- Email: [email protected]
High frequency scanning response of an APD photocurrent for laser range finder
Sensors and Actuators A 110 (2004) 289–293
Conference
High frequency scanning response of an APD photocurrent for laser range finder David Dupuy∗ , Marc Lescure, Hélène Tap-Béteille ENSEEIHT, Electronic Laboratory, 2 rue Camichel, 31071 Toulouse, France Received 27 June 2003; received in revised form 27 June 2003; accepted 3 September 2003
Abstract In this paper, the scanning response of the photocurrent emitted by a large area avalanche photodiode (APD) is studied for a 3D laser camera. This 3D camera is based on a phase-shift laser range-finder to measure distance from 1 to 20 m. To obtain a large field of view of the optical head, a large area APD working as an optoelectronic mixer is used. Photocurrent response versus light spot position above the APD active area is analysed for high frequency measurements. Optoelectronic mixing permits to measure the scanning response phase of the internal photoelectric current. Moreover, it is demonstrated that the signal phase depends on the photoelectric gain. Signal-to-noise ratio and distance measurement error for the 3D camera are then discussed. © 2003 Elsevier B.V. All rights reserved. Keywords: 3D camera; Optical distance measurement; Laser range-finder; Optoelectronic mixing; Avalanche photodiode
1. Introduction A 3D camera for distance measurement from 1 to 20 m, based on phase-shift time-of-flight technique has been developed [1]. This technique is particularly well adapted for this distance range (Fig. 1) [2]. The dc current of the laser diode is modulated by a sine wave generated by the main oscillator at frequency fRF . After reflection from the rough target, a part of the laser beam is collected by a photodiode through a focusing lens. Distance measurement D is deduced from the phase-shift ϕ between the photoelectric current and the modulated laser signal: ϕ = 2πfRF
2D c
(1)
where c is the light speed. When the target is Lambertian and the target surface is as large as the area illuminated by the transmitter, the APD photocurrent is given by the relationship [3]: iAPD (t) = TT TR MSλ ρd
2 /4 πDR Popt (t) cos α π D2
(2)
where TT ρd Popt (t)/πcos α = Iopt (t) = photometric intensity. Here, TT is the collection and transmission efficiency of the transmitter; TR the transmission efficiency of the receiver ∗ Corresponding author. Tel.: +33-5-615-88317; fax: +33-5-615-88237. E-mail addresses: [email protected] (D. Dupuy), [email protected] (M. Lescure).
0924-4247/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2003.09.001
optics; ρd the Lambertian reflection coefficient of the target; α the laser beam incident angle on the target; DR the diameter of receiver lenses; M the APD photoelectric gain; Sλ the sensitivity of the APD. The pupil diameter DR of the receiver lenses must be wide in order to obtain a high signal-to-noise ratio. However, this is in conflict with a large field of view of the 3D camera [1]. In fact, when distance D is much larger than the lens focal length f, the minimal APD diameter DAPD depends on the field of view characterized by the angle θ max (Fig. 1): DR sin θmax DAPD = 2f sin θmax = (3) NA where NA is the numerical aperture of the lens. For example, the minimal diameter of the photodiode is DAPD = 0.34DR when θmax = 20◦ and NA = 1. So, a large area photodiode is necessary to take into account a high signal-to-noise ratio and a large field of view. The use of a silicon APD instead of a PIN photodiode provides a better signal-to-noise ratio because of the photoelectric gain M. Large area APD exist but have a large junction capacitance which strongly affects the photoelectric current bandwidth. To obtain a large bandwidth and an optimal signal-to-noise ratio, a transimpedance amplifier is usually associated with a photodiode [4]. For the laser range finder phase-shift technique, the photoelectric signal is mixed with a local oscillator signal fLO by a balanced modulator in order to realize the phase-shift mea-
290
D. Dupuy et al. / Sensors and Actuators A 110 (2004) 289–293
Scanning by micro mirrors reference
fIF
∆ϕ
signal
fRF
osc. LO
fIF
Diffusive Target
LD osc. RF
fRF Optical head
APD
θmax D
Fig. 1. Block diagram of the laser range-finder using phase-shift method. Micro mirrors are used to deflect the laser diode (LD) beam. The light spot moves above the APD active area.
