Multipoint vibrometry with dynamic and static holograms T. Haist, C. Lingel, W. Osten, M. Winter, M. Giesen, F. Ritter, K. Sandfort, C. Rembe, and K. Bendel Citation: Review of Scientific Instruments 84, 121701 (2013); doi: 10.1063/1.4845596 View online: http://dx.doi.org/10.1063/1.4845596 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/84/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Frequency Shifted Digital Holography for the Measurement of Vibration with Very Small Amplitudes AIP Conf. Proc. 1253, 415 (2010); 10.1063/1.3455485 Low level free vibration measurements using high speed digital holography AIP Conf. Proc. 992, 810 (2008); 10.1063/1.2926975 Measurement of dynamic full-field internal stresses through surface laser Doppler vibrometry Appl. Phys. Lett. 91, 134101 (2007); 10.1063/1.2790379 Photorefractive correlation filtering of time-varying laser speckles for vibration monitoring Appl. Phys. Lett. 73, 1466 (1998); 10.1063/1.122216 Holographic study of a vibrating bell: An undergraduate laboratory experiment Am. J. Phys. 66, 380 (1998); 10.1119/1.18877
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
REVIEW OF SCIENTIFIC INSTRUMENTS 84, 121701 (2013)
Multipoint vibrometry with dynamic and static holograms T. Haist,1 C. Lingel,1 W. Osten,1 M. Winter,2 M. Giesen,2 F. Ritter,2 K. Sandfort,2 C. Rembe,2 and K. Bendel3 1 Institut für Technische Optik, Stuttgart Research Center of Photonic Engineering (SCOPE), University of Stuttgart, D-70569 Stuttgart, Germany 2 Polytec GmbH, Polytec-Platz 1-7, D-76337 Waldbronn, Germany 3 Corporate Sector Research and Advanced Engineering, Robert Bosch GmbH, Gerlingen, Germany
(Received 7 June 2013; accepted 18 November 2013; published online 17 December 2013) We report on two multipoint vibrometers with user-adjustable position of the measurement spots. Both systems are using holograms for beam deflection. The measurement is based on heterodyne interferometry with a frequency difference of 5 MHz between reference and object beam. One of the systems uses programmable positioning of the spots in the object volume but is limited concerning the light efficiency. The other system is based on static holograms in combination with mechanical adjustment of the measurement spots and does not have such a general efficiency restriction. Design considerations are given and we show measurement results for both systems. In addition, we analyze the sensitivity of the systems which is a major limitation compared to single point scanning systems. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4845596] I. INTRODUCTION
The measurement of vibrations of technical objects is of considerable importance in industrial quality control and applied research. Typically, Doppler-based interferometric methods are employed because very small vibrating amplitudes xmax in the range of nanometers and even picometers, which are not detectable by other methods, can be measured. Even very small amplitudes at high frequencies result in large Doppler shifts f = 2v/λ, where we denote the wavelength of the light by λ and the speed of the movement by v.1 For typical applications in mechanical engineering, Doppler shifts of up to several MHz are to be detected. At such high detection frequencies two main problems have to be taken into account. First, of course, the signal has to be sampled with a high enough sampling frequency. Second, enough light needs to be available in order to deliver enough photons on the detector for the short measurement time corresponding to the inverse of the frequency resolution when the spectrum of the vibration is calculated. For periodic vibrations, both problems can be approached by using time-averaging or periodic sampling. Of course, transient or aperiodic vibrations cannot be measured using such methods. Therefore, for industrial measurements, interferometry typically is used. In order to achieve a satisfactory signal-to-noise level at the sufficiently high frequencies heterodyne detection is employed. Single point systems are extended by scanning using electro-mechanical scanning devices and three-dimensional vibrations are measured using a measurement from different directions. A lot of interesting full-field measurement systems for measuring vibrations at a lot of points (some tens of thousands to several × 106 ) are available. Typical approaches rely on speckle techniques, e.g., electronic speckle pattern interferometry or digital holography.22 Due to the limited number of photons one, however, is limited to averaging2, 3 or sam0034-6748/2013/84(12)/121701/8/$30.00
pling approaches, e.g., with double-pulse systems or stroboscopic illumination.4–6 Current commercial systems are not suitable for the recording of transient phenomena at multiple points because scanning in this case is not possible. Full-field interferometric (holographic) detection by using fast camera systems as proposed by different authors7–10 is limited to small or medium Doppler shifts due to the aforementioned limited number of photons which are available during the short effective measurement time. Considerable improvement is possible by sacrificing one dimension, e.g., using a line illumination in combination with a line-scan camera, as proposed, e.g., by MacPherson et al.8 Still, high frequencies cannot be reached with such approaches. Further improvement necessarily means that the number of simultaneous measurement points has to be further reduced. This leads to so-called multi-channel systems which have a limited number of measurement channels. Several such systems have been realized with fixed measurement geometries.11–19 A low-noise laser source is necessary and, therefore, restrictions of the laser power have to be considered. Consequently, the user wants to control at least the position of the measurement points on a given object. This, of course, cannot be achieved using fixed-geometry systems. In this contribution we describe two systems that achieve a flexible measurement geometry using a holographic approach for beam deflection. Section II shows one approach based on dynamic holography using a spatial light modulator (SLM; multipoint vibrometry with dynamic holograms, MVDH). The measurement geometry can be changed very fast (video rate) but due to the limitation of current commercially available SLMs the light efficiency is strongly limited for satisfactory beam deflections. The second approach (multipoint vibrometry with static holograms, MVSH) is presented in Sec. III and employs static holograms in combination with mechanical adjustment of the measurement positions. This
84, 121701-1
© 2013 AIP Publishing LLC
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
121701-2
Haist et al.
Rev. Sci. Instrum. 84, 121701 (2013)
FIG. 1. Object path of an heterodyne interferometer using a spatial light modulator (LCD) for non-mechanical beam deflection. Shown here without the object-sided telescope that might be used in order to increase the scanning range. Depending on the programmed grating different deflections can be realized.
leads to improved light efficiency at the cost of an increased setup time for a new measurement-grid configuration.
II. VIBROMETRY USING A SPATIAL LIGHT MODULATOR
The basic idea of using dynamic holography within an interferometric vibrometer as described in Ref. 20 is depicted in Fig. 1. A hologram is used for beam deflection and beam splitting. This way, mechanical beam deflection which might introduce spurious vibrations and inaccuracies of the beam position is eliminated. Since the basic optical design considerations will also apply to a multipoint configuration we will shortly review the most important relationships. The most simple hologram is a grating and it directly leads to beam deflection by the angle φ = asin(λ/d) with the grating period d. If the grating is not a perfectly blazed phase grating only part of the light will be diffracted into the desired deflection. In order to achieve a satisfactory efficiency the blazed grating has to be approximated by at least 3 to 4 discrete and quantized pixels. For high quality commercial spatial light modulators the pixel pitch is in the range of 10 μm and, therefore, the maximum usable deflection is in the range of about 1◦ for visible light in the green spectral region. For a lot of applications this deflection is not large enough and as a result a telescope is necessary to amplify the deflection. Unfortunately, an amplification of the deflection by a magnification M leads to a reduction of the diameter of the pupil of the optical system by the same factor and consequently the light efficiency of the detection is reduced by a factor of M2 (area of the receiving pupil). As a result, the pupil size is completely determined by the number of pixels of the SLM and the desired maximum deflection. Compared to static systems this leads to a lower light efficiency.
