Full-field heterodyne interferometry using a complementary metal-oxide semiconductor digital signal processor camera for high-resolution profilometry

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1 46 9, September 2007 Full-field heterodyne interferometry using a complementary metal-oxide semiconductor digital signal processor camera for high-resolution profilometry Mauro V. Aguanno European Commission Joint Research Center Institute for Health and Consumer Protection Photonics Group Ispra, Varese I Italy and University of Limerick Department of Electronic and Computer Engineering Optical Communications Research Group Limerick, Ireland Fereydoun Lakestani Maurice P. Whelan European Commission Joint Research Center Institute for Health and Consumer Protection Photonics Group Ispra, Varese I Italy Abstract. We describe a heterodyne interferometry system based on a complementary metal-oxide semiconductor digital signal processor CMOS-DSP camera that is utilized for full-field optical phase measurement using a carrier-based phase retrieval algorithm, with no need for electro-mechanical scanning. Camera characterization test results support the adoption of a single-pixel approach to perform quasiinstantaneous differential phase measurements, which are immune to mechanical vibrations and thermal drifts. We developed an optical configuration based on a Mach-Zehnder heterodyne interferometer to perform a static test on a mirror surface. The profiles of the mirror surface set at two angular positions, the relative displacements in the range of nanometers, and the corresponding tilt angle were determined Society of Photo-Optical Instrumentation Engineers. DOI: / Subject terms: metrology; interferometry; profiling; signal processing; cameras. Paper R received Mar. 1, 2007; revised manuscript received Apr. 10, 2007; accepted for publication Apr. 11, 2007; published online Sep. 20, Michael J. Connelly University of Limerick Department of Electronic and Computer Engineering Optical Communications Research Group Limerick, Ireland 1 Introduction High-resolution optical profilometry is typically performed using modern full-field techniques such as temporal phasestepping TPS, spatial carrier method SCM, and digital holography DH. 1 5 TPS methods are popular because they are simple to implement and offer good sensitivity for modest computational effort. The basic concept behind TPS methods is to introduce a set of controlled phase-steps between the object and reference paths in a dual-wavefront interferometer, acquiring an interferogram at each step. 4 The phase-stepped interferograms are then used to calculate a wrapped phase-map that can be subsequently unwrapped and scaled appropriately to produce a quantitative 2-D surface profile. In a practical setup, however, TPS measurements can exhibit appreciable uncertainty due to the sensitivity of the phase-stepping process to translational vibrations and thermo-mechanical drift of the interferometer s optical elements. Additionally, typical TSP algorithms are not very effective in averaging out random noise due to the modest number of samples acquired to calculate the phase-map /2007/$ SPIE Optical profilometers that rely on SCM and DH for phase determination are nearly immune to translational vibrations and thermo-mechanical drift compared to a TPS approach since only a single interferogram is required to calculate the wrapped phase-map. 6 The tradeoff, however, is the fact that the lateral spatial resolution of the profile measurement is lower because the spatial carrier must be sufficiently resolved by the imaging system and camera employed. This makes it more difficult to accurately follow steep gradients in the object profile. Similar to TSP methods, SCM techniques are also sensitive to random noise because the phase calculation is based on a low number of samples of the spatial carrier. An alternative to TPS and SCM phase-retrieval approaches is optical heterodyning OH. OH techniques typically rely on the mixing of mutually coherent wavefronts, each with a different optical frequency, to generate a beat carrier-signal at a frequency inside the measurement bandwidth of the optical detector used. Reflection of the optical carrier from an object surface results in a relative phase modulation that can be extracted using a variety of digital signal processing algorithms. Generally heterodyne phaseretrieval methods are insensitive to translational vibrations

