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Instruments for Optical and Radio Astronomy 2 > Practice Questions > Flashcards

Practice Questions Flashcards

1
Q

M(obj) =

A

I(obj)(max)-I(obj)(min) / I(obj)(max)+I(obj)(min)

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2
Q

I(obj)(max)

A

b0 + b1

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3
Q

I(obj)(min) =

A

b0 - b1

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4
Q

M(img) =

A

I(img)(max) - I(img)(min) / I(img)(max) + I(img)(min)

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5
Q

I(img)(max) =

A

c0 + c1

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6
Q

I(img)(min) =

A

c0 - c1

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7
Q

M =

A

M(img)/M(obj)

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8
Q

What happens to the image contrast and the modulation transfer function if the value of c1 is halved

A

contrast is halved

harder to distinguish edge of image

the peak of the PSF is reduced

the image is dimmer, less contrast

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9
Q

<ε(iso)^2> =

A

(θ/θ(0))^5/3

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10
Q

θ(0) =

A

r(0)/h

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11
Q

Seeing =

A

β = 0.98 λ/r(0)

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12
Q

Strehl ratio =

A

S = (r(0)/D)^2

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13
Q

<ε(fit)^2> =

A

k/N^(5/6) (D/r(0))^(5/3)

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14
Q

Marechal approximation

A

S ~ e^(<ε^2>)

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15
Q

fewer actuators means

A

design and operation of AO system is easier

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16
Q

angular resolution

A

α = 1.22 λ/D

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17
Q

cut off frequency of the modulation transfer function

A

f(c) = D/λF

most cases F = 1

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18
Q

phase structure function is

A

a measure of the phase variance between two locations on the phase front separated by r

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19
Q

phase structure function =

A

D(φ)(r) = <|φ(x) - φ(x+r)|^2>

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20
Q

coherence function is

A

an indication of the correlation of the phase front between two locations on the phase front

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21
Q

coherence function =

A

B(φ)(r) = <|φ(x) φ(x+r)|>

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22
Q

qualitatively explain this expression

D(φ)(r) = 2[B(φ)(0) - B(φ)(r)]

A

phase structure function eq and definition

coherence function eq and definition

B(φ)(0) is the correlation of the phase value with itself at the same location (since the shift parameter r is 0).

2[B(φ)(0) - B(φ)(r)] is then equivalent to the evaluation of the phase structure function.

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23
Q

Show that

D(φ)(r) = k^2δh (∞ ∫ -∞) [D(N)(r,z) - D(N)(0,z)] dz

A

B(φ)(r) = k^2δh (∞ ∫ -∞) B(N)(r,z)dz

substitue into

D(φ)(r) = 2[B(φ)(0) - B(φ)(r)]

inserting B(N)(0,0)-B(N)(0,0)

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24
Q

re-express the fried parameter in terms of temperature T and its corresponding structure constant C(T)

A

r(0) ∝ [ ∫ C^2(N)(h) dh]^(-3/5)

n - 1 ∝ P/T

dn/dT ∝ -P/T^2

C^2(N) = C^2(T) |dn/dT| ∝ C^2(T) P/T^2

=> r(0) ∝ [ ∫ C^2(T)(h) P/T^2dh]^(-3/5)

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25
Q

Should the Fried parameter vary with zenith angle

A

r(0) ∝ [0.423k^2(cosγ)^-2 ∫ C^2(N)(h) dh]^(-3/5)

and r(0) ∝ (cosγ)^(3/5)

where γ is the zenith angle. We see that at large zenith angles, cosγ goes to 0. So the fried paramter is smaller which is expected for stronger turbulence

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26
Q

Show that the phase structure function can be expressed as

D(φ)(r) = 6.88 (τ/τ(0))^(5/3)

A

D(φ)(r) = 6.88 (r/r(0))^(5/3)

r = v(bar)τ

and τ(0) = r(0)/v(bar)

substituting into D(φ)(r)

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27
Q

<ε(servo)^2> =

A

(τ(0) f(3dB)^(-5/3)

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28
Q

τ(3dB) =

A

1/f(3dB)

where f(3dB) is the bandwidth of the servo

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29
Q

Littrow configuration

A

θ(i) = θ(B)

θ(m) = -θ(B)

θ(m) = -θ(i)

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30
Q

how should the FSR be considered when designing a spectrograph

A

can adjust the free spectral range by changing the spacing between grating rules

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31
Q

groove separation

A

a measured in m

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32
Q

optical path difference

A

OPD = Δnl

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33
Q

refractive index =

A

n = 1+7.8x10^-7 P/T

34
Q

turbulence occurs around the

A

tropopause at an altitude of 10km

with pressure 100mbar

and temperature 200K

35
Q

number of grooves

A

N = 2π/Δφ

where Δφ = Δl k

36
Q

in terms of 1 rad <ε(fit)^2> =

A

(N(1 rad)/N)^(5/6)

37
Q

<ε(total)^2> =

A

sum of different <ε^2> =

38
Q

for a loseless system

A

G(s) = G(r)

39
Q

Kolmogorov Model

A

describes how the Kelvin-Helmholtz instabilities are broken up into smaller eddies

40
Q

The main points of the Kolmogorov Model

A
  1. The kinetic energy is added to the system at the outer scale
  2. The energy then cascades down to the smaller scales
  3. when the scale is sufficiently small, the air viscosity dissipates the kinetic energy and the formation of new eddies stops. The average diameter at the smaller eddies is 1mm.
41
Q

Shack-Hartmann wavefront sensor scheme

A
  1. an array of lenslets to focus the incoming wavefront onto an array of CCDs.
  2. Senses the position by measuring the gradient of wavefronts and is therefore, achromatic
  3. a plane wavefront would be focused to a grid of equally spaced images
  4. any distortion in wavefront will cause image to be focused away from central position
42
Q

Shack-Hartmann WS diagram

A

see notes

43
Q

Re-express the Fourier transform U in polar coordinates and evaluate the Fourier transform.