A. Fourteen-channel multipoint vibrometry with dynamic holograms
In order to realize a multipoint system the SLM is used to generate multiple object beams. To this end different hologram multiplexing schemes are possible.21 All of these schemes lead to the same overall light efficiency because the overall pupil area stays the same. Still, differences between the schemes exist, especially concerning the size of the measurement spot on the object and the number and distribution of unwanted diffraction orders. No matter which scheme is employed it is mandatory to work in a “confocal-mode” where the same sizes of the illumination and the detection pupils for each channel of the vibrometer are used. This way, speckle-induced contrast loss of the interference signal is avoided. One major challenge of such a system that realizes multiple measurement spots simultaneously using a thin hologram is the unavoidable crosstalk of the holograms. There is crosstalk between the sending and receiving parts of the hologram (mostly reduced by using several polarizing components and aperture elements), crosstalk between the individual holograms for each measurement spot, and crosstalk due to imperfect modulation characteristics of the spatial light modulator. The optical design as well as the computation of the hologram have to consider these effects because any unwanted (interfering) light contribution that will fall onto one of the detectors might lead to measurement errors. The best multiplexing approach concerning resolution and flexibility is a complex superposition of the holograms for the individual channels. The resulting complicated spurious diffraction orders are filtered using pinhole masks in a plane conjugate to the object. This filtering in combination with hologram optimization as described in Ref. 21 avoids that unwanted diffraction orders of the hologram fall onto detectors and lead to measurement errors. Fig. 2 depicts one of the optical setups that we have investigated. It consists of a heterodyne interferometer using
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
121701-3
Haist et al.
Rev. Sci. Instrum. 84, 121701 (2013)
FIG. 2. Experimental setup for programmable multipoint vibrometry (MVDH). The central element is the liquid crystal modulator that is used for illumination (red) and detection (blue). The detector unit consists of a pinhole array in combination with a microlens array and multimode fibers (see text for details). Reprinted with permission from AIP Conf. Proc. 1457, 234 (2012). Copyright 2012 American Institute of Physics.26
acousto-optical modulation (AOM) where a spatial light modulator is located in a near-Fourier plane of the object. The AOM consists of two cells working at 84 MHz and 79 MHz, giving a 5 MHz frequency difference which is used for heterodyning. The laser source is a 20 mW diode-pumped solid state (DPSS) laser at 532 nm wavelength. As described, we use a Kepler telescope with a magnification of four to increase the object field. In order to achieve the maximum possible light efficiency we use a phase-only Liquid-Crystal on silicon (LCoS) modulator, namely a Holoeye Pluto modulator (1920 × 1080 pixels, 8 μm pixel-pitch, compare Sec. II B). The optical design (see Fig. 2) achieves diffraction limited reconstruction and imaging using standard achromatic lenses over the whole field. Residual aberrations, e.g., due to bad alignment can be eliminated by modifying the holograms. One half of the rectangular SLM is used for the illumination of the object. The light being scattered/reflected at the object is modulated only by the second half of the SLM. To this end we use a combination of a λ/4 plate and a split λ/2 plate located in a plane conjugate to the SLM. This way, the polarization of the light that is backreflected from the object and
that falls onto the first half of the SLM will be rotated by 90◦ and, therefore, will not be modulated by the SLM. Additionally, in another plane conjugate to the SLM such unwanted light contributions are blocked. After the SLM, the backreflected light is imaged by the same Kepler telescope that has been used for the illumination in combination with another lens onto an intermediate image plane (PA) with a pinhole mask which is conjugate to the receiving multimode fibers that lead to discrete photodiodes. The pinhole mask pattern corresponds to the detector/fiber pattern and is used to eliminate all remaining unwanted diffraction orders. A microlens array (MLA) is located after this pinhole mask for generating one collimated beamlet of appropriate size for every fiber. The superposition with the reference beam then leads to the heterodyne interference signal at the entrance of the fibers. For complex multiplexing, the whole area of the SLM and the entrance pupil is used for each channel. But since the holograms are thin (in contrast to volume holograms) the light coming from one object point is deflected to N different directions and only one of these directions leads to the desired detector. Concerning the light efficiency we end up with the
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
121701-4
Haist et al.
Rev. Sci. Instrum. 84, 121701 (2013)
TABLE I. Comparison of different spatial light modulators.
Resolution (pixel) Pixel pitch (μm) Max. angle (◦ ) Diffraction efficiency (%) Reflectivity (%) Max. phase shift (rad) Price (Euro)
SDE1280
Pluto-VIS
X10468-01
BNS-DM
1280 × 720 9.5 1.19 ≈40 68@5◦ 0.85pi 1000
1920 × 1080 8.0 2.27 69 60 >2pi 8300
800 × 600 20 0.91 85 75@5◦ >2pi 8000–10 000
512 × 512 15 1.2 66 90 >2pi 20 000
same result that we directly obtain for spatial multiplexing: Due to the N channels the efficiency is reduced by 1/N2 . This is an important general limitation and it applies to all multipoint concepts if the pupil size is kept constant. Therefore, good signal-to-noise ratios for large numbers of channels can be only achieved if the overall pupil size is large and/or the laser power is strong. Unfortunately, for SLM-based vibrometry the pupil size is limited by the area of the spatial light modulator. B. Spatial light modulator
Different SLMs have been considered as the core element of our system and four of these modulators have been tested in detail:
r r r r
Cambridge Correlator SDE1280 Holoeye Pluto-VIS Hamamatsu X10468-01 Boulder Nonlinear Systems BNS-XY-Ph-P512-DM
In Table I some of the main specifications are given. Finally, the Holoeye Pluto modulator has been chosen because of the good experimental results and the availability as an OEM (original equipment manufacturer) version. It is a high definition liquid crystal phase-only modulator with 1920 × 1080 pixels, a pixel pitch of 8 μm, and a fill factor of 87%. Using such an SLM several factors which influence the diffraction efficiency have to be considered:20 Fill factor: Between the pixels of the SLM the modulation is not as desired. The active area (SLM area without the pixel gaps) divided by the SLM area is the area-related fill factor. For absorbing pixel gaps, the efficiency of the hologram reconstruction is proportional to the square of the fill factor. Fringing field effect: For small pixels we have the problem of crosstalk between adjacent pixels. That means that the liquid crystals of one pixel are influenced by the electric fringing field of the neighboring pixels causing a smoothing of a sharp phase step. This blurring effect results in an inaccurate representation of the hologram and, in consequence, in some loss of diffraction efficiency and unwanted diffraction orders. Discretization and quantization: Because the SLM is pixelated it is only possible to image discretized and quantized holograms. Again, part of the light will be redirected to spurious diffraction orders.
Temporal effects: The SLM-elements are modulated with a certain time-dependent signal to realize the phase delay. The phase delay can be defined, for example, by the amplitude of a sine excitation or by the duty cycle of a pulse signal. The kind of realization influences strongly the phase modulation of the beam reflected by the SLM which leads to spurious signals in the vibration signal of the vibrometer. Our investigations have shown that the analog control of the Hamamatsu SLM shows the lowest influence of such spurious effects. Modulation: Typically, even for a “phase-only” modulator some amplitude modulation is still present, which leads to a loss of diffraction efficiency. Also a nonlinear phase response leads to unwanted diffraction orders.
