Two major participants: JPL o Modeling wavefront quality (mid-to-high spatial frequency) vs. telescope tilt. o Optical block bonding oddard o Program

Transcription

1 SFC JPL ESA LISA Optics in the U.S. Eugene Waluschka NASA/oddard Space Flight Center reenbelt, Maryland 20771

2 Two major participants: JPL o Modeling wavefront quality (mid-to-high spatial frequency) vs. telescope tilt. o Optical block bonding oddard o Program office o Systems engineering equirements definition End-to-end modeling Structural, Thermal, Optical (STOP) and self gravity SFC JPL ESA

3 Laser Interferometer Space Antenna Counts fringes (about a million/second) Deduce a variable strain (within the band of interest) between freely falling proof masses Magnitude of strain is about About 10 picometers Out of 5 million kilometers. To accomplish this, the LISA experiment has: Three spacecraft, Two telescopes in each spacecraft, for a total of six identical telescopes, Each telescope tracks a distant spacecraft and sends and receives light (at a slightly different angle), Collimated (quasi) monochromatic, light centered on microns. Circularly polarized beam SFC JPL ESA

4 Knowing the relative positions of optical elements is a good starting point. SFC JPL ESA HELIOCENTIC COODINATE FAME AND KEPLEIAN OBITS S 1 (t ) S 2 (t ) kˆ0 ecliptic S 3 (t ) j 0 O0 iˆ0

5 A Keplerian orbit in the ecliptic is given by (from L&L Mechanics) SFC JPL ESA x (ξ ) a (cos ξ e) S (t ) = y (ξ ) = a 1 e 2 sin ξ 0 0 where t = a3 (ξ e sin ξ ) M sun a is the major axis of the ellipse e is the eccentricity is the universal constant of gravitation Msun is the mass of the sun A complete passage round the ellipse corresponds to ξ increasing by 2π, so that when t = 0 then ξ = 0 and S (0) = ( ae,0,0).

6 Three LISA like orbits are obtained by the following rotations and time translations: S1 (t ) = y ( β ) S (t ) o S 2 (t ) = z (120 ) y ( β ) S (t 1 year ) 3 o S3 (t ) = z (240 ) y ( β ) S (t 2 year ) 3 Z (γ ) and Y (β ) are rotation matrices about the heliocentric z and y axes. If β = 0.948o then a roughly equilateral triangle leg length and angles varying about 1% SFC JPL ESA

7 Three Orbits SFC JPL ESA

8 SPACECAFT AND OPTICAL BENCH SFC JPL ESA Spacecraft O12 O1 J J J JJ S1 (t ) O13

9 SFC JPL ESA

10 Optical Block + Telescope = Optical Assembly SFC JPL ESA detector y fold telescope O12 z proof mass laser toward spacecraft 2

11 Far field intensity pattern SFC JPL ESA LISA O ptics M odel,penn State,22 July 2002

12 Far field phase variations sensitivity analysis SFC JPL ESA

13 POINT AHEAD SFC JPL ESA S 2 (t + t12 ) S1 (t + t12 ) s s S 2 (t t12 ) S 1 ( t t12 ) θ 12 ( t ) t ) S 3 ( t + 13 Θ 23 ( t ) S1 s t ) S 1 (t + 13 s S 3 (t t13 ) S 1 (t t13 )

14 Computing the point ahead positions Light transit time about 16 seconds. S 2 (t + t12 ) S1 (t + t12 ) = c t12 S S 2 (t t12 ) S1 (t t12s ) = c t12s Table 1: The positions of all three when transmitting and receiving light from the other spacecraft. eceive position of spacecraft Inertial frame Send position of spacecraft S 2 (t + t ) S1 (t + t ) S1 S 2 (t t12s ) S1 (t t12s ) S3 (t + t13 ) S1 (t + t13 ) S1 S3 (t t13s ) S1 (t t13s ) S1 (t + t 21 ) S 2 (t + t21 ) S2 S S1 (t t21 ) S2 (t t21s ) S3 (t + t23 ) S2 (t + t 23 ) S2 S3 (t t23s ) S2 (t t23s ) S1 (t + t31 ) S3 (t + t31 ) S3 S1 (t t31s ) S3 (t t31s ) S 2 (t + t32 ) S3 (t + t32 ) S3 S 2 (t t32s ) S3 (t t32s ) SFC JPL ESA

15 In a local inertial frame attached to a spacecraft the motion of a distant spacecraft. SFC JPL ESA

16 adial velocity of spacecraft SFC JPL ESA

17 Angle between two telescopes SFC JPL ESA

18 DISTUBANCE EDUCTION SYSTEM 18 degrees of freedom SIMULINK DS 6 degrees of freedom for spacecraft 6 degrees of freedom for each proof mass SFC JPL ESA

19 FOM LASE TO DETECTO Light leaving laser SFC JPL ESA Elaser ( x, y, z, t ) = Alaser ( x, y, z, t )e [ i ω t +φlaser ( x, y, z, t )] then by tracing a sufficient number of rays, we get the outgoing wavefront at the telescope aperture. i ωt +φoutgoing ( x, y, z,t ) Eoutgoing (x, y, z, t) = Aoutgoing (x, y, z, t)e (6) The (far) field at the aperture of the distant spacecraft is given by i(φoutgoing ( x, y, z,t )+ iω (t + t12 ) Eincomin g (x, y, z,t + t ) = Afare 12 A Eoutgoing (x, y, z,t)e S 2πS ) λ da

20 At the detector As local ( x, y, z, t ) ei[ ωlocal (t ) t +ϕ local ( x, y, z,t )] Elocal ( x, y, z, t ) = p i t t x y z t [ ( ) (,,, )] ω + ϕ p A local local local ( x, y, z, t ) e s As ( x, y, z, t ) ei[ ω far ( t ) t +ϕ far ( x, y, z,t )] far E far ( x, y, z, t ) = p A p ( x, y, z, t ) ei[ ω far (t ) t +ϕ far ( x, y, z,t )] far s Jones vectors to remind us of the fact that the light really is polarized. The intensity of the light at any point (x,y,z) on the detector: 2 I ( x, y, z, t ) Elocal ( x, y, z, t ) + E far ( x, y, z, t ) + scattered light. SFC JPL ESA

21 Signal extraction Over the detector area SFC JPL ESA { } 2 I (t ) Alocal (t ) + A2far (t ) + 2 Alocal (t ) Afar (t ) cos (ωlocal ω far (t ) ) t + φlocal (t ) φ far (t ) Doppler beat note ωlocal ω far (t) φlocal (t ) φ far (t ) = φnoise (t ) + φsignal (t ) φnoise (t ) optical path noise from the sending laser to the receiving detector φ signal (t ) is the gravitational signal

22 Conclusion oal of the optics model guide us in the spacecraft and mission design extend standard optical practice Perfect LISA + telescope SFC JPL ESA