- Email: [email protected]
Heterodyne speckle interferometer for full-field velocity profile measurements of a vibrating membrane by electronic scanning
ARTICLE IN PRESS
Optics and Lasers in Engineering 45 (2007) 677–683
Heterodyne speckle interferometer for full-field velocity profile measurements of a vibrating membrane by electronic scanning Mauro V. Aguannoa,b, Fereydoun Lakestanib, Maurice P. Whelanb, Michael J. Connellya, a
Optical Communications Research Group, Department of Electronic and Computer Engineering, University of Limerick, Limerick, Ireland Photonics Group, Institute for Health and Consumer Protection, European Commission Joint Research Centre, Ispra, (VA) I-21020, Italy
b
Received 21 September 2006; received in revised form 4 December 2006; accepted 4 December 2006 Available online 22 January 2007
Abstract Dynamic deformation measurements were carried out by combining full-field speckle interferometry and heterodyne interferometry. A digital demodulation technique based on the evaluation of the instantaneous frequency have been implemented in the digital signal processor of a complementary metal-oxide semiconductor (CMOS)-based camera to extract velocity measurements from phase modulated optical carrier signals. The purpose of this experimental investigation was to demonstrate a full-field laser vibrometer system that could replace electro-mechanical scanning with electronic scanning within a programmable stand-alone and relatively low-cost digital camera. Velocity profiles of a vibrating membrane in the order of few microns per second were reconstructed automatically by performing an electronic scanning of the surface over the image sensor. r 2006 Elsevier Ltd. All rights reserved. Keywords: Metrology; Vibrometry; Speckle interferometer; CMOS camera; Signal processing
1. Introduction Quantitative phase measurement methods such as the temporal phase-stepping (TPS) technique [1–4] set a new standard in the precision achievable from full-field interferometry. Phase stepping (or phase shifting) can be applied in almost any dual-wavefront interferometer whether classical or based on speckle. The approach is based on the acquisition of a sequence of interferograms acquired after the introduction of known amounts of relative phase step between the object and the reference path. Simple arithmetic operations on the interferogram set then allow the calculation of relative optical (wrapped) phase over the entire area of interest. Although phasestepping routines have become an important part of most full-field optical metrology systems they can suffer from errors in phase calculation due to phase-step miscalibration and unwanted mechanical vibration in the optical set-up Corresponding author. Tel.: +353 61 202173; fax: +353 61 338176.
E-mail addresses: [email protected] (M.V. Aguanno), [email protected] (M.P. Whelan), [email protected] (M.J. Connelly). 0143-8166/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2006.12.001
during image acquisition. Moreover, most full-field systems utilise standard CCD cameras which typically limits image acquisition to video rates (25 Hz) and in turn, restricts the speed at which phase maps can be calculated. In general therefore, full-field optical metrology systems that use phase-stepping and standard CCD cameras can only be used for static or quasi-static measurements. Full-field dynamic measurements usually require the use of techniques employing expensive fast CCD cameras [5,6], which allow the time history reconstruction of a transient event and as a result thousands of images need to be acquired for successive post processing. Synchronising pulsed lasers with the exposure of standard CCDs has demonstrated non-stationary event analysis [7,8]. However, this approach is usually limited to measurements of periodic motion. An alternative is the spatial phasestepping (SPS) technique, also known as spatial carrier method. In SPS, a known phase shift is implemented spatially using polarisation optics, a diffraction grating or a beam lateral offset. With SPS only a single frame is needed to estimate the measurement phase [9–11]. The advantages of this technique are fast phase measurements and insensitivity to TPS fluctuations. However, spatial
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resolution is reduced compared to TPS and there exists alignment difficulties requiring sub-pixel accuracy. Optical heterodyning [12–14] is a carrier-based approach for optical phase detection that is capable of following fast dynamic events with extremely high sensitivity [15] and accuracy. Heterodyne techniques [16–20] rely on mixing mutually coherent stabilised laser beams, each with a different optical frequency, to generate a beat carrier signal at frequency inside the bandwidth of the optical detector. The heterodyne carrier signal can be modulated in phase through the interaction with a test object and subsequently demodulated using various phase retrieval methods [21] to provide, for example, a measurement of velocity. When heterodyne techniques are used in conjunction with fast optical detectors such as single photodiodes, detection of the optical carrier and demodulation of its phase signal can be made very rapidly. The laser Doppler vibrometer (LDV) [22,23] is a well known example of