СOMPENSATION OF LASER BEAM WAVEFRONT ABERRATIONS BASED ON ATMOSPHERIC BACKSCATTERING. Viktor Banakh, Igor Smalikho

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1 Wave Propagaton Lab СOMPENSATION OF LASER BEAM WAVEFRONT ABERRATIONS BASED ON ATMOSPHERIC BACKSCATTERING Vktor Banakh, Igor Smalkho Insttute of Atmospherc Optcs of the Russan Academy of Scences

2 Wave Propagaton Lab Formulaton of the task Schematc dagram of the setup: pulsed laser PL, lens telescopes for the prncpal and probng beams LT1 and LT2, deformable mrror DM, contrreflector CR and reflector R of the transmttng telescope, objectve Ob of the recevng telescope, daphragm D, photodetector PhD, deformable mrror control unt CU

3 Basc equatons P 2 2 s 2 2 N N 2a0 f D Wave Propagaton Lab ce P ( x) ( x) d ρ" I ( x, ρ") d ρ I ( x, ρ" ρx/ f) s the mean power of the backscattered radaton from probed volume, 2 d /2 d /2 R d ρ dz dy, D d /2 d /2 R R R f s the focal length of the recevng telescope, ( x) s the backscatterng coeffcent ρ' 2 2 ρ T ρ 2 0 ρ 0 ρ ρ ρ ρ x 2a F x 0 IN( x, ") d ρ ' ( ') j[ ( ') ( ') ' ( ' ") ] s the ntensty of the Gaussan probng beam wth the ntal radus a 0 and pulse energy E P focused at the dstance F, T ( ρ ') s the pupl functon of the transmttng aperture, s the wavelength I N( x, ρ") d ρ ' R( ρ')exp j ρ' j ( ρ' ρ") x F x 2 2 s the ntensty of the back propagated vrtual beam wth the unform ntal feld dstrbuton over the pupl functon of the recevng aperture

4 Phase aberratons and effectveness of aberraton compensaton 0 0 ( ρ') CZ( ρ') 0 are aberratonal phase (wave front) dstortons ( ρ') CZ ( ρ') 0 s the phase change ntroduced by the deformable mrror, Wave Propagaton Lab Z ( ρ ') s the Zernke polynomal C C TASK Ix (,0)/[(,0) Ix ] C C s the parameter of effcency of aberraton compensaton I ( x, 0 ) and I( x,0) C C are the ntensty at the prncpal beam axs and that n the absence of aberratons

5 Wave Propagaton Lab Smulaton Pˆ P (1 / SNR) s s 1 x/2 Ps dx' Ps( F x') x x/2 x s the mean power of the radaton scattered from the probed volume near the focus ( x F ), s the Gaussan random varable wth zero mean and unt varance SNR P s N M 2 2 s Ps P P P h /( ) (NEP) /(2 ) x x, km Normalzed mean power of backscattered radaton for probng beam focused at the dstance F 5km n the vcnty of focus. M s the number of accumulated soundng shots, NEP s the nose equvalent power, h s the Plank s constant, s the quantum effcency x N p s the longtudnal sze of the probed volume p pulse x c P s the length and P s the duraton of the N x - degree of freedom of averagng along the path (number of averaged pulse length)

6 Wave Propagaton Lab = 1.06 µm Smulaton parameters h, km = 67 ns ( p = 10 m) P PRF = 50 khz radus of transmttng aperture R = 50 cm, F = 5 km radus of recevng aperture r = 10 cm feld-of-vew angle d / f = 10 µrad, = 0.8 N = 50 ( x = 500 m), M = 50 x R Heght profles of molecular backscatter coeffcent m( h ) (), aerosole backscatter coeffcent a( h ) ( ) and sum atmospherc backscatter coeffcent ( h) ( h) ( h) ( ) x 1,( msr) m a

7 Computer smulaton of the ntal partally coherent laser beam wave front collmaton based on the atmospherc backscatter

8 Computer smulaton of the ntal partally coherent laser beam wave front collmaton based on the atmospherc backscatter

9 Computer smulaton of the ntal partally coherent laser beam wave front collmaton based on the atmospherc backscatter

10 SIMULATION RESULTS Wave Propagaton Lab SNR (a), mean power of probng beam backscattered radaton (b) and normalzed ntensty of prncpal beam (c) as functons of teraton number E P = 1 mj E P = 4 mj (b) (a) (a) Wt Wt (c) (b) (b) Iteraton number SNR= (c) (c) Iteraton number 1 C ( 1) 10, -15 NEP 10 Wt/Hz 1/2 Iteraton number

11 SIMULATION RESULTS Wave Propagaton Lab SNR (a), mean power of probng beam backscattered radaton (b) and normalzed ntensty of prncpal beam (c) as functons of teraton number (a) (a) Wt Wt (b) (b) (c) (c) C 1 ( 1) 15, Iteraton number -15 NEP 10 Wt/Hz 1/2, E P = 4 mj C 1 ( 1) 15, Iteraton number -16 NEP 5 10 Wt/Hz 1/2, E P = 2 mj

12 Wave Propagaton Lab EXPERIMENTAL MODELING Schematc dagram of the setup: deformable mrror DM, objectve Ob, daphragm D, photodetector PhD, deformable mrror control unt CU, amplfer A

13 Wave Propagaton Lab MEAN POWER OF PROBING BEAM BACKSCATTERED RADIATION Compensaton regme Compensaton regme Wthout compensaton Wthout compensaton Reflecton from dffuse target Aerosol backscatterng

14 Wave Propagaton Lab COMPENSATION OF SPHERICAL ABERRATION Dffuse screen Schematc dagram of the setup: deformable mrror DM, objectve Ob, daphragm D, photodetector PhD, deformable mrror control unt CU, amplfer A

15 Wave Propagaton Lab COMPENSATION OF SPHERICAL ABERRATION Intensty dstrbuton of probng beam (green) and prncpal beam (red)

16 Wave Propagaton Lab COMPENSATION OF SPHERICAL ABERRATION Intensty dstrbuton of probng beam (green) and prncpal beam (red) Deformable mrror swtch off Deformable mrror swtch on

17 Wave Propagaton Lab Summary Numercal smulaton and expermental modelng show that atmospherc backscatter can be used as control sgnal n the system of the ntal wave front collmaton