= Polarized light microscopy
\b[Polarized light microscopy] uses controlled <polarization (waves)> of illumination and detection to reveal optical properties of a specimen. A <polarizer> before the specimen sets the incident <polarization (waves)>; a second <polarizer>, called the analyzer, selects which outgoing component reaches the image. With the two pass axes perpendicular, an ideal empty optical path is dark. A specimen can alter this result through <birefringence> or polarization-dependent absorption.<Polarized Light Microscopy in Nikon MicroscopyU>[Polarized Light Microscope Configuration and specimen contrast]{ref}
For an ideal nonabsorbing birefringent plate between crossed <polarizers>, the transmitted <light intensity> is
$$
I=I_0\sin^2(2\theta)\sin^2(\delta/2),\qquad \delta=\frac{2\pi\Delta n\,d}{\lambda},
$$
where $I_0$ is the intensity after the first <polarizer>, $\theta$ is the angle of a plate axis to its pass axis, $d$ is thickness, $\Delta n$ the <birefringence>, and $\lambda$ the vacuum <wavelength>. The <phase retardation> $\delta$ comes from different <optical path lengths>. With $\delta=\pi$, the plate is bright at $\theta=45^\circ$ and dark at $\theta=0$: rotating a specimen changes contrast without removing material.<Polarized Light Microscopy in Nikon MicroscopyU>[Rotating-stage discussion: extinction and maximum brightness at45degrees]{ref}
This sensitivity is useful for oriented biological materials. A2018 <ivory> study combined polarized-light observations with <X-ray scattering> and <scanning electron microscopy> to investigate mineralized <collagen> architecture. Brightness alone does not uniquely identify a substance: orientation, thickness, <wavelength> and optical properties all contribute.<The three-dimensional arrangement of the mineralized collagen fibers in elephant ivory and its relation to mechanical and optical properties by M. Albéric and others>[Abstract: complementary methods and proposed origin of the Schreger pattern]{ref}
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