 360 https://www.imeko.org/publications/wc-2006/PWC-2006-TC22-007u.pdf https://www.imeko.org/publications/wc-2006/PWC-2006-TC22-007u.pdf http://www.imeko2009.it.pt/Papers/FP_495.pdf https://dx.doi.org/10.1088/0026-1394/46/5/013 https://doi.org/10.1063/1.4730555 https://doi.org/10.1016/j.measurement.2012.11.044 INTRODUCTION EXISTING METHODS STIMULATION BY AMPLITUDE MODULATED LASER SOURCE SIGNAL GENERATION AND PROCESSING Determination of time delays RESULTS OUTLOOK References