Flashcards in Observational Techniques Deck (63):

1

## New discoveries come from extending obsevational parameter space (5)

###
Fainter - larger telescopes

Faster - fast, low noise detectors

Higher spatial resolution - AO

Higher spectral resolution - FTS (fourier transform spectroscopy)

New wavebands - eg UV observations in space

2

## Effects of Earth's atomosphere (4)

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Absorption

Dispersion

Emission

Atmosphereic turbulence and seeing

3

##
Limiting factors for optical imaging (3)

Characterising image quality

###
Earth's atmosphere, turbulence

Telescope and Instrument

Detectors, noise

Metrics : FWHM, Strehl ratio, included ratio. Variation with time and image position

4

## Strehl ratio

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Central intensity/diffraction limited central intensity

For small sigma_phi^2: S ~ exp(-sigma_phi^2)

5

## Factors in locations of observatories (4)

### Clear skies, good seeing, dark sky, little water vapour

6

## Telescopes - key factors (3) & why large/reflectors? Mounts

###
Key factors: difffraction, tracking, aberrations

Large telescopes collect more light and achieve better resolution. Reflectors not reflactors because mirrors can be large and supported from behind, don't suffer from chromatic dispersion, can be made more powerful.

Equatorial Mount or Alt-Az mount - almost impossible to use equitorial for large telescopes.

7

## Focal ratio, plate scale, distance on detector

###
Focal ratio = effective focal length/ aperture diameter

Plate scale: angle on sky projected on to unit distance on detector

Distance on detector = focal length x angle on sky

8

##
Diffraction limited angular resolution (FWHM)

Spatial frequency cut off

###
theta fwhm = lamda / D

Rayleigh criterion is x 1.22

Spatial freq. cut off: D/lamda (or r_0 over lamda in seeing limited case)

9

## Optical aberrations

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Chromatic aberration

Field Curvature

Spherical aberration

Vignetting

10

## CCD specs, typical and normal

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Spec, typical, perfect

QE, 50-95%, 100%

Well depth, ~50,000 electrons, infinate

Array, 20 micro m pixels, 2000^2, perfect is tiny

Resolution, 16/32 bit, infinate

Gain, ~linear, linear

Read noise, < 5e^-, 0

Dark current, <<1e per sec, 0

((queer eye was a really great re discovery))

11

## Flux of V=0 magnitude star at top of earth's atmosphere

### 1000 photons s^-1 cm^-2 A^-1 (a = amstrong)

12

## No. photons detected

### Ndet = (1000). 10^(-m/2.5). pi (D/2)^2. T. delta lamda. mu

13

## SNR

### SNR = signal/root(signal+n(background + read^2 + dark))

14

## Exoplanet discover methods

### Transits, transit timing variations, dopler radial velocity spectroscopy, direct imaging, astrometry, gravitational micro lensing, pulsar timing

15

## Super WASP

### Aim to find exoplanets, needs high SNR and field of view. 8 small lenses on a single mount, 2 instruments survey whole sky in <1 month.

16

## Positional accuracy

### sigma_ast ~ image width/ SNR_phot

17

## Ideal imaging system

### 1:1 correspondance between points on object and image. Points on object are infinitesimmaly small as are points on image. Location and brightness of one point relative to another should also be the same in image as object. Colour spectrum of image should be identical to object.

18

## Diffraction pattern

### Can be calculated numerically for a general pupil function vai FT. Diffraction pattern calculated thus is equivalent to power spectrum of aperture function.

19

## PSF and OTF

###
Point spread function, optical transfer function

PSF OTF

FT

20

## Calculating image from PSF

###
Image = object x PSF

x = convolution

F(image) = F(object) x F(PSF) (OTF)

21

## Shannon's sampling theorum

### Sigmal must be sampled at freq. at least twice the feq. of the highest harmonic in the signal.

22

## Apodization & Coronagraphy

###
Square telescope - different diffraction pattern and can search for planets where it is dark

Coronagraphy - blocking out central portion of sun to avoid it saturating image. 2 masksone in image plane to block out central portion of star and one in pupil plane to block out most of the residual light.

