<s>
Retinomorphic	B-Algorithm
sensors	I-Algorithm
are	O
a	O
type	O
of	O
event-driven	B-Application
optical	B-Application
sensor	I-Application
which	O
produce	O
a	O
signal	O
in	O
response	O
to	O
changes	O
in	O
light	O
intensity	O
,	O
rather	O
than	O
to	O
light	O
intensity	O
itself	O
.	O
</s>
<s>
This	O
is	O
in	O
contrast	O
to	O
conventional	O
optical	B-Application
sensors	I-Application
such	O
as	O
charge	B-Algorithm
coupled	I-Algorithm
device	I-Algorithm
(	O
CCD	O
)	O
or	O
complementary	B-Architecture
metal	I-Architecture
oxide	I-Architecture
semiconductor	I-Architecture
(	O
CMOS	O
)	O
based	O
sensors	B-Application
,	O
which	O
output	O
a	O
signal	O
that	O
increases	O
with	O
increasing	O
light	O
intensity	O
.	O
</s>
<s>
Because	O
they	O
respond	O
to	O
movement	O
only	O
,	O
retinomorphic	B-Algorithm
sensors	I-Algorithm
are	O
hoped	O
to	O
enable	O
faster	O
tracking	O
of	O
moving	O
objects	O
than	O
conventional	O
image	B-Algorithm
sensors	I-Algorithm
,	O
and	O
have	O
potential	O
applications	O
in	O
autonomous	O
vehicles	O
,	O
robotics	O
,	O
and	O
neuromorphic	O
engineering	O
.	O
</s>
<s>
These	O
silicon-based	O
sensors	B-Application
were	O
based	O
on	O
small	O
circuits	O
involving	O
differential	O
amplifiers	O
,	O
capacitors	O
,	O
and	O
resistors	O
.	O
</s>
<s>
The	O
sensors	B-Application
produced	O
a	O
spike	O
and	O
subsequent	O
decay	O
in	O
output	O
voltage	O
in	O
response	O
to	O
a	O
step-change	O
in	O
illumination	O
intensity	O
.	O
</s>
<s>
The	O
name	O
silicon	B-Algorithm
retina	I-Algorithm
has	O
hence	O
been	O
used	O
to	O
describe	O
these	O
sensors	B-Application
.	O
</s>
<s>
The	O
term	O
received	O
wider	O
use	O
by	O
Stanford	O
Professor	O
of	O
Engineering	O
Kwabena	O
Boahen	O
,	O
and	O
has	O
since	O
been	O
applied	O
to	O
a	O
wide	O
range	O
of	O
event-driven	B-Application
sensing	O
strategies	O
.	O
</s>
<s>
The	O
word	O
is	O
analogous	O
to	O
neuromorphic	O
,	O
which	O
is	O
applied	O
to	O
hardware	O
elements	O
(	O
such	O
as	O
processors	B-General_Concept
)	O
designed	O
to	O
replicate	O
the	O
way	O
the	O
brain	O
processes	O
information	O
.	O
</s>
<s>
There	O
are	O
several	O
retinomorphic	B-Algorithm
sensor	I-Algorithm
designs	O
which	O
yield	O
a	O
similar	O
response	O
.	O
</s>
<s>
Since	O
the	O
1980	O
's	O
these	O
sensors	B-Application
have	O
evolved	O
into	O
much	O
more	O
complex	O
and	O
robust	O
circuits	O
.	O
</s>
<s>
A	O
more	O
compact	O
design	O
of	O
retinomorphic	B-Algorithm
sensor	I-Algorithm
consists	O
of	O
just	O
a	O
photosensitive	O
capacitor	O
and	O
a	O
resistor	O
in	O
series	O
.	O
</s>
<s>
The	O
output	O
voltage	O
of	O
these	O
retinomorphic	B-Algorithm
sensors	I-Algorithm
,	O
,	O
is	O
defined	O
as	O
voltage	O
dropped	O
across	O
the	O
resistor	O
.	O
</s>
<s>
If	O
a	O
constant	O
voltage	O
,	O
is	O
applied	O
across	O
this	O
RC	B-Algorithm
circuit	I-Algorithm
it	O
will	O
act	O
as	O
a	O
passive	O
high-pass	O
filter	O
and	O
all	O
voltage	O
will	O
be	O
dropped	O
across	O
the	O
capacitor	O
(	O
i.e.	O
</s>
<s>
Conventional	O
cameras	B-Device
capture	O
every	O
part	O
of	O
an	O
image	O
,	O
regardless	O
of	O
whether	O
it	O
is	O
relevant	O
to	O
the	O
task	O
.	O
</s>
<s>
Because	O
every	O
pixel	O
is	O
