Lecture 8 Flashcards
General scheme of adaptive optics
Laser guide star + natural guide star
Spectral lines
stellar bodies emit radiation at a variety of wavelengths
emission if spectra is hot
absorption spectre if cold (lit)
what can be determined by observing a stellar bodies spectrum
its chemical composition
doppler shift
large planets cause star to ‘wobble’ leading to a doppler shift
Resolving power
R = λ/Δλ = mN
spectrometer
tune wavelength by rotating grating
spectrograph
spectrum recorded on camera
slit-less spectrographs
spectrographs made without a slit
prisms
disperse light into a spectrum
blue is deviated more than red
a diffraction grating
is typically used to separate or disperse the various wavelengths present
Grating equation
sinθ(m) - sinθ(i) = mλ/a
incident angle = θ(i)
diffraction order angle = θ(m)
Angular dispersion
D = dθ(m)/dλ = m/(acosθ(m))
Instrumental Width
Δθ = λ/(Nacosθ(m))
Free-Spectral Range
Δλ(FSR) = λ/m
grating equation derivation
Δl = mλ = a(sinθ(m) - sinθ(i))
sinθ(m) - sinθ(i) = mλ/a
Diffraction pattern
I = I(0) [(sin(Nφ/2))/(sin(φ/2))]^2
where φ = (2πa)/λ (sinθ(m) - sinθ(i))
maxima occurs when
φ = 2πm
or sinθ(m) = mλ/a
angular dispersion derivation
differentiating the grating equation with respect to wavelength
linear dispersion derivation
x = Lθ
and dx/dλ = L dθ/dλ
substituting with the angular dispersion relation
resolution limit
when the first minimum of λ(1) coincides with the maximum λ(2) (Rayleigh Criterion)
Instrumental width is
the angular separation to the first minimum
first minimum occurs
φ = 2π/N
N = number of grating lines
Instrumental width derivation
differentiating, φ = (2πa)/λ (sinθ(m) - sinθ(i))
then substituting φ = 2π/N
Resolution limit is
the minimum resolvable difference in wavelength Δλ corresponds to an angular seperation given by the instrumental width
Resolving power derivation
instrumental width = angular dispersion
replacing angular dispersion for m/(acosθ(m))
then substituting λ/N = mΔλ
Free spectral range is
the difference in wavelength for which you start to get an overlap of adjacent orders
Free spectral range derivation
mλ’ = (m+1)λ
Δλ(FSR) = λ-λ’ = λ/m
two sources of error associated with guide stars are
the cone effect
and
tip-tilt anisoplanatism
spectroscopic instruments are
used to study the spectral content of light from astronomical objects