surement at the intermediate frequency fIF = |fRF –fLO |. In fact, the phase measurement resolution is better at low frequency fIF than at high frequency fRF . The sensitivity SD = D/φ is proportional to 1/fRF . So, the sensitivity SD increases when the frequency fRF increases. For example, for fRF = 100 MHz, the sensitivity is equal to SD = 4.17 mm per degree. If the phasemeter resolution is equal to 0.1 degree, we obtain a distance resolution close to 0.4 mm. We have shown that the photodetection system can be improved by using an APD working as an optoelectronic mixer [5]. The mixing output is then mainly attributed to the dependence of the photoelectric gain M on the APD bias voltage. This photoelectric gain is modulated by the local oscillator voltage vLO . However, the scanning response of the APD photocurrent versus the laser spot position is not uniform [9]. That involves a low signal-to-noise ratio and a distance measurement error of the 3D camera for some laser spot positions. In this paper, the scanning response of a large area APD working as an optoelectronic mixer is studied when the light power is modulated in a high frequency range. Amplitude variation and phase-shift variation of the APD photocurrent are analyzed.
2. Experimental The experimental set-up shown on Fig. 2 enables us to measure the intrinsic scanning response (amplitude and phase-shift) of the large area APD working as an optoelectronic mixer. The laser diode wavelength is well adapted to the Si APD sensitivity (λ = 780 nm). The case temperature of the APD is fixed to TC = 37 ◦ C in order to avoid a breakdown voltage shift. The laser diode power is modulated by the main oscillator LO1 at frequency fRF . APD photoelectric gain M is modulated by the local oscillators LO2 working at frequency fLO . The biasing circuit using a low static resistance (R1 = 200 ) is necessary to keep the bias voltage VAPD independent of the dc photocurrent IAPD . As a consequence, power supply VHT and bias voltage VAPD are quasi equals. The laser beam is focused by a lens to realize
fIF LO2 LO1
fLO
ref. R1
fRF
C1 VHT
δϕ
APD
Popt
fIF
LD lens
mV L2
C2
Fig. 2. Experimental set-up to record the scanning response of the APD photoelectric signal. When the APD is working as an optoelectronic mixer, the multiplication factor M is modulated by the voltage of the local oscillator LO2. The signal-to-noise ratio is improved by the resonant circuit tuned at the intermediate frequency fIF .
a small light spot size (diameter around 25 m). Cartesian coordinate positions of the light spot above the APD area are measured by two X and Y position sensors. The resonant circuit L2 C2 tuned at the intermediate frequency fIF = 13.3 kHz improves the photoelectric signal-to-noise ratio. Phase-shift variation δϕ is measured between the photoelectric signal and the reference signal at the intermediate frequency fIF . The reference signal is generated by a balanced modulator which mixes fRF and fLO signals. With optoelectronic mixing technique, the phasemeter operates at low frequency (fIF = 13.3 kHz). That is why no error due to amplitude variation is introduced by the phasemeter. 3. Scanning response of the APD photocurrent The dc photocurrent IAPD of an uniform gain APD is given by the Miller’s formula [6]: IAPD = MIph =
1 Iph 1 − (VAPD /BV)n
(4)
where Iph = Sλ Popt the primary dc photocurrent; BV the breakdown voltage; n the concavity index of the avalanche zone.
D. Dupuy et al. / Sensors and Actuators A 110 (2004) 289–293
Fig. 3. Experimental results of APD photocurrent amplitude versus light spot position on active area section (“classical” photodetection at low frequency fRF = 13.3 kHz). VAPD = 423 V, 461 V, 478 V, 487 V from bottom to top and TC = 37 ◦ C (APD C30872 n◦ 2) (the same scanning response is given by the optoelectronic mixing technique for fRF = 10 MHz).