a device which is based on heterodyne detection and it usually incorporates a single photo-detector with a fast response time. A major drawback of the LDV, however, is the fact that a single detector only allows a measurement to be made at a single point in space. To carry out full-field measurements, scanning LDV (SLDVs) systems have been developed [24–27] that combine a single-detector LDV with sophisticated electro-mechanical scanning units. This allows the rapid sequential measurement of the velocity or displacement of an array of points over an area of interest. However, such systems are typically very expensive, bulky and they lack versatility. Considering the aspects of both phase-stepping full-field techniques and optical heterodyne methods, in this paper it is proposed that a full-field optical metrology system would combine the advantages of both approaches. In essence the system should employ optical heterodyning for rapid high resolution phase measurement, and utilise an image sensor and imaging optics to allow high resolution spatial measurements without the need for electro-mechanical scanning. The solution presented here adopts a low-cost approach to combine the advantages of speckle full-field interferometry with the benefits of carrier-based systems [28]. The key element on which the solution is based is a complementary metal-oxide semiconductor (CMOS) image sensor [29], which offers independent and direct pixel access, both in space and time. This is made possible by novel active pixel sensor (APS) architecture [30]. Using this type of sensor, which is integrated into a digital camera, high acquisition bandwidths can be achieved (i.e. 10 s kHz) when acquiring from a small number of pixels (e.g. 10–100). This facilitates the acquisition of high frequency optical carrier signals. By sequentially switching from pixel to pixel, or from one set of pixels to another set of pixels, an electronic scan of any or every point on a test surface can be made. The spatial resolution obtainable (at the object surface) depends on the CMOS pixel size and the magnification factor of the imaging system employed. The spatial density
of measurements acquired depends simply on the number and location of the pixels accessed. The random, direct access in space and time is particularly useful and efficient when specific regions (or points) of interest are chosen for analysis rather than the entire field of view. The CMOS camera employed also incorporated a dedicated digital signal processor (DSP) which permitted rapid on-board demodulation of the optical carrier signals through the implementation of real-time signal processing routines dedicated to the specific measurement requirements. In the experimental investigations described in this paper, the CMOS-DSP camera was combined with a heterodyne interferometer to produce a versatile, compact optical metrology system capable of rapid high-resolution measurement of velocity profiles of engineering surfaces [31,32]. In particular, vibration analysis was carried out on a thin vibrating membrane within a speckle heterodyne interferometer and validated using a commercial LDV system. 2. Instantaneous frequency (IF) detection Digital demodulation methods based on the evaluation of the IF can be applied to frequency- and phasemodulated signals for very precise analysis, such as velocity measurements. The IF is given by the time derivative of the phase of a complex signal [33–37]. A logarithmic active CMOS image sensor array can be considered as a multidetector system connected to a DSP demodulation unit, where broadband signals, acquired from single pixels and acting as single detectors, can be analysed. The approach adopted to retrieve the velocity and displacement information from a vibrating surface, mainly consists in the determination of the IF using the analytic signal argument of a real signal. This method is termed single pixel carrier based demodulation (SPCBD) and the algorithm was implemented directly on the DSP [38]. Analytic signals are well established as an important tool for processing one-dimensional real signals, in that they provide a direct access to the signal amplitude and phase. The analytic signal z(t) of a real signal s(t), is a complex signal having the actual signal as the real part and the Hilbert transform H of the same signal as the imaginary component: zðtÞ ¼ sðtÞ þ jH½sðtÞ ¼ aðtÞ ejjðtÞ ,
(1)
where the amplitude a(t) and the phase j(t) are given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (2) aðtÞ ¼ ðsðtÞÞ2 þ ðH½sðtÞÞ2 , H½sðtÞ jðtÞ ¼ tan . sðtÞ 1
(3)
The Hilbert transform is given by the principal value of the integral Z 1 1 sðtÞ dt. (4) H½sðtÞ ¼ p 1 t t
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pixel output signal is equal to the imaginary part of the ratio of the time derivative of the analytic signal to the analytic signal. In the implementation of the algorithm the analytic signal and its time derivative were calculated in the frequency domain. From the IF, the velocity and the displacement are easily retrieved. The mean value of f(t), calculated over the acquisition interval, of the original FM signal equals the carrier frequency. Fig. 1. Magnitude of the gate filter transfer function vs. frequency.
Fig. 2. Flowchart of the SPCBD algorithm.
