
378 15. Plane Grating Spectrometers
The relevant relations for slit- and seeing-limited cases are Eqs. (13.4.12) and
(12.2.1a), repeated here for convenience,
2di sin
5
cos 0
D cos a
2^1,
(in general) (15.2.1)
= --^tan^, (Littrow) (15.2.2)
w' = rw(/2//i) = r(/>Z)F2, (15.2.3)
= 2A (optimum match)
0^2 = 2A/D (optimum match) (15.2.4)
where F2 =^2/^1 ^^^ ^ is the pixel width.
To illustrate the utility of these relations, we apply Eqs. (15.2.2) and (15.2.4) to
an echelle spectrometer in Littrow mode on a 4-m telescope with tan
(5
= 2,
^1= 200 mm, and A = 20|im. The results are ^0 = 0.2 ^ 40,000 arc-sec,
0F2 = 2 arc-sec. Note that a change to an