<s>
In	O
physics	O
,	O
ray	B-Algorithm
tracing	I-Algorithm
is	O
a	O
method	O
for	O
calculating	O
the	O
path	O
of	O
waves	O
or	O
particles	O
through	O
a	O
system	O
with	O
regions	O
of	O
varying	O
propagation	O
velocity	O
,	O
absorption	O
characteristics	O
,	O
and	O
reflecting	O
surfaces	O
.	O
</s>
<s>
Ray	B-Algorithm
tracing	I-Algorithm
solves	O
the	O
problem	O
by	O
repeatedly	O
advancing	O
idealized	O
narrow	O
beams	O
called	O
rays	B-Device
through	O
the	O
medium	O
by	O
discrete	O
amounts	O
.	O
</s>
<s>
Simple	O
problems	O
can	O
be	O
analyzed	O
by	O
propagating	O
a	O
few	O
rays	B-Device
using	O
simple	O
mathematics	O
.	O
</s>
<s>
More	O
detailed	O
analysis	O
can	O
be	O
performed	O
by	O
using	O
a	O
computer	O
to	O
propagate	O
many	O
rays	B-Device
.	O
</s>
<s>
When	O
applied	O
to	O
problems	O
of	O
electromagnetic	O
radiation	O
,	O
ray	B-Algorithm
tracing	I-Algorithm
often	O
relies	O
on	O
approximate	O
solutions	O
to	O
Maxwell	O
's	O
equations	O
that	O
are	O
valid	O
as	O
long	O
as	O
the	O
light	O
waves	O
propagate	O
through	O
and	O
around	O
objects	O
whose	O
dimensions	O
are	O
much	O
greater	O
than	O
the	O
light	O
's	O
wavelength	O
.	O
</s>
<s>
Ray	B-Algorithm
tracing	I-Algorithm
works	O
by	O
assuming	O
that	O
the	O
particle	O
or	O
wave	O
can	O
be	O
modeled	O
as	O
a	O
large	O
number	O
of	O
very	O
narrow	O
beams	O
(	O
rays	B-Device
)	O
,	O
and	O
that	O
there	O
exists	O
some	O
distance	O
,	O
possibly	O
very	O
small	O
,	O
over	O
which	O
such	O
a	O
ray	O
is	O
locally	O
straight	O
.	O
</s>
<s>
The	O
ray	B-Algorithm
tracer	I-Algorithm
will	O
advance	O
the	O
ray	O
over	O
this	O
distance	O
,	O
and	O
then	O
use	O
a	O
local	B-Algorithm
derivative	I-Algorithm
of	O
the	O
medium	O
to	O
calculate	O
the	O
ray	O
's	O
new	O
direction	O
.	O
</s>
<s>
This	O
process	O
is	O
repeated	O
with	O
as	O
many	O
rays	B-Device
as	O
are	O
necessary	O
to	O
understand	O
the	O
behavior	O
of	O
the	O
system	O
.	O
</s>
<s>
Ray	B-Algorithm
tracing	I-Algorithm
is	O
being	O
increasingly	O
used	O
in	O
astronomy	O
to	O
simulate	O
realistic	O
images	O
of	O
the	O
sky	O
.	O
</s>
<s>
Unlike	O
conventional	O
simulations	O
,	O
ray	B-Algorithm
tracing	I-Algorithm
does	O
not	O
use	O
the	O
expected	O
or	O
calculated	O
PSF	O
of	O
a	O
telescope	O
and	O
instead	O
traces	O
journey	O
of	O
each	O
photon	O
from	O
entering	O
the	O
upper	O
atmosphere	O
to	O
the	O
detector	O
.	O
</s>
<s>
Most	O
of	O
the	O
dispersion	O
and	O
distortion	O
,	O
arising	O
mainly	O
from	O
atmosphere	O
,	O
optics	B-Algorithm
and	O
detector	O
are	O
taken	O
into	O
account	O
.	O
</s>
<s>
Notable	O
examples	O
include	O
Large	O
Synoptic	O
Survey	O
Telescope	O
where	O
this	O
kind	O
of	O
ray	B-Algorithm
tracing	I-Algorithm
was	O
first	O
used	O
with	O
PhoSim	O
to	O
create	O
simulated	O
images	O
.	O
</s>
<s>
One	O
particular	O
form	O
of	O
ray	B-Algorithm
tracing	I-Algorithm
is	O
radio	O
signal	O
ray	B-Algorithm
tracing	I-Algorithm
,	O
which	O
traces	O
radio	O
signals	O
,	O
modeled	O
as	O
rays	B-Device
,	O
through	O
the	O
ionosphere	O
where	O
they	O
are	O
refracted	O
and/or	O
reflected	O
back	O
to	O
the	O
Earth	O
.	O
</s>
<s>
This	O
form	O
of	O
ray	B-Algorithm
tracing	I-Algorithm