The IF, f(t) is given by f ðtÞ ¼
1 djðtÞ . 2p dt
(5)
An analytic signal can be generated in the frequency domain by suppressing the negative frequency components of the original signal. The analytic signal of the real signal s(t) acquired from a pixel can be obtained by multiplying the fast Fourier transform (FFT) of s(t) by a bandpass filter centred at Df, whose response is zero at negative frequencies and then by taking the inverse FFT, Df ¼ 962 Hz and the filter bandwidth ¼ 100 Hz. This is large enough not to alter the spectrum of the frequency modulated signals and also removes the noise components from the sampled signal as well as the harmonics generated by the CMOS pixel logarithmic response. The shape of the filter produced an undistorted analytic signal, avoiding aliasing problems due to the sampling of a finite signal. The magnitude of the gate filter transfer function is shown in Fig. 1. The impulse response of the filter decreases as 1/t6 for large values of t which greatly reduces the aliasing. The implementation of the SPCBD algorithm is graphically presented in the flowchart of Fig. 2. The IF of the
3. Experimental investigation In the two-wavefront interferometer employed, shown in Fig. 3, a laser beam (532 nm) is divided by beam splitter BS-1 into object and reference beams. Along these paths two acousto-optic modulators (AOMs) are driven at 80 MHz and 80 MHz+102 Hz. This shifts the laser frequency in each branch in order to produce a heterodyne effect upon recombination and interference at the camera, with a carrier frequency of 102 Hz. The object beam was expanded by expanding lens Ex-1 onto the object surface and the light reflected back was recombined with the second beam by beam splitter BS-2 with the reference beam expanded by expanding lens Ex-2. The interfering wavefronts travelling from BS-2 were then imaged by the CMOS sensor fitted with a zoom camera lens. The light signal reflected on the loudspeaker is Doppler shifted by the membrane vibration driven by a CW 10 Hz signal. The camera is focused on the membrane. The frequency modulated carrier is detected using single-pixel acquisition and by electronically scanning the CMOS sensor and performing a real-time demodulation processing on the camera DSP in order to extract the velocity of the membrane surface. The CMOS-DSP on-board processing used the algorithm described above. The carrier/ modulation ratio in this experiment was equal to 10 to allow a large separation between the frequency components and to improve the demodulation and the extraction of the IF. The optical signal was sampled at 2.7 kHz, using single buffers of 1024 samples for a corresponding acquisition window of approximately 0.4 s. A typical detected heterodyne optical carrier frequency at 102 Hz modulated by the vibrating surface at 10 Hz is shown in Fig. 4 in the time and spectral domains. The bandwidth widening during the modulation was low suggesting that the Doppler frequency shift was small enough such that the
Fig. 3. Heterodyne speckle interferometer experimental setup.
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Fig. 4. Experimental single pixel acquisition of FM optical carrier; (a) time domain, (b) frequency domain representation (carrier frequency ¼ 102 Hz; modulation frequency ¼ 10 Hz).
Fig. 6. Spectrum of the IF signal showing the 10 Hz membrane vibration frequency.
Fig. 5. Instantaneous frequency of a given point on the vibrating membrane surface.
IF calculated through analytic signal was in fact proportional to the membrane velocity. The extracted IF output, shown in Fig. 5, contains the information needed to determine the velocity of the membrane. A frequency domain representation of the membrane vibration in terms of the IF is shown in Fig. 6. As expected, the spectrum of the retrieved IF shows the frequency peak at the modulating frequency of 10 Hz. The noise in Fig. 6 possibly originates from translational vibrations of the mirrors, temperature fluctuations along optical paths and frequency instability of the carrier and of the sampling clock. These errors could be reduced by subtracting the vibration measured on a reference pixel, which is another
advantage of full field quasi-instantaneous electronic scanning compared to mechanical systems. In another test, a commercial LDV, isolated from the vibration source, was included in the set-up by using a system of mirrors and stepper motor translation stages. The LDV laser beam was positioned onto the vibrating surface in order to compare with the results from the CMOS camera system. One of the measurement grids adopted over the membrane surface for the horizontal and the vertical section scan (numbered star points) performed during the LDV comparison is shown in Fig. 7. A comparison of the velocity of the vibrating membrane detected with the LDV and CMOS-DSP camera system, along sections A-A and B-B is shown in Fig. 8. In Fig. 8(a), the extracted profiles were measured along the horizontal section A-A. The maximum values detected (RMS) were 2.82 mm/s for the CMOS-DSP system and 2.93 mm/s using the LDV. The difference between the amplitudes of the velocity measurements between the
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systems was of the order of 4% of the average velocity at a given point on the membrane surface. In this test the vibration frequency adopted was set to 150 Hz with an acquisition window of 80 ms corresponding to almost 11 cycles. Repeatability tests were performed to check the consistency of the data retrieved from the scanned pixels. For a given pixel accessed 20 times during the electronic scanning with a maximum velocity value detected equal to 1.61 mm/s, the standard deviation was equal to 0.042 mm/s. The slow variations suggest that the most probable reason is temperature variation that affects the membrane elastic properties. Initially, the electronic scanning procedure was performed with step-by-step user interaction, choosing the pixels manually with the aid of real time signal visualisation on the monitor in order to change the sensor analog-to-digital converter parameters and increasing the digitisation levels or rejecting those pixels with a poor response. Several pixels along a section of the membrane were thus manually chosen to determine the velocities over the surface, moving from one pixel to another. All of the velocity amplitudes were extracted and stored to plot a profile of the first mode of vibration. The time required to execute a single measurement was less than 1 s.
As an example of a basic stand-alone application, an automatic procedure as shown in Fig. 9 was implemented on the CMOS-DSP camera to perform electronic scanning and processing. The threshold level visibility for the pixel selection process wave is included in the procedure. The number of the pixels considered along a membrane section during the scanning is chosen at the beginning of the process. As mentioned above, the amplitude velocity data calculated by the analysis of IF signals was used to reconstruct a velocity shape profile. A typical membrane velocity profile derived from experimental velocity data
Fig. 7. Circular vibrating membrane and measurement grid.
