A. Fabry-Perot (text: Sect. 3-7, Figure 3-56)

— multiple passes between partially reflecting surfaces

— if paths differ by ml — constructive interference

l = 2d/m — normal incidence

— if beam enters at angle lead to "fringes" as spacing changes

l = 2d/m (cos q)

free spectral range: Dl_f = l/(m+1) ~ l/m =2d/m² = l²/2d

sharpness of interference depends on reflectivity (coefficient of finesse)

C_F = 4r/(1-r)²

use: — couple to monochromator à enhance resolution to Dli

— etalon in laser select mode — narrowline

B. Michaelson Interferometer (ref: see Griffiths & DeHaseth and/or Marshall & Verdun)

encode frequency (wave number) by position (Dx) of moving mirror

interference at beam splitter on recombining from moving and fixed mirrors creates signal

interpret by Fourier transform of intensity (response) vs. Dx

1. Monochromatic light — interferogram is sine wave

retardation — measure path difference waves: d = 4pDx/l = (4pDx)n/c

constant move mirror at n: f = 2v/l = 2vn/c Note: n/c = 1/l = wavenumber

modulates signal:

spectral response (F.T.):

if truncate scan at xm

this restricts resolution of spectral lines

2. Polychromatic light: interference between wave different frequency leads to envelope on interferogram oscillation — reflect spectrum

Two frequencies–get beat pattern

Broader, must integrate over all contributions, envelop decays:

low Dx à broad base line, high Dx à interference of close frequencies

Finite motion of mirror — limit resolution, bandshape

resolution — ideal: Dn/c = (2x_m)^-1 -- if D n too small, then no interference

apodization — modify bandshape by convolving D(x), apold. Fct., reslti in lower resolution but cleaner line shape

boxcar (no alternation), triangular (ramp), others (or more continuous variants)

Jacquinot — no slit — throughout enhanced, but small aperture high res

Fellgett — multiplex — all frequencies simultaneously detected

Connes — frequency accuracy (compare/correct spectra)

lack modulation depth (at large Dx values)–only can transform modulation

phase errors need correction/distort bandshape

Digital spectra — can miss Dx = 0:

Electronic frequency response — e à e() — "chirp"--lose symmetry at x=0

Result — S(x) has sine components — B^c() has derivative shapes

Correct — complex FT derive Re [~cos e] and Im [~sin e] component

Mertz algorithm

measure over small Dx range (assume  slow vary )

5. Alignment error and Aperture — lower resolution

solid angle accepted: W = 2pa² = 2pDn/n

divergence causes — loss modulation at large Dx (loss resolution — like apodize)

— loss of frequency accuracy n’ = n[1-Dn/n]

mirror align cause loss intensity, resolution high (favor IR), rooftop or corner cube can reduce

6. Indirect measure — need F.T. — computer must be fast, accurate co-add

7. Survey of Drive systems (handouts) older: 3-interferometer system (IR, White, laser), modern: 60deg B/S, Genzel interferometer (vacuum), FT-Raman setup