<s>
The	O
ring-imaging	O
Cherenkov	O
,	O
or	O
RICH	O
,	O
detector	O
is	O
a	O
device	O
for	O
identifying	O
the	O
type	O
of	O
an	O
electrically	O
charged	O
subatomic	O
particle	O
of	O
known	O
momentum	B-Algorithm
,	O
that	O
traverses	O
a	O
transparent	O
refractive	O
medium	O
,	O
by	O
measurement	O
of	O
the	O
presence	O
and	O
characteristics	O
of	O
the	O
Cherenkov	O
radiation	O
emitted	O
during	O
that	O
traversal	O
.	O
</s>
<s>
RICH	B-Algorithm
detectors	I-Algorithm
were	O
first	O
developed	O
in	O
the	O
1980s	O
and	O
are	O
used	O
in	O
high	O
energy	O
elementary	O
particle	O
-	O
,	O
nuclear	O
-	O
and	O
astro-physics	O
experiments	O
.	O
</s>
<s>
This	O
article	O
outlines	O
the	O
origins	O
and	O
principles	O
of	O
the	O
RICH	B-Algorithm
detector	I-Algorithm
,	O
with	O
brief	O
examples	O
of	O
its	O
different	O
forms	O
in	O
modern	O
physics	O
experiments	O
.	O
</s>
<s>
Their	O
research	O
and	O
development	O
,	O
of	O
high	O
precision	O
single-photon	O
detectors	O
and	O
related	O
optics	O
,	O
lay	O
the	O
foundations	O
for	O
the	O
design	O
development	O
and	O
construction	O
of	O
the	O
first	O
large-scale	O
Particle	O
Physics	O
RICH	B-Algorithm
detectors	I-Algorithm
,	O
at	O
CERN	O
's	O
OMEGA	O
facility	O
and	O
LEP	O
(	O
Large	O
Electron	O
–	O
Positron	O
Collider	O
)	O
DELPHI	O
experiment	O
.	O
</s>
<s>
A	O
ring-imaging	O
Cherenkov	O
(	O
RICH	O
)	O
detector	O
allows	O
the	O
identification	O
of	O
electrically	O
charged	O
subatomic	O
particle	O
types	O
through	O
the	O
detection	O
of	O
the	O
Cherenkov	O
radiation	O
emitted	O
(	O
as	O
photons	B-Application
)	O
by	O
the	O
particle	O
in	O
traversing	O
a	O
medium	O
with	O
refractive	O
index	O
>	O
1	O
.	O
</s>
<s>
Knowledge	O
of	O
the	O
particle	O
's	O
momentum	B-Algorithm
and	O
direction	O
(	O
normally	O
available	O
from	O
an	O
associated	O
momentum-spectrometer	O
)	O
allows	O
a	O
predicted	O
for	O
each	O
hypothesis	O
of	O
the	O
particles	O
type	O
;	O
using	O
the	O
known	O
of	O
the	O
RICH	O
radiator	O
gives	O
a	O
corresponding	O
prediction	O
of	O
that	O
can	O
be	O
compared	O
to	O
the	O
of	O
the	O
detected	O
Cherenkov	O
photons	B-Application
,	O
thus	O
indicating	O
the	O
particle	O
's	O
identity	O
(	O
usually	O
as	O
a	O
probability	O
per	O
particle	O
type	O
)	O
.	O
</s>
<s>
A	O
typical	O
(	O
simulated	O
)	O
distribution	O
of	O
vs	O
momentum	B-Algorithm
of	O
the	O
source	O
particle	O
,	O
for	O
single	O
Cherenkov	O
photons	B-Application
,	O
produced	O
in	O
a	O
gaseous	O
radiator	O
(	O
n	O
~	O
1.0005	O
,	O
angular	O
resolution	O
~	O
0.6mrad	O
)	O
is	O
shown	O
in	O
the	O
following	O
figure	O
:	O
</s>
<s>
The	O
different	O
particle	O
types	O
follow	O
distinct	O
contours	O
of	O
constant	O
mass	O
,	O
smeared	O
by	O
the	O
effective	O
angular	O
resolution	O
of	O
the	O
RICH	B-Algorithm
detector	I-Algorithm
;	O
at	O
higher	O
momenta	O
each	O
particle	O
emits	O
a	O
number	O
of	O
Cherenkov	O
photons	B-Application
which	O
,	O
taken	O
together	O
,	O
give	O
a	O
more	O
precise	O
measure	O
of	O
the	O
average	O
than	O
does	O
a	O
single	O
photon	B-Application
,	O
allowing	O
effective	O
particle	O
separation	O
to	O
extend	O
beyond	O
100	O
GeV	O
in	O
this	O
example	O
.	O
</s>
<s>
The	O