Fig. 9. Flowchart of the electronic scanning procedure.
Fig. 8. Velocity profiles of: (a) section A-A, and (b) section B-B of a vibrating membrane using a commercial LDV and the CMOS camera system.
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measurement points as in a laboratory or in-line production environment. This compact and powerful tool achieved very precise measurements suggesting a novel single-pixel approach in the field of optical metrology. Acknowledgements This work was supported through a collaboration contract (]18487-2001-10 SOFD ISPIE) between the Institute for Health and Consumer Protection (IHCP), Photonics Sector, European Commission Joint Research Centre (Ispra, Italy) and the Department of Electronic and Computer Engineering of the University of Limerick (Limerick, Ireland). The project was also supported by Enterprise Ireland International Collaboration Grant and the University of Limerick/Tellabs Foundation. Fig. 10. Typical reconstructed velocity profile of the vibrating membrane.
References collected during one of the automatic electronic scans is shown in Fig. 10. 4. Discussion and conclusion Dynamic measurements were achieved combining both speckle and heterodyne interferometry for velocity profile reconstruction by single-pixel acquisition and electronic scanning of a vibrating thin membrane. Several profile measurements describing the typical Gaussian shape of the first symmetric mode of vibration of the membrane tested showed the potential of the approach. As expected by the adoption of an algorithm based on the frequency analysis, small variations in the amplitudes of the acquired signal and between the pixels accessed, did not affect the extraction of the final velocity results. Amplitudes and shapes were also confirmed by a LDV scan, by simulation tests and by the qualitative analysis of an interferogram recorded at a low vibration frequency. A low standard deviation of 0.042 mm/s determined from many measurements was obtained. An automatic electronic scan procedure enabled the velocity profile of the vibrating membrane to be determined in a relatively short time depending on the number of pixels used; considering that each complete measurement required less than 1 s/pixel scanned. Although it is a quasi-instantaneous technique, in the measuring process of full-field dynamic stationary events this methodology can minimise both environmental noise and thermal drifts. The integrated machine vision system presented can be considered a versatile, simple and low-cost alternative to expensive and complex devices. Moreover, as it is programmable it can be adapted for specific problems in different applications in order to perform several types of measurements combining the benefits of laser Doppler and full-field speckle techniques. For example, in experimental mechanics, this system can also be applied to ensure an elevated accuracy in the monitoring of a sparse number of
[1] Yamaguchi I. Holography, speckle, and computers. Opt Laser Eng 2003;39:411–29. [2] Creath K. Phase-measurement interferometry techniques. In: Wolf E, editor. Progress in optics, vol. XXVI. Elsevier Science Publishers; 1988. p. 349–93. [3] Greivenkamp JE, Bruning JH. In: Malacara D, editor. Phase shifting interferometers, in optical shop Testing. New York: Wiley; 1992. p. 501–98. [4] Huntley J, Kaufmann GH, Kerr D. Phase-shifted dynamic speckle pattern interferometry at 1 kHz. Appl Opt 1999;38(31):6556–63. [5] Moore AJ, Hand DP, Barton JS, Jones JSJDC. Transient deformation measurement with electronic speckle pattern interferometry and a high-speed camera. Appl Opt 1999;38(7):1159–62. [6] Chen F, Luo WD, Dale M, Petniunas A, Harwood P, Brown GM. High-speed ESPI and related techniques: overview and its application in the automotive industry. Opt Laser Eng 2003;40(5–6):459–85. [7] Pedrini G, Tiziani HJ. Double pulse electronic speckle interferometry for vibration analysis. Appl Opt 1994;33:7857–63. [8] Chambarda JP, et al. Pulsed TV-holography recording for vibration analysis applications. Opt Laser Eng 2002;38:131–43. [9] Millerd J, Brock N, Hayes J, North-Morris M, Novak M, Wyant J. Pixelated phase-mask dynamic interferometer. In: Creath K, Schmit J, editors. Proceedings of the SPIE on Interferometry XII. Techniques and analysis, vol. 5531, 2004. [10] Burke J. Application and optimisation of the spatial phase shifting technique in digital speckle interferometry. PhD thesis, Dissertation at Carl von Ossietzky University Oldenburg, Department of Physics and Applied Optics, October 2000. [11] Burke J, Helmers H. Spatial vs. temporal phase shifting in ESPI: noise comparison in phase maps. Appl Opt 2000;38(25):4598–606. [12] Massie NA, Nelson RD, Holly S. High-performance real-time heterodyne interferometry. Appl Opt 1979;18(11):1180–797. [13] Kobayashi T, Shudong J. Optical FM heterodyne interferometry for range and displacement measurements. Precis Electromagn Meas CPEM 1988;88:133–4. [14] Hageli M, Dual J. Heterodyne laser-interferometer with phasedemodulation. /http://www.ifm.mavt.ethz.ch/research-98S, 1998. [15] Gasco´n F, Bayo´n A, Varade´ A. Measurement of longitudinal vibrations in a slender rod by optical heterodyne interferometry. Eur J Mech A/Solids 1998;17:167–77. [16] Fu Y, Tay CJ, Quan C, Miao H. Wavelet analysis of speckle patterns with a temporal carrier. Appl Opt 2005;44(6):959–65. [17] Yoneyama S, Morimoto Y, Fujigaki M, Yabe M. Phase-measuring profilometry of moving object without phase-shifting device. Opt Laser Eng 2003;40:153–61.
