Lecture 7 Flashcards
Wavefront reconstruction limited by the fact that
there is a finite spacing between the actuators of the mirror
-> gives rise to fitting error
fitting error
<ε^2(fit)> = k/N^(5/6) (D/r0)^(5/3)
N - number of actuators
k = constant
fitting error of 1 rad^2
<ε^2(fit)> = (N(1 rad)/N)^(5/6)
Phase structure function
D(φ)(r) ∝ (r/r0)^(5/3)
for a inter-actuator spacing d the phase variance due to the fitting error is given by
<ε^2(fit)> = k (d/r0)^(5/3)
where k = 1
fitting error derivation
N = ( π(D/2)^2 / d^2 )
d = D(π/4N)^(1/2)
<ε^2(fit)> = k/N^(5/6) (D/r0)^(5/3)
The finite bandwidth of servo system will also lead to
residual phase error that will limit the Strehl ratio
servo with bandwidth has associated time constant
τ(3dB) = 1/f(3dB)
residual phase error
<ε(BW)>^2 = (τ(3dB)/τ(0))^(5/3)
or
<ε(BW)>^2 = (τ(0)f(3dB))^(-5/3)
Natural Guide Stars
Bright stars
have limited coverage for complete correction of errors. however they are essential for the correction of Tip-Tilt Anisoplanatism
Laser Guide Stars
laser or artificial stars created that is above the typical altitudes at which turbulence occurs
angular anisoplanatism
<ε^2(iso)> = (θ/θ(0))^(5/3)
<ε^2(iso)> ∝
1/λ^2
cone effect
laser guide star samples only part of the turbulent layer through which light from the target star passes
cone effect error
<ε^2(cone)> = (D/3θ(0)H)^(5/3)