For large area APD, the gain uniformity is not a valid hypothesis anymore. Representative examples of experimental results of the APD photocurrent (amplitude and phase-shift) versus light spot position on active area are shown (Figs. 3–7). The “reach-through” structure of the large area (7 mm2 ) APD C30872 provides very low noise performance at high gain M. 3.1. Variation in photocurrent amplitude versus light spot position Variation in amplitude of the APD photocurrent IAPD is mainly due to a low variation of the APD breakdown voltage BV. In fact, BV depends on thickness and doping con-
291
Fig. 5. Experimental results of APD photocurrent versus light spot position on active area section for fRF = 500 MHz (phase-shift and amplitude from top to bottom). APD C30872 n◦ 2.
centration of the APD multiplication layer, which can vary slightly versus position on active area. When the bias voltage VAPD is close to the avalanche zone, Eq. (4) shows a large IAPD variation for a low BV variation. This is true for quasi-darkness conditions. When the average incident light power is high, the amplitude spatial response is flatter, because concavity index n (Eq. (4)) decreases. Amplitude variation increases with the bias voltage VAPD (Fig. 3). Fig. 4 shows that the relative scanning response of the a.c. photocurrent variation amplitude is quasi identical from low frequencies (fRF = 1 MHz ) to 1 GHz. However, we estimate that the internal cutoff frequency of the photoelectric current is close to 400 MHz for the APD C30872. This result agrees with [7] which demonstrates the mixing output of the APD is almost independent of frequency fRF .
Fig. 4. Experimental results of normalized photocurrent amplitude versus light spot position on active area section (APD C30872 n◦ 2) for fRF = 1 MHz, 100 MHz, 700 MHz, 1 GHz with the optoelectronic mixing technique.
292
D. Dupuy et al. / Sensors and Actuators A 110 (2004) 289–293
When the APD is working as an optoelectronic mixer, the scanning response of the photoelectric signal is independent of the time constant associated with the junction capacitance and with the distributed series resistance of the APD frontal zone. In fact, the useful photoelectric current is at low frequency (fIF = 13.3 kHz) thanks to the heterodyne photodetection. 3.2. Variation in photocurrent phase-shift 3.2.1. APD response time The intrinsic response time tr of the APD photoelectric signal is expressed by: tr = tt + tmult
(5)
where tt is the transit time and tmult is the multiplication time of the carriers. The transit time due to the absorption layer is expressed by: dabs dabs tt = (6) + vn vp where dabs is the absorption layer thickness of the APD, vn and vp are the saturation velocity of electrons and holes respectively. The multiplication time is random, but can be evaluated by [8]: dmult dmult + (7) tmult = κM vn vp
Fig. 6. Experimental results of APD photocurrent versus light spot position on active area section for fRF = 100 MHz (a) and fRF = 300 MHz (b) (phase-shift and amplitude from top to bottom). APD C30872 n◦ 3.
where κ is the ionization ratio and dmult is the multiplication layer thickness of the APD. Multiplication time tmult is lower than transit time tt . However, as will be shown below, the phase shift variation is mainly due to the multiplication time. 3.2.2. Relationship between phase-shift variation and gain variation Fig. 5 presents the scanning response (amplitude and phase-shift) at fRF = 500 MHz. Both recorder curves can be divided into three parts. Zone A has a low and constant gain M. In this zone, the phase-shift is also constant. It proves that the scanning response is independent of the distributed series resistance of the front layer. Zone B is a transition zone where the photoelectric gain increases progressively. A phase-shift step appears between zone A and zone B. To our knowledge, this is due to a state change of the APD multiplication layer. Zone C presents a high gain. For zone B and zone C, phase-shift variation δϕ is function to gain variation δM. In fact, multiplication time tmult depends essentially on the gain M when this one gets high (Eq. (7)). In this case, the phase-shift variation is mainly due to the gain variation: δϕ = 2πfRF δtmult = 2πfRF κ
dmult δM vn
(8)
Phase-shift variation δϕ is also proportional to the modulation signal frequency. This hypothesis is verified by the recording of Fig. 6. The scanning response of the APD selected for the optical head of the range finder is shown on Fig. 7. One can see that the phase-shift variation versus spot position is lower than ±2.5◦ at fRF = 30 MHz. According to Eq. (1), this variation involves a distance error δD ≈ ±3.5 cm for the 3D camera.
Fig. 7. Experimental results of APD photocurrent versus light spot position on active area section for fRF = 30 MHz and VAPD = 491 V (phase-shift and relative amplitude from top to bottom).