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[28] Pedrin G, Schedin S, Tiziani HJ. Pulsed digital holography combined with laser vibrometry for 3D measurements of vibrating objects. Opt Laser Eng 2002;38:117–29. [29] Helmers H, Schellenberg M. CMOS vs. CCD sensors in speckle interferometry. Opt Laser Technol 2003;35:587–95. [30] Dierickx B, Scheffer D, Meynants G, Ogiers W, Vlummens J. Random addressable active pixel image sensors. In: Proceedings of the SPIE. AFPAEC/EUROPTO96, vol. 1, 1996. p. 2950. [31] Aguanno MV, Lakestani F, Whelan MP, Connelly MJ. Speckle interferometry using a CMOS-DSP camera for static and dynamic deformation measurements. In: Proceedingas of the 12th international conference on experimental mechanics. ICEM12, paper ]260, Bari: EURASEM—Politecnico di Bari; 2004. [32] Aguanno MV. Heterodyne interferometry using a CMOS based digital camera for experimental mechanics applications. PhD thesis dissertation, University of Limerick, Limerick, Ireland, May 2005. [33] Randall RB. Frequency analysis. Copenaghen: Bruel & Kjaer; 1987. [34] Lovell BC, Williamson RC, Boashash B. The relationship between instantaneous frequency and time-frequency representations. IEEE Trans Sig Process 1993;41(3):1458–61. [35] Boashash B. Estimating and interpreting the instantaneous frequency of a signal-part; part I: fundamentals, II: algorithms. Proc IEEE 1992;80(4):519–69. [36] Boashash B. Algorithms for instantaneous frequency estimation: a comparative study. Adv Sig Process Algorithm Architect Implement 1990;1348:126–48. [37] Girolami G, Vakman D. Instantaneous frequency estimation and measurement: a quasi-local method. Meas Sci Technol 2002;13: 909–17. [38] Aguanno MV, Lakestani F, Whelan MP, Connelly MJ. Single pixel carrier based approach for full field laser interferometry using a CMOS-DSP camera. Proc SPIE 2003;5251-42:304–12.
Optics and Lasers in Engineering 45 (2007) 677–683
Heterodyne speckle interferometer for full-field velocity profile measurements of a vibrating membrane by electronic scanning Mauro V. Aguannoa,b, Fereydoun Lakestanib, Maurice P. Whelanb, Michael J. Connellya, a
Optical Communications Research Group, Department of Electronic and Computer Engineering, University of Limerick, Limerick, Ireland Photonics Group, Institute for Health and Consumer Protection, European Commission Joint Research Centre, Ispra, (VA) I-21020, Italy
b
Received 21 September 2006; received in revised form 4 December 2006; accepted 4 December 2006 Available online 22 January 2007
Abstract Dynamic deformation measurements were carried out by combining full-field speckle interferometry and heterodyne interferometry. A digital demodulation technique based on the evaluation of the instantaneous frequency have been implemented in the digital signal processor of a complementary metal-oxide semiconductor (CMOS)-based camera to extract velocity measurements from phase modulated optical carrier signals. The purpose of this experimental investigation was to demonstrate a full-field laser vibrometer system that could replace electro-mechanical scanning with electronic scanning within a programmable stand-alone and relatively low-cost digital camera. Velocity profiles of a vibrating membrane in the order of few microns per second were reconstructed automatically by performing an electronic scanning of the surface over the image sensor. r 2006 Elsevier Ltd. All rights reserved. Keywords: Metrology; Vibrometry; Speckle interferometer; CMOS camera; Signal processing
1. Introduction Quantitative phase measurement methods such as the temporal phase-stepping (TPS) technique [1–4] set a new standard in the precision achievable from full-field interferometry. Phase stepping (or phase shifting) can be applied in almost any dual-wavefront interferometer whether classical or based on speckle. The approach is based on the acquisition of a sequence of interferograms acquired after the introduction of known amounts of relative phase step between the object and the reference path. Simple arithmetic operations on the interferogram set then allow the calculation of relative optical (wrapped) phase over the entire area of interest. Although phasestepping routines have become an important part of most full-field optical metrology systems they can suffer from errors in phase calculation due to phase-step miscalibration and unwanted mechanical vibration in the optical set-up Corresponding author. Tel.: +353 61 202173; fax: +353 61 338176.
