A Lyot filter (polarization-interference monochromator, birefringent filter), named for its inventor and French astronomer Bernard Lyot, is a type of optical filter that uses birefringence to produce a narrow passband of transmitted wavelengths. Lyot filters are used in astronomy, particularly for solar astronomy, lasers, biomedical photonics and Raman chemical imaging.
Basic principles This section describes how the Lyot filter's wavelength dependent transmission of light arises from birefringence.
Single-plate optical filter The Lyot filter relies on light's polarization property, a vector (Jones vector) perpendicular to light's path that has a fixed direction (linear polarization) or a time-varying rotating direction (circular or elliptical polarization). For a typical single-plate Lyot filter, light passes through three consecutive optical elements that modify the light's polarization: the first horizontal polarizer, a waveplate (retarder) and a second horizontal polarizer. Linearly polarized light travels fastest when aligned with the waveplate's fast F direction, and slowest when aligned with the waveplate's orthogonal slow S direction. The speed difference depends on the difference between the waveplate's ordinary refractive index and extraordinary refractive index. This example assumes that the horizontal makes a 45-degree angle with the waveplate's F and S directions. The first horizontal polarizer transforms the incoming light's polarization to horizontally polarized light by passing only the incoming light's horizontal polarization component. The waveplate may modify the incoming horizontally polarized light to a different polarization based on the light's wavelength. The second horizontal polarizer passes only the horizontal polarization component of the light exiting the waveplate. For example, at one wavelength, if the light exiting the waveplate is horizontally polarized, then the light passes through the second horizontal polarizer fully, exiting the optical filter with no attenuation. At a different wavelength, if the light exiting the waveplate is vertically polarized, then no light passes through the second horizontal polarizer, and no light exits the optical filter. At most wavelengths, some wavelength-dependent attenuation will occur. This single-plate optical filter transmits light intensity I T {\displaystyle I_{T}} from an input of horizontally polarized light intensity I X {\displaystyle I_{X}} with wavelength λ {\displaystyle \lambda } , waveplate thickness d {\displaystyle d} , waveplate ordinary refractive index n o {\displaystyle n_{o}} and waveplate extraordinary refractive index n e {\displaystyle n_{e}} :
I T = I X ⋅ cos 2 ( π ( n o − n e ) d λ ) {\displaystyle I_{T}=I_{X}\cdot \operatorname {cos} ^{2}\left({\frac {\pi (n_{o}-n_{e})d}{\lambda }}\right)}
Multiplate optical filter Multiplate filters are a series of consecutive single-plate filters, with each waveplate half the thickness of the preceding plate. Using this design, a graph describing the transmitted light intensity at each wavelength will show sharper major peaks (narrower bandwidth) of transmitted light and a greater wavelength interval between the major peaks of transmitted light (free spectral range). As an example, extending the single-plate equation to a 3-plate optical filter with maximum waveplate thickness d {\displaystyle d} , this multiplate optical filter transmits light intensity I T {\displaystyle I_{T}} from an input of horizontally polarized light intensity I X {\textstyle I_{X}} :
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