23

## Atmospheric turbulence and seeing

###
Wind shear in atmosphere causes turbulent mixing of air of different temperatures, and hence fluctuations of refractive index

Effects: speckle image (image breaks up but total intensity is constant), scintillation (intensity fluctuation or twinnkling)

24

## Structure function

###
D(rho) =

Kolmogorov showed optical effects of turbulence can be characterised by sturcture funciton Dn

Dn(r) = = Cn^2(h) r^2/3

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

r0 is proportional to lamda ^ 6/5

25

## Quantifying atmospheric seeing

###
Fried parameter (coherance length) - r0 omega_seeing = lamda/r0, diameter of an equivalent diffraction limited telescope that would have the same limiting resoluiton in the sabsence of turbulence

Coherance time tau0 - time over which the rms phase fluctuation at a single point is ~ 1 radian tau0 = 0.314 r0/veff

Coherance angle - on axis beam suffers phase aberration due to the tubulence at height h . theta0 = 0.314 r0/h_eff

26

## Dependence on wavelength of r_0, t_0, theta_0

###
r_0 ~ lamda ^ 6/5

t_0 ~ lamda ^ 6/5

theta_0 ~ lamda ^ 6/5

-> easier at larger wavelengths

27

## Mean optical phase variance over telescope of diameter DT

### sigma^2_phi = 1.03 (D/r0)^5/3

28

## Atmospheric turbules 2 main effets on telescope images and methods for image compensation

###
Resolution is degraded ~ lamda/r0

Intensity ( SNR) is degraded by factor of about ~ (D/r0)^2

Go to space (good but expensive), post-exposure sharpening (de-convolution, inexpensive but no improvement in SNR), adaptive optics (real time correction and improvement of SNR and resolution)

29

## Adaptive optics 3 basic components

###
1. Wavefront corrector

2. Wavefront sensor

3. Controls and feeback loop

30

## Types of AO wavefront corrector

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Segmented mirrors - can tilt each section with piezo (with voltage)

Deformable face-sheet masks

Bimorph mirrors - apply voltage, actuators extend length and make mirror curve

Liquid crystal devices

Correction is normally 2 step process: tip-tilt mirror followed by deformable mirror

31

## Performance of wavefront corrector limited by

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Number of actuators

Response time

32

## Types of Wavefront sensor

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Shack-Hartman WFS (measures wavefront slope)

Curvature sensor

(can also use interferometry and phase retrival techniques)

33

## Performance of AO eq.

###
sigma = s

s^2_phi, total = fit + wfs + servo + isoplanatic

Strehl = exp(-sigma^2_phi,total) or:

Strehl_fit x strehl_wfs x strehl_servo x strehl_isoplanatic

34

## Wavefront sensor error

###
Ability of wfs to determine aberrations limited by SNR of wfs. Image width for sub-aperture width d is lamda/d position error is ~ lamda/d.

sigma^2_phi,wfs = alpha/n

-more photons per channel - ower error

35

## Fitting error

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wf correctors can be characterized by fitting error - how well the wf corrector ca for the approprite wavefront shape

sigma^2_phi,fit = 0.134[D/n_actuators r0]^5/3

36

## Servo error

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Chacterises finite response time of AO system, variance of resulting phase error approximated as:

sigma^2_phi, servo = (tau_exp/tau_0)^5/3

37

## Isoplanatic error

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Rays from off-axis objecst pass through a slighly diffrent part of the atomosphere, theferefore need error that increases with angular separation from guide star, depends on isoplanatic angle theta_0

sigma^2_phi,iso = (theta/theta_0)^5/3

38

## Laser beacon

###
Solution to lack of guide stars is to create artificial one.

Types: rayleigh: uses rayleigh backscatter, height ~ 20 km, requires time-gating to set height

Sodium D: uses excitation of Na, beacon height 80-90 km, no time-gating, laser tuned to sodium D line

39

## Focal anisoplanatism error

###
Rays from a laser beacon pass through slightly different (conical) volume of atomsphere to target, variance of phase error is:

sigma^2_phi, cone = (D/d_0)^5/3

d_0 - r_0 h_lgs/h_turb

40

## Lucky imaging

### For a given aperture size there is a finite probabiltih that instantaneous phase varience will be less than 1 rad ^2. - image motion can be ignored, shift and add individual frames later. Resolution improved, not SNR

41

## Stellar interferometry definition

### Combo of light from separate telescopes in order to synthesise a telescope with the same resolution as the maximum spacing between the telescopes - aperture synthesis. eg michelson stellar interferometry.

