Optimal Recognition Algorithm for Cameras of Lasers Evanescent

Transcription

1 Otimal Recognition Algorithm for Cameras of Lasers Evanescent T. Gaudo * Abstract An algorithm based on the Bayesian aroach to detect and recognise off-axis ulse laser beams roagating in the atmoshere is resented. This method otimises the off-axis measurement of ulse laser with low energy level by ultra fast cameras. The erformance of this technique is validated with simulated signals obtained from array sensor. Index Terms Array, Bayesian, detection, laser, sensor. INTRODUCTION As lasers are coming into more and more widesread use in target-designation, countermeasures, range finding, and surveying oerations, the otential for accidental damage to human eyes or sensors on the battlefield increases. Initial indications are off-axis laser beam detection shows romise for use as an early laser warning system. The laser beams can indeed be off-axis detected when roagating in the lower atmoshere by their scattering track on natural aerosols [1]. In the last years, several laboratories have conducted studies to detect off-axis non cooerative ulsed laser beams in the lower atmoshere. A roblem of interest in laser imager rocessing occurs when Signal to Noise Ratio is very low. For instance, for a sub-otimum leading-edge level detection rocedure, the noise may increased the robability false alarm (fa if the level is low. To decrease the fa a Bayesian aroach is used in which a robability density function (df for the signal amlitude is used as rior distribution in determining the df for signal lus noise []. This aer describes an analytic model of scattered light under different atmosheric and angle conditions in a 3D geometry, giving the hotometry, the geometry and the temoral arameters of the detected signal. Then, to evaluate the detection technique, a comuter code is develoed. Following this theoretical art, simulations in the visible and near infrared bands are resented with a kilometric scale of free laser roagation. The technique develoed for this urose confirms a fa reduction that allows to imrove Off- Axis Laser Warning detection. In section, an analytic model describing the hysics of the detection is resented. Section 3 is devoted to the simulations and detection analysis. Section 4 summarizes and concludes the discussion. LASER DETECTION DEL DESCRIPTION The objective of the model is to calculate the arameters of the light scattered by a ulsed beam onto atmoshere aerosols, in order to estimate the otential erformances of a dedicated warning sensor. So, the ower received on a D array of detectors is calculated, coming from the scattered beam, the geometric image of the beam on the focal lane array, and the time and duration of the ixel illumination. This energy is assumed to be detected by a D-array sensor. Photometry in 3D geometry Considering the laser beam and the sensor in a 3D geometry as in Fig. 1. O is the center of the detection otics. A is the source of the laser beam : D = OA. The orthogonal distance from O to the beam is : d = B. M is a oint on the beam, observed with an angle from O, in resect with the source direction. θ is the angle between the observation axis and the beam. A is observed with an angle from. θ is the angle between the observation axis and the beam. The laser beam is modeled as a thin line, i.e. the image of its right section is smaller than the ixel in the focal lane. The atmosheric arameters deending on altitude h are : α( h : absortion coefficient (m -1, assumed to be constant on the beam, β(h : scattering coefficient (m -1, assumed to be constant on the beam. The scattering distribution is given by the hase function ϕ(θ,h. A c is the sensor collection area, E e is the ulse energy. Pe(t is the time deendent transmitted ower of the laser. Pe(t is suosed having a gaussian shae with a 1/e width τ e. Time origin t= is set at the center of the ulse. * T. Gaudo is with the Office National Études et de Recherches Aérosatiales O.N.E.R.A (The French Aerosace Lab, Palaiseau France (hone: ; thierry.gaudo@ onera.fr. P (t E ex 8 A t e = e τ e π τe (1 ISBN: WCECS 7

2 θ = arccos AB (7 AB = θ θ (8 ( + Ac cos dω = (9 The cosine term comes from the field angle between the scattered beam and the otical axis. d dl = = cdt sin ( θ (1 Figure 1 Detection geometry 3D and lane view The incident laser ower at M is exressed as : β } M A AM P i (t = P e (t ex + AM c The scattered ower at M by a beam element of length dl in the direction θ into a solid angle dω is : M d A i dp (t = P (t βϕ Ω dl (3 Geometric considerations as in Fig. 1 give : ABct AM = (4 AB j = AO AM ( (5 After roagation from M to O, the received ower at the sensor aerture, coming from the beam in the direction θ into the angle element d is : M A dp r (t = P d (t ex + c β } (11 By relacing the exressions (, (3, (4, (5, (6,(7, (8, (9, (1 into (11 the ower received on O becomes : O dp r (t A Ac cos ( + c = P e (t τ βϕ G(t dt (1 G(t = ex α + β AM + β}( with the arrival time on the lens : τ = AM + c The otical arameters deends of the instrumental transmission factor τ i, of the focal F, of the otic modulation resonse and of the array dimension. (13 Considering the detection lane arallels to the lane formed by the sensor inut lens, the vector drawing the laser trace on the array is exressed as : OF= F OM j OM i OM j OM k (14 h = OM k (6 ISBN: WCECS 7