2 and drift due to their characteristically short measurement times, and they offer very high sensitivity since a large number of samples is used to determine the phase at a particular measurement location. 7 9 However, a major drawback of most heterodyne systems, is the reliance on a single wide-bandwidth photodetector to resolve the highfrequency optical carrier. Therefore, to carry out a full-field measurement, electro-mechanical scanning of a focused beam must be employed 10 since standard CCD sensors are too slow. Ideally, an optical profilometry system should combine the full-field capability and opto-mechanical simplicity of TPS, SCM, or DH setups, with the high resolution and robustness of heterodyne phase-retrieval methods. Such a system would offer the full lateral spatial resolution attainable with the imaging optics and camera employed, while still delivering a very high-resolution profile measurement owing to its insensitivity to translational vibrations, drift, and random noise. To achieve this, the solution proposed here exploited the distinctive properties of a logarithmic CMOS imaging chip whose active pixel sensor APS architecture facilitated direct independent pixel access in both space and time. Using this type of image sensor, a highfrequency optical carrier could be recorded with sufficient acquisition bandwidth at any point in the field of view, allowing a profile or height measurement to be made at any or every point on a test surface. The camera also incorporated a dedicated digital signal processor DSP that permitted rapid on-board demodulation of optical carrier signals through the implementation of real-time signal processing routines. We have demonstrated in prior work that the attractive features of this type of CMOS-DSP camera can be utilized effectively in different optical metrology applications Description and Characterization of the CMOS-DSP Camera The CMOS camera we used was an imvs-135 model from AKAtech, Switzerland. This digital camera incorporates a 40-MHz DSP from Analog Devices 32-bit floating-point SHARC family series digitally interfaced with a Fuga model logarithmic CMOS APS. The APS consisted of 512 x 512 square pixels of 12.5 m size and a single onchip 8-bit flash analog-to-digital-converter ADC placed next to the matrix. 14 Within the APS, the photocurrent generated by absorbed light is converted into a low-impedance voltage by each pixel. 15 Since the conversion process is continuous, the accessing of a pixel is not limited by an integration time or shift register as in a CCD. Therefore, it can be randomly addressed in a very rapid fashion i.e., 410 ns to have its voltage read directly. This gives the opportunity to perform fast electronic scanning over the sensor, or to efficiently jump from one particular set of pixels to another. To give an indication of the acquisition speeds that can be obtained, characterization tests have been carried out to determine pixel access rates in the random single-pixel acquisition mode. 16,17 As illustrated in Fig. 1, the frequency at which pixel values can be read and transferred into DSP memory was 57, 112, and 500 khz for ten, five, and one pixel, respectively. Although the electronic acquisition rates achievable are impressive, in practice the recording of an optical carrier Fig. 1 Electronic acquisition rate as a function of numbers of pixels accessed. signal from a pixel must take into account not only the electronic access time, but also the response time of the pixel itself to the incoming light. Within an APS, the voltage-intensity response time is highly dependent on the average intensity; therefore, the illumination power can dictate the actual sampling rate that can be obtained to detect a dynamic signal. As indicated in the technical specifications from the manufacturer and experimentally verified, for 40 mw/m 2 of light intensity, the time response is of the order of 4 ms, while increasing the source intensity to 400 mw/m 2 reduces pixel reaction to 400 s. Therefore, the pixel time response is inversely proportional to the average light intensity. A large variation in the illumination intensity over the whole field can result in different time responses between the pixels. This introduces a timedependent error in the detected signal phase due to the time-varying signal amplitude, which impacts in particular on the high-frequency components of the detected signal. Ideally one wishes to use a sufficient degree of uniform illumination to ensure a short pixel rise-time to allow the use of a high-frequency optical carrier, which results in faster measurement times and greater immunity to spurious vibrations and drift. As presented below, the interferometer employed to make the profile measurements conducted in this study used an illumination intensity of 200 mw, which comfortably permitted a sampling rate of 820 Hz to acquire a heterodyne carrier frequency of 82 Hz. 3 Differential Phase-Sensitive Detection Digital demodulation methods are an attractive alternative to analog approaches for differential phase retrieval. 18 In the scheme employed here, the carrier signal s p recorded at each pixel of interest was compared to the signal s ref of a reference pixel to determine the relative phase across the field. The phase difference was determined using a mathematical approach based on classical phase-sensitive detection theory implemented on a DSP, 19 which uses an internally generated comparator signal s int. To illustrate how

