Nonlinear MSM Photodetector Model for High Resolution Laser Impulse Radar Imaging

Transcription

1 Nonlinear MSM Photodetector Model for High Resolution Laser Imulse Radar Imaging M. DJEBARI *, M. BENSEBTI *, A. ANOU *, M. MEHDI * AND G. KOMPA ** * Deartment of electronic University Saad Dahlab of Blida BP 7, Blida 9 ALGERIA ** Fachgebiet Hochfrequenztechnik, University of Kassel, GERMANY Abstract: - Based on the recently develoed modulation scheme of highly dynamic and strong carrier injection into the active zone of a single-heterostructure (SH) laserdiode, laser ulses of some hundreds of watts and ulse widths (FWHM) of about s are available. Such otical ulses are useful for high recision near-field ranging. Until now suitable otical receivers are not available. This aer concerns a broadband otical receiver using a very fast large area MSM hotodiode. We resent nonlinear CAD Models for hotodiode derived from measurement which can be to analyze the nonlinear transfer function versus the otical large signal stimulus. Accurate models correction of the distorted signals can be erformed to making time interval measurement more accurate. Measurement uncertainties in the micrometer range could be attained by data range error correction using a nonlinear equivalent network for the device. The results are demonstrated on the basis of D and D maed objects. Key-Words: - Nonlinear, MSM, Photodiode, Laser, Imulse, Radar, Distance, D, Imaging. Introduction The erformance of laser imulse radar (LIR) systems has continuously imroved during the last two decades. Such systems are destined to quality control [], distance and contour maing [, ] or involved to acquire medical images as D surface oints of anatomical art to be oerate []. In articular a develoed modulation scheme [] has led to ultra short otical ulses which require corresonding broadband receiving units. Different aroaches are known [, 5]. One main roblem of highly recise measurements originates in the nonlinearities of the used hotodiodes []. In many investigations, discussing the hase difference ranging aroach, a hase uncertainty of about 55 degree has been observed under high dynamics of the received signal. For PIN detectors more than 5 degree hase shifting versus inut signal amlitude can be measured. Therefore, submillimeter uncertainties are rather difficult to be obtained without taking into account the device nonlinearities. We have also observed similar effects utilizing ulse-traveling ranging methods. Ranging errors of several millimeters are observed with high received signal dynamics, which originate from the nonlinearities of the hotodiode used. Fig. shows the time significant oint, defined in this case at % of the amlitude, varies with the received otical ower. Therefore exact knowledge of the nonlinearities of the hotodiodes and the following amlifier is strongly needed to access the submillimeter and micrometer measurement uncertainty range. Commonly, avalanche hotodiodes are used in laser imulse radar (LIR) systems with tyical rise time of about s. In this aer and for the first time an MSM hotodiode with much higher bandwidth is used in a short range LIR. It is shown that an MSM hotodiode based LIR has suerior erformance with resect to ranging uncertainty.

2 and using a Taylor series develoment eq. () can be written as []: H + + n n ( ω) = jω + ( jω) + ( ) ( jω) n () Eq. may be further rewritten in the following form: Fig. : Measured received ulse resonse of a laser radar system for different otical ower Nonlinear Model of MSM Photodiode Regarding recise LIRs for D imaging, the nonlinearities of the used hotodiode must be taken into account. The model consists of a hysics-based O/Econverter (hysical art) and an electrical network with nonlinear current, charge sources and series resistance (Fig. ) [7]. Ii ( ω) H( ω) = V ( ω) [ + ( n + ) jω] () Eq.() gives very good aroximation u to 5 GHz. Eq.() is considered as a second order low ass filter. Using network synthesis aroach a lumed-element RLC circuit with L( n, ), C( n, ) and R (Fig. ) can be derived from it. The lumed model of the MSM is given in Fig.. For CAD imlementation the otical inut ower is normalized to V = (P i ot/a). Fig. : Lumed element nonlinear model of a MSM hotodiode The nonlinear transfer function of the ideal MSM hotodiode converter similar to [, 9, and ] may be written as follows: H oe ( ω) = a n an ( e + a ) ( a j n n + ωn) ( an + jω n ) e + ( an + jωn) a e ( a + jω ) + + a ( e + a ) ( a j ) ( a j + ω + ω ) () This equation characterizes the generation of the electron-hole airs and the drift of the carriers in the deletion layer. n and are the electron and hole transit times. are a n and a are the resective transit time to lifetime ratios (a n = n / e, and a = / h, with e and h the electron and hole lifetime, resectively). When e >> n and h >> Fig. : Equivalent descrition of eq. () by RLC network (V = P i ot/a, P i ot : Inut otical ower). Model Imlementation First, the small signal elements are extracted from the measured bias deendent electrical reflection coefficient []. The nonlinear current and charge sources are obtained by twodimensional integration over the known small signal quantities. They are resented in Figs. a- c. Their bias deendent values are imlemented in MDS (Microwave Design System) as Citi-Files (twodimensional look-u tables). The nonlinear lumed element model of Fig. is imlemented in MDS. The nonlinear elements are modeled in MDS as a six ort symbolically defined device (SDD) and the residual linear elements as a lumed elements circuit. All arameters needed for the simulation are in the circuit age. The data for the bias deendent elements are sline-interoled from data-set variables. The relation between the different arameters are imlemented as

