Physics 681: Solar Physics and Instrumentation –

Lecture 8

Carsten Denker

NJIT Physics DepartmentCenter for Solar–Terrestrial

Research

September 27, 2005 Center for Solar-Terrestrial Research

SpectroscopyGrating SpectrographLyot FilterFabry-Pérot Interferometer

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September 27, 2005 Center for Solar-Terrestrial Research

Grating Spectrograph Collimate light beam on spectrograph slit

Focal ratio of collimator

Grating equation

Angular dispersion

Linear dispersion

1D

f N

S

S

f f

D D

sin sin with m a

cos

d m

d a

with cosS s

dx d mf f

d d a

http://outreach.atnf.csiro.au/education/senior/astrophysics/spectrographs.html

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

Phase difference and birefringence

Interference of two waves passing a single element

12 with 1, 2,...nne e n

2 / with o e o ee n n J n n

cos cos cos / 2 cos / 22 2

A AA

September 27, 2005 Center for Solar-Terrestrial Research

Intensity

Transmission maxima

Separation

N elements between N + 1 polarizers

Individual transmission maxima at

Central wavelength

2 2max mincos / 2 with 2 and 2 1I A k k

/eJ k

2/ for large eJ k k

2 2 2 2

2 1

cos / cos 2 / cos 4 /

... cos 2 /N

I A eJ eJ eJ

eJ

1/ , 2 / , 4 / , ... 2 /NeJ k eJ k eJ k eJ k

12 /N eJ k

September 27, 2005 Center for Solar-Terrestrial Research

NIR Lyot-Filter Design½ Wave Plate

LC Crystal

Polarizer

Calcite Plates

September 27, 2005 Center for Solar-Terrestrial Research

Band width

Birefringence (calcite J = –0.172 and quartz J = 0.0092)

1 1 21 12 2 /

1/ 2 1/ 2N NeJ eJ k

k k

1 22 /N e J

September 27, 2005 Center for Solar-Terrestrial Research

Fabry-Pérot Interferometer Phase difference

Outgoing wave

Intensity

2 / 4 cos / with 2 cosnd nd

2( ) 2

2 2

...

1 Re ...1 Re

i ti t i t i t

i ii

Ae Te TRe TR e

TA T R e

2 2

22 2

2

max max 22

2

1 2 cos 1 4 sin / 2

1 with

4 11 sin21

T TI AA

R R R R

TI I I

R RR

September 27, 2005 Center for Solar-Terrestrial Research

Band width

Finesse

/FSR F

1

R

R

F

http://www.physicsdaily.com/physics/Fabry-Perot

September 27, 2005 Center for Solar-Terrestrial Research

Coating Curves

September 27, 2005 Center for Solar-Terrestrial Research

Filter Transmission and Spectrum