D. Dupuy et al. / Sensors and Actuators A 110 (2004) 289–293
4. Conclusion The optoelectronic mixing technique permits to measure amplitude and phase-shift variations of the APD photocurrent versus light spot position from low frequencies to high frequencies. Frequency response of the optoelectronic mixing is the same as the intrinsic frequency response of the direct detection photocurrent. For large area APD, photocurrent amplitude variation versus light spot position shows a non-uniform response. Furthermore, phase-shift variation depends mainly on the photoelectric gain variation when this parameter is getting high. This phase-shift variation is approximately proportional to the modulation signal frequency. Thanks to the optoelectronic mixing, the scanning response keeps independent of the distributed series resistance of the front zone because the useful photoelectric signal is at low frequency. As a direct consequence of the non-uniform APD gain, the 3D camera, based on a phase-shift laser range-finder, has a variable signal-to-noise ratio and an additional distance error. At modulation frequency fRF = 30 MHz, the error value due to the non-uniform APD response, calculated for the APD C30872 (active area: 7 mm2 ) is approximately 3 cm. To minimize distance errors and to obtain a high signal-to-noise ratio, an APD array seems to be more interesting than a large area APD.
References [1] M. Lescure, C. Ganibal, C. Lemaire, R. Prajoux, A large field-of-view range-finder associated with silicon micro-mirrors to design a 3d perception system for robotics applications, in: ODIMAP III Symposium, Pavia, Italy, 2001, pp. 383–388. [2] T. Bosch, M. Lescure, Crosstalk analysis of 1 m to 10 m phase-shift range finder, IEEE Trans. Instrum. Measurement 46 (6) (1997) 1224– 1228. [3] M.C. Amann, T. Bosch, M. Lescure, R. Myllylä, M. Rioux, Laser ranging: a critical review of usual techniques for distance measurement, Optical Engineering 40 (1) 1-0 (2001) 1–10.
293
[4] S.D. Personick, Receiver design for optical fiber systems, Proc. IEEE 65 (12) (1977) 1670–1678. [5] D. Dupuy, M. Lescure, M. Cousineau, A FMCW laser range-finder based on a delay line technique, IEEE rediscovering measurement in the age of informatics, IMTC Symposium 2 (2001) 1084–1088. [6] S.L. Miller, Avalanche breakdown in germanium, Phys. Rev. 99 (4) (1955) 1234–1241. [7] L. Li, F.V.C. Mendis, M.K. Haldar, M. Nakajima, Frequency characteristics of an avalanche photodiode in super-high-speed optical demodulation with electronic mixing, J. Opt. Commun. 18 (1997) 202–207. [8] B.E.A. Saleh, M.C. Teich, Fundamentals of Photonics, Wiley, USA, 1991, ISBN 0-471-83965-5. [9] T.F. Refaat, G.E. Halama, R.J. De Young, Characterization of advanced avalanche photodiodes for water vapor lidar receivers, NASA/TP-2000-210096, 2000.
Biographies David Dupuy was born in France, on 28 July, 1975. He started his school career at the Faculty of sciences, Université Paul Sabatier (UPS), Toulouse, France. He is currently working toward the PhD degree in optoelectronics at the INP-ENSEEIHT, Toulouse, France. His research interests are the FMCW laser range finder and the phase-shift laser range finder. Marc Lescure was born in Auch, France in 1945. He received the PhD degrees in electronics engineering from the University of Toulouse in 1972, and the Doctorat d’Etat in 1985. Since 1972, he has been working at the electronics laboratory (ENSEEIHT) of the National Polytechnics Institute of Toulouse. From 1972 to 1985, his research includes characterization of optoelectronic devices (LED, solar cell, MIS) by frequential method. Currently, he is professor with the electronics department. His current teaching/research interests include design of analog circuits, wireless infrared communications and optoelectronic sensors. He has published two books with A. Dziadowiec by Eyrolles, France on the subject of Analog Circuits and he is co-editor with T. Bosch of a selected papers on laser distance measurements, in SPIE Millestones Series. Hélène Tap-Béteille was born in 1973. She received her PhD in microelectronics-microsystems in 1999, prepared at the Laboratoire d’Analyse et d’Architecture des Systèmes of the French Centre National de la Recherche Scientifique (LAAS-CNRS). In 2001, she became assistant professor in the electronics laboratory of ENSEEIHT in Toulouse. She is currently working on integrated circuits and optoelectronics.