essence	O
of	O
the	O
ring-imaging	O
method	O
is	O
to	O
devise	O
an	O
optical	O
system	O
with	O
single-photon	O
detectors	O
,	O
that	O
can	O
isolate	O
the	O
Cherenkov	O
photons	B-Application
that	O
each	O
particle	O
emits	O
,	O
to	O
form	O
a	O
single	O
"	O
ring	O
image	O
"	O
from	O
which	O
an	O
accurate	O
can	O
be	O
determined	O
.	O
</s>
<s>
A	O
polar	O
plot	O
of	O
the	O
Cherenkov	O
angles	O
of	O
photons	B-Application
associated	O
with	O
a	O
22	O
GeV/c	O
particle	O
in	O
a	O
radiator	O
with	O
=	O
1.0005	O
is	O
shown	O
below	O
;	O
both	O
pion	O
and	O
kaon	B-Application
are	O
illustrated	O
;	O
protons	B-Application
are	O
below	O
Cherenkov	O
threshold	O
,	O
</s>
<s>
producing	O
no	O
radiation	O
in	O
this	O
case	O
(	O
which	O
would	O
also	O
be	O
a	O
very	O
clear	O
signal	O
of	O
particle	O
type	O
=	O
proton	B-Application
,	O
since	O
fluctuations	O
in	O
the	O
number	O
of	O
photons	B-Application
follow	O
Poisson	O
statistics	O
about	O
the	O
expected	O
mean	O
,	O
so	O
that	O
the	O
probability	O
of	O
e.g.	O
</s>
<s>
a	O
22	O
GeV/c	O
kaon	B-Application
producing	O
zero	O
photons	B-Application
when	O
~	O
12	O
were	O
expected	O
is	O
very	O
small	O
;	O
e−12	O
or	O
1	O
in	O
162755	O
)	O
The	O
number	O
of	O
detected	O
photons	B-Application
shown	O
for	O
each	O
particle	O
type	O
is	O
,	O
for	O
illustration	O
purposes	O
,	O
the	O
average	O
for	O
that	O
type	O
in	O
a	O
RICH	O
having	O
~	O
25	O
(	O
see	O
below	O
)	O
.	O
</s>
<s>
Note	O
that	O
,	O
because	O
the	O
points	O
of	O
emission	O
of	O
the	O
photons	B-Application
can	O
be	O
at	O
any	O
place	O
on	O
the	O
(	O
normally	O
straight	O
line	O
)	O
trajectory	O
of	O
the	O
particle	O
through	O
the	O
radiator	O
,	O
the	O
emerging	O
photons	B-Application
fill	O
a	O
light-cone	O
in	O
space	O
.	O
</s>
<s>
In	O
a	O
RICH	B-Algorithm
detector	I-Algorithm
the	O
photons	B-Application
within	O
this	O
light-cone	O
pass	O
through	O
an	O
optical	O
system	O
and	O
impinge	O
upon	O
a	O
position	O
sensitive	O
photon	B-Application
detector	O
.	O
</s>
<s>
The	O
resolving	O
power	O
of	O
this	O
method	O
is	O
illustrated	O
by	O
comparing	O
the	O
Cherenkov	O
angle	O
per	O
photon	B-Application
,	O
see	O
the	O
first	O
plot	O
above	O
,	O
with	O
the	O
mean	O
Cherenkov	O
angle	O
per	O
particle	O
(	O
averaged	O
over	O
all	O
photons	B-Application
emitted	O
by	O
that	O
particle	O
)	O
obtained	O
by	O
ring-imaging	O
,	O
shown	O
below	O
;	O
the	O
greatly	O
enhanced	O
separation	O
between	O
particle	O
types	O
is	O
very	O
clear	O
:	O
</s>
<s>
The	O
effective	O
angular	O
resolution	O
per	O
photon	B-Application
,	O
</s>
<s>
The	O
maximum	O
number	O
of	O
detected	O
photons	B-Application
in	O
the	O
ring-image	O
,	O
</s>
<s>
is	O
a	O
measure	O
of	O
the	O
intrinsic	O
optical	O
precision	O
of	O
the	O
RICH	B-Algorithm
detector	I-Algorithm
.	O
</s>
<s>
is	O
a	O
measure	O
of	O
the	O
optical	O
response	O
of	O
the	O
RICH	O
;	O
it	O
can	O
be	O
thought	O
of	O
as	O
the	O
limiting	O
case	O
of	O
the	O
number	O
of	O
actually	O
detected	O
photons	B-Application
produced	O
by	O
a	O
particle	O
whose	O
velocity	O
approaches	O
that	O
of	O
light	O
,	O
averaged	O
over	O
all	O
relevant	O
particle	O
trajectories	O
in	O
the	O
RICH	B-Algorithm