C. Experimental results and limitations
The system has been tested on mirrors and objects prepared with retro-reflecting tape. The wavefront has been optimized by a special algorithm for illuminating the object points in order to achieve the best signal-to-noise ratio. This way, aberrations and dark speckles are avoided.24 The hologram deflections have been calibrated in such a way that a desired position on the object automatically triggers the generation of a corresponding detection hologram that will deflect the scattered light onto the desired detector. The hologram computation has been implemented on the graphics processing unit (GPU) of a GT8800-based consumer graphics board using NVidia’s CUDA programming methodology. Figs. 3 and 4 show typical results for a three channel measurement using spatial multiplexing (compare Ref. 21). The measurement object has been a loudspeaker with retroreflective tape driven by a frequency generator. The measurement positions on the loudspeaker can be freely chosen using computer-controlled change of the hologram. It is obvious that the light efficiency is strongly reduced compared to a conventional single-point vibrometer and this is the main problem of the method. Measurements on a mirror are always possible but on retro-reflective tape at a distance of about 1 m the light efficiency with the employed 18.3 mW laser is not sufficient to measure more than four channels simultaneously. Although heterodyne interferometry is extremely sensitive down to the shot noise limit the received light power needs to exceed the noise power in the demodulation bandwidth. Especially
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
121701-5
Haist et al.
Rev. Sci. Instrum. 84, 121701 (2013)
FIG. 3. One channel of a simultaneous measurement on a loudspeaker with retroreflective tape for a three channel measurement. Reprinted with permission from AIP Conf. Proc. 1457, 234 (2012). Copyright 2012 American Institute of Physics.26
the low numerical aperture for a maximum necessary beamdeflection angle of approximately 5◦ for standard measurement tasks has posed a major restriction. Even a 100 mW laser would not solve the general problem. We have estimated that at least 10 × 106 pixels are required for the reception and detection SLM area in combination with 100 mW laser power. Ten times more pixels correspond to a ten times larger sensitivity. The size of the entrance/exit pupil D = ySLM /M of the optical system, of course, is finally limited by the size of the light modulator ySLM . Since the number of pixels in one direction of the SLM NSLM , the pixel pitch pp, and the size of the SLM are related via ySLM = NSLM · pp, the size of the (rectangular) entrance/exit pupil is given by NSLM · z · pp λ NSLM pp = tan arcsin (1) D= M y 2 pp ≈
NSLM · pp · z λ y 2 pp
(2)
NSLM · z λ . 2y
(3)
=
The overall light efficiency depends on a lot of factors (see Ref. 23) but is proportional to the square of the linear
FIG. 5. Schematic of the 12 channel heterodyne interferometer with static holograms (MVSH). There are 6 further channels under the 6 visible ones.
extension of the entrance pupil and—as described—inversely proportional to the square of the number of measurement channels N: η∼
2 z 2 λ2 NSLM D2 ≈ . N2 4 y2 N 2
(4)
III. MULTIPOINT VIBROMETRY USING STATIC HOLOGRAMS
Because of the efficiency problems mentioned in Sec. II we decided to realize another multipoint vibrometer based on static holograms. In this approach the splitting of the laser beam into multiple channels is accomplished by two static diffractive optical elements (DOE) instead of the SLM. Positioning of the measurement point is done manually by mechanical means. Therefore, a larger pupil per channel can be used and the light efficiency is strongly increased. One disadvantage of this design is that the number of measurement spots is not variable and, therefore, it is not possible to combine several channels into one. The second disadvantage is, of course, the necessity to align the positions on the object by hand. A. Twelve-channel interferometer and optical head
FIG. 4. Second channel of a simultaneous measurement on a loudspeaker with retroreflecting tape for a two channel measurement. Reprinted with permission from AIP Conf. Proc. 1457, 234 (2012). Copyright 2012 American Institute of Physics.26
The optical setup of the vibrometer is depicted in Fig. 5. We use a 532 nm diode-pumped solid state laser which is split into measurement and reference light by a polarizing beam splitter (PBS). The light in the object arm is frequency-shifted by 5 MHz using two combined Bragg cells. The reference and the object beam are divided into 3 × 4 parallel beams utilizing two DOEs, see Sec. III B. After the second DOE every group of 4 measurement beams are split again by a single PBS. Every single beam of the object path is coupled into a monomode fiber. At the output of the fiber an objective lens
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
121701-6
Haist et al.
Rev. Sci. Instrum. 84, 121701 (2013)
FIG. 6. Combination of two CGHs for 12-channel splitting.
focuses the beam onto the object. In addition, a quarter wave plate is placed to every fiber to make sure that the polarization of the returning light is rotated by 90◦ and, thus, is reflected at the PBS in direction of the detectors. On the way back, the reference and object beams are superimposed by non-polarizing beam splitters and each of the 12 beams is focused on a multimode fiber. These are connected to photodetectors providing a broadband heterodyne signal. To solve the problem of the adaptive measurement position the fibers are passed to a sensor head inside which every fiber and the objective lens are mounted in a tilting bearing. The objectives can be focused between a working distance of 80 mm to infinity. A spot diameter of 30 m at a distance of 80 mm and of 124 m at a distance of 500 mm have been achieved. The objectives are arranged in a square around a camera which can be used to control the position of the measurement spots. Each tilting bearing can be used to adjust the corresponding objectives in an angular range of ±10.5◦ (horizontally and vertically) manually. The maximum distance where a reasonable signal can be obtained is approximately 3 m. Thus, an object with the size of approximately 1 m diameter can be measured in a maximum working distance of 2.7 m. The 12-channel demodulator consists of two 8-channel analog-digital (A/D) converters (40 MSamples/s) which have been synchronized with one common clock for all channels. Thus, our A/D converter can digitize up to 16 channels synchronously. Since we need only 12 signal channels for our 12channel interferometer we have four free channels to realize a trigger and to obtain reference signals. The digital signals are evaluated using a field-programmable-gate-array (FPGA) processor. The detectors of the multibeam interferometer provide also an analog signal-strength voltage signal. These signals have a very low bandwidth and are converted to digital values by an additional A/D converter from National Instruments and transferred to the PC via USB. The signal strength can be used to optimize the laser focus and position. B. Static hologram
The fiber coupling is necessary to ensure a large enough distance between individual detectors to avoid electrical crosstalk between the detectors. For achieving a stable geom-
etry for the fiber coupling and a minimization of the necessary alignment elements we employ a splitting of the laser into 12 beamlets using two computer generated holograms (CGHs). The output of these two CGHs is 12 accurately aligned beamlets which are collinear with the incoming beam, see Fig. 6. The first CGH generates 12 beam deflections while the second CGH ensures the collinearity. The second hologram which gives a recollimation of the beams consists just of 12 blazed gratings with different grating periods. The first hologram which achieves the 1:12 splitting into the desired geometry has been optimized using a direct binary search algorithm. Because of the given symmetry of the desired reconstruction we chose the first CGH to be a binary pattern. The optimized hologram is tiled to its final size of 5 × 5 mm. It is therefore larger than the laser beam diameter to achieve insensitivity concerning lateral alignment errors. These two CGHs must be aligned accurately and then they can be used as a combined module. A graytone lithographic process is used for the fabrication of the elements where a Circular Laser Writing System CLWS 300 radial plotter is utilized to expose the photoresist which is spin-coated onto a quartz substrate.25 After lowcontrast development of the exposed resist we get the desired height profile which is transferred to the quartz using reactive ion etching. The binary elements are fabricated by using wet etching of chromium coated quartz. We can improve the DOEs concerning manufacturing errors by using a special edge optimization algorithm and increase the efficiency by 10%, so that the first hologram has an overall diffraction efficiency (including Fresnel losses for the uncoated element) of 72%. For the second DOE we obtain a diffraction efficiency of 58% because here we are not able to take advantage of the symmetry as for the first element where the +1st and −1st order lead to the desired deflection angles. C. Measurement examples
One interesting transient event we investigated with the multipoint vibrometer was the bouncing of a valve. Considering valves with conical seats the needle may strike the center only after some bounces on the cone. This process is complex and not repeatable (see Fig. 7). For this reason it is necessary to measure multiple points simultaneously to get the deflection shape of the valve. Therefore we arranged eight ro-
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
121701-7
Haist et al.