E-mail addresses: [email protected] (M.V. Aguanno), [email protected] (M.P. Whelan), [email protected] (M.J. Connelly). 0143-8166/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2006.12.001
during image acquisition. Moreover, most full-field systems utilise standard CCD cameras which typically limits image acquisition to video rates (25 Hz) and in turn, restricts the speed at which phase maps can be calculated. In general therefore, full-field optical metrology systems that use phase-stepping and standard CCD cameras can only be used for static or quasi-static measurements. Full-field dynamic measurements usually require the use of techniques employing expensive fast CCD cameras [5,6], which allow the time history reconstruction of a transient event and as a result thousands of images need to be acquired for successive post processing. Synchronising pulsed lasers with the exposure of standard CCDs has demonstrated non-stationary event analysis [7,8]. However, this approach is usually limited to measurements of periodic motion. An alternative is the spatial phasestepping (SPS) technique, also known as spatial carrier method. In SPS, a known phase shift is implemented spatially using polarisation optics, a diffraction grating or a beam lateral offset. With SPS only a single frame is needed to estimate the measurement phase [9–11]. The advantages of this technique are fast phase measurements and insensitivity to TPS fluctuations. However, spatial
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resolution is reduced compared to TPS and there exists alignment difficulties requiring sub-pixel accuracy. Optical heterodyning [12–14] is a carrier-based approach for optical phase detection that is capable of following fast dynamic events with extremely high sensitivity [15] and accuracy. Heterodyne techniques [16–20] rely on mixing mutually coherent stabilised laser beams, each with a different optical frequency, to generate a beat carrier signal at frequency inside the bandwidth of the optical detector. The heterodyne carrier signal can be modulated in phase through the interaction with a test object and subsequently demodulated using various phase retrieval methods [21] to provide, for example, a measurement of velocity. When heterodyne techniques are used in conjunction with fast optical detectors such as single photodiodes, detection of the optical carrier and demodulation of its phase signal can be made very rapidly. The laser Doppler vibrometer (LDV) [22,23] is a well known example of a device which is based on heterodyne detection and it usually incorporates a single photo-detector with a fast response time. A major drawback of the LDV, however, is the fact that a single detector only allows a measurement to be made at a single point in space. To carry out full-field measurements, scanning LDV (SLDVs) systems have been developed [24–27] that combine a single-detector LDV with sophisticated electro-mechanical scanning units. This allows the rapid sequential measurement of the velocity or displacement of an array of points over an area of interest. However, such systems are typically very expensive, bulky and they lack versatility. Considering the aspects of both phase-stepping full-field techniques and optical heterodyne methods, in this paper it is proposed that a full-field optical metrology system would combine the advantages of both approaches. In essence the system should employ optical heterodyning for rapid high resolution phase measurement, and utilise an image sensor and imaging optics to allow high resolution spatial measurements without the need for electro-mechanical scanning. The solution presented here adopts a low-cost approach to combine the advantages of speckle full-field interferometry with the benefits of carrier-based systems [28]. The key element on which the solution is based is a complementary metal-oxide semiconductor (CMOS) image sensor [29], which offers independent and direct pixel access, both in space and time. This is made possible by novel active pixel sensor (APS) architecture [30]. Using this type of sensor, which is integrated into a digital camera, high acquisition bandwidths can be achieved (i.e. 10 s kHz) when acquiring from a small number of pixels (e.g. 10–100). This facilitates the acquisition of high frequency optical carrier signals. By sequentially switching from pixel to pixel, or from one set of pixels to another set of pixels, an electronic scan of any or every point on a test surface can be made. The spatial resolution obtainable (at the object surface) depends on the CMOS pixel size and the magnification factor of the imaging system employed. The spatial density
of measurements acquired depends simply on the number and location of the pixels accessed. The random, direct access in space and time is particularly useful and efficient when specific regions (or points) of interest are chosen for analysis rather than the entire field of view. The CMOS camera employed also incorporated a dedicated digital signal processor (DSP) which permitted rapid on-board demodulation of the optical carrier signals through the implementation of real-time signal processing routines dedicated to the specific measurement requirements. In the experimental investigations described in this paper, the CMOS-DSP camera was combined with a heterodyne interferometer to produce a versatile, compact optical metrology system capable of rapid high-resolution measurement of velocity profiles of engineering surfaces [31,32]. In particular, vibration analysis was carried out on a thin vibrating membrane within a speckle heterodyne interferometer and validated using a commercial LDV system. 2. Instantaneous frequency (IF) detection Digital demodulation methods based on the evaluation of the IF can be applied to frequency- and phasemodulated signals for very precise analysis, such as velocity measurements. The IF is given by the time derivative of the phase of a complex signal [33–37]. A logarithmic active CMOS image sensor array can be considered as a multidetector system connected to a DSP demodulation unit, where broadband signals, acquired from single pixels and acting as single detectors, can be analysed. The approach adopted to retrieve the velocity and displacement information from a vibrating surface, mainly consists in the determination of the IF using the analytic signal argument of a real signal. This method is termed single pixel carrier based demodulation (SPCBD) and the algorithm was implemented directly on the DSP [38]. Analytic signals are well established as an important tool for processing one-dimensional real signals, in that they provide a direct access to the signal amplitude and phase. The analytic signal z(t) of a real signal s(t), is a complex signal having the actual signal as the real part and the Hilbert transform H of the same signal as the imaginary component: zðtÞ ¼ sðtÞ þ jH½sðtÞ ¼ aðtÞ ejjðtÞ ,
(1)
where the amplitude a(t) and the phase j(t) are given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (2) aðtÞ ¼ ðsðtÞÞ2 þ ðH½sðtÞÞ2 , H½sðtÞ jðtÞ ¼ tan . sðtÞ 1
(3)
The Hilbert transform is given by the principal value of the integral Z 1 1 sðtÞ dt. (4) H½sðtÞ ¼ p 1 t t
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pixel output signal is equal to the imaginary part of the ratio of the time derivative of the analytic signal to the analytic signal. In the implementation of the algorithm the analytic signal and its time derivative were calculated in the frequency domain. From the IF, the velocity and the displacement are easily retrieved. The mean value of f(t), calculated over the acquisition interval, of the original FM signal equals the carrier frequency. Fig. 1. Magnitude of the gate filter transfer function vs. frequency.
