Lecture 9 Flashcards
0th order is
direct reflection from surface or specular reflection
θr = θi
Grating is described mathematically as
a convolution of a single slit of width b with an array of delta functions spaced apart by a
Diffraction pattern is
Fourier transform of the grating transfer function which, by the Convolution theorem, is the product of the Fourier transforms of the individual functions
Diffraction pattern =
I = I0 [ sin(β) ]2 [ sin(Nφ/2) ]2
Reflection grating is inefficient
solution Blazed Grating
Blazed Grating
Gratings are most efficient when rays emerge from the grating as if by direct reflection
tilted faces or a blaze in the grating
Select blaze angle γ so that specular reflection coincides with angle of diffraction
θi - γ = γ + θm
θi - θm = 2γ
the diffraction pattern is produced by
a white light source incident on an unblazed and blazed diffraction grating,
Unblazed
Spectra get fainter as the order increases
Blazed case
Most of the light is directed into the order of interest,
Littrow Configuration
Incident beam normal to face of facet
Specular reflection retro-reflected
Radial velocity of the star is given by
vr = m2 √(G/r2m1)
doppler shift of a spectral line
Δλ/λ = vr/c = 1/Nm
The Grating Equation equally applies to
a Reflection Grating
A Blazed Grating concentrates
light into the desired order and makes efficient use of power
The Littrow Configuration is
auto- collimating and needs only one lens
The Resolving Power indicates
whether spectral lines can be resolved
Extrasolar Planets cause
the star to wobble and its light to become Doppler shifted
Doppler shift can be resolved via
using a grating in High Order
The downside of using gratings in high order is that
Orders Overlap
contamination of the spectrum
Echelle Spectrograph overcomes
Orders overlap
by using an Echelle Grating followed by a Cross Disperser to create a 2D Echellogram in which overlapping orders are separated