Rev. Sci. Instrum. 84, 121701 (2013)
FIG. 7. Surface velocity on the valve in one measurement point for 8 impacts of a closing valve.
FIG. 8. Measurement setup with 8 mirrors for measuring up to 9 sides of the valve simultaneously from one direction. The schematic of the setup as top view is presented in (a) while (b) shows a photo of the front view of the setup.
FIG. 9. Measurement grid and two examples for the deflection of the valve 250 μs after the impact.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
121701-8
Haist et al.
tatable mirrors around the valve to get a detailed view (see Fig. 8). In Fig. 9 we measured the radial velocity of the valve on two perpendicular rows each consisting of 6 measurement points. In Fig. 9 we show the maximum deflection of the valve at 250 μs after the impact. IV. CONCLUSION
We have described two holographic approaches for performing multipoint vibrometry using heterodyne interferometry. In both setups the user can freely choose the positions of the measurement spots. This is the main advantage of the method compared to other techniques. Dynamic holograms implemented using a spatial light modulator can be used in order to program the position of the measurement spots by optimizing the sending and receiving hologram. The disadvantage of this method is the limited space-bandwidth of the commercially available light modulators. This leads to a limitation concerning the light efficiency, especially if larger object fields are to be measured. The system with static holograms avoids this disadvantage but needs mechanical adjustment of the measurement positions. Measurements for both systems have been presented. In general, one main limitation for multipoint systems in combination with transient phenomena is the light efficiency because the receiving pupil area is reduced by the square of the number of measurement channels. ACKNOWLEDGMENTS
The authors would like to thank the German Bundesministerium für Bildung und Forschung (BMBF) for financial support under the project HoloVib (No. 13N9339). 1 L.
E. Drain, The Laser Doppler Principle (John Wiley and Sons, 1980).
2 C. Joenathan, “Vibration fringes by phase stepping on an electronic speckle
pattern interferometer: an analysis,” Appl. Opt. 30, 4658–4665 (1991). Bavigadda, R. Jallapuram, E. Mihaylova, and V. Toal, “Electronic speckle-pattern interferometer using holographic optical elements for vibration measurements,” Opt. Lett. 35, 3273–3275 (2010). 4 P. Hariharan, B. F. Oreb, and C. H. Freund, “Stroboscopic holographic interferometry: measurements of vector components of a vibration,” Appl. Opt. 26, 3899–3903 (1987). 5 I. Alexeenko, M. Gusev, and V. Gurevich, “Separate recording of rationally related vibration frequencies using digital stroboscopic holographic interferometry,” Appl. Opt. 48, 3475–3480 (2009). 6 R. Pawluczyk, Z. Kraska, and Z. Pawlowski, “Holographic investigations of skin vibrations,” Appl. Opt. 21, 759–765 (1982). 3 V.
Rev. Sci. Instrum. 84, 121701 (2013) 7 A.
Styk, M. Kujawinska, P. Lambelet, A. Royset, and S. Beer, “Microelements vibration measurement using quasi-heterodyning method and smartpixel camera,” in Fringe 2009, edited by W. Osten and M. Kujawinska (Springer, 2009), pp. 523–527. 8 W. N. MacPherson, M. Reeves, D. P. Towers, A. J. Moore, J. D. C. Jones, M. Dale, and C. Edwards, “Multipoint laser vibrometer for modal analysis,” Appl. Opt. 46, 3126–3132 (2007). 9 M. J. Connelly, P. M. Szecówka, R. Jallapuram, S. Martin, V. Toal, and M. P. Whelan, “Multipoint laser Doppler vibrometry using holographic optical elements and a CMOS digital camera,” Opt. Lett. 33, 330–332 (2008). 10 M. J. Connelly, P. M. Szecowka, R. Jallapuram, S. Martin, V. Toal, and M. P. Whelan, “Laser Doppler Vibrometry system using the syntheticheterodyne interferometric demodulation scheme implemented on a CMOS DSP camera,” in Proceedings of the 6th International Symposium on Communication Systems, Networks and Digital Signal Processing 2008 (IEEE, 2008), pp. 133–136. 11 W. Zheng, R. V. Kruzelecky, and R. Changkakoti, “Multichannel laser vibrometer and its applications,” Proc. SPIE 3411, 376–384 (1998). 12 E. Cupido, S. Morel, and D. Smith, “Multipoint laser doppler vibrometer for transient analysis,” in Proceedings of IMAC XXI, Orlando, USA (Springer, 2003). 13 E. Li, J. Xi, J. Chicharo, J. Yao, and D. Yu, “Multi-point laser Doppler velocimeter,” Opt. Commun. 245, 309–313 (2005). 14 V. Aranchuk, A. Lal, C. Hess, and J. M. Sabatier, “Multi-beam laser Doppler vibrometer for landmine detection,” Opt. Eng. 45, 104302 (2006). 15 A. K. Lal, C. F. Hess, H. Zhang, L. E. Hurtado, V. B. Markov, and V. Aranchuk, “Multi-beam heterodyne laser Doppler vibrometer,” U.S. patent 6,972,846 (2005). 16 A. K. Lal, C. F. Hess, E. Hurtado, V. B. Markov, V. Aranchuk, and V. V. Doushkina, “Multi-beam heterodyne laser Doppler vibrometer,” U.S. patent 7,477,498 B3 (2009). 17 A. T. Waz, P. R. Kaczmarek, and K. M. Abramski, “Laser-fibre vibrometry at 1550 nm,” Meas. Sci. Technol. 20, 105301 (2009). 18 J. Kilpatrick, A. Apostol, and V. Markov, “System for transient spatiotemporal (4D) vibration imaging and non-destructive inspection,” in Fringe 2009, edited by W. Osten and M. Kujawinska (Springer, 2009), pp. 519– 522. 19 J. Kilpatrick and V. Markov, “Multi-pixel (matrix) laser vibrometer,” Imaging 3, 2–4 (2010). 20 S. Zwick, M. Warber, T. Haist, F. Schaal, W. Osten, S. Boedecker, and C. Rembe, “Advanced scanning laser-Doppler vibrometer with computer generated holograms,” AIP Conf. Proc. 1253, 279–290 (2010). 21 T. Haist, A. Tarbeyevskaya, M. Warber, W. Osten, C. Rembe, M. Ludwig, and W. Stork, “SLM-based multipoint vibrometry,” Proc. SPIE 8082, 80821V (2011). 22 R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge University Press, 1989). 23 S. Zwick, T. Haist, M. Warber, and W. Osten, “Dynamic holography using pixelated light modulators,” Appl. Opt. 49, F47–F58 (2010). 24 S. Mayer, B. Tibken, and C. Rembe, “A new approach for signal loss compensation in a vibrometer,” in American Control Conference (ACC) (IEEE, 2011), pp. 2645–2650. 25 W. Osten, G. Baer, M. Häfner, W. Lyda, C. Pruss, R. Reichle, and F. Schaal, “Making, testing, applying: some progress in the field of micro-optics at ITO,” Proc. SPIE 8769, 876905–870611 (2013). 26 T. Haist et al., AIP Conf. Proc. 1457, 234 (2012).
