AOI Shift Concept Calculator

Estimate bandpass filter center-wavelength shift versus angle of incidence (AOI).

Inputs

Center wavelength at normal incidence λ₀ (nm) Valid range: 193 to 1940 nm. Effective refractive index n_eff

n_eff presets (approximate stack types)

Typical thin-film effective index is about 1.7 to 2.5. Angle of incidence, θ (deg) Use 0 to 85 degrees (collimated-beam approximation). AOI slider (θ) Slider control for angle θ from 0 to 85 degrees.

Incident medium is fixed to air: n₀ = 1.000.

How to choose n_eff

Use the filter vendor datasheet when available. As a quick starting point, many dielectric interference filters are often approximated in the range n_eff ≈ 1.7 to 2.5.

Estimated Results

Conceptual estimate only: values are rounded and should not be used as final specification numbers. For design sign-off, rely on measured AOI data for the actual filter.

Shifted center wavelength λ_θ (nm)

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Wavelength shift Δλ (nm)

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Relative shift (%)

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Concept Visuals

Visuals are conceptual only: they show AOI shift behavior, not exact filter transmission.

Model and References

λ_θ = λ₀ · √( 1 − ( n₀ / n_eff )² · sin²θ )

Equivalent form when the incident medium is air (n₀ = 1): λ_θ = λ₀ · √( 1 − sin²θ / n_eff² )

λ₀: center wavelength at normal incidence (θ = 0)
λ_θ: shifted center wavelength at incidence angle θ
n_eff: effective refractive index of the filter stack
Model assumption: collimated beam and effective-index approximation

References: