Interferometry Fringe Calculator
Calculate the fringe spacing produced when two coherent beams intersect at a given angle and wavelength. Use it when setting up laser interferometers, holographic recording setups, or optical metrology systems.
About this calculator
When two coherent beams of light intersect at a half-angle θ, they form a sinusoidal interference pattern whose fringe spacing Λ is given by: Λ = λ / (2 × sin θ), where λ is the wavelength and θ is the half-angle between the beams. The formula used here converts wavelength from nanometres to millimetres (dividing by 1000) so that Λ is returned in millimetres. Smaller intersection angles produce widely spaced fringes; larger angles compress the fringes. At θ = 90° (counter-propagating beams), fringe spacing equals λ/2 — the theoretical minimum. Fringe visibility, a separate metric, depends on the amplitude balance and coherence length of the two beams; a coherence length longer than the optical path difference is required for high-contrast fringes. This calculation is fundamental in holography, laser Doppler velocimetry, and surface metrology.
How to use
Example: wavelength λ = 532 nm (green laser), beam intersection half-angle θ = 15°. Step 1 — convert wavelength: 532 / 1000 = 0.532 μm... using the formula in mm: (532/1000) / (2 × sin 15°). Step 2 — sin(15°) ≈ 0.2588. Step 3 — denominator: 2 × 0.2588 = 0.5176. Step 4 — Λ = 0.532 / 0.5176 ≈ 1.028 μm (0.001028 mm). Fringe spacing is about 1.03 μm — fine enough to require a high-resolution holographic recording medium. Increasing θ to 30° would halve the spacing to ~0.53 μm.
Frequently asked questions
How does beam intersection angle affect fringe spacing in laser interferometry?
Fringe spacing and beam angle share an inverse relationship through the sine function: doubling the intersection angle roughly halves the fringe spacing for small angles. At very small angles (nearly co-propagating beams), fringes are widely spaced and easy to resolve with standard cameras. As the angle increases toward 90°, fringes approach the diffraction limit of λ/2 and require specialised high-resolution detectors or recording media. In holographic setups, the chosen angle determines whether a standard silver-halide film or a finer-grained photopolymer is needed to resolve the pattern.
What is coherence length and why does it matter for fringe visibility in interferometry?
Coherence length is the maximum optical path difference over which a light source can produce visible interference fringes. It is determined by the spectral bandwidth of the source: coherence length ≈ λ² / Δλ. If the path difference between the two arms of an interferometer exceeds the coherence length, fringe contrast (visibility) drops toward zero and fringes disappear. This is why highly coherent single-mode lasers are preferred in precision interferometry — they can have coherence lengths of metres to kilometres, allowing large path differences without losing fringe contrast. Broadband sources like LEDs have coherence lengths of only a few micrometres.
What are the main applications of fringe spacing calculations in optical metrology?
Fringe spacing calculations are essential in holographic data storage, where the recording density depends directly on fringe spacing — tighter fringes store more data per unit volume. In laser Doppler velocimetry, particles scatter light as they cross the fringe pattern, and their velocity is inferred from the crossing frequency and known fringe spacing. Surface profilometry systems use fringe projection to map height variations across a sample, with finer fringes giving higher lateral resolution. In all these cases, knowing the fringe spacing before building the setup allows engineers to choose appropriate sensors, recording media, and mechanical tolerances.