Optimization of Separated spacecraft Interferometer Trajectories in the Absence of A Gravity-Well Edmund M. Kong Prof david w. miller MIT Space Systems Laboratory 20th March 1998 Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Optimization of Separated Spacecraft Interferometer Trajectories in the Absence of A Gravity-Well Optimization of Separated Spacecraft Optimization of Separated Spacecraft Interferometer Trajectories in the Interferometer Trajectories in the Absence of A Gravity Absence of A Gravity-Well Edmund M. Edmund M. Kong Prof David W. Miller David W. Miller MIT Space Systems Laboratory MIT Space Systems Laboratory 20th March 1998 March 1998
Objective Approach Objective: Determine the optimal synthetic imaging trajectory for a Separated Spacecraft Interferometer Image Quality Optimization Trajectory Optimization Mass metric Time metric Comparison with Other Alternatives Uniformly spaced DS3 U-v points Other considerations Optimal Systel Performance Metric Trade-offs Mass Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Objective & Approach Objective & Approach Objective : Determine the optimal synthetic imaging trajectory for a Determine the optimal synthetic imaging trajectory for a Separated Spacecraft Interferometer Separated Spacecraft Interferometer Image Quality Optimization Image Quality Optimization Comparison with Other Alternatives Comparison with Other Alternatives Other Considerations Other Considerations Trajectory Optimization Trajectory Optimization Mass Metric Mass Metric Time Metric Time Metric Uniformly Spaced Uniformly Spaced U-V Points V Points DS3 Performance Metric Performance Metric Optimal System Optimal System Trade Mass Trade-offs
Image quality Model 2 Collector and 1 Combiner Interferometer (DS 3) Physics Average Image Intensity q,9)=∑ R I(+COSO)D(J1(X 丌 2Cos:(, xk+O, yR) a pixx+p yk cOS - Nominal Point Spread Function(2601 U-V Points) k=1(A Combiner 807 0.5 1.3 Collector Collector Psi milli-arcsecs -1.3-1.3 Psi milli-arcsecs Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Image Quality Image Quality Model : 2 Collector and 1 Combiner Interferometer (DS 3) Physics : Average Image Intensity Combiner Collector Collector ∑ ∑ = = ⎟⎠⎞ ⎜⎝⎛ ⎟ + ⎠⎞ ⎜⎝⎛ ≈ ⎟⎠⎞ ⎜⎝⎛ + ⎟⎟⎠⎞ ⎜⎜⎝⎛ ⎟⎠⎞ ⎜⎝⎛ + = N k i k j k N k D i k j k D i j x y D N x y D J N I 1 2 2 1 2 sin sin 1 2 2 2 cos ( ) 1 2 2 cos ( ) 1 (1 cos ) ( ) ( , ) ϕ ϕ λ π λ π ϕ ϕ λ π λ π θ ϕ ϕ λ π θ λ π θ
Image Quality. Mean Square Error omo Minimize M△B=(-.) Best mse Performance 15r n×n Approach: Choose N subset of all points Compare with Nominal psf o Simulated Annealing c Optimization Technique Optimized MSE Imaging Locations(N= 201 Poir 500 05 100 200 300 400 No of Imaging Points Results Image quality increases with no of imaging points(N) 500 Diminishing rate of return X(m) Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Image Quality Image Quality - Mean Square Error Mean Square Error Minimize : ( ) m m I I MSE m i m j o i j i j × − = ∑∑ = = 1 1 ( , ) ( , ) 2 ϕ ϕ ϕ ϕ Approach : Choose N subset of all points : Compare with Nominal PSF : Simulated Annealing Optimization Technique Results : Image quality increases with no. of imaging points (N) : Diminishing rate of return 0 100 200 300 400 0 0.5 1 1.5 No. of Imaging Points MSE, (W m-2 ) 2 (x 1 0-3 ) Best MSE Performance
Point spread Function Images MsE=14x103Wm2)2 MSE=2.97x 10-0Wm2 05 Psi, milli-arcsecs -1.3-1.3 Psik milli Psi milli-arcsec Psi mi‖ Arcsec 41 Imaging points 121 Imaging Points MsE=123×104wm2 MsE=572×105Wm2 907 05 milli-arcsecs 13-13 Psi milli-arcsecs -1.3-13 201 Imaging points 281 Imaging Points Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Point Spread Function Images Point Spread Function Images 41 Imaging Points 201 Imaging Points 281 Imaging Points 121 Imaging Points