Lecture 5 Flashcards
Fried parameter is an
indication of the strength of phase fluctuations
Cn^2 (refractive index structure parameter) describes
the strength of turbulent fluctuations of refractive index
Fried parameter describes
length of wavefront over which phase changes by 1 radian
turbulent cells evolve on longer timescales than
time it takes the wind to move a cell by its own size
wind velocity V(bar) at the altitude of the turbulence determines
temporal variation of the wavefronts entering the telescope
turbulent cell moves by its own size in time
t0= t2 - t1
atmospheric time constant or coherence time
τ0 = r0/V(bar)
the coherence time is the
timescale on which wavefront sensor and deformable mirror of an adaptive optic system must operate
exposure time:
τ < τ0 , short
τ > τ0 , long
Seeing
is the equivalent resolution one would get by viewing through a diffraction-limited telescope of diameter r0
Angular width of seeing-limited image
β = 0.98λ/r0
Kolmogorov
r0 ∝ λ^(6/5)
better seeing in infrared as
optical path length changes a smaller proportion of the wavelength
r0 determines sizes of
individual lenslets and mirror segments in wavefront sensors and deformable mirrors
adaptive optics correction in the infrared requires
fewer elements than in the optical
Isoplanatic angle
angle over which turbulence pattern shifted by distance r0.
angular separation at which light from two stars becomes uncorrelated
Isoplanatic angle =
θ0 = r0/h
θ0 determines
area of sky over which adaptive optics are effective
wavefront compensation
light from point source becomes distorted as it passed through the atmosphere
wavefront disturbance measured to produce path length error
original wavefront restored by inserting equal and opposite path length corrections producing corrected image
adaptive optic scheme
compensate the wavefront by sensing the wavefront then actuating on a deformable mirror
Strehl ratio
effect of wavefront compensation on the intensity profile of a turbulent-degraded image of a star
no compensation
seeing disc
strehl ratio «_space;1
fully compensated
airy disc
strehl ratio = 1
partially compensated
core and halo
strehl ratio < 1
Compensating the wavefront transfers energy from the halo to the core of the image
increases the peak intensity
Strehl ratio derivation
S = I(PSF)(0) / I(Airy)(0)
Intensity = Power/Area
Airy disc ∝ (λ/D)^2
Seeing Disc ∝ (λ/r0)^2
S = (r0/D)^2
atmospheric time constant is
the timescale over which a turbulence cell moves by its own size