3 with (1 and (14 the ower received on the detector lane is : ( + F dp r (t A Ac cos c = τ ip e (t τ βϕ G(t dt β }( G(t = ex + AM + (15 By considering the quasi-erfect objective, the otic modulation resonse is a sot of Airy. The geometrical form of this resonse can be aroached by S a circular surface of angular r radius limited by solid angle dω (9. Surface lit according to direction x and y in the array lane is: S (x, F, y = 1 x y dω if arctan + arctan < r < F F S (x, F, y = elsewhere With (16 laser trace drawn on the detection lane (15 becomes (* convolution oerator : dp F r (t = dp r (t *S dt dt (16 (17 Detection lane dimensions describes by a matrix D are of N sit ixels in vertical direction N gis ixels in horizontal direction. the ixels are of width lgis, length l gis. From these arameters the laser trace imaged by the array sensor is exressed by : dp r (t,m, n = dt lsit lgis N 1 ym + x N 1 gis n + sit F dp r (tdxdy δ m= n= lsit l y gis m x n ( F n (18 its satial samling ste if one considers the axis of the lens in the array center and the located ixel (m, n = (, laced as shown in the Fig. 1 is: F n 1 Ngis n + l xn = y = m Nsit 1 m l gis sit (19 An electronic device, connected to the array sensor, amlifies filters and samles each ixel. The deterministic signal at the outut of filter modeled with the H(t ulse resonse is assumed to take the form : V(t,m, n = H(t,m, n*p r (t,m, n ( Electronic signal from each ixel line is rocessed in one channel data samler working at T s. The V signal rovides the amlitude evolution of received ower for different ixels in vertical and horizontal lane. This signal imaging laser sot on array sensor is written : N 1M 1 ( = V( kt,m,n (1 V kts n= m= s This electronic architecture decreases rocessing time and answer to real time need of the laser detection systems. It rovides in real time the index of the most illuminated ixel as well as the starting time of illumination of these ixels. However, with this electronic device, amlitude evolution of a individual ixel becomes inaccessible and noise variance is increased of a factor MN (ixel number. That may decrease the erformances of the Bayesian detection, but strongly reduces the data flow to be rocessed, answering to real-time goals of a laser warning system. Descrition of the Bayesian detection technique The detection technique is based on decision test on line. The roblem is to select, using a window sliing of P- samles, one of both hyothesis : H 1 : There is a laser in camera field. H : There isn't any. With 1 and U-samled temoral vector (window size t = [ t m,ts t m,..., ( U 1 Ts t m ] the hyothesis as exressed (vector in bold tye : z = A v + w ( H 1 : H : z = w (3 where w is a white noise with centered normal df N ( σ w,, and A is the maximum amlitude of normalized V at time t m. The decision criterion between H 1 and H is constructed with Bayes risk function. This function verifies than the detection is otimal with the likelihood ratio : ( z H1 ( z H < η H Λ ( z = = then select > η H 1 (4 ISBN: WCECS 7