detector	I-Algorithm
.	O
</s>
<s>
Given	O
the	O
known	O
momentum	B-Algorithm
of	O
the	O
emitting	O
particle	O
and	O
the	O
refractive	O
index	O
of	O
the	O
radiator	O
,	O
the	O
expected	O
Cherenkov	O
angle	O
for	O
each	O
particle	O
type	O
can	O
be	O
predicted	O
,	O
and	O
its	O
difference	O
from	O
the	O
observed	O
mean	O
Cherenkov	O
angle	O
calculated	O
.	O
</s>
<s>
The	O
following	O
figure	O
shows	O
the	O
'	O
number	O
of	O
sigma	O
 '	O
deviation	O
of	O
the	O
kaon	B-Application
hypothesis	O
from	O
a	O
true	O
pion	O
ring	O
image	O
( π	O
not	O
k	O
)	O
and	O
of	O
the	O
pion	O
hypothesis	O
from	O
a	O
true	O
kaon	B-Application
ring	O
image	O
(	O
k	O
not	O
π	O
)	O
,	O
as	O
a	O
function	O
of	O
momentum	B-Algorithm
,	O
for	O
a	O
RICH	O
with	O
=	O
1.0005	O
,	O
=	O
25	O
,	O
=	O
0.64	O
milliradians	O
;	O
</s>
<s>
Also	O
shown	O
are	O
the	O
average	O
number	O
of	O
detected	O
photons	B-Application
from	O
pions(Ngπ )	O
or	O
from	O
kaons(Ngk )	O
.	O
</s>
<s>
In	O
practice	O
,	O
for	O
the	O
multi-particle	O
final	O
states	O
produced	O
in	O
a	O
typical	O
collider	O
experiment	O
,	O
separation	O
of	O
kaons	B-Application
from	O
other	O
final	O
state	O
hadrons	O
,	O
mainly	O
pions	O
,	O
is	O
the	O
most	O
important	O
purpose	O
of	O
the	O
RICH	O
.	O
</s>
<s>
In	O
that	O
context	O
the	O
two	O
most	O
vital	O
RICH	O
functions	O
,	O
which	O
maximise	O
signal	O
and	O
minimise	O
combinatorial	O
backgrounds	O
,	O
are	O
its	O
ability	O
to	O
correctly	O
identify	O
a	O
kaon	B-Application
as	O
a	O
kaon	B-Application
and	O
its	O
ability	O
not	O
to	O
misidentify	O
a	O
pion	O
as	O
a	O
kaon	B-Application
.	O
</s>
<s>
The	O
related	O
probabilities	O
,	O
which	O
are	O
the	O
usual	O
measures	O
of	O
signal	O
detection	O
and	O
background	O
rejection	O
in	O
real	O
data	O
,	O
are	O
plotted	O
below	O
to	O
show	O
their	O
variation	O
with	O
momentum	B-Algorithm
(	O
simulation	O
with	O
10%	O
random	O
background	O
)	O
;	O
</s>
<s>
Note	O
that	O
the	O
~	O
30%	O
π	O
→	O
k	O
misidentification	O
rate	O
at	O
100	O
GeV	O
is	O
,	O
for	O
the	O
most	O
part	O
,	O
due	O
to	O
the	O
presence	O
of	O
10%	O
background	O
hits	O
(	O
faking	O
photons	B-Application
)	O
in	O
the	O
simulated	O
detector	O
;	O
the	O
3-sigma	O
separation	O
in	O
the	O
mean	O
Cherenkov	O
angle	O
(	O
shown	O
in	O
the	O
4th	O
plot	O
above	O
)	O
would	O
,	O
by	O
itself	O
,	O
only	O
account	O
for	O
about	O
6%	O
misidentification	O
.	O
</s>
<s>
More	O
detailed	O
analyses	O
of	O
the	O
above	O
type	O
,	O
for	O
operational	O
RICH	B-Algorithm
detectors	I-Algorithm
,	O
can	O
be	O
found	O
in	O
the	O
published	O
literature	O
.	O
</s>
<s>
The	O
following	O
figure	O
shows	O
,	O
on	O
the	O
left	O
,	O
the	O
π+π−	O
mass	O
distribution	O
without	O
RICH	O
identification	O
,	O
where	O
all	O
particles	O
are	O
assumed	O
to	O
be	O
π	O
;	O
the	O
B0	O
→	O
π+π−	O
signal	O
of	O
interest	O
is	O
the	O
turquoise-dotted	O
line	O
and	O
is	O
completely	O
swamped	O
by	O
background	O
due	O
to	O
B	O
and	O
Λ	O
decays	O
involving	O
kaons	B-Application
and	O
protons	B-Application
,	O
and	O
combinatorial	O
background	O
from	O
particles	O
not	O
associated	O
with	O
the	O
B0	O
decay	O
.	O
</s>
<s>
On	O
the	O
right	O
are	O
the	O
same	O
