Lecture 4

Question 1

wavefronts

Answer 1

are locus of points having the same phase

Question 2

variations in atmosphere distort

Answer 2

wavefront of incoming signal

wavefront no longer parallel when it arrives at telescope

Question 3

turbulent layer of the atmosphere

Answer 3

pockets of air, each of varying size
move around erratically
leads to variations in the refractive index

Question 4

varying refractive index distorts

Answer 4

plane waves entering the atmosphere

Question 5

the variation of refractive index (formula)

Answer 5

dn/dT ∝ - P/T^2

Question 6

the phase lag/lead introduced into the wavefront relative to the reference wavefront (formula)

Answer 6

ΔΦ = l Δn/λ ∝ P/λT^2 LΔT

Question 7

for visible wavelengths and standard pressures and temperatures (formula)

Answer 7

ΔΦ = 2LΔT

Question 8

Phase structure function

Answer 8

D(Φ)(r) = D(Φ) (|x’-x|)

Question 9

Long exposure OTF

Answer 9

< H(r) > = H(atm) . H(tel)

< H(r) > - Ensemble average OTF

H(atm) OTF of atmosphere

H(tel) OTF of telescope

Question 10

Ensemble-average PSF in focal plane

Answer 10

|h|^2 = F^-1 {H(atm) . H{tel)}

Question 11

For a high quality telescope with a large primary, the effects of the atmosphere dominate and

Answer 11

<H(r)> = e^(-DΦ(r)/2)

Question 12

Coherence function

Answer 12

B(r) = e^(-DΦ(r)/2)

Question 13

Kolmogorov Model

Answer 13

Simple model of turbulence in the atmosphere

Wind-shears gives rise to Kelvin-Helmholtz Instabilites

Turbulent energy is generated on a large scale, Lo

These get smaller and smaller until kinetic energy is dissipated through viscosity at a length scale, lo

Question 14

universal description for turbulence spectrum

Answer 14

inertial range between lo and L0

Question 15

strength of the turbulence as a function

Answer 15

of the eddy size or spatial frequency

Question 16

two parameters determine the strength and spectrum of Kolmogorov turbulence

Answer 16

rate of energy generation per unit mass

kinematic viscosity

Question 17

structure function of velocity field (formula)

Answer 17

D(v) (R1,R2) = α . f (|R1-R2|/β)

Question 18

Temperature Cells

Answer 18

Turbulence mixes different layers of air carries around cells of air with different temperatures

these cells are in pressure equilibrium have different densities and, therefore, different indices of refraction, n

Question 19

Turbulent atmosphere can be modelled as

Answer 19

layers of distortion driven by the wind, moving with velocity v.

Question 20

Light travelling through high refractive index regions is

Answer 20

delayed compared to other regions

Question 21

Phase Structure function

Answer 21

D(r) = 6.88(r/r0)^(5/3)

Question 22

Turbulent fluctuations of refractive index are described by the refractive index structure parameter and determine

Answer 22

the Fried parameter

Question 23

Atmospheric time constant (formula)

Answer 23

τ0 = r0/V(bar)

r0 = turbulence strength or fried parameter

V(bar) is the wind velocity

Question 24

images exposed on a time longer than τ0 are called

Answer 24

long-exposure images and are dominated by the effects of atmospheric aberrations

Question 25

images exposed on a time shorter than τ0 are called

Answer 25

short-exposure images and are free from atmospheric aberrations

Question 26

Atmospheric Seeing

Answer 26

β = 0.98λ/r0

Question 27

resolution of diffraction-limited telescope

Answer 27

α = 1.03λ/D

Question 28

Variations in refractive index alead to

Answer 28

Wavefront Distortion

Question 29

The OTF can be expressed in terms of a

Answer 29

Phase structure function

Question 30

turbulence generates

Answer 30

temperature cells

Question 31

the Kolmogorov model describes

Answer 31

the variation of temperature and refractive index over a wide range of scales

Question 32

the strength of the turbulence is characterised by the

Answer 32

Fried Parameter r0

Question 33

the long exposure OTF is given by an

Answer 33

integral of the Phase Structure Parameter C(N)^2 with height

Question 34

The seeing is the

Answer 34

FWHM of the atmospheric PSF and can be interpreted as the resolution given by an equivalent diffraction-limited telescope diameter r0.