Observational Techniques Flashcards
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
Effects of Earth’s atomosphere (4)
Absorption
Dispersion
Emission
Atmosphereic turbulence and seeing
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
Strehl ratio
Central intensity/diffraction limited central intensity
For small sigma_phi^2: S ~ exp(-sigma_phi^2)
Factors in locations of observatories (4)
Clear skies, good seeing, dark sky, little water vapour
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.
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
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)
Optical aberrations
Chromatic aberration
Field Curvature
Spherical aberration
Vignetting
CCD specs, typical and normal
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))
Flux of V=0 magnitude star at top of earth’s atmosphere
1000 photons s^-1 cm^-2 A^-1 (a = amstrong)
No. photons detected
Ndet = (1000). 10^(-m/2.5). pi (D/2)^2. T. delta lamda. mu
SNR
SNR = signal/root(signal+n(background + read^2 + dark))
Exoplanet discover methods
Transits, transit timing variations, dopler radial velocity spectroscopy, direct imaging, astrometry, gravitational micro lensing, pulsar timing
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.
Positional accuracy
sigma_ast ~ image width/ SNR_phot
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.
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.
PSF and OTF
Point spread function, optical transfer function
PSF OTF
FT
Calculating image from PSF
Image = object x PSF x = convolution F(image) = F(object) x F(PSF) (OTF)
Shannon’s sampling theorum
Sigmal must be sampled at freq. at least twice the feq. of the highest harmonic in the signal.
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.
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)
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
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
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
Mean optical phase variance over telescope of diameter DT
sigma^2_phi = 1.03 (D/r0)^5/3
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)
Adaptive optics 3 basic components
- Wavefront corrector
- Wavefront sensor
- Controls and feeback loop
Types of AO wavefront corrector
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
Performance of wavefront corrector limited by
Number of actuators
Response time
Types of Wavefront sensor
Shack-Hartman WFS (measures wavefront slope)
Curvature sensor
(can also use interferometry and phase retrival techniques)
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
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
Fitting error
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
Servo error
Chacterises finite response time of AO system, variance of resulting phase error approximated as:
sigma^2_phi, servo = (tau_exp/tau_0)^5/3
Isoplanatic error
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
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
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
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
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.
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.
Fringe analysis - double source & line source
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)
van-Cittert Zernike Theorum
The object Intensity distribution is equal to the Fourier transform of the fring visibility function
Earth Rotation Synthesis
Use fixed interferometer baselines (separations) and allow rotation of Earth to change their orientation wrt sky
Fringe tracking
Number of fringe cycles within fringe envelope is given by lamda/ delta lamda
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
Types of spectograph
Refraction (prisms, rarely used now)
Diffraction - gratings
Interference - Fabry-Perot, Michelson Interferometer
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.
Key components of a grating spectrometer
Slit Collimator Diffraction grating Camera Detector
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
Resolving power
R = lamda/delta lamda
= m rho W
= mN
R = m rho lamda W / chi D_T
Doppler shift
Shift = v/c = delta lamda / lamda = 1/R
Multi-Object/Area spectroscopy
Muti-object: Allow several spectra from separated objects to be recorded simultaneously
Area: take spectra of several coniguous pixels simultaneously
Muti fibre spectroscopy
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
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
Pros/cons FT spectograph
+ 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.
Diffraction limited omega_FWHF & seeing limited
Diffraction limited lamda/D
Seeing limited lamda/r_0
Parts of Michelson Stellar Interferometer
Unit telescopes Beam lines Delay lines Beam combiner Fringe tracker Fringe detector
Scintillation
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.
Role of each part in grating spectograph
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
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.
Image spread due to defocus
Added in quadrature