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
REVIEW OF SCIENTIFIC INSTRUMENTS 84, 121701 (2013)
Multipoint vibrometry with dynamic and static holograms T. Haist,1 C. Lingel,1 W. Osten,1 M. Winter,2 M. Giesen,2 F. Ritter,2 K. Sandfort,2 C. Rembe,2 and K. Bendel3 1 Institut für Technische Optik, Stuttgart Research Center of Photonic Engineering (SCOPE), University of Stuttgart, D-70569 Stuttgart, Germany 2 Polytec GmbH, Polytec-Platz 1-7, D-76337 Waldbronn, Germany 3 Corporate Sector Research and Advanced Engineering, Robert Bosch GmbH, Gerlingen, Germany
(Received 7 June 2013; accepted 18 November 2013; published online 17 December 2013) We report on two multipoint vibrometers with user-adjustable position of the measurement spots. Both systems are using holograms for beam deflection. The measurement is based on heterodyne interferometry with a frequency difference of 5 MHz between reference and object beam. One of the systems uses programmable positioning of the spots in the object volume but is limited concerning the light efficiency. The other system is based on static holograms in combination with mechanical adjustment of the measurement spots and does not have such a general efficiency restriction. Design considerations are given and we show measurement results for both systems. In addition, we analyze the sensitivity of the systems which is a major limitation compared to single point scanning systems. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4845596] I. INTRODUCTION
The measurement of vibrations of technical objects is of considerable importance in industrial quality control and applied research. Typically, Doppler-based interferometric methods are employed because very small vibrating amplitudes xmax in the range of nanometers and even picometers, which are not detectable by other methods, can be measured. Even very small amplitudes at high frequencies result in large Doppler shifts f = 2v/λ, where we denote the wavelength of the light by λ and the speed of the movement by v.1 For typical applications in mechanical engineering, Doppler shifts of up to several MHz are to be detected. At such high detection frequencies two main problems have to be taken into account. First, of course, the signal has to be sampled with a high enough sampling frequency. Second, enough light needs to be available in order to deliver enough photons on the detector for the short measurement time corresponding to the inverse of the frequency resolution when the spectrum of the vibration is calculated. For periodic vibrations, both problems can be approached by using time-averaging or periodic sampling. Of course, transient or aperiodic vibrations cannot be measured using such methods. Therefore, for industrial measurements, interferometry typically is used. In order to achieve a satisfactory signal-to-noise level at the sufficiently high frequencies heterodyne detection is employed. Single point systems are extended by scanning using electro-mechanical scanning devices and three-dimensional vibrations are measured using a measurement from different directions. A lot of interesting full-field measurement systems for measuring vibrations at a lot of points (some tens of thousands to several × 106 ) are available. Typical approaches rely on speckle techniques, e.g., electronic speckle pattern interferometry or digital holography.22 Due to the limited number of photons one, however, is limited to averaging2, 3 or sam0034-6748/2013/84(12)/121701/8/$30.00
pling approaches, e.g., with double-pulse systems or stroboscopic illumination.4–6 Current commercial systems are not suitable for the recording of transient phenomena at multiple points because scanning in this case is not possible. Full-field interferometric (holographic) detection by using fast camera systems as proposed by different authors7–10 is limited to small or medium Doppler shifts due to the aforementioned limited number of photons which are available during the short effective measurement time. Considerable improvement is possible by sacrificing one dimension, e.g., using a line illumination in combination with a line-scan camera, as proposed, e.g., by MacPherson et al.8 Still, high frequencies cannot be reached with such approaches. Further improvement necessarily means that the number of simultaneous measurement points has to be further reduced. This leads to so-called multi-channel systems which have a limited number of measurement channels. Several such systems have been realized with fixed measurement geometries.11–19 A low-noise laser source is necessary and, therefore, restrictions of the laser power have to be considered. Consequently, the user wants to control at least the position of the measurement points on a given object. This, of course, cannot be achieved using fixed-geometry systems. In this contribution we describe two systems that achieve a flexible measurement geometry using a holographic approach for beam deflection. Section II shows one approach based on dynamic holography using a spatial light modulator (SLM; multipoint vibrometry with dynamic holograms, MVDH). The measurement geometry can be changed very fast (video rate) but due to the limitation of current commercially available SLMs the light efficiency is strongly limited for satisfactory beam deflections. The second approach (multipoint vibrometry with static holograms, MVSH) is presented in Sec. III and employs static holograms in combination with mechanical adjustment of the measurement positions. This
84, 121701-1
© 2013 AIP Publishing LLC
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
121701-2
Haist et al.
Rev. Sci. Instrum. 84, 121701 (2013)
FIG. 1. Object path of an heterodyne interferometer using a spatial light modulator (LCD) for non-mechanical beam deflection. Shown here without the object-sided telescope that might be used in order to increase the scanning range. Depending on the programmed grating different deflections can be realized.
leads to improved light efficiency at the cost of an increased setup time for a new measurement-grid configuration.
II. VIBROMETRY USING A SPATIAL LIGHT MODULATOR
The basic idea of using dynamic holography within an interferometric vibrometer as described in Ref. 20 is depicted in Fig. 1. A hologram is used for beam deflection and beam splitting. This way, mechanical beam deflection which might introduce spurious vibrations and inaccuracies of the beam position is eliminated. Since the basic optical design considerations will also apply to a multipoint configuration we will shortly review the most important relationships. The most simple hologram is a grating and it directly leads to beam deflection by the angle φ = asin(λ/d) with the grating period d. If the grating is not a perfectly blazed phase grating only part of the light will be diffracted into the desired deflection. In order to achieve a satisfactory efficiency the blazed grating has to be approximated by at least 3 to 4 discrete and quantized pixels. For high quality commercial spatial light modulators the pixel pitch is in the range of 10 μm and, therefore, the maximum usable deflection is in the range of about 1◦ for visible light in the green spectral region. For a lot of applications this deflection is not large enough and as a result a telescope is necessary to amplify the deflection. Unfortunately, an amplification of the deflection by a magnification M leads to a reduction of the diameter of the pupil of the optical system by the same factor and consequently the light efficiency of the detection is reduced by a factor of M2 (area of the receiving pupil). As a result, the pupil size is completely determined by the number of pixels of the SLM and the desired maximum deflection. Compared to static systems this leads to a lower light efficiency.
