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.
About this calculator
In a two-beam interferometer (such as Young's double-slit or a Michelson setup), the fringe spacing Δy is given by Δy = λ × L / d, where λ is the wavelength of light, L is the distance from the source/slits to the screen, and d is the separation between the two beams or slits. The fringe visibility V = (I_max − I_min) / (I_max + I_min) depends on source coherence: V = cos(2π × ΔP / λ) × exp(−|ΔP| / l_c), where ΔP is the optical path difference and l_c is the coherence length of the source. When the path difference exceeds the coherence length, fringes wash out and visibility drops toward zero. This calculator combines both effects, returning a visibility-weighted fringe amplitude that accounts for spatial coherence loss.
How to use
Take a 532 nm laser (λ = 532 nm), beam separation d = 1 mm, screen distance L = 500 mm, path difference ΔP = 0.5 μm, and coherence length l_c = 100 μm. First, base fringe spacing: Δy = (532 × 10⁻⁶ mm × 500 mm) / 1 mm = 0.266 mm. For the visibility factor, compute (λ/1,000,000 × L) / d = (532/1,000,000 × 500) / 1 = 0.266 mm. Then multiply by cos(2π × 0.5 / 532) × exp(−0.5/100) ≈ cos(0.00590) × exp(−0.005) ≈ 0.99998 × 0.99502 ≈ 0.99500. So the output ≈ 0.266 × 0.995 ≈ 0.2645 mm — fringes remain nearly fully visible because the path difference is far smaller than the coherence length.
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.