Conference
High frequency scanning response of an APD photocurrent for laser range finder David Dupuy∗ , Marc Lescure, Hélène Tap-Béteille ENSEEIHT, Electronic Laboratory, 2 rue Camichel, 31071 Toulouse, France Received 27 June 2003; received in revised form 27 June 2003; accepted 3 September 2003
Abstract In this paper, the scanning response of the photocurrent emitted by a large area avalanche photodiode (APD) is studied for a 3D laser camera. This 3D camera is based on a phase-shift laser range-finder to measure distance from 1 to 20 m. To obtain a large field of view of the optical head, a large area APD working as an optoelectronic mixer is used. Photocurrent response versus light spot position above the APD active area is analysed for high frequency measurements. Optoelectronic mixing permits to measure the scanning response phase of the internal photoelectric current. Moreover, it is demonstrated that the signal phase depends on the photoelectric gain. Signal-to-noise ratio and distance measurement error for the 3D camera are then discussed. © 2003 Elsevier B.V. All rights reserved. Keywords: 3D camera; Optical distance measurement; Laser range-finder; Optoelectronic mixing; Avalanche photodiode
1. Introduction A 3D camera for distance measurement from 1 to 20 m, based on phase-shift time-of-flight technique has been developed [1]. This technique is particularly well adapted for this distance range (Fig. 1) [2]. The dc current of the laser diode is modulated by a sine wave generated by the main oscillator at frequency fRF . After reflection from the rough target, a part of the laser beam is collected by a photodiode through a focusing lens. Distance measurement D is deduced from the phase-shift ϕ between the photoelectric current and the modulated laser signal: ϕ = 2πfRF
2D c
(1)
where c is the light speed. When the target is Lambertian and the target surface is as large as the area illuminated by the transmitter, the APD photocurrent is given by the relationship [3]: iAPD (t) = TT TR MSλ ρd
2 /4 πDR Popt (t) cos α π D2
(2)
where TT ρd Popt (t)/πcos α = Iopt (t) = photometric intensity. Here, TT is the collection and transmission efficiency of the transmitter; TR the transmission efficiency of the receiver ∗ Corresponding author. Tel.: +33-5-615-88317; fax: +33-5-615-88237. E-mail addresses: [email protected] (D. Dupuy), [email protected] (M. Lescure).
0924-4247/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2003.09.001
optics; ρd the Lambertian reflection coefficient of the target; α the laser beam incident angle on the target; DR the diameter of receiver lenses; M the APD photoelectric gain; Sλ the sensitivity of the APD. The pupil diameter DR of the receiver lenses must be wide in order to obtain a high signal-to-noise ratio. However, this is in conflict with a large field of view of the 3D camera [1]. In fact, when distance D is much larger than the lens focal length f, the minimal APD diameter DAPD depends on the field of view characterized by the angle θ max (Fig. 1): DR sin θmax DAPD = 2f sin θmax = (3) NA where NA is the numerical aperture of the lens. For example, the minimal diameter of the photodiode is DAPD = 0.34DR when θmax = 20◦ and NA = 1. So, a large area photodiode is necessary to take into account a high signal-to-noise ratio and a large field of view. The use of a silicon APD instead of a PIN photodiode provides a better signal-to-noise ratio because of the photoelectric gain M. Large area APD exist but have a large junction capacitance which strongly affects the photoelectric current bandwidth. To obtain a large bandwidth and an optimal signal-to-noise ratio, a transimpedance amplifier is usually associated with a photodiode [4]. For the laser range finder phase-shift technique, the photoelectric signal is mixed with a local oscillator signal fLO by a balanced modulator in order to realize the phase-shift mea-
290
D. Dupuy et al. / Sensors and Actuators A 110 (2004) 289–293
Scanning by micro mirrors reference
fIF
∆ϕ
signal
fRF
osc. LO
fIF
Diffusive Target
LD osc. RF
fRF Optical head
APD
θmax D
Fig. 1. Block diagram of the laser range-finder using phase-shift method. Micro mirrors are used to deflect the laser diode (LD) beam. The light spot moves above the APD active area.