Fig. 2. Flowchart of the SPCBD algorithm.
The IF, f(t) is given by f ðtÞ ¼
1 djðtÞ . 2p dt
(5)
An analytic signal can be generated in the frequency domain by suppressing the negative frequency components of the original signal. The analytic signal of the real signal s(t) acquired from a pixel can be obtained by multiplying the fast Fourier transform (FFT) of s(t) by a bandpass filter centred at Df, whose response is zero at negative frequencies and then by taking the inverse FFT, Df ¼ 962 Hz and the filter bandwidth ¼ 100 Hz. This is large enough not to alter the spectrum of the frequency modulated signals and also removes the noise components from the sampled signal as well as the harmonics generated by the CMOS pixel logarithmic response. The shape of the filter produced an undistorted analytic signal, avoiding aliasing problems due to the sampling of a finite signal. The magnitude of the gate filter transfer function is shown in Fig. 1. The impulse response of the filter decreases as 1/t6 for large values of t which greatly reduces the aliasing. The implementation of the SPCBD algorithm is graphically presented in the flowchart of Fig. 2. The IF of the
3. Experimental investigation In the two-wavefront interferometer employed, shown in Fig. 3, a laser beam (532 nm) is divided by beam splitter BS-1 into object and reference beams. Along these paths two acousto-optic modulators (AOMs) are driven at 80 MHz and 80 MHz+102 Hz. This shifts the laser frequency in each branch in order to produce a heterodyne effect upon recombination and interference at the camera, with a carrier frequency of 102 Hz. The object beam was expanded by expanding lens Ex-1 onto the object surface and the light reflected back was recombined with the second beam by beam splitter BS-2 with the reference beam expanded by expanding lens Ex-2. The interfering wavefronts travelling from BS-2 were then imaged by the CMOS sensor fitted with a zoom camera lens. The light signal reflected on the loudspeaker is Doppler shifted by the membrane vibration driven by a CW 10 Hz signal. The camera is focused on the membrane. The frequency modulated carrier is detected using single-pixel acquisition and by electronically scanning the CMOS sensor and performing a real-time demodulation processing on the camera DSP in order to extract the velocity of the membrane surface. The CMOS-DSP on-board processing used the algorithm described above. The carrier/ modulation ratio in this experiment was equal to 10 to allow a large separation between the frequency components and to improve the demodulation and the extraction of the IF. The optical signal was sampled at 2.7 kHz, using single buffers of 1024 samples for a corresponding acquisition window of approximately 0.4 s. A typical detected heterodyne optical carrier frequency at 102 Hz modulated by the vibrating surface at 10 Hz is shown in Fig. 4 in the time and spectral domains. The bandwidth widening during the modulation was low suggesting that the Doppler frequency shift was small enough such that the
Fig. 3. Heterodyne speckle interferometer experimental setup.
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Fig. 4. Experimental single pixel acquisition of FM optical carrier; (a) time domain, (b) frequency domain representation (carrier frequency ¼ 102 Hz; modulation frequency ¼ 10 Hz).
Fig. 6. Spectrum of the IF signal showing the 10 Hz membrane vibration frequency.
Fig. 5. Instantaneous frequency of a given point on the vibrating membrane surface.
