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Physics 681: Solar Physics and
Instrumentation – Lecture 8
Carsten Denker
NJIT Physics Department
Center for Solar–Terrestrial Research
Spectroscopy
 Grating
Spectrograph
 Lyot Filter
 Fabry-Pérot Interferometer
 Please
September 27, 2005
check your TurnItIn.com account!
Center for Solar-Terrestrial Research
Grating Spectrograph

Collimate light beam on spectrograph slit
D 1

f N

Focal ratio of collimator
fS
f

DS D

Grating equation
m  a  sin   sin   with      
Angular dispersion
d
m

d  a cos 

Linear dispersion

http://outreach.atnf.csiro.au/education/senior/astrophysics/spectrographs.html
dx
d
m
 fS
 fs
with 
d
d
a cos 
September 27, 2005

Center for Solar-Terrestrial Research
September 27, 2005
Center for Solar-Terrestrial Research
Lyot Filter






Birefringent filter
Alternating sequence of polarizers and birefringent crystals
Polarizers are mounted parallel to each other
Uniaxial crystals cut parallel to their optical axis
Optical axis of crystals and polarizers make a 45º angle
Thickness of the nth crystal plate
en  2n 1 e with n  1, 2,...

Phase difference and birefringence
  2 e  no  ne  /  with J  no  ne

Interference of two waves passing a single element
A
A
cos      cos   A cos  / 2  cos    / 2 
2
2
September 27, 2005
Center for Solar-Terrestrial Research

Intensity
I  A2 cos2  / 2 with  max  2k and  min   2k 1 
  eJ / k

Transmission maxima

Separation

N elements between N + 1 polarizers
eJ / k 2 for large k
I  A2 cos2  eJ /   cos2  2 eJ /   cos 2  4 eJ /  

... cos2 2 N 1 eJ / 


Individual transmission maxima at
  eJ / k ,   2eJ / k ,   4eJ / k , ...   2 N 1 eJ / k

Central wavelength
September 27, 2005
  2 N 1 eJ / k
Center for Solar-Terrestrial Research
NIR Lyot-Filter Design
½ Wave Plate
Polarizer
September 27, 2005
LC Crystal
Calcite Plates
Center for Solar-Terrestrial Research

Band width
1 
 1
N 1
2
  2 N 1 eJ 


2
eJ
/
k

k

1/
2
k

1/
2


 2 N 1 e   2 / J 

Birefringence (calcite J = –0.172 and quartz J = 0.0092)
September 27, 2005
Center for Solar-Terrestrial Research
Fabry-Pérot Interferometer


Phase difference
  2 /   4 nd cos /  with   2nd cos
Outgoing wave
Aeit  Teit  TRei (t  )  TR 2eit  2   ...
T
A  T 1  Rei  R 2 e 2i  ... 
1  Rei



Intensity
T2
T2
I  AA 

2
2
1  2 R cos   R
1  R   4 R sin 2  / 2 

I  I max
1
1
4R
1  R 
September 27, 2005
2
sin
2 
with I max 
T2
1  R 
2
2
Center for Solar-Terrestrial Research

Band width
  FSR / F

Finesse
F
 R
1 R
http://www.physicsdaily.com/physics/Fabry-Perot
September 27, 2005
Center for Solar-Terrestrial Research
Coating Curves
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Center for Solar-Terrestrial Research
Filter Transmission and Spectrum
September 27, 2005
Center for Solar-Terrestrial Research