大 Example: Image Construction Image quality is determined by the point spread function of aperture configuration πDsin0 π(1+cose)D 2 V exp π Dsin e (v n +vin) Aperture dependence Geometry dependence The geometry dependence can be expanded into terms which only depend on relative position 丌 I()=1A()N+cosy, (=x2))+cos/w, ( DIl EMFF Final review ug.29,2003
DII EMFF Final Review Aug. 29, 2003 Example: Image Construction Example: Image Construction • Image quality is determined by the point spread function of aperture configuration ( ) 2 1 1 ( ) 2 exp sin sin (1 cos ) , ⎥⎥⎥⎥⎦⎤ ⎢⎢⎢⎢⎣⎡ ∑ ⎟⎠⎞ ⎜⎝⎛ ψ + ψ λπ − ⎟⎟⎟⎟⎠⎞ ⎜⎜⎜⎜⎝⎛ λ π θ ⎟⎠⎞ ⎜⎝⎛ λ π θ ⎟⎠⎞ ⎜⎝⎛ λ π + θ ψ ψ = =Nn i j i n j n x y i DD J D I • The geometry dependence can be expanded into terms which only depend on relative position Aperture dependence Geometry dependence I ψi ( ) = IAp ψi ( ) N + cos 2πλψi(x1 − x2) ⎛ ⎝ ⎞ ⎠ + cos 2πλψi(x1 − x3) ⎛ ⎝ ⎞ ⎠ + ... ⎡⎣ ⎢ ⎤ ⎦ ⎥
大 Comparison -Golay Configurations Ss 3 spacecraft Point Spread Function 6 spacecraft Point Spread Function 13.1 13.1 s0书 0 50 -13.1 13.1 50131013.1500 5013.1013.1 x(m 8. (arcmin) x(m) 8. ( arcmin) 9 spacecraft Point Spread Function 12 spacecraft Point Spread Function 50 13.1 50 13.1 0 ! 50 -13.1 -13.1 05013.1013150 5013.10 3.1 (arcmin) x(m) e, ( arcmin) PSFs for the golay configurations shown here will not change if the apertures are shifted in any direction DIl EMFF Final review ug.29,2003
DII EMFF Final Review Aug. 29, 2003 Comparison Comparison - Golay Configurations Configurations PSFs for the Golay configurations shown here will not change if the apertures are shifted in any direction
大 Question /l What forces must be transmitted between satellites to allow for all relative degrees of freedom to be controlled? In 2-D, N spacecraft have 3N DOFS, but we are only interested in controlling(and are able to control)3N-2 (no translation of the center of mass For 2 spacecraft, that's a total of 4 All except case(4 )can be generated using axial forces(such as electrostatic monopoles)and torques provided by reaction wheels Complete instantaneous control requires a transverse force which can be provided using either electrostatic or electromagnetic dipoles DIl EMFF Final review ug.29,2003
DII EMFF Final Review Aug. 29, 2003 Question III: Question III: • What forces must be transmitted between satellites to allow for all relative degrees of freedom to be controlled? – In 2-D, N spacecraft have 3N DOFs, but we are only interested in controlling (and are able to control) 3N-2 (no translation of the center of mass) – For 2 spacecraft, that’s a total of 4: • All except case (4) can be generated using axial forces (such as electrostatic monopoles) and torques provided by reaction wheels • Complete instantaneous control requires a transverse force, which can be provided using either electrostatic or electromagnetic dipoles 1 2 3 4
大 What is it Not good for? Orbit Raising Bulk Plane Changes De-Orbit All these require rotating the system angular momentum vector or changing the energy of the orbit None of these is possible using only internal forces DIl EMFF Final review ug.29,2003
DII EMFF Final Review Aug. 29, 2003 What is it NOT good for? What is it NOT good for? • Orbit Raising • Bulk Plane Changes • De-Orbit • All these require rotating the system angular momentum vector or changing the energy of the orbit • None of these is possible using only internal forces
大 Forces and Torques: Conceptual In the Far Field the dipole field structure for electrostatic and electromagnetic dipoles are the same The electrostatic analogy is useful in getting a physical feel for how the transverse force is applied Explanation B DIl EMFF Final review ug.29,2003
DII EMFF Final Review Aug. 29, 2003 Forces and Torques: Conceptual Forces and Torques: Conceptual S N S N S N S N B A A B • In the Far Field, the dipole field structure for electrostatic and electromagnetic dipoles are the same • The electrostatic analogy is useful in getting a physical feel for how the transverse force is applied • Explanation …