surement at the intermediate frequency fIF = |fRF –fLO |. In fact, the phase measurement resolution is better at low frequency fIF than at high frequency fRF . The sensitivity SD = D/φ is proportional to 1/fRF . So, the sensitivity SD increases when the frequency fRF increases. For example, for fRF = 100 MHz, the sensitivity is equal to SD = 4.17 mm per degree. If the phasemeter resolution is equal to 0.1 degree, we obtain a distance resolution close to 0.4 mm. We have shown that the photodetection system can be improved by using an APD working as an optoelectronic mixer [5]. The mixing output is then mainly attributed to the dependence of the photoelectric gain M on the APD bias voltage. This photoelectric gain is modulated by the local oscillator voltage vLO . However, the scanning response of the APD photocurrent versus the laser spot position is not uniform [9]. That involves a low signal-to-noise ratio and a distance measurement error of the 3D camera for some laser spot positions. In this paper, the scanning response of a large area APD working as an optoelectronic mixer is studied when the light power is modulated in a high frequency range. Amplitude variation and phase-shift variation of the APD photocurrent are analyzed.
2. Experimental The experimental set-up shown on Fig. 2 enables us to measure the intrinsic scanning response (amplitude and phase-shift) of the large area APD working as an optoelectronic mixer. The laser diode wavelength is well adapted to the Si APD sensitivity (λ = 780 nm). The case temperature of the APD is fixed to TC = 37 ◦ C in order to avoid a breakdown voltage shift. The laser diode power is modulated by the main oscillator LO1 at frequency fRF . APD photoelectric gain M is modulated by the local oscillators LO2 working at frequency fLO . The biasing circuit using a low static resistance (R1 = 200 ) is necessary to keep the bias voltage VAPD independent of the dc photocurrent IAPD . As a consequence, power supply VHT and bias voltage VAPD are quasi equals. The laser beam is focused by a lens to realize
fIF LO2 LO1
fLO
ref. R1
fRF
C1 VHT
δϕ
APD
Popt
fIF
LD lens
mV L2
C2
Fig. 2. Experimental set-up to record the scanning response of the APD photoelectric signal. When the APD is working as an optoelectronic mixer, the multiplication factor M is modulated by the voltage of the local oscillator LO2. The signal-to-noise ratio is improved by the resonant circuit tuned at the intermediate frequency fIF .
a small light spot size (diameter around 25 m). Cartesian coordinate positions of the light spot above the APD area are measured by two X and Y position sensors. The resonant circuit L2 C2 tuned at the intermediate frequency fIF = 13.3 kHz improves the photoelectric signal-to-noise ratio. Phase-shift variation δϕ is measured between the photoelectric signal and the reference signal at the intermediate frequency fIF . The reference signal is generated by a balanced modulator which mixes fRF and fLO signals. With optoelectronic mixing technique, the phasemeter operates at low frequency (fIF = 13.3 kHz). That is why no error due to amplitude variation is introduced by the phasemeter. 3. Scanning response of the APD photocurrent The dc photocurrent IAPD of an uniform gain APD is given by the Miller’s formula [6]: IAPD = MIph =
1 Iph 1 − (VAPD /BV)n
(4)
where Iph = Sλ Popt the primary dc photocurrent; BV the breakdown voltage; n the concavity index of the avalanche zone.
D. Dupuy et al. / Sensors and Actuators A 110 (2004) 289–293
Fig. 3. Experimental results of APD photocurrent amplitude versus light spot position on active area section (“classical” photodetection at low frequency fRF = 13.3 kHz). VAPD = 423 V, 461 V, 478 V, 487 V from bottom to top and TC = 37 ◦ C (APD C30872 n◦ 2) (the same scanning response is given by the optoelectronic mixing technique for fRF = 10 MHz).