4 where, with and 3, ( z H and, z A v ex σ w 1 = U ( πσ w (5 With exression 7 and the assumtion made on the noise, it comes : l( z N ( SNR v, SNR v under H (3 l( z N (SNR v, SNR v under H1 where SNR signal to noise ower ratio at filter outut is defined by SNR A v σ w ( v root mean square (rms value. ( z H z ex σ w = U ( πσ w The decision criterion 4 becomes the logarithmic exression : ( z l( z = ln Λ ( = H 1 z z Av > ln( w H < η σ This exression more simle which has the same roerties than 4 is a likelihood test between signals recorded and simulated. (6 (7 Equation 4 suggests to use Neyman-Pearson test [3] which takes into consideration the fa and d (robability of detection to determine the level. From 7, it follows directly that : fa d + = (l H dl (8 + = (l H 1dl (9 In 8 and 9 likelihood ratio l( (l H i reresents df of logarithmic z when H i is true. Equations 8 and 9 become : + SNR v fa = 1 erf SNR v SNR v d = 1 erf SNR v where erf is the error function ( erf ( l 1 π ex l dl. (31 Exressions 8 and 9 allow to lot receiver oerating characteristics (roc to select theoretic value. These curves show the detection erformances of algorithm with different signal models simulated. Simulation arameters SIMULATIONS AND DETECTION ANALYSIS The goal is to validate the Bayesian laser beam detection model by simulated field trials. This base allowed to deal with kilometric roagation and detection distances. The ulse is generated by a laser, emitting either in near Infrared (IR. The ulse duration is around 1 ns. The laser roagates freely over a controlled distance of km with a divergence less than 1mrad. The scattered beam detection under secific atmosheric conditions can be evaluated with off-axis observation angles from 5 to 9 degrees. The laser beam warning sensor. comrises a focal lane array (fa 8 x 8 of IR hotodiodes. A f/1 lan-convex single lens focuses the beam on the fa. The field of view (fov is 16 x 16. The ixel fov is. Electronic signal from each ixel is amlified in 15MHz band and the channels are samled at 1MHz for time real oerational use. ISBN: WCECS 7

5 Above three sets of numerical models is resented, summarized in Table I and Fig.. For each set, D,d, and thus θ and are given. For each set, summed signals (1 are simulated in stable atmosheric conditions. The atmoshere arameters are derived from Fascode data for a continental climate, 3 km visibility. Position D(m d (m θ ( ( A B C Table I Geometric arameters of field observations Fig. 4 illustrates fa and d evolution according to for a value of SNR, two t m and osition A. Pd is equal to 1 for >. The erformances of detections are not very deendent on the delay (t m=t a/4 or t m=3*t a/4 between acquisition window and signal, in the case of otimal recovery (overlaing suerior to 5%. Pfa has an instantaneous variation from 1 to around for all snr values, in the case where the signal is not in acquisition window (tm< -Ta/4. This roerty forces to choose always higher than to ensure a very weak fa. Figure - Observation geometry Values of are smaller than the half field of view, so that laser source is observed. For each of the three oints of observation, in the case of a laser source laced at m of altitude, the simulated signals are resented in Fig. 3. Figure 4 -Pd for t m=t a/4 or t m=3*t a/4 fa :for t m<-t a/4 according snr=18db and osition A. Fig. 5 makes it ossible to determine the level otimal for a d=99.9 according to SNR and simulated signals. =1.8 is the otimal threshold which ensures a d=99.9 and a fa near to for the three ositions of laser source and snr near to 1dB. Figure 3 - Simulated signals with T a=16t s=16ns (acquisition time and t m=4t s=t a/4=4ns (delay time of enveloe max. Figure 5 - maximum value ensuring d=99.9% for t m=t a/4 or t m=3*t a/4 according to snr and ositions A,B and C. ISBN: WCECS 7

6 This Bayesian method has erformances much higher than the technique of detection er threshold. The latter gives results satisfying for osition A only starting from snr of 4dB. Detection and recognition algorithm 7 runs in line and rocesses into continuous ermanent samles flow delivered by camera. Its comuting ower around 6 M Flos is adated to current rocessing systems. CONCLUSION The model derived analytic formulas for comuting, array sensor ower of backscattered light incoming from a beam roagating in the atmoshere, has been develoed in a 3D geometry. Off-axis laser camera detection erformances can so be calculated for different observation geometries and atmosheric conditions. Using a generic sensor array, field trials is conducted for validating Bayesian detection algorithm. Simulation results allow to set correctly algorithm and otimise rocessing time. The model is therefore able to redict Bayesian detection erformance in many oerational situations and can be extended to different cameras. In the near future, the algorithm will be imrove, and validate with signals bank based on many more geometric conditions and for very different atmosheric conditions. REFERENCES [1] B.H. Björkman, Aaratus for determining the ath of a ulsed light beam, United States Patent, U.S. Philis Cororation, New York, [] D. V. Lindley, Introduction to robability and statistics from a Bayesian viewoint I, II, Cambridge Univ. Press, [3] J. Neyman and E. S. Pearson, Contributions to the theory of testing statistical hyotheses I, II, Statist. Res. Mem. London Univ., 1 (1936, l-37; (1938, ISBN: WCECS 7