data	O
with	O
RICH	O
identification	O
used	O
to	O
select	O
only	O
pions	O
and	O
reject	O
kaons	B-Application
and	O
protons	B-Application
;	O
the	O
B0	O
→	O
π+π−	O
signal	O
is	O
preserved	O
but	O
all	O
kaon	B-Application
-	O
and	O
proton-related	O
backgrounds	O
are	O
greatly	O
reduced	O
,	O
so	O
that	O
the	O
overall	O
B0	O
signal/background	O
has	O
improved	O
by	O
a	O
factor	O
~	O
6	O
,	O
allowing	O
much	O
more	O
precise	O
measurement	O
of	O
the	O
decay	O
process	O
.	O
</s>
<s>
In	O
a	O
focusing	O
RICH	B-Algorithm
detector	I-Algorithm
,	O
the	O
photons	B-Application
are	O
collected	O
by	O
a	O
spherical	O
mirror	O
with	O
focal	O
length	O
and	O
focused	O
onto	O
the	O
photon	B-Application
detector	O
placed	O
at	O
the	O
focal	O
plane	O
.	O
</s>
<s>
This	O
scheme	O
is	O
suitable	O
for	O
low	O
refractive	O
index	O
radiators	O
(	O
i.e.	O
,	O
gases	O
)	O
with	O
their	O
larger	O
radiator	O
length	O
needed	O
to	O
create	O
enough	O
photons	B-Application
.	O
</s>
<s>
In	O
the	O
more	O
compact	O
proximity-focusing	O
design	O
a	O
thin	O
radiator	O
volume	O
emits	O
a	O
cone	O
of	O
Cherenkov	O
light	O
which	O
traverses	O
a	O
small	O
distance	O
,	O
the	O
proximity	O
gap	O
,	O
and	O
is	O
detected	O
on	O
the	O
photon	B-Application
detector	O
plane	O
.	O
</s>
<s>
An	O
example	O
of	O
a	O
proximity	O
gap	O
RICH	B-Algorithm
detector	I-Algorithm
is	O
the	O
High	O
Momentum	B-Algorithm
Particle	O
Identification	O
(	O
)	O
,	O
one	O
of	O
the	O
detectors	O
of	O
ALICE	O
(	O
A	O
Large	O
Ion	O
Collider	O
Experiment	O
)	O
,	O
which	O
is	O
one	O
of	O
the	O
five	O
experiments	O
at	O
the	O
LHC	O
(	O
Large	O
Hadron	O
Collider	O
)	O
at	O
CERN	O
.	O
</s>
<s>
In	O
a	O
DIRC	B-Algorithm
(	O
Detection	B-Algorithm
of	I-Algorithm
Internally	I-Algorithm
Reflected	I-Algorithm
Cherenkov	I-Algorithm
light	I-Algorithm
)	O
,	O
another	O
design	O
of	O
a	O
RICH	B-Algorithm
detector	I-Algorithm
,	O
light	O
that	O
is	O
captured	O
by	O
total	O
internal	O
reflection	O
inside	O
the	O
solid	O
radiator	O
reaches	O
the	O
light	O
sensors	O
at	O
the	O
detector	O
perimeter	O
,	O
the	O
precise	O
rectangular	O
cross	O
section	O
of	O
the	O
radiator	O
preserving	O
the	O
angular	O
information	O
of	O
the	O
Cherenkov	O
light	O
cone	O
.	O
</s>
<s>
One	O
example	O
is	O
the	O
DIRC	B-Algorithm
of	O
the	O
BaBar	O
experiment	O
at	O
SLAC	O
.	O
</s>
<s>
The	O
LHCb	O
experiment	O
on	O
the	O
Large	O
Hadron	O
Collider	O
uses	O
two	O
RICH	B-Algorithm
detectors	I-Algorithm
for	O
differentiating	O
between	O
pions	O
and	O
kaons	B-Application
.	O
</s>
<s>
The	O
first	O
(	O
RICH-1	O
)	O
is	O
located	O
immediately	O
after	O
the	O
Vertex	O
Locator	O
(	O
VELO	O
)	O
around	O
the	O
interaction	O
point	O
and	O
is	O
optimised	O
for	O
low-momentum	O
particles	O
and	O
the	O
second	O
(	O
RICH-2	O
)	O
is	O
located	O
after	O
the	O
magnet	O
and	O
particle-tracker	O
layers	O
and	O
optimised	O
for	O
higher-momentum	O
particles	O
.	O
</s>
<s>
The	O
Alpha	O
Magnetic	O
Spectrometer	O
device	O
AMS-02	O
,	O
recently	O
mounted	O
on	O
the	O
International	O
Space	O
Station	O
uses	O
a	O
RICH	B-Algorithm
detector	I-Algorithm
in	O
combination	O
with	O
other	O
devices	O
to	O
analyze	O
cosmic	O
rays	O
.	O
</s>
