Lecture 10: Echelle Spectrograph & Etendue

Question 1

spectrum of a particular order is contaminated by light from adjacent orders - solution

Answer 1

use a second, vertical grating to separate the overlapping orders

basis of echelle technique

Question 2

echelle spectrograph

Answer 2

collimating mirror
echelle grating - high order diffraction
cross disperser grating
detector

Question 3

cross disperser grating

Answer 3

grooves perpendicular to echelle grating so that the spectral orders are mapped out in 2D

Question 4

solid angle

Answer 4

area of segment on a unit sphere

units of sr

Question 5

full space solid angle

Answer 5

4 pi sr

Question 6

radiance

Answer 6

flux emitted per unit projected area per unit solid angle

“brightness”

Question 7

lambertian

Answer 7

radiance independent of angle

Question 8

etendue

Answer 8

G=A omega

from small angle approx and simplifying integral

Question 9

etendue is a geometric quantity and can be thought of as

Answer 9

a measure of the flux gathering capability of an optical system

Question 10

the greater the area

Answer 10

the greater the flux collected

Question 11

etendue - the solid angle takes into account

Answer 11

all the directions from which light can arrive at the aperture and so contribute to the flux

Question 12

the stop

Answer 12

the limiting aperture in an optical system

Question 13

Once set by the stop, the etendue of an optical system remains

Answer 13

unchanged as the light is transformed by the lenses, mirrors and other optical components

etendue is conserved

Question 14

can also derive the entendue in terms of

Answer 14

half angle measured from the optical axis
small angle approx gives G=piA theta^2

Question 15

The instrumental width gives

Answer 15

the angular separation at
which individual spectral lines
are just resolved

this assumes the slit has zero width

Question 16

with a finite width
the entrance slit also

Answer 16

introduces an angular spread due to diffraction

Question 17

• In designing a spectrometer, the slit width is chosen so that

Answer 17

the spread in wavelengths due to diffraction from the slit matches the spread in wavelengths due to diffraction from the grating

Question 18

if the slit is too large

Answer 18

it will degrade resolution

Question 19

if the slit is too narrow

Answer 19

it won’t pass enough light

Question 20

A good compromise is if the resolution

Answer 20

is degraded equally by diffraction from the slit and diffraction from the grating

Question 21

resolution delta lambda=

Answer 21

d lambda/dx deltax0

inverse of linear disp x width of exit slit

Question 22

the exit slit width is chosen so that

Answer 22

the resolution of the device is set by the diffraction limit of the beam at the focusing lens

smaller than this - lose signal
larger - degrade resolution

Question 23

minimum wavelength
resolution that can be achieved taking into account diffraction
from both the grating and from the entrance slit

Answer 23

delta xi = dx/dlambda delta lambda_bp

Question 24

etendue at the entrance slit is proportional to

Answer 24

height of slit
bandpass
order number
illuminated area

Question 25

etendue can be increased by

Answer 25

increasing the height of the slit but this can increase amount of stray light entering the system

Question 26

an echelle spectrograph overcomes order overlap using

Answer 26

an echelle grating followed by a cross disperser to create a 2D echellogram

Question 27

etendue is the product of

Answer 27

area and solid angle measure of the flux gathering ability of an optical system

Question 28

bandpass of a spectrometer is

Answer 28

the minimum wavelength resolution, achieved by matching diffraction from the entrance slit with that from the grating