Optical Delay lines Steering with optical delay lines Collector s/c trajectory in propagation Collector s/c follow R, =Ro elliptical trajectory vectors(X)frame from architecture 2 cosy siny 01 0 Delay lines to image off-nadir targets(Regt. 1) =I-siny cosy 00 cos p sin p Collector-Combiner s/c distance 010- sing sing=」mn D=R (osm)2(1 v 4Ip+iPn cosnt +8+ 25-PA+ P2 Imaginary Paraboloid Elliptical Trajectory 下 At Geo Maximum delay length from GEO (X,D) Delav/R D =0.310R 06◆=0,v=162° -03 Minimum semi-minor axis projection 0.6 Cross Range(Z/Ro) yz)=0.914R。 Space Systems Laboratory Massachusetts Institute of TechnologySpace Systems Laboratory Massachusetts Institute of Technology Optical Delay Lines Optical Delay Lines -1.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 -0.6 -0.3 0 0.3 0.6 x1" x2" Imaginary Paraboloid Elliptical Trajectory D1 D2 Delay/Ro = |D1 - D2| φ = 0o, ψ = 162o Combiner (Focus) dtarget Cross Range (z/Ro) Ze n ith ( x / R o ) −180 −90 0 90 180 180 90 0 GEO LEO φ (degrees) ψ (degrees) Delay/Ro 0 1 2 3 4 Steering with optical delay lines • Collector s/c follow Rz = Ro elliptical trajectory from Architecture 2 • Delay lines to image off-nadir targets (Reqt. 1) Hill z y x z y x ⎥⎥⎥⎦⎤ ⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤ ⎢⎢⎢⎣⎡⎥ − ⎥⎥⎦⎤ ⎢⎢⎢⎣⎡ = − ⎥⎥⎥⎦⎤ ⎢⎢⎢⎣⎡ ′′′ φ φ ψ ψ φ φ ψ ψ 0 sin sin 0 cos sin 1 0 0 0 0 1 sin cos 0 cos sin 0 2 2 2 1 256 25 8 5 cos 16 1 5 4 (cos ) n n n n o P P nt P P nt D R + + + ⎟⎟⎠⎞ ⎜⎜⎝⎛ = + + At GEO • Maximum delay length from GEO (x’,D) = 0.310Ro • Minimum semi-minor axis projection (y’,z’) = 0.914Ro Collector s/c trajectory in propagation vector’s (x’) frame: Collector-Combiner s/c distance: