From the gradient-optics.org website...

Gradient-index, or GRIN, materials are optical materials with a varying index of
refraction. They provide additional design parameters over conventional
refractive optics, which use homogenous materials (a constant refractive index).
GRIN media can complement or even replace other design parameters, such as
surface curvature. Using a GRIN material increases the design options, with
gradient-index materials providing new opportunities to reduce element count,
balance imaging aberrations, control wavelength-dependent behaviors over the
spectrum of interest, and manage thermal effects. GRIN materials can be used for
imaging and non-imaging designs.

The effects of a GRIN medium are a common part of life. Documented almost 200
years ago, the mirage is the best known optical effect from a GRIN profile,
explained as a result of temperature variations causing a refractive index
variation in the air. An example is commonly seen driving on a hot day: the
shimmering appearance of a water-like pool on the road ahead. The index of
refraction of air increases from the hottest region at the road’s surface to the
cooler air above. The variation causes the light rays to be refracted, or bent,
into the driver’s line of sight.

Gradient-index optics are also part of living creatures. In the late 19th
century, insect eyes were discovered to be composed of rods which act as lenses
due to their varying index of refraction. The human eye’s lens, too, has a
radial gradient-index profile.

The simplest, and broadest view, of GRIN materials, is that it is an additional
material type, with additional design parameters, to choose from when designing
an optical system. GRIN optics given the designer more options to work with. A
conventional imaging system would use refractive elements, choosing the glass
type to optimize the design performance. Each lens would be have a constant
index of refraction (at a given wavelength) chosen to optimize the design. The
GRIN optic opens up the design space to have a varying refractive index within
an element. As the surface curvature can be varied to reduce classical
aberrations, so the index profile can be varied to improve system performance.
Below is an illustration of the “Wood” lens, named after its inventor. A
radially varying index profile makes what would otherwise be a window into a
lens: a collimated wavefront is brought to a focus solely due to the GRIN
material.

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