3 the algorithm works, we can express the periodic signals s int and s p,ref with identical carrier frequency f as s int = A cos 2 ft + int, s p,ref = B cos 2 ft + p,ref, 1 2 where A and B are the signal amplitudes, and p and ref are the two phase values we want to retrieve. As mentioned above, s int is used as a comparator to calculate the unknown phase between the two input signals s p and s ref and is generated internally in the DSP. The method works by extracting the part of each input signal whose frequency and phase match the internal reference, which in practice means multiplying both input signals by s int. With the assumption of an internal signal phase int =0, the output of the PSD after multiplication with either s p or s ref will be a new signal with two components: one centered at frequency 2 f, and the other centerd at zero frequency. For example, multiplying s int with s p and low pass filtering to extract the component centered at zero frequency gives the in-phase component signal X = AB 2 cos p. 3 Multiplying s p by the s int shifted by 90 deg and filtering as above gives the quadrature component signal Y = AB 2 sin p. 4 From Eqs. 3 and 4, weget p = tan 1 Y/X. 5 Due to the form of Eq. 5, this demodulation technique is also called the arctangent phase demodulation method. 20 The processing described above can then be used to determine p and ref. The relative or differential phase between the measurement pixel and the reference pixel is determined by subtracting the two phase values. This relative phase value is proportional to the difference in optical path length traveled by the light reflected from the corresponding measurement and reference points on the object surface. The algorithm was implemented on the DSP of the CMOS camera to allow the on-line processing of the signals sequentially acquired from user-selected sets of measurement pixels. 4 Experimental Investigation The experimental setup that was employed for full-field heterodyne interferometry to perform static profile measurements is shown in Fig. 2. It was based on a Mach- Zehnder configuration that incorporated two acousto-optic modulators AOMs Crystal Technology Inc., model # and used light from a 532-nm laser source Coherent, model 2W Verdi. A mirror M1 directed the laser into the interferometer toward the first beamsplitter BS1. A variable neutral density filter NDF was used to fineadjust the light intensity in order to optimize the exposure of the CMOS sensor. After separation by BS1, the two Fig. 2 Full-field Mach-Zehnder heterodyne interferometer for static profile measurement, consisting of a 512-nm laser, a variable neutral density filter NDF, two acousto-optic modulators AOM, beamsplitters BS1 and BS2, reference mirror M ref, and the CMOS-DSP camera. The test object in this case was a simple flat mirror mounted on a rotation stage. beams were frequency-shifted by AOMs placed in each arm. The two AOMs were driven by separate stabilized radio-frequency drivers one set at a frequency of 80 MHz, and the other at 80 MHz plus f. The frequency difference f, in effect the frequency of the optical carrier being generated, was controlled by an external signal generator and a phase locked loop PLL circuit, and could be varied from 10 Hz to 1 khz. For this experiment the carrier frequency was set at 82.2 Hz. After reflection of the reference wavefront from the mirror M ref and the object wavefront from the surface of the test object in this case, a flat mirror, the two beams were recombined by a second beamsplitter BS2 and projected onto the sensor of the CMOS-DSP camera. The test object flat mirror was mounted on a rotational stepper-stage Micro-Controle, Newport Inc. that could be used to tilt the mirror with a step precision of 0.01 deg. The aim of the experiment was to measure the profile of the object mirror at two different positions on the rotation stage, and from those profiles to determine the imposed rotation. The experiment proceeded as follows. With the object mirror in its first position, a horizontal line-profile measurement was made across the center of the mirror, which corresponded to a row of 256 pixels on the CMOS sensor. Each pixel in the row was sampled 1024 times at a sampling rate of approximately 1.3 khz per pixel. Therefore, the periodic signal acquired for each pixel represented approximately 80 cycles of the optical carrier. Taking the first pixel in the row as the reference pixel and employing the differential phase retrieval algorithm described earlier, we calculated the relative phase for each pixel along the profile. This yielded a wrapped modulo 2 phase plot as illustrated in Fig. 3. The continuous unwrapped phase profile was retrieved by applying a simple 1-D phase unwrapping algorithm. In a second step, the object mirror was rotated by 0.13 deg about its vertical axis. The phase measurement was repeated once more for the same horizontal line profile. Therefore, a second linear profile was obtained that corresponded to the new mirror position. Subtracting the two unwrapped phase plots, the relative phase change between

