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    Gradient Index (GRIN) optics: radial quadratic - MIT

    fabrication 
by 
melding 
& 
grinding Stack Meld Grind & polish to a sphere Result: Spherical refractive surface with axial index profile n(z) Correction of spherical aberration by axial GRIN lenses aberrated corrected

    MIT OpenCourseWare

    material with variable optical “density” P’ light ray P “optical path length” Let’s take a break from optics ...

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    s: 
parameterization 
of 
the 
ray 
trajectory q(s): 
position 
vector 
for 
the 
ray 
trajectory 
at 
s; 
p(s): 
tangent 
vector 
to 
the 
ray 
trajectory 
at 
s s p(s) p(s) q(s+Δs) q(s) p(s+Δs) s ∇n(q) = 
low 
index 
n min = 
high 
index 
nmax

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    Rays 
are 
continuous 
and 

piecewise 
differentiable

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    Momentum 
changes 
along 
trajectory 
arc 
length 
in 
proportion 
to 
the 
local 
refractive 
index 
gradient These are the “equations of motion,” i.e. they yield the ray trajectories.

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