For large area APD, the gain uniformity is not a valid hypothesis anymore. Representative examples of experimental results of the APD photocurrent (amplitude and phase-shift) versus light spot position on active area are shown (Figs. 3–7). The “reach-through” structure of the large area (7 mm2 ) APD C30872 provides very low noise performance at high gain M. 3.1. Variation in photocurrent amplitude versus light spot position Variation in amplitude of the APD photocurrent IAPD is mainly due to a low variation of the APD breakdown voltage BV. In fact, BV depends on thickness and doping con-
291
Fig. 5. Experimental results of APD photocurrent versus light spot position on active area section for fRF = 500 MHz (phase-shift and amplitude from top to bottom). APD C30872 n◦ 2.
centration of the APD multiplication layer, which can vary slightly versus position on active area. When the bias voltage VAPD is close to the avalanche zone, Eq. (4) shows a large IAPD variation for a low BV variation. This is true for quasi-darkness conditions. When the average incident light power is high, the amplitude spatial response is flatter, because concavity index n (Eq. (4)) decreases. Amplitude variation increases with the bias voltage VAPD (Fig. 3). Fig. 4 shows that the relative scanning response of the a.c. photocurrent variation amplitude is quasi identical from low frequencies (fRF = 1 MHz ) to 1 GHz. However, we estimate that the internal cutoff frequency of the photoelectric current is close to 400 MHz for the APD C30872. This result agrees with [7] which demonstrates the mixing output of the APD is almost independent of frequency fRF .
Fig. 4. Experimental results of normalized photocurrent amplitude versus light spot position on active area section (APD C30872 n◦ 2) for fRF = 1 MHz, 100 MHz, 700 MHz, 1 GHz with the optoelectronic mixing technique.
292
D. Dupuy et al. / Sensors and Actuators A 110 (2004) 289–293
When the APD is working as an optoelectronic mixer, the scanning response of the photoelectric signal is independent of the time constant associated with the junction capacitance and with the distributed series resistance of the APD frontal zone. In fact, the useful photoelectric current is at low frequency (fIF = 13.3 kHz) thanks to the heterodyne photodetection. 3.2. Variation in photocurrent phase-shift 3.2.1. APD response time The intrinsic response time tr of the APD photoelectric signal is expressed by: tr = tt + tmult
(5)
where tt is the transit time and tmult is the multiplication time of the carriers. The transit time due to the absorption layer is expressed by: dabs dabs tt = (6) + vn vp where dabs is the absorption layer thickness of the APD, vn and vp are the saturation velocity of electrons and holes respectively. The multiplication time is random, but can be evaluated by [8]: dmult dmult + (7) tmult = κM vn vp
Fig. 6. Experimental results of APD photocurrent versus light spot position on active area section for fRF = 100 MHz (a) and fRF = 300 MHz (b) (phase-shift and amplitude from top to bottom). APD C30872 n◦ 3.
where κ is the ionization ratio and dmult is the multiplication layer thickness of the APD. Multiplication time tmult is lower than transit time tt . However, as will be shown below, the phase shift variation is mainly due to the multiplication time. 3.2.2. Relationship between phase-shift variation and gain variation Fig. 5 presents the scanning response (amplitude and phase-shift) at fRF = 500 MHz. Both recorder curves can be divided into three parts. Zone A has a low and constant gain M. In this zone, the phase-shift is also constant. It proves that the scanning response is independent of the distributed series resistance of the front layer. Zone B is a transition zone where the photoelectric gain increases progressively. A phase-shift step appears between zone A and zone B. To our knowledge, this is due to a state change of the APD multiplication layer. Zone C presents a high gain. For zone B and zone C, phase-shift variation δϕ is function to gain variation δM. In fact, multiplication time tmult depends essentially on the gain M when this one gets high (Eq. (7)). In this case, the phase-shift variation is mainly due to the gain variation: δϕ = 2πfRF δtmult = 2πfRF κ
dmult δM vn
(8)
Phase-shift variation δϕ is also proportional to the modulation signal frequency. This hypothesis is verified by the recording of Fig. 6. The scanning response of the APD selected for the optical head of the range finder is shown on Fig. 7. One can see that the phase-shift variation versus spot position is lower than ±2.5◦ at fRF = 30 MHz. According to Eq. (1), this variation involves a distance error δD ≈ ±3.5 cm for the 3D camera.
Fig. 7. Experimental results of APD photocurrent versus light spot position on active area section for fRF = 30 MHz and VAPD = 491 V (phase-shift and relative amplitude from top to bottom).