42

## Interferance fringes FO

###
I[theta] = I [1+cos(k d theta) ] sinc^2 (k b theta)

Interference fringes are nmodulated by envelope term that becomes narrower as slit width b is increased.

43

## Fringe analysis - double source & line source

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Double star: phi = lamda / 2d

Rectangular star: phi = lamda / d

For point source, fringe visibility = 1

For double soruce, fringe visibility = cos(kd phi/2)

For uniform source, fringe visiblity = sinc(kdphi/2)

Fringe visibility = gamma = (I_max -I_min)/(I_max + I_min)

44

## van-Cittert Zernike Theorum

### The object Intensity distribution is equal to the Fourier transform of the fring visibility function

45

## Earth Rotation Synthesis

### Use fixed interferometer baselines (separations) and allow rotation of Earth to change their orientation wrt sky

46

## Fringe tracking

### Number of fringe cycles within fringe envelope is given by lamda/ delta lamda

47

## Spectroscopy and applications

###
Feature & Info

Wavelength of peak intensity - temp

Presence and depth of absorption + emission lines - composition and temp

Line widths and shapes - temperature, density, rotation vel, turbulence, B fields

Doppler shift - line of sight velocity

48

## Types of spectograph

###
Refraction (prisms, rarely used now)

Diffraction - gratings

Interference - Fabry-Perot, Michelson Interferometer

49

## Diffraction grating

### In practice, DG is not a series of slits but a series of rulings or indentations on a reflecting plate, not an amplitude grating, physics of the two is identical.

50

## Key components of a grating spectrometer

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Slit

Collimator

Diffraction grating

Camera

Detector

51

## Blazing

### Technique which shifts peak of the single slit diffraction pattern, but does not change grating function. ~70% of light can be directed into first or higher order spectrum to greatly incrase efficiency of spectograph

52

## Resolving power

###
R = lamda/delta lamda

= m rho W

= mN

R = m rho lamda W / chi D_T

53

## Doppler shift

### Shift = v/c = delta lamda / lamda = 1/R

54

## Multi-Object/Area spectroscopy

###
Muti-object: Allow several spectra from separated objects to be recorded simultaneously

Area: take spectra of several coniguous pixels simultaneously

55

## Muti fibre spectroscopy

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Use fibres as light pipes to ransport object images to spectograph slit.

+ : wide field, large mutiplex gain, high dispersion possible

- : sky measurements not adjacent to object at slit or in field, throughput < 80%, throughput stability leads to fibre-to-fibre stability issues

56

## Fourier Transform Spectograph

###
Michelson-Morley interferometer with a movable mirror, single pixel detector. Measure output intensity as function of path difference, path lengths must be stable and measured accurately using laser interfereometer

R = lamda / delta lamda = delta / lamda

57

## Pros/cons FT spectograph

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+ v high spectral resolution, independent of telescope size. No slit required, all wavelengths contribute to all measurements - big advantage when detector is noise limited

- photon noise from al wavelenths contribute to noise in each measurement: big advantage when photon noise limited.

58

## Diffraction limited omega_FWHF & seeing limited

###
Diffraction limited lamda/D

Seeing limited lamda/r_0

59

## Parts of Michelson Stellar Interferometer

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Unit telescopes

Beam lines

Delay lines

Beam combiner

Fringe tracker

Fringe detector

60

## Scintillation

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Fluctuation in observed intensity for light source from Fresnel diffraction. Only happens from high altitude rubulence, propagation distance sufficient to produce fluctuations.

Doesn't happen for planets becuase their angular size is large relative to isoplanatic error.

61

## Role of each part in grating spectograph

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Slit - isolates region of interest on sky

Collimator - projects light emerging from slit into parallel beam onto diffraction grating

Diffraction grating - ruled grating that produces angular dispersion of starlight

Re-iager - optical system to refocused spectrum onto detector

Detector - recors spectral intensity as funciton of wavelength

62

## Focal length

###
Short focal lengths: large field of view so that the sky can be mapped quickly using a relatively small number of images. Long focal length: high magnification, i.e. a small

number of arcsec per detector pixel, to allow high resolution imaging of small scale structures.

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