involves	O
the	O
integration	O
of	O
differential	O
equations	O
that	O
describe	O
the	O
propagation	O
of	O
electromagnetic	O
waves	O
through	O
dispersive	O
and	O
anisotropic	O
media	O
such	O
as	O
the	O
ionosphere	O
.	O
</s>
<s>
An	O
example	O
of	O
physics-based	O
radio	O
signal	O
ray	B-Algorithm
tracing	I-Algorithm
is	O
shown	O
to	O
the	O
right	O
.	O
</s>
<s>
Radio	O
communicators	O
use	O
ray	B-Algorithm
tracing	I-Algorithm
to	O
help	O
determine	O
the	O
precise	O
behavior	O
of	O
radio	O
signals	O
as	O
they	O
propagate	O
through	O
the	O
ionosphere	O
.	O
</s>
<s>
Unlike	O
optical	B-Device
ray	B-Algorithm
tracing	I-Algorithm
where	O
the	O
medium	O
between	O
objects	O
typically	O
has	O
a	O
constant	O
refractive	O
index	O
,	O
signal	O
ray	B-Algorithm
tracing	I-Algorithm
must	O
deal	O
with	O
the	O
complexities	O
of	O
a	O
spatially	O
varying	O
refractive	O
index	O
,	O
where	O
changes	O
in	O
ionospheric	O
electron	O
densities	O
influence	O
the	O
refractive	O
index	O
and	O
hence	O
,	O
ray	O
trajectories	O
.	O
</s>
<s>
Ray	B-Algorithm
tracing	I-Algorithm
may	O
be	O
used	O
to	O
calculate	O
the	O
path	O
of	O
sound	O
through	O
the	O
ocean	O
up	O
to	O
very	O
large	O
distances	O
,	O
incorporating	O
the	O
effects	O
of	O
the	O
SOFAR	O
channel	O
,	O
as	O
well	O
as	O
reflections	O
and	O
refractions	O
off	O
the	O
ocean	O
surface	O
and	O
bottom	O
.	O
</s>
<s>
Ray	B-Algorithm
tracing	I-Algorithm
may	O
be	O
used	O
in	O
the	O
design	O
of	O
lenses	O
and	O
optical	B-Algorithm
systems	O
,	O
such	O
as	O
in	O
cameras	O
,	O
microscopes	O
,	O
telescopes	O
,	O
and	O
binoculars	O
,	O
and	O
its	O
application	O
in	O
this	O
field	O
dates	O
back	O
to	O
the	O
1900s	O
.	O
</s>
<s>
Geometric	O
ray	B-Algorithm
tracing	I-Algorithm
is	O
used	O
to	O
describe	O
the	O
propagation	O
of	O
light	B-Device
rays	I-Device
through	O
a	O
lens	O
system	O
or	O
optical	B-Algorithm
instrument	O
,	O
allowing	O
the	O
image-forming	O
properties	O
of	O
the	O
system	O
to	O
be	O
modeled	O
.	O
</s>
<s>
The	O
following	O
effects	O
can	O
be	O
integrated	O
into	O
a	O
ray	B-Algorithm
tracer	I-Algorithm
in	O
a	O
straightforward	O
fashion	O
:	O
</s>
<s>
Thin	O
film	O
interference	O
(	O
optical	B-Algorithm
coating	O
,	O
soap	O
bubble	O
)	O
can	O
be	O
used	O
to	O
calculate	O
the	O
reflectivity	O
of	O
a	O
surface	O
.	O
</s>
<s>
In	O
a	O
focal	O
point	O
,	O
rays	B-Device
from	O
a	O
point	O
light	O
source	O
meet	O
again	O
and	O
may	O
constructively	O
or	O
destructively	O
interfere	O
with	O
each	O
other	O
.	O
</s>
<s>
Within	O
a	O
very	O
small	O
region	O
near	O
this	O
point	O
,	O
incoming	O
light	O
may	O
be	O
approximated	O
by	O
plane	O
waves	O
which	O
inherit	O
their	O
direction	O
from	O
the	O
rays	B-Device
.	O
</s>
<s>
The	O
optical	B-Algorithm
path	O
length	O
from	O
the	O
light	O
source	O
is	O
used	O
to	O
compute	O
the	O
phase	O
.	O
</s>
<s>
The	O
derivative	B-Algorithm
of	O
the	O
position	O
of	O
the	O
ray	O
in	O
the	O
focal	O
region	O
on	O
the	O
source	O
position	O
is	O
used	O
to	O
obtain	O
the	O
width	O
of	O
the	O
ray	O
,	O
and	O
from	O
that	O
the	O
amplitude	B-Application
of	O
the	O
plane	O
wave	O
.	O
</s>
<s>
The	O
result	O
is	O
the	O