D. Dupuy et al. / Sensors and Actuators A 110 (2004) 289–293
4. Conclusion The optoelectronic mixing technique permits to measure amplitude and phase-shift variations of the APD photocurrent versus light spot position from low frequencies to high frequencies. Frequency response of the optoelectronic mixing is the same as the intrinsic frequency response of the direct detection photocurrent. For large area APD, photocurrent amplitude variation versus light spot position shows a non-uniform response. Furthermore, phase-shift variation depends mainly on the photoelectric gain variation when this parameter is getting high. This phase-shift variation is approximately proportional to the modulation signal frequency. Thanks to the optoelectronic mixing, the scanning response keeps independent of the distributed series resistance of the front zone because the useful photoelectric signal is at low frequency. As a direct consequence of the non-uniform APD gain, the 3D camera, based on a phase-shift laser range-finder, has a variable signal-to-noise ratio and an additional distance error. At modulation frequency fRF = 30 MHz, the error value due to the non-uniform APD response, calculated for the APD C30872 (active area: 7 mm2 ) is approximately 3 cm. To minimize distance errors and to obtain a high signal-to-noise ratio, an APD array seems to be more interesting than a large area APD.
References [1] M. Lescure, C. Ganibal, C. Lemaire, R. Prajoux, A large field-of-view range-finder associated with silicon micro-mirrors to design a 3d perception system for robotics applications, in: ODIMAP III Symposium, Pavia, Italy, 2001, pp. 383–388. [2] T. Bosch, M. Lescure, Crosstalk analysis of 1 m to 10 m phase-shift range finder, IEEE Trans. Instrum. Measurement 46 (6) (1997) 1224– 1228. [3] M.C. Amann, T. Bosch, M. Lescure, R. Myllylä, M. Rioux, Laser ranging: a critical review of usual techniques for distance measurement, Optical Engineering 40 (1) 1-0 (2001) 1–10.
293
[4] S.D. Personick, Receiver design for optical fiber systems, Proc. IEEE 65 (12) (1977) 1670–1678. [5] D. Dupuy, M. Lescure, M. Cousineau, A FMCW laser range-finder based on a delay line technique, IEEE rediscovering measurement in the age of informatics, IMTC Symposium 2 (2001) 1084–1088. [6] S.L. Miller, Avalanche breakdown in germanium, Phys. Rev. 99 (4) (1955) 1234–1241. [7] L. Li, F.V.C. Mendis, M.K. Haldar, M. Nakajima, Frequency characteristics of an avalanche photodiode in super-high-speed optical demodulation with electronic mixing, J. Opt. Commun. 18 (1997) 202–207. [8] B.E.A. Saleh, M.C. Teich, Fundamentals of Photonics, Wiley, USA, 1991, ISBN 0-471-83965-5. [9] T.F. Refaat, G.E. Halama, R.J. De Young, Characterization of advanced avalanche photodiodes for water vapor lidar receivers, NASA/TP-2000-210096, 2000.
Biographies David Dupuy was born in France, on 28 July, 1975. He started his school career at the Faculty of sciences, Université Paul Sabatier (UPS), Toulouse, France. He is currently working toward the PhD degree in optoelectronics at the INP-ENSEEIHT, Toulouse, France. His research interests are the FMCW laser range finder and the phase-shift laser range finder. Marc Lescure was born in Auch, France in 1945. He received the PhD degrees in electronics engineering from the University of Toulouse in 1972, and the Doctorat d’Etat in 1985. Since 1972, he has been working at the electronics laboratory (ENSEEIHT) of the National Polytechnics Institute of Toulouse. From 1972 to 1985, his research includes characterization of optoelectronic devices (LED, solar cell, MIS) by frequential method. Currently, he is professor with the electronics department. His current teaching/research interests include design of analog circuits, wireless infrared communications and optoelectronic sensors. He has published two books with A. Dziadowiec by Eyrolles, France on the subject of Analog Circuits and he is co-editor with T. Bosch of a selected papers on laser distance measurements, in SPIE Millestones Series. Hélène Tap-Béteille was born in 1973. She received her PhD in microelectronics-microsystems in 1999, prepared at the Laboratoire d’Analyse et d’Architecture des Systèmes of the French Centre National de la Recherche Scientifique (LAAS-CNRS). In 2001, she became assistant professor in the electronics laboratory of ENSEEIHT in Toulouse. She is currently working on integrated circuits and optoelectronics.