measured	O
,	O
conventional	O
image	B-Algorithm
sensors	I-Algorithm
are	O
only	O
able	O
to	O
sample	O
the	O
visual	O
field	O
at	O
relatively	O
low	O
frame	O
rates	O
,	O
typically	O
30	O
-	O
240	O
frames	O
per	O
second	O
.	O
</s>
<s>
Even	O
in	O
professional	O
high	O
speed	O
cameras	B-Device
used	O
for	O
motion	O
picture	O
,	O
the	O
frame	O
rate	O
is	O
limited	O
to	O
a	O
few	O
10	B-Algorithm
's	I-Algorithm
of	I-Algorithm
thousands	I-Algorithm
of	I-Algorithm
frames	I-Algorithm
per	I-Algorithm
second	I-Algorithm
for	O
a	O
full	O
resolution	O
image	O
.	O
</s>
<s>
By	O
contrast	O
,	O
retinomorphic	B-Algorithm
sensors	I-Algorithm
identify	O
movement	O
by	O
design	O
.	O
</s>
<s>
This	O
means	O
that	O
they	O
do	O
not	O
have	O
a	O
frame	O
rate	O
and	O
instead	O
are	O
event-driven	B-Application
,	O
responding	O
only	O
when	O
needed	O
.	O
</s>
<s>
For	O
this	O
reason	O
,	O
retinomorphic	B-Algorithm
sensors	I-Algorithm
are	O
hoped	O
to	O
enable	O
identification	O
of	O
moving	O
objects	O
much	O
more	O
quickly	O
than	O
conventional	O
real-time	O
image	B-Application
analysis	I-Application
strategies	I-Application
.	O
</s>
<s>
Retinomorphic	B-Algorithm
sensors	I-Algorithm
are	O
therefore	O
hoped	O
to	O
have	O
applications	O
in	O
autonomous	O
vehicles	O
,	O
robotics	O
,	O
and	O
neuromorphic	O
engineering	O
.	O
</s>
<s>
Retinomorphic	B-Algorithm
sensor	I-Algorithm
operation	O
can	O
be	O
quantified	O
using	O
similar	O
techniques	O
to	O
simple	O
RC	B-Algorithm
circuits	I-Algorithm
,	O
the	O
only	O
difference	O
being	O
that	O
capacitance	O
is	O
not	O
constant	O
as	O
a	O
function	O
of	O
time	O
in	O
a	O
retinomorphic	B-Algorithm
sensor	I-Algorithm
.	O
</s>
<s>
Because	O
capacitance	O
in	O
retinomorphic	B-Algorithm
sensors	I-Algorithm
is	O
a	O
function	O
of	O
time	O
,	O
cannot	O
be	O
taken	O
out	O
of	O
the	O
derivative	O
as	O
a	O
constant	O
.	O
</s>
<s>
Using	O
the	O
product	O
rule	O
,	O
we	O
get	O
the	O
following	O
general	O
equation	O
of	O
retinomorphic	B-Algorithm
sensor	I-Algorithm
response	O
:	O
</s>
<s>
While	O
real-world	O
applications	O
of	O
retinomorphic	B-Algorithm
sensors	I-Algorithm
are	O
unlikely	O
to	O
be	O
accurately	O
described	O
by	O
such	O
events	O
,	O
it	O
is	O
a	O
useful	O
way	O
to	O
understand	O
and	O
benchmark	O
the	O
performance	O
of	O
retinomorphic	B-Algorithm
sensors	I-Algorithm
.	O
</s>
<s>
Since	O
is	O
linearly	O
proportional	O
to	O
charge	O
density	O
,	O
and	O
capacitance	O
is	O
linearly	O
proportional	O
to	O
charges	O
on	O
the	O
plates	O
for	O
a	O
given	O
voltage	O
,	O
the	O
capacitance	O
of	O
a	O
retinomorphic	B-Algorithm
sensor	I-Algorithm
also	O
has	O
a	O
power-law	O
dependence	O
on	O
.	O
</s>
<s>
The	O
retinomorphic	O
figure	O
of	O
merit	O
,	O
,	O
is	O
defined	O
as	O
the	O
ratio	O
of	O
the	O
capacitance	O
prefactor	O
and	O
the	O
capacitance	O
of	O
the	O
retinomorphic	B-Algorithm
sensor	I-Algorithm
in	O
the	O
dark	O
:	O
</s>
<s>
This	O
can	O
be	O
carried	O
out	O
by	O
measuring	O
the	O
peak	O
height	O
,	O
,	O
of	O
a	O
retinomorphic	B-Algorithm
sensor	I-Algorithm
in	O
response	O
to	O
a	O
step	O
change	O
in	O
light	O
intensity	O
from	O
0	O
to	O
,	O
for	O
a	O
range	O
of	O
values	O
.	O
</s>