A. Fourteen-channel multipoint vibrometry with dynamic holograms
In order to realize a multipoint system the SLM is used to generate multiple object beams. To this end different hologram multiplexing schemes are possible.21 All of these schemes lead to the same overall light efficiency because the overall pupil area stays the same. Still, differences between the schemes exist, especially concerning the size of the measurement spot on the object and the number and distribution of unwanted diffraction orders. No matter which scheme is employed it is mandatory to work in a “confocal-mode” where the same sizes of the illumination and the detection pupils for each channel of the vibrometer are used. This way, speckle-induced contrast loss of the interference signal is avoided. One major challenge of such a system that realizes multiple measurement spots simultaneously using a thin hologram is the unavoidable crosstalk of the holograms. There is crosstalk between the sending and receiving parts of the hologram (mostly reduced by using several polarizing components and aperture elements), crosstalk between the individual holograms for each measurement spot, and crosstalk due to imperfect modulation characteristics of the spatial light modulator. The optical design as well as the computation of the hologram have to consider these effects because any unwanted (interfering) light contribution that will fall onto one of the detectors might lead to measurement errors. The best multiplexing approach concerning resolution and flexibility is a complex superposition of the holograms for the individual channels. The resulting complicated spurious diffraction orders are filtered using pinhole masks in a plane conjugate to the object. This filtering in combination with hologram optimization as described in Ref. 21 avoids that unwanted diffraction orders of the hologram fall onto detectors and lead to measurement errors. Fig. 2 depicts one of the optical setups that we have investigated. It consists of a heterodyne interferometer using
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
121701-3
Haist et al.
Rev. Sci. Instrum. 84, 121701 (2013)
FIG. 2. Experimental setup for programmable multipoint vibrometry (MVDH). The central element is the liquid crystal modulator that is used for illumination (red) and detection (blue). The detector unit consists of a pinhole array in combination with a microlens array and multimode fibers (see text for details). Reprinted with permission from AIP Conf. Proc. 1457, 234 (2012). Copyright 2012 American Institute of Physics.26
acousto-optical modulation (AOM) where a spatial light modulator is located in a near-Fourier plane of the object. The AOM consists of two cells working at 84 MHz and 79 MHz, giving a 5 MHz frequency difference which is used for heterodyning. The laser source is a 20 mW diode-pumped solid state (DPSS) laser at 532 nm wavelength. As described, we use a Kepler telescope with a magnification of four to increase the object field. In order to achieve the maximum possible light efficiency we use a phase-only Liquid-Crystal on silicon (LCoS) modulator, namely a Holoeye Pluto modulator (1920 × 1080 pixels, 8 μm pixel-pitch, compare Sec. II B). The optical design (see Fig. 2) achieves diffraction limited reconstruction and imaging using standard achromatic lenses over the whole field. Residual aberrations, e.g., due to bad alignment can be eliminated by modifying the holograms. One half of the rectangular SLM is used for the illumination of the object. The light being scattered/reflected at the object is modulated only by the second half of the SLM. To this end we use a combination of a λ/4 plate and a split λ/2 plate located in a plane conjugate to the SLM. This way, the polarization of the light that is backreflected from the object and
that falls onto the first half of the SLM will be rotated by 90◦ and, therefore, will not be modulated by the SLM. Additionally, in another plane conjugate to the SLM such unwanted light contributions are blocked. After the SLM, the backreflected light is imaged by the same Kepler telescope that has been used for the illumination in combination with another lens onto an intermediate image plane (PA) with a pinhole mask which is conjugate to the receiving multimode fibers that lead to discrete photodiodes. The pinhole mask pattern corresponds to the detector/fiber pattern and is used to eliminate all remaining unwanted diffraction orders. A microlens array (MLA) is located after this pinhole mask for generating one collimated beamlet of appropriate size for every fiber. The superposition with the reference beam then leads to the heterodyne interference signal at the entrance of the fibers. For complex multiplexing, the whole area of the SLM and the entrance pupil is used for each channel. But since the holograms are thin (in contrast to volume holograms) the light coming from one object point is deflected to N different directions and only one of these directions leads to the desired detector. Concerning the light efficiency we end up with the
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
121701-4
Haist et al.
Rev. Sci. Instrum. 84, 121701 (2013)
TABLE I. Comparison of different spatial light modulators.
Resolution (pixel) Pixel pitch (μm) Max. angle (◦ ) Diffraction efficiency (%) Reflectivity (%) Max. phase shift (rad) Price (Euro)
SDE1280
Pluto-VIS
X10468-01
BNS-DM
1280 × 720 9.5 1.19 ≈40 68@5◦ 0.85pi 1000
1920 × 1080 8.0 2.27 69 60 >2pi 8300
800 × 600 20 0.91 85 75@5◦ >2pi 8000–10 000
512 × 512 15 1.2 66 90 >2pi 20 000
same result that we directly obtain for spatial multiplexing: Due to the N channels the efficiency is reduced by 1/N2 . This is an important general limitation and it applies to all multipoint concepts if the pupil size is kept constant. Therefore, good signal-to-noise ratios for large numbers of channels can be only achieved if the overall pupil size is large and/or the laser power is strong. Unfortunately, for SLM-based vibrometry the pupil size is limited by the area of the spatial light modulator. B. Spatial light modulator
Different SLMs have been considered as the core element of our system and four of these modulators have been tested in detail:
r r r r
Cambridge Correlator SDE1280 Holoeye Pluto-VIS Hamamatsu X10468-01 Boulder Nonlinear Systems BNS-XY-Ph-P512-DM
In Table I some of the main specifications are given. Finally, the Holoeye Pluto modulator has been chosen because of the good experimental results and the availability as an OEM (original equipment manufacturer) version. It is a high definition liquid crystal phase-only modulator with 1920 × 1080 pixels, a pixel pitch of 8 μm, and a fill factor of 87%. Using such an SLM several factors which influence the diffraction efficiency have to be considered:20 Fill factor: Between the pixels of the SLM the modulation is not as desired. The active area (SLM area without the pixel gaps) divided by the SLM area is the area-related fill factor. For absorbing pixel gaps, the efficiency of the hologram reconstruction is proportional to the square of the fill factor. Fringing field effect: For small pixels we have the problem of crosstalk between adjacent pixels. That means that the liquid crystals of one pixel are influenced by the electric fringing field of the neighboring pixels causing a smoothing of a sharp phase step. This blurring effect results in an inaccurate representation of the hologram and, in consequence, in some loss of diffraction efficiency and unwanted diffraction orders. Discretization and quantization: Because the SLM is pixelated it is only possible to image discretized and quantized holograms. Again, part of the light will be redirected to spurious diffraction orders.
Temporal effects: The SLM-elements are modulated with a certain time-dependent signal to realize the phase delay. The phase delay can be defined, for example, by the amplitude of a sine excitation or by the duty cycle of a pulse signal. The kind of realization influences strongly the phase modulation of the beam reflected by the SLM which leads to spurious signals in the vibration signal of the vibrometer. Our investigations have shown that the analog control of the Hamamatsu SLM shows the lowest influence of such spurious effects. Modulation: Typically, even for a “phase-only” modulator some amplitude modulation is still present, which leads to a loss of diffraction efficiency. Also a nonlinear phase response leads to unwanted diffraction orders.
C. Experimental results and limitations
The system has been tested on mirrors and objects prepared with retro-reflecting tape. The wavefront has been optimized by a special algorithm for illuminating the object points in order to achieve the best signal-to-noise ratio. This way, aberrations and dark speckles are avoided.24 The hologram deflections have been calibrated in such a way that a desired position on the object automatically triggers the generation of a corresponding detection hologram that will deflect the scattered light onto the desired detector. The hologram computation has been implemented on the graphics processing unit (GPU) of a GT8800-based consumer graphics board using NVidia’s CUDA programming methodology. Figs. 3 and 4 show typical results for a three channel measurement using spatial multiplexing (compare Ref. 21). The measurement object has been a loudspeaker with retroreflective tape driven by a frequency generator. The measurement positions on the loudspeaker can be freely chosen using computer-controlled change of the hologram. It is obvious that the light efficiency is strongly reduced compared to a conventional single-point vibrometer and this is the main problem of the method. Measurements on a mirror are always possible but on retro-reflective tape at a distance of about 1 m the light efficiency with the employed 18.3 mW laser is not sufficient to measure more than four channels simultaneously. Although heterodyne interferometry is extremely sensitive down to the shot noise limit the received light power needs to exceed the noise power in the demodulation bandwidth. Especially
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
121701-5
Haist et al.
