Majority of interference filters are designed to be used at normal angle of incidence (AOI). The primary effect of an increase in the incident angle on an interference coating is a shift in spectral performance toward shorter wavelengths. In other words, the principal wavelength $$\lambda$$ of all types of interference filters decreases as the AOI increases,
$\lambda(\theta) = \lambda_0 \sqrt{1 – \left(\frac{\sin\theta}{n_{\rm eff}}\right)^2},$ where $$\theta$$ stands for the AOI and $$n_{\rm eff}$$ is an effective index of refraction with value typically between 1.4 and 2.2. Small tilts are commonly used to tune the peak of a filter to the desired wavelength even though they have an adverse ef fect on the angular field of the filter and its transmittance.

The performance of the filter depends on a polarization of the input light for $$\textrm{AOI}>0$$, as S and P polarization modes can be distinguished and interfere differently. The shift of the central or principal wavelength towards shorter wavelengths can be more pronounced for P-polarized light (smaller effective index of refraction). The bandwidth of the filter broadens slightly for P-polarized light while narrowing for S-polarized light. The most striking feature is the decrease in transmission for S-polarized light, while the P-polarized light maintains high transmission.

References

1) M. Bass ed., Handbook of optics, Volume I (2nd edition, McGRAW-HILL, New York 1995), chapter 42: Optical properties of films and coatings, pages 42 .89-91.

2) P.H. Lissberger and W.L. Wilcock, Properties of All-Dielectric Interference Filters. II. Filters in Parallel Beams of Light Incident Obliquely and in Convergent Beams, J. Opt. Soc. Am. 49, 126-128 (1959).

4) Omega Optical: Angle of Incidence and Polarization

Interference filters at off-normal angles of incidence

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• 2016/07/07 at 06:56