Interferometer Fringe Calculator
Calculate fringe spacing and visibility in optical interferometers based on wavelength, beam separation, and source coherence length. Used in precision metrology, optical testing, and physics experiments.
Last updated: September 2026
Formula below · 2 sources (optica.org, Wikipedia) · Updated Sep 2026
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About this calculator
Two coherent beams separated by a distance d produce straight interference fringes on a screen at distance L with spacing Δy = λ·L / d (small-angle approximation, valid when d ≪ L). The wavelength is entered in nm and converted to mm (÷ 10⁶), so with L and d in mm the spacing comes out in mm. The optical path difference and the source's coherence length change the fringe contrast (visibility), not the spacing: for a source of coherence length l_c, visibility falls roughly as exp(−|ΔOPD| / l_c), and fringes disappear when the path difference exceeds l_c. An earlier version multiplied the spacing by a cosine of the path difference, which is not physical, so those two inputs were removed.
How to use
Take a 532 nm laser, beam separation d = 1 mm and screen distance L = 500 mm. Δy = (532 × 10⁻⁶ mm × 500 mm) / 1 mm = 0.266 mm. The defaults (633 nm, 2 mm, 1,000 mm) give 0.32 mm. To keep the fringes visible, keep the path difference between the arms well below the source's coherence length (a few cm for a stabilised HeNe, under a millimetre for a diode laser, about 1 µm for white light).
Frequently asked questions
What is fringe visibility in interferometry and what causes it to decrease?
Fringe visibility (also called fringe contrast) measures how clearly defined the bright and dark fringes are, defined as V = (I_max − I_min) / (I_max + I_min), ranging from 0 (no fringes) to 1 (perfect contrast). Visibility decreases when the optical path difference between the two beams approaches or exceeds the coherence length of the light source. Thermal light sources like incandescent bulbs have very short coherence lengths (micrometers), so fringes disappear with even tiny path differences. Stabilized lasers can have coherence lengths of meters or more, maintaining high visibility over long path differences. Misalignment, polarization mismatch, and unequal beam intensities also degrade visibility.
How does coherence length affect interference fringe formation?
Coherence length l_c = λ² / Δλ is the path difference over which a light source can interfere with itself. It is inversely related to the source's spectral bandwidth Δλ. When the optical path difference in an interferometer exceeds l_c, the wavefronts from the two paths are no longer correlated, and their superposition produces no stable fringe pattern — fringes wash out. This is why white light (very short l_c ≈ 1 μm) produces only a few fringes near zero path difference, while monochromatic laser light can produce fringes over path differences of kilometers. Coherence length is therefore a critical design parameter when selecting a light source for a given interferometric measurement range.
What is the formula for fringe spacing in a double-slit or two-beam interferometer?
The fringe spacing (distance between adjacent bright or dark fringes on the screen) is Δy = λL / d, where λ is the wavelength of light, L is the perpendicular distance from the slits (or beam splitter) to the observation screen, and d is the separation between the two interfering beams or slits. Smaller slit separations produce wider, more easily resolved fringes, while larger separations pack fringes closer together. This relationship is widely used in optics education and metrology: by measuring Δy experimentally, you can determine an unknown wavelength, or by knowing λ precisely, you can measure tiny changes in L or d with nanometer accuracy, as in gravitational wave detectors and surface profilometers.