Rev. Sci. Instrum. 84, 121701 (2013)
FIG. 3. One channel of a simultaneous measurement on a loudspeaker with retroreflective tape for a three channel measurement. Reprinted with permission from AIP Conf. Proc. 1457, 234 (2012). Copyright 2012 American Institute of Physics.26
the low numerical aperture for a maximum necessary beamdeflection angle of approximately 5◦ for standard measurement tasks has posed a major restriction. Even a 100 mW laser would not solve the general problem. We have estimated that at least 10 × 106 pixels are required for the reception and detection SLM area in combination with 100 mW laser power. Ten times more pixels correspond to a ten times larger sensitivity. The size of the entrance/exit pupil D = ySLM /M of the optical system, of course, is finally limited by the size of the light modulator ySLM . Since the number of pixels in one direction of the SLM NSLM , the pixel pitch pp, and the size of the SLM are related via ySLM = NSLM · pp, the size of the (rectangular) entrance/exit pupil is given by NSLM · z · pp λ NSLM pp = tan arcsin (1) D= M y 2 pp ≈
NSLM · pp · z λ y 2 pp
(2)
NSLM · z λ . 2y
(3)
=
The overall light efficiency depends on a lot of factors (see Ref. 23) but is proportional to the square of the linear
FIG. 5. Schematic of the 12 channel heterodyne interferometer with static holograms (MVSH). There are 6 further channels under the 6 visible ones.
extension of the entrance pupil and—as described—inversely proportional to the square of the number of measurement channels N: η∼
2 z 2 λ2 NSLM D2 ≈ . N2 4 y2 N 2
(4)
III. MULTIPOINT VIBROMETRY USING STATIC HOLOGRAMS
Because of the efficiency problems mentioned in Sec. II we decided to realize another multipoint vibrometer based on static holograms. In this approach the splitting of the laser beam into multiple channels is accomplished by two static diffractive optical elements (DOE) instead of the SLM. Positioning of the measurement point is done manually by mechanical means. Therefore, a larger pupil per channel can be used and the light efficiency is strongly increased. One disadvantage of this design is that the number of measurement spots is not variable and, therefore, it is not possible to combine several channels into one. The second disadvantage is, of course, the necessity to align the positions on the object by hand. A. Twelve-channel interferometer and optical head
FIG. 4. Second channel of a simultaneous measurement on a loudspeaker with retroreflecting tape for a two channel measurement. Reprinted with permission from AIP Conf. Proc. 1457, 234 (2012). Copyright 2012 American Institute of Physics.26
The optical setup of the vibrometer is depicted in Fig. 5. We use a 532 nm diode-pumped solid state laser which is split into measurement and reference light by a polarizing beam splitter (PBS). The light in the object arm is frequency-shifted by 5 MHz using two combined Bragg cells. The reference and the object beam are divided into 3 × 4 parallel beams utilizing two DOEs, see Sec. III B. After the second DOE every group of 4 measurement beams are split again by a single PBS. Every single beam of the object path is coupled into a monomode fiber. At the output of the fiber an objective lens
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
121701-6
Haist et al.
Rev. Sci. Instrum. 84, 121701 (2013)
FIG. 6. Combination of two CGHs for 12-channel splitting.
focuses the beam onto the object. In addition, a quarter wave plate is placed to every fiber to make sure that the polarization of the returning light is rotated by 90◦ and, thus, is reflected at the PBS in direction of the detectors. On the way back, the reference and object beams are superimposed by non-polarizing beam splitters and each of the 12 beams is focused on a multimode fiber. These are connected to photodetectors providing a broadband heterodyne signal. To solve the problem of the adaptive measurement position the fibers are passed to a sensor head inside which every fiber and the objective lens are mounted in a tilting bearing. The objectives can be focused between a working distance of 80 mm to infinity. A spot diameter of 30 m at a distance of 80 mm and of 124 m at a distance of 500 mm have been achieved. The objectives are arranged in a square around a camera which can be used to control the position of the measurement spots. Each tilting bearing can be used to adjust the corresponding objectives in an angular range of ±10.5◦ (horizontally and vertically) manually. The maximum distance where a reasonable signal can be obtained is approximately 3 m. Thus, an object with the size of approximately 1 m diameter can be measured in a maximum working distance of 2.7 m. The 12-channel demodulator consists of two 8-channel analog-digital (A/D) converters (40 MSamples/s) which have been synchronized with one common clock for all channels. Thus, our A/D converter can digitize up to 16 channels synchronously. Since we need only 12 signal channels for our 12channel interferometer we have four free channels to realize a trigger and to obtain reference signals. The digital signals are evaluated using a field-programmable-gate-array (FPGA) processor. The detectors of the multibeam interferometer provide also an analog signal-strength voltage signal. These signals have a very low bandwidth and are converted to digital values by an additional A/D converter from National Instruments and transferred to the PC via USB. The signal strength can be used to optimize the laser focus and position. B. Static hologram
The fiber coupling is necessary to ensure a large enough distance between individual detectors to avoid electrical crosstalk between the detectors. For achieving a stable geom-
etry for the fiber coupling and a minimization of the necessary alignment elements we employ a splitting of the laser into 12 beamlets using two computer generated holograms (CGHs). The output of these two CGHs is 12 accurately aligned beamlets which are collinear with the incoming beam, see Fig. 6. The first CGH generates 12 beam deflections while the second CGH ensures the collinearity. The second hologram which gives a recollimation of the beams consists just of 12 blazed gratings with different grating periods. The first hologram which achieves the 1:12 splitting into the desired geometry has been optimized using a direct binary search algorithm. Because of the given symmetry of the desired reconstruction we chose the first CGH to be a binary pattern. The optimized hologram is tiled to its final size of 5 × 5 mm. It is therefore larger than the laser beam diameter to achieve insensitivity concerning lateral alignment errors. These two CGHs must be aligned accurately and then they can be used as a combined module. A graytone lithographic process is used for the fabrication of the elements where a Circular Laser Writing System CLWS 300 radial plotter is utilized to expose the photoresist which is spin-coated onto a quartz substrate.25 After lowcontrast development of the exposed resist we get the desired height profile which is transferred to the quartz using reactive ion etching. The binary elements are fabricated by using wet etching of chromium coated quartz. We can improve the DOEs concerning manufacturing errors by using a special edge optimization algorithm and increase the efficiency by 10%, so that the first hologram has an overall diffraction efficiency (including Fresnel losses for the uncoated element) of 72%. For the second DOE we obtain a diffraction efficiency of 58% because here we are not able to take advantage of the symmetry as for the first element where the +1st and −1st order lead to the desired deflection angles. C. Measurement examples
One interesting transient event we investigated with the multipoint vibrometer was the bouncing of a valve. Considering valves with conical seats the needle may strike the center only after some bounces on the cone. This process is complex and not repeatable (see Fig. 7). For this reason it is necessary to measure multiple points simultaneously to get the deflection shape of the valve. Therefore we arranged eight ro-
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
121701-7
Haist et al.
