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.
Camera
Layers
Quality
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.