4 Fig. 3 Typical sawtooth wrapped phase plot of the relative phase measured along a line profile of the object mirror. This was then unwrapped to obtain a continuous distribution of relative phase. the two positions was obtained. The phase was then converted into the corresponding relative displacement d of the mirror using the expression Fig. 4 Profiles measured for initial profile1 and rotated profile 2 positions of object mirror and the resulting relative displacement. Fig. 5 Plot of residuals obtained after subtracting the ideal linear profile from the corresponding measured profile. The standard deviation is 5.3 nm. d = 2, 8 where is the laser wavelength, and is the relative phase change measured between the two positions of the object mirror. The profiles measured for each position of the mirror, and the resulting relative displacement, are shown in Fig. 4. The insertion of a precision Ronchi grating allowed us to determine the magnification factor of the imaging system, which in turn facilitated the relating of pixelpitch at the image plane to lateral dimension on the object surface. At this point the amount by which the mirror had been rotated was calculated as deg. The difference between the rotation imposed 0.13 deg and the experimental result obtained was only deg, well below the resolution 0.01 deg of the stepper micro-stage used. We assumed that for the small angle of rotation the object mirror was perfectly smooth and determined the measurement noise by subtracting the actual measured profile from a linear fit. A typical result is shown in Fig. 5, where the residuals obtained after subtraction were plotted along the profile. These residuals were used to calculate the standard deviation, equal to 5.3 nm. This effective noise-floor was attributed to electronic noise of the sensor and camera electronics, and could possibly be reduced by improving the digital filtering implemented in the phase retrieval algorithm. 5 Discussion The heterodyne methodology scheme used in this paper, which is possible due to the CMOS APS sensor s high acquisition speed, is comparable to a classical phase-shifting technique repeated continuously with a large number of steps over many periods of 2 shifts. This allows a higher SNR and displacement resolution through the averaging of the errors added by the CMOS sensor along all of the many sampled values. However, the main advantage of adopting a carrier-based technique for a static test is increased accuracy from its immunity to mechanical vibration and thermal drift in the phase calculation, with respect to TPS or scanning techniques. The quasi-instantaneous parallel acquisition of the phase between two points/pixels during surface analysis reduces the influence of the phase noise. In addition, the differential nature of the signal-processing algorithm eliminates errors induced by mirror translations and the need for the preliminary fixed pattern noise calibration procedure. Moreover, the spatial resolution obtained by electronic scanning without the need for electro-mechanical devices was of the same order as expected from full-field imaging systems. Also, the measurement speed and the accuracy matched the performance of heterodyne systems. 6 Conclusion We have described a functional machine vision system based on a digital CMOS-DSP camera and heterodyne interferometry that achieved automated high-precision measurements in a Mach-Zehnder optical configuration. The profile of a mirror and its rotation angle were obtained. The on-chip digital integration between the CMOS image sensor and a DSP allowed the on-board implementation of

