Presets
Playback
Light source
Each source has its own spectrum, so its own coherence length.
Mirror
Coarse = micrometer screw, fine = piezo; the motor scans at a constant speed.
Fringe display
Extended source gives rings, a collimated beam with a tilted mirror gives straight fringes.
Optics
Gas cell in the moving arm
Vent or pump the cell and count fringes.
Layers
Model checks
The science
What the instrument does
A beam splitter sends light into two arms; both beams return and recombine. The screen brightness depends only on the path difference OPD = 2 d + 2 L (n - 1), where d is the mirror offset from equal arms and the gas cell of length L is crossed twice:
I = (I0 / 2) [1 + V cos(2 pi OPD / lambda)]
Fringe counting
Moving the mirror by Delta d changes the OPD by 2 Delta d, so N = 2 Delta d / lambda bright fringes pass any point. A micrometer plus a fringe counter is a length gauge with a resolution of a fraction of a wavelength.
Circular and straight fringes
With an extended source each ray leaves at an angle theta: OPD = 2 d cos(theta), so bright rings obey 2 d cos(theta_m) = m lambda. The closer to equal arms, the fewer and wider the rings. Tilting a mirror by alpha adds 2 alpha x across the beam: straight fringes of spacing lambda / (2 alpha).
Coherence and visibility
Every wavelength in the source makes its own fringes. Summing them, the visibility is the modulus of the Fourier transform of the spectrum (Wiener-Khinchin): V(OPD) = | integral S(sigma) exp(2 pi i sigma OPD) d sigma | with sigma = 1/lambda. For a Gaussian line of width Delta sigma this is exp[-(pi Delta sigma OPD)^2 / (4 ln 2)], so V falls to one half at OPD = 0.441 / Delta sigma. A top-hat spectrum (white light) gives |sinc(pi Delta sigma OPD)|; a doublet multiplies the envelope by |cos(pi Delta sigma_sep OPD)|, which is why the sodium fringes vanish and return every 290 um of mirror travel.
Gas refractometer
Letting a gas into an evacuated cell changes the OPD by 2 L (n - 1), so the number of fringes crossed gives n - 1 = N lambda / (2 L). The model scales n - 1 with pressure and temperature as (p / p0)(T0 / T).
Why a compensator plate
The beam splitter plate sits in one path only. Glass is dispersive, so without a matching compensator the arms have different group delays and the white-light fringes smear out. The glass slider adds that mismatch using a fused-silica Cauchy fit.
Simplifications
Ideal lossless 50/50 splitter, no polarization, perfectly flat mirrors, Gaussian or top-hat line shapes with representative widths, gas dispersion neglected (n - 1 is quoted near 633 nm), the screen drawn at 112 x 112 pixels. Spectral widths of real lamps depend on temperature and pressure.
What to try
- HeNe laser: set the motor scan speed to 2 um/s and read the fringe counter; 10 fringes mean 3.16 um of mirror travel.
- Switch to Straight fringes and change the tilt: the fringe spacing is lambda / (2 alpha).
- Sodium lamp: raise the coarse position slowly. Contrast fades and returns about every 0.29 mm of travel.
- White light: set equal arms (button). One dark central fringe with coloured fringes either side appears only within about a micrometre. Now add uncompensated glass and watch it wash out.
- Gas cell: choose the straight-fringe view, pump to vacuum, then vent it. Compare the fringe count with the graph for air and for carbon dioxide.