Rev. Sci. Instrum. 84, 121701 (2013)
FIG. 7. Surface velocity on the valve in one measurement point for 8 impacts of a closing valve.
FIG. 8. Measurement setup with 8 mirrors for measuring up to 9 sides of the valve simultaneously from one direction. The schematic of the setup as top view is presented in (a) while (b) shows a photo of the front view of the setup.
FIG. 9. Measurement grid and two examples for the deflection of the valve 250 μs after the impact.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
121701-8
Haist et al.
tatable mirrors around the valve to get a detailed view (see Fig. 8). In Fig. 9 we measured the radial velocity of the valve on two perpendicular rows each consisting of 6 measurement points. In Fig. 9 we show the maximum deflection of the valve at 250 μs after the impact. IV. CONCLUSION
We have described two holographic approaches for performing multipoint vibrometry using heterodyne interferometry. In both setups the user can freely choose the positions of the measurement spots. This is the main advantage of the method compared to other techniques. Dynamic holograms implemented using a spatial light modulator can be used in order to program the position of the measurement spots by optimizing the sending and receiving hologram. The disadvantage of this method is the limited space-bandwidth of the commercially available light modulators. This leads to a limitation concerning the light efficiency, especially if larger object fields are to be measured. The system with static holograms avoids this disadvantage but needs mechanical adjustment of the measurement positions. Measurements for both systems have been presented. In general, one main limitation for multipoint systems in combination with transient phenomena is the light efficiency because the receiving pupil area is reduced by the square of the number of measurement channels. ACKNOWLEDGMENTS
The authors would like to thank the German Bundesministerium für Bildung und Forschung (BMBF) for financial support under the project HoloVib (No. 13N9339). 1 L.
E. Drain, The Laser Doppler Principle (John Wiley and Sons, 1980).
2 C. Joenathan, “Vibration fringes by phase stepping on an electronic speckle
pattern interferometer: an analysis,” Appl. Opt. 30, 4658–4665 (1991). Bavigadda, R. Jallapuram, E. Mihaylova, and V. Toal, “Electronic speckle-pattern interferometer using holographic optical elements for vibration measurements,” Opt. Lett. 35, 3273–3275 (2010). 4 P. Hariharan, B. F. Oreb, and C. H. Freund, “Stroboscopic holographic interferometry: measurements of vector components of a vibration,” Appl. Opt. 26, 3899–3903 (1987). 5 I. Alexeenko, M. Gusev, and V. Gurevich, “Separate recording of rationally related vibration frequencies using digital stroboscopic holographic interferometry,” Appl. Opt. 48, 3475–3480 (2009). 6 R. Pawluczyk, Z. Kraska, and Z. Pawlowski, “Holographic investigations of skin vibrations,” Appl. Opt. 21, 759–765 (1982). 3 V.
Rev. Sci. Instrum. 84, 121701 (2013) 7 A.
Styk, M. Kujawinska, P. Lambelet, A. Royset, and S. Beer, “Microelements vibration measurement using quasi-heterodyning method and smartpixel camera,” in Fringe 2009, edited by W. Osten and M. Kujawinska (Springer, 2009), pp. 523–527. 8 W. N. MacPherson, M. Reeves, D. P. Towers, A. J. Moore, J. D. C. Jones, M. Dale, and C. Edwards, “Multipoint laser vibrometer for modal analysis,” Appl. Opt. 46, 3126–3132 (2007). 9 M. J. Connelly, P. M. Szecówka, R. Jallapuram, S. Martin, V. Toal, and M. P. Whelan, “Multipoint laser Doppler vibrometry using holographic optical elements and a CMOS digital camera,” Opt. Lett. 33, 330–332 (2008). 10 M. J. Connelly, P. M. Szecowka, R. Jallapuram, S. Martin, V. Toal, and M. P. Whelan, “Laser Doppler Vibrometry system using the syntheticheterodyne interferometric demodulation scheme implemented on a CMOS DSP camera,” in Proceedings of the 6th International Symposium on Communication Systems, Networks and Digital Signal Processing 2008 (IEEE, 2008), pp. 133–136. 11 W. Zheng, R. V. Kruzelecky, and R. Changkakoti, “Multichannel laser vibrometer and its applications,” Proc. SPIE 3411, 376–384 (1998). 12 E. Cupido, S. Morel, and D. Smith, “Multipoint laser doppler vibrometer for transient analysis,” in Proceedings of IMAC XXI, Orlando, USA (Springer, 2003). 13 E. Li, J. Xi, J. Chicharo, J. Yao, and D. Yu, “Multi-point laser Doppler velocimeter,” Opt. Commun. 245, 309–313 (2005). 14 V. Aranchuk, A. Lal, C. Hess, and J. M. Sabatier, “Multi-beam laser Doppler vibrometer for landmine detection,” Opt. Eng. 45, 104302 (2006). 15 A. K. Lal, C. F. Hess, H. Zhang, L. E. Hurtado, V. B. Markov, and V. Aranchuk, “Multi-beam heterodyne laser Doppler vibrometer,” U.S. patent 6,972,846 (2005). 16 A. K. Lal, C. F. Hess, E. Hurtado, V. B. Markov, V. Aranchuk, and V. V. Doushkina, “Multi-beam heterodyne laser Doppler vibrometer,” U.S. patent 7,477,498 B3 (2009). 17 A. T. Waz, P. R. Kaczmarek, and K. M. Abramski, “Laser-fibre vibrometry at 1550 nm,” Meas. Sci. Technol. 20, 105301 (2009). 18 J. Kilpatrick, A. Apostol, and V. Markov, “System for transient spatiotemporal (4D) vibration imaging and non-destructive inspection,” in Fringe 2009, edited by W. Osten and M. Kujawinska (Springer, 2009), pp. 519– 522. 19 J. Kilpatrick and V. Markov, “Multi-pixel (matrix) laser vibrometer,” Imaging 3, 2–4 (2010). 20 S. Zwick, M. Warber, T. Haist, F. Schaal, W. Osten, S. Boedecker, and C. Rembe, “Advanced scanning laser-Doppler vibrometer with computer generated holograms,” AIP Conf. Proc. 1253, 279–290 (2010). 21 T. Haist, A. Tarbeyevskaya, M. Warber, W. Osten, C. Rembe, M. Ludwig, and W. Stork, “SLM-based multipoint vibrometry,” Proc. SPIE 8082, 80821V (2011). 22 R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge University Press, 1989). 23 S. Zwick, T. Haist, M. Warber, and W. Osten, “Dynamic holography using pixelated light modulators,” Appl. Opt. 49, F47–F58 (2010). 24 S. Mayer, B. Tibken, and C. Rembe, “A new approach for signal loss compensation in a vibrometer,” in American Control Conference (ACC) (IEEE, 2011), pp. 2645–2650. 25 W. Osten, G. Baer, M. Häfner, W. Lyda, C. Pruss, R. Reichle, and F. Schaal, “Making, testing, applying: some progress in the field of micro-optics at ITO,” Proc. SPIE 8769, 876905–870611 (2013). 26 T. Haist et al., AIP Conf. Proc. 1457, 234 (2012).
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 202.28.191.34 On: Tue, 23 Dec 2014 01:03:18