5 efficient, real-time, carrier-based phase-retrieval routines. This flexible, compact, and relatively inexpensive system was able to combine the advantages of full-field interferometry with the benefits offered by single-point carrierbased measurement. Acknowledgments This work was supported through a collaboration contract # SOFD ISPIE between the University of Limerick Ireland and the Institute for Health and Consumer Protection IHCP, Photonics Sector, European Commission Joint Research Centre Ispra, Italy. The project was also supported by Enterprise Ireland International Collaboration Grant and the University of Limerick- Tellabs Foundation. References 1. R. Jones and C. Wykes, Holographic and Speckle Interferometry, 2nd ed., Cambridge Univ. Press H. J. Tiziani, Optical methods for precision measurements, Opt. Quantum Electron. 21, J. E. Greivenkamp and J. H. Bruning, Phase shifting interferometers, in Optical Shop Testing, D. Malacara, Ed., Wiley, New York, pp K. 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Lakestani, and M. P. Whelan, Random depth access full-field heterodyne low coherence interferometry utilizing acousto-optic modulation and a complementary metal-oxide semiconductor camera, Opt. Lett. 31 7, January P. Egan, F. Lakestani, M. P. Whelan, and M. J. Connelly, Full-field optical coherence tomography with a CMOS-DSP camera, Opt. Eng. 45, 1 6 January N. Ricquier and B. Dierickx, Active pixel CMOS image sensor with on-chip non-uniformity correction, presented at IEEE Workshop on Charge-Coupled Devices and Advanced Image Sensors, April 1995, California. 15. S. Kavadias, B. Dierickx, D. ScheDer, A. Alaerts, D. Uwaerts, and J. Bogaerts, A logarithmic response CMOS image sensor with on-chip calibration, IEEE J. Solid-State Circuits 35 8, M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, Single-pixel carrier based approach for full-field laser interferometry using a CMOS-DSP camera, Proc. SPIE 5251, P. Egan, F. Lakestani, M. P. Whelan, and M. J. Connelly, Threedimensional machine vision utilising optical coherence tomography with a direct read-out CMOS camera, Proc. SPIE 5856, June P. A. Temple, An introduction to phase-sensitive amplifiers: an inexpensive student instrument, Am. J. Phys. 43 9, P. Embree, C Algorithms for Real-Time DSP, Prentice Hall, Upper Saddle River, NJ J. A. Smith and C. P. Burger, Digital phase demodulation in heterodyne interferometry, in Review of Progress in Quantitative Nondestructive Evaluation, Vol. 14, D. O. Thompson and D. E. Chimenti, Eds., Plenum Press, New York Mauro Aguanno obtained the Laurea degree in Aeronautical Engineering from the Politecnico di Milano, Italy, in Carrying out a project on composite material structures monitoring using embedded optical fibre sensors and interferometric laser techniques he completed a 12-months stage at the Photonics and Diagnostics Group of the European Commission Joint Research Centre in Italy. In 2000 he took a postgraduate position at the Electronic and Computer Engineering Department of the University of Limerick. Enduring a successful active collaboration with the Photonics and Diagnostics Group, his research was mainly focused on the development of a machine vision system using heterodyne interferometric techniques and a CMOS based digital camera for experimental mechanics applications. In 2005 he received his Ph.D. from the University of Limerick. In January 2006 he joined the Stokes Research Institute at the University of Limerick as a Research Fellow working on the High Radiating Compartment Testing project funded by Aribus. Maurice P. Whelan is currently head of the Photonics Sector of the European Commission Joint Research Centre, based in Italy and adjunct professor at the Stokes Research Institute in Ireland. He obtained his doctorate in 1994 from the University of Limerick, Ireland, in the field of computational and experimental stress analysis. Since then he has worked on the development and application of full-field optical metrology techniques, optical fiber sending, and biomedical imaging. He is the author of 13 international patents in these fields. His current interests include interference microscopy for cell and tissue diagnostics in vitro, hyperspectral fluorescence imaging for endoscopy, and optical waveguide biosensors. Fereydoun Lakestani received his engineering degree from Ecole Nationale Supérieure d Electromique et de Radioélectricité de Grenoble, France, in He taught physics and nondestructive techniques at the Institut National des Sciences Appliquées de Lyon, France, for 13 years, where he received his doctorate degree in science. He has been working at European Commission Joint Research Centre since His research activities until 1997 were in various fields of ultrasonic applications: transducers, NDT, material characterization and medicine. From 1997 to 2001 he worked on thermal waves, and since 2001 he has been involved in various applications of laser interferometry. Throughout his research activities, he has acquires skill in ultrasonic, optical and thermal wave propagation and the use of electronic instrumentation, signal processing, and data analysis. Michael J. Connelly received his Ph.D. in electronic engineering from University College Dublin in He is a senior lecturer in electronic engineering at the University of Lemerick, where he leads a research group working on optoelectronic device modeling, semiconductor optical amplifiers, optical coherence tomography, and optical metrology