A

X = pcosθ and Y = psinθ
dXdY= |J|dpdθ = pdpdθ
x = ωcosψ and y = ωsinψ
substitute into U

Bessel function

identify Bessel function in U

n=0 , sigma = (θ-ψ) and x = kpω

use Bessel function identities

U(P) = U(0) = [2J(1)(ka)/(ka)]

44
Q

How does the fourier transform U change with a

A

the intensity takes the form of an Airy function -> resulting image an Airy disc

for an ideal telescope the PSF is described by an airy function

as a changes the height of the central peak of the airy function will increase and its width decreases

a is the radius of the primary mirror.

as a increases the width of the central spot of the Airy disc will decrease and the central spot will be brighter

45
Q

Fried parameter describes

A

the strength of the wave front distortion due to atmospheric turbulence

46
Q

the value of the Fried parameter is

A

the equivalent diameter of an ideal telescope for observations limited by random inhomogeneities in the atmosphere’s refractive index

47
Q

Strehl ratio

A

the ratio between the intensity of the central spot of the point spread function with that expected in the ideal case

48
Q

the Strehl ratio compares

A

the observed intensity peak to that for a telescope working at the diffraction limit

49
Q

For telescopes with large primary mirrors, the observed image will be limited by

A

the length scale of atmospheric turbulence which is characterized by the Fried parameter

50
Q

for a wavefront sensing scheme that uses the same wavelength as the observation

A

α(SA) = λ/d

51
Q

The fried parameter is a measure

A

of the characteristic coherence length of the distorted wavefront

52
Q

isoplanatic angle is

A

the greatest angular distance between the guide star and the observing target. Where light from both pass through the same turbulent region.

53
Q

Why does the isoplanatic angle vary with zenith

A

The isoplanatic angle is smaller with increasing zenith angle because light passes through more turbulent atmosphere at larger zenith angles.

54
Q

Sodium Laser Guide Stars

A

There is a layer of sodium at altitudes of about 90km above sea level.

Laser light is used to excite an atomic resonance line in this layer of sodium to produce an artificial guide star.

55
Q

How do laser guide stars improve the sky coverage

A

laser guide stars improve the sky coverage of AO systems because observations no longer need to be close to natural guide stars

56
Q

The cone effect is

A

the result of laser guide stars being much closer to the observer than their targets.

As a result, light from the laser guide star probe all the turbulent air that distorts the observed wavefront for light from a distant star

57
Q

cone effect diagram

A

see notes

58
Q

As a increases the PSF

A

becomes narrower tending towards a delta function

59
Q

S =

A

I(0)PSF/I(0)airy

60
Q

as a increases the height

A

of the PSF increases thus the Strehl function decreases as a increases

61
Q

how to obtain an image from the point spread function

A

I(x,y) = O(x,y) * P(x,y)

62
Q

DΦ(r) = <|Φ(x) - Φ(x+r)|^2> =

A

(∞ ∫ -∞) |Φ(x) - Φ(x+r)|^2 dx

63
Q

<ε(iso)^2> =

A

(∞ ∫ h(0)) DΦ(r) dh

64
Q

PSF tells us

A

how the light from a source spreads out in an image

65
Q

Modulation transfer function

A

measure of how contrast is lost in the image

66
Q

Optical transfer function can be expressed

A

in terms of a phase structure function

67
Q

turbulence generates

A

temperature cells

68
Q

the long exposure OTF is given by

A

the phase structure parameter C^2(N) with height

69
Q

the seeing is

A

the FWHM of the atmospheric PSF

70
Q

atmospheric time constant

A

is the timescale over which a turbulence cell moves by its own size

71
Q

adaptive optics compensate

A

the wavefront by sensing the wavefront then actuating on a deformable mirror

72
Q

fitting error comes from

A

finite actuator spacing

73
Q

bandwidth error comes from

A

finite servo bandwidth

74
Q

free spectral range

A

is the wavelength difference at which orders start to overlap

75
Q

a blazed grating

A

concentrates light into the desired order and makes efficient use of power

76
Q

wavefront correction

A

is carried out by segmented or deformable mirrors

77
Q

Curvature WFS is

A

a simple alternative to SHWS

78
Q

doppler shift can be resolved by

A

using a grating in High order

downside is that orders overlap contaminating the spectrum

an echelle spectrograph overcomes this by using echelle grating followed by a cross disperser to create a 2D echellogram

79
Q

the etendue of a system is set by

A

the stop

80
Q

the bandpass of a spectrometer is

A

the minimum wavelength resolution achieved by matching diffraction from the entrance slit with that from the grating

Instruments for Optical and Radio Astronomy 2 (12 decks)

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