3 equations. The model is used for a transient ulse simulation Fig. a: Current source I(I i,v i ) Fig. 5: Simulated and measured ulse resonse of MSM Photodiode (µm x µm) Fig. b: Charge source Q(I i,v i ).... Laser Radar Set U Figure shows a schematic view of a ulsed laser radar setu []. The laser beam from the laser transmitter is focused via scanning s. The ulse is reflected back to the scanning s, collected and focused by the receiver otics onto the hotodetector. In addition, the reference signal is reflected back by a reference-ulse and focused onto the hotodetector. The distance to the illuminated oint on the target can be calculated from the time interval between the detected reference and the measured signal (Fig. ), where the time is roortional to the distance. As a laser transmitter, a laser diode LD- with a small emission strie of 7. µm is used []. The ulse reetition frequency is tyically KHz. Fig. c: Small signal series resistance R S (I i,v i ) Target Laser transmitter Galvanometer scanning Semi-transarent Reference-ulse In Fig. 5 the measured and the simulated ulse resonse are resented. The Inset figure of Fig. 5 is the otical inut ulse with t rise = s and t FWHM = 5 s. MSM hotodetector Fig. : Schematic of the ulsed laser radar

4 5 Distance Measurements Constant distance is measured using a large area (µm x µm) MSM Photodetector. The measurement is reeated times using -oint averaging in each case Fig7. The measurement uncertainty is about 5 µm. Fig. shows the detected ulse for the distance measurement. One of the advantages of using the MSM hotodiode is the short tail of the received ulse which leads to less interference between the reference and received ulses. As a result time-measurement window can be used which imroves the radial resolution of the measurements and shortens the measurement range nominal distance deviation Fig. 9: Distribution of the distance deviation (σ MSM = 5.5 µm) D and D Alications Figures and show the scanned small salt shaker, imaged from a distance of cm, as intensity and wireframe images, resectively. The lateral resolution is.5 mm in both directions. The black area in Fig. reresents a holder which was used to clam the model shaker in lace during the scanning rocess. Fig. 7: Distance measurements (uncertainty = 5. µm) 9 reference ulse reflected ulse 7 5 Fig. : Scanned image of a small salt shaker Real size:.5x5.5 mm time / ns Fig. Detected ulses for distance of a MSM hotodiode (Active area: µm x µm). The distribution of the distance measurements versus the distance deviation is resented in Fig. 9. The standard deviation range is 5 µm. Fig. : D Wireframe of the small Salt shaker median filtered. Lateral resolution:.5 mm Scan distance: cm

5 7 Conclusion In this aer an MSM hotodiode has been used for near field LIR ranging. The influence of the high signal dynamics on the erformance of otoelectronic devices has generally been discussed. Exemlarily, a MSM hotodiode has been investigated. Considering this roblem there is no rincial difference between MSM-, PIN- or avalanche hotodiodes. The device can be modelled by a lumed element RLC network with nonlinear current and charge sources derived from measurement. Simulation based on the nonlinear CAD model shows strong influence of the otical inut ower on the ulseshae of the received electrical signal, and thus, the osition of the time significant oint for timeinterval measurement. Knowing accurate nonlinear device models, error-correction of the distorted received signals can be erformed. It has been shown also that the ranging uncertainty could be drastically reduced in comarison with a radar system that uses an avalanche hotodiode in the receiving unit. References: [] G. Koma, Extended Time Samling for accurate Otical Pulse Reflection Measurement in Level Control, IEEE Trans. on Instrumentation and Measurement, Vol. IM-, No., 9, 97-. [] G. Koma et al, Powerful icosecond-ulsed laser radar with micrometer ranging resolution, Proc. th Eur. Microwave Conf. Prague, 99, 7-5. [] A. Biernat and G. Koma, Powerful icosecond laser ulses enabling high-resolution ulsed laser radar, Journal of Otics Vol. 9, 99, 5-. [] G. Kamucha and G. Koma, A non-invasive aroach to atient registration in comuter assisted hijoint surgey using ulsed laser radar imaging, roceedings of ODIMAPIII, rd Toical Meeting of Otoelectronic Distance measurement an alications, University of Pavia, Italy, 5-, Set.. [5] H. Höfler and G. Schmidtke, D contouring by an otical radar system, Proc. Laser Dimensional Metrology, Vol., SPIE Conference (Brighton UK) 7, 99. [] M. Djebari, G. Koma and A. Stolze, Error Correction of the Resonse Delay due to the Nonlinearities of Photoreceivers, Journal of Otics Nr. 9, 99, 9-9. [7] M. Djebari, G. Koma and A. Stolze, A Simlified Physic-based Quasi-static MSM Photodiode Model, 7 th Euroean Microwave Conference. Jerusalem, Setember -, 7, 997. [] J. E. Bowers und C. A. Burrus, Ultrawide-Band Long-Wavelength -i-n Photodetectors, Journal of Lightwave Technology, Vol. LT-5, No., October 97. [9] J. W. Chen et al, Transit-Time Limited High- Frequency Resonse Characteristics of MSM Photodetectors, IEEE Transactions on Electron Devices, Vol., No., November 99. [] A. Stolze and G. Koma: Nonlinear modelling of disersive hotodiodes based on frequency- and time-domain measurements, th Euro. Microwave Conference Proceedings, Prague, P.5, 99. [] M. Djebari, PhD Thesis, Deartment of High Frequency Engineering, University of Kassel, Photoemfänger für Pikosekunden-Laserimulsradar, by the edition Kassel University Press,. XI, 97 S.:III., ISBN Germany. htt:// [] G. Koma, Modelling of disersive microwave FET devices using a quasi-static aroach, International Journal of Microwave and Millimeterwave Comuter Aided Engi-neering Vol. 5 No.. 7 9, 995. [] M. Djebari, G. Kom, MSM Photodiode Based Higly Accurate D Laser Imulse Radar, 9 th Euroean Microwave Conference, TuC-, Munich, - October, 999.