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Filter Angle Shift Calculator

Calculate the wavelength shift of interference filters due to angle of incidence. Supports both collimated beams (fixed AOI) and convergent beams (f-number).

Interference filters — bandpass, longpass, notch, and dichroic designs — are fabricated for normal incidence. Tilting the filter or using it in a convergent beam shifts its center wavelength toward shorter wavelengths according to λ(θ) = λ₀ √(1 − sin²θ / n_eff²), where n_eff is the effective refractive index of the filter stack (typically 1.5–2.1 depending on coating design). This tool handles two cases. In Collimated Beam mode, a single angle of incidence (0–30°) is applied uniformly and the tool returns the shifted center wavelength and shift magnitude. In Convergent Beam mode, a beam f-number defines the cone half-angle, producing both a net blueshift of the effective passband center and a broadening of the passband — both effects degrade spectral selectivity. Use it to anticipate filter performance in tilted or focused-beam configurations.

Input
Collimated Beam Shift
Shifted CWL (λθ)
λθ = λ₀ × √(1 − sin²θ / n_eff²)
529.65nm
Wavelength shift (Δλ)
Negative = blue shift
-2.3488nm
Shift as % of CWL
-0.44150%
Abridged Optics — Filter Angle Shift Calculator v1.0Uses the standard thin-film angle-shift formula λθ = λ₀√(1 − sin²θ/n_eff²). Valid for moderate angles (0–30°). For convergent beams, the effective CWL shift is approximated as half the collimated shift at the cone half-angle, and bandwidth broadening as the full collimated shift.

All information, equations, and calculations have been compiled and verified to the best of our ability. For mission-critical applications, we recommend independent verification of all values. If you find an error, please let us know.