IF calculated through analytic signal was in fact proportional to the membrane velocity. The extracted IF output, shown in Fig. 5, contains the information needed to determine the velocity of the membrane. A frequency domain representation of the membrane vibration in terms of the IF is shown in Fig. 6. As expected, the spectrum of the retrieved IF shows the frequency peak at the modulating frequency of 10 Hz. The noise in Fig. 6 possibly originates from translational vibrations of the mirrors, temperature fluctuations along optical paths and frequency instability of the carrier and of the sampling clock. These errors could be reduced by subtracting the vibration measured on a reference pixel, which is another
advantage of full field quasi-instantaneous electronic scanning compared to mechanical systems. In another test, a commercial LDV, isolated from the vibration source, was included in the set-up by using a system of mirrors and stepper motor translation stages. The LDV laser beam was positioned onto the vibrating surface in order to compare with the results from the CMOS camera system. One of the measurement grids adopted over the membrane surface for the horizontal and the vertical section scan (numbered star points) performed during the LDV comparison is shown in Fig. 7. A comparison of the velocity of the vibrating membrane detected with the LDV and CMOS-DSP camera system, along sections A-A and B-B is shown in Fig. 8. In Fig. 8(a), the extracted profiles were measured along the horizontal section A-A. The maximum values detected (RMS) were 2.82 mm/s for the CMOS-DSP system and 2.93 mm/s using the LDV. The difference between the amplitudes of the velocity measurements between the
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systems was of the order of 4% of the average velocity at a given point on the membrane surface. In this test the vibration frequency adopted was set to 150 Hz with an acquisition window of 80 ms corresponding to almost 11 cycles. Repeatability tests were performed to check the consistency of the data retrieved from the scanned pixels. For a given pixel accessed 20 times during the electronic scanning with a maximum velocity value detected equal to 1.61 mm/s, the standard deviation was equal to 0.042 mm/s. The slow variations suggest that the most probable reason is temperature variation that affects the membrane elastic properties. Initially, the electronic scanning procedure was performed with step-by-step user interaction, choosing the pixels manually with the aid of real time signal visualisation on the monitor in order to change the sensor analog-to-digital converter parameters and increasing the digitisation levels or rejecting those pixels with a poor response. Several pixels along a section of the membrane were thus manually chosen to determine the velocities over the surface, moving from one pixel to another. All of the velocity amplitudes were extracted and stored to plot a profile of the first mode of vibration. The time required to execute a single measurement was less than 1 s.
As an example of a basic stand-alone application, an automatic procedure as shown in Fig. 9 was implemented on the CMOS-DSP camera to perform electronic scanning and processing. The threshold level visibility for the pixel selection process wave is included in the procedure. The number of the pixels considered along a membrane section during the scanning is chosen at the beginning of the process. As mentioned above, the amplitude velocity data calculated by the analysis of IF signals was used to reconstruct a velocity shape profile. A typical membrane velocity profile derived from experimental velocity data
Fig. 7. Circular vibrating membrane and measurement grid.
Fig. 9. Flowchart of the electronic scanning procedure.
Fig. 8. Velocity profiles of: (a) section A-A, and (b) section B-B of a vibrating membrane using a commercial LDV and the CMOS camera system.
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measurement points as in a laboratory or in-line production environment. This compact and powerful tool achieved very precise measurements suggesting a novel single-pixel approach in the field of optical metrology. Acknowledgements This work was supported through a collaboration contract (]18487-2001-10 SOFD ISPIE) between the Institute for Health and Consumer Protection (IHCP), Photonics Sector, European Commission Joint Research Centre (Ispra, Italy) and the Department of Electronic and Computer Engineering of the University of Limerick (Limerick, Ireland). The project was also supported by Enterprise Ireland International Collaboration Grant and the University of Limerick/Tellabs Foundation. Fig. 10. Typical reconstructed velocity profile of the vibrating membrane.
References collected during one of the automatic electronic scans is shown in Fig. 10. 4. Discussion and conclusion Dynamic measurements were achieved combining both speckle and heterodyne interferometry for velocity profile reconstruction by single-pixel acquisition and electronic scanning of a vibrating thin membrane. Several profile measurements describing the typical Gaussian shape of the first symmetric mode of vibration of the membrane tested showed the potential of the approach. As expected by the adoption of an algorithm based on the frequency analysis, small variations in the amplitudes of the acquired signal and between the pixels accessed, did not affect the extraction of the final velocity results. Amplitudes and shapes were also confirmed by a LDV scan, by simulation tests and by the qualitative analysis of an interferogram recorded at a low vibration frequency. A low standard deviation of 0.042 mm/s determined from many measurements was obtained. An automatic electronic scan procedure enabled the velocity profile of the vibrating membrane to be determined in a relatively short time depending on the number of pixels used; considering that each complete measurement required less than 1 s/pixel scanned. Although it is a quasi-instantaneous technique, in the measuring process of full-field dynamic stationary events this methodology can minimise both environmental noise and thermal drifts. The integrated machine vision system presented can be considered a versatile, simple and low-cost alternative to expensive and complex devices. Moreover, as it is programmable it can be adapted for specific problems in different applications in order to perform several types of measurements combining the benefits of laser Doppler and full-field speckle techniques. For example, in experimental mechanics, this system can also be applied to ensure an elevated accuracy in the monitoring of a sparse number of
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