point	O
spread	O
function	O
,	O
whose	O
Fourier	B-Algorithm
transform	I-Algorithm
is	O
the	O
optical	B-Algorithm
transfer	O
function	O
.	O
</s>
<s>
However	O
,	O
when	O
the	O
rays	B-Device
come	O
close	O
together	O
or	O
even	O
cross	O
,	O
the	O
wavefront	O
approximation	O
breaks	O
down	O
.	O
</s>
<s>
Interference	O
of	O
spherical	O
waves	O
is	O
usually	O
not	O
combined	O
with	O
ray	B-Algorithm
tracing	I-Algorithm
,	O
thus	O
diffraction	O
at	O
an	O
aperture	O
cannot	O
be	O
calculated	O
.	O
</s>
<s>
Field	O
Tracing	O
is	O
a	O
modelling	O
technique	O
,	O
combining	O
geometric	O
optics	B-Algorithm
with	O
physical	O
optics	B-Algorithm
enabling	O
to	O
overcome	O
the	O
limitations	O
of	O
interference	O
and	O
diffraction	O
in	O
designing	O
.	O
</s>
<s>
The	O
ray	B-Algorithm
tracing	I-Algorithm
techniques	O
are	O
used	O
to	O
optimize	O
the	O
design	O
of	O
the	O
instrument	O
by	O
minimizing	O
aberrations	O
,	O
for	O
photography	O
,	O
and	O
for	O
longer	O
wavelength	O
applications	O
such	O
as	O
designing	O
microwave	O
or	O
even	O
radio	O
systems	O
,	O
and	O
for	O
shorter	O
wavelengths	O
,	O
such	O
as	O
ultraviolet	B-Application
and	O
X-ray	B-Library
optics	B-Algorithm
.	O
</s>
<s>
Before	O
the	O
advent	O
of	O
the	O
computer	O
,	O
ray	B-Algorithm
tracing	I-Algorithm
calculations	O
were	O
performed	O
by	O
hand	O
using	O
trigonometry	O
and	O
logarithmic	O
tables	O
.	O
</s>
<s>
The	O
optical	B-Algorithm
formulas	O
of	O
many	O
classic	O
photographic	O
lenses	O
were	O
optimized	O
by	O
roomfuls	O
of	O
people	O
,	O
each	O
of	O
whom	O
handled	O
a	O
small	O
part	O
of	O
the	O
large	O
calculation	O
.	O
</s>
<s>
Now	O
they	O
are	O
worked	O
out	O
in	O
optical	B-Algorithm
design	O
software	O
.	O
</s>
<s>
A	O
simple	O
version	O
of	O
ray	B-Algorithm
tracing	I-Algorithm
known	O
as	O
ray	O
transfer	O
matrix	O
analysis	O
is	O
often	O
used	O
in	O
the	O
design	O
of	O
optical	B-Algorithm
resonators	O
used	O
in	O
lasers	O
.	O
</s>
<s>
The	O
basic	O
principles	O
of	O
the	O
most	O
frequently	O
used	O
algorithm	O
could	O
be	O
found	O
in	O
Spencer	O
and	O
Murty	O
's	O
fundamental	O
paper	O
:	O
"	O
General	O
ray	B-Algorithm
tracing	I-Algorithm
Procedure	O
"	O
.	O
</s>
<s>
In	O
seismology	O
,	O
geophysicists	O
use	O
ray	B-Algorithm
tracing	I-Algorithm
to	O
aid	O
in	O
earthquake	O
location	O
and	O
tomographic	B-Algorithm
reconstruction	O
of	O
the	O
Earth	O
's	O
interior	O
.	O
</s>
<s>
Ray	B-Algorithm
tracing	I-Algorithm
may	O
be	O
used	O
to	O
compute	O
paths	O
through	O
a	O
geophysical	O
model	O
,	O
following	O
them	O
back	O
to	O
their	O
source	O
,	O
such	O
as	O
an	O
earthquake	O
,	O
or	O
deducing	O
the	O
properties	O
of	O
the	O
intervening	O
material	O
.	O
</s>
<s>
In	O
general	O
relativity	O
,	O
where	O
gravitational	O
lensing	O
can	O
occur	O
,	O
the	O
geodesics	O
of	O
the	O
light	B-Device
rays	I-Device
receiving	O
at	O
the	O
observer	O
are	O
integrated	O
backwards	O
in	O
time	O
until	O
they	O
hit	O
the	O
region	O
of	O
interest	O
.	O
</s>
<s>
Image	O
synthesis	O
under	O
this	O
technique	O
can	O
be	O
view	O
as	O
an	O
extension	O
of	O
the	O
usual	O
ray	B-Algorithm
tracing	I-Algorithm
in	O
computer	O
graphics	O
.	O
</s>
