<s>
Holographic	B-Algorithm
interferometry	I-Algorithm
(	O
HI	O
)	O
is	O
a	O
technique	O
which	O
enables	O
static	O
and	O
dynamic	O
displacements	O
of	O
objects	O
with	O
optically	O
rough	O
surfaces	O
to	O
be	O
measured	O
to	O
optical	O
interferometric	O
precision	O
(	O
i.e.	O
</s>
<s>
Holography	B-Algorithm
is	O
the	O
two-step	O
process	O
of	O
recording	O
a	O
diffracted	O
light	O
field	O
scattered	O
from	O
an	O
object	O
,	O
and	O
performing	O
image	O
rendering	O
.	O
</s>
<s>
This	O
process	O
can	O
be	O
achieved	O
with	O
traditional	O
photographic	O
plates	O
or	O
with	O
a	O
digital	O
sensor	O
array	O
,	O
in	O
digital	B-Algorithm
holography	I-Algorithm
.	O
</s>
<s>
This	O
technique	O
is	O
known	O
as	O
live	O
holographic	B-Algorithm
interferometry	I-Algorithm
.	O
</s>
<s>
This	O
is	O
known	O
as	O
'	O
frozen	O
fringe	O
 '	O
holography	B-Algorithm
.	O
</s>
<s>
Several	O
research	O
groups	O
published	O
papers	O
in	O
1965	O
describing	O
holographic	B-Algorithm
interferometry	I-Algorithm
.	O
</s>
<s>
While	O
the	O
first	O
observations	O
of	O
phenomena	O
that	O
could	O
be	O
ascribed	O
to	O
holographic	B-Algorithm
interferometry	I-Algorithm
were	O
made	O
by	O
Juris	O
Upatnieks	O
in	O
1963	O
the	O
essential	O
feature	O
of	O
the	O
process	O
was	O
not	O
understood	O
until	O
the	O
work	O
of	O
Powell	O
and	O
Stetson	O
.	O
</s>
<s>
This	O
was	O
demonstrated	O
by	O
recording	O
a	O
hologram	B-Algorithm
of	O
the	O
view	O
over	O
one	O
of	O
the	O
mirrors	O
.	O
</s>
<s>
In	O
one	O
of	O
the	O
holograms	B-Algorithm
,	O
however	O
,	O
a	O
dark	O
band	O
was	O
observed	O
in	O
the	O
closest	O
image	O
to	O
the	O
hologram	B-Algorithm
,	O
and	O
it	O
was	O
observed	O
to	O
shift	O
position	O
with	O
perspective	O
.	O
</s>
<s>
This	O
band	O
was	O
not	O
observable	O
in	O
the	O
original	O
laser	O
beam	O
and	O
had	O
to	O
be	O
something	O
created	O
by	O
the	O
holographic	B-Algorithm
process	O
.	O
</s>
<s>
The	O
multiple	O
laser	O
modes	O
were	O
incoherent	O
and	O
did	O
not	O
interfere	O
in	O
the	O
observable	O
laser	O
beam	O
,	O
so	O
why	O
did	O
they	O
interfere	O
in	O
the	O
hologram	B-Algorithm
reconstruction	O
?	O
</s>
<s>
Stetson	O
put	O
forth	O
the	O
idea	O
that	O
each	O
mode	O
existed	O
in	O
both	O
the	O
object	O
and	O
in	O
the	O
reference	O
beam	O
,	O
and	O
each	O
pair	O
recorded	O
a	O
separate	O
hologram	B-Algorithm
in	O
the	O
photographic	O
plate	O
.	O
</s>
<s>
Powell	O
objected	O
to	O
this	O
idea	O
,	O
because	O
it	O
implied	O
that	O
the	O
hologram	B-Algorithm
had	O
the	O
power	O
to	O
coherently	O
reconstruct	O
fields	O
that	O
were	O
incoherent	O
during	O
its	O
recording	O
.	O
</s>
<s>
These	O
consisted	O
of	O
:	O
(	O
1	O
)	O
Recording	O
the	O
reflection	O
of	O
a	O
concentrated	O
laser	O
beam	O
while	O
capturing	O
the	O
entire	O
reference	O
beam	O
on	O
the	O
hologram	B-Algorithm
and	O
adjusting	O
the	O
laser	O
for	O
combinations	O
of	O
off-axis	O
modes	O
.	O
</s>
<s>
(	O
2	O
)	O
Recording	O
double-exposure	O
holograms	B-Algorithm
of	O
an	O
object	O
where	O
the	O
object	O
,	O
the	O
reference	O
beam	O
mirror	O
,	O
and	O
the	O
hologram	B-Algorithm
itself	O
were	O
rotated	O
slightly	O
between	O
exposures	O
.	O
</s>
<s>
(	O
3	O
)	O
Recording	O
holograms	B-Algorithm
of	O
the	O
bottom	O
of	O
a	O
35mm	O
film	O
can	O
while	O
it	O
was	O
vibrating	O
.	O
</s>
<s>
Later	O
,	O
in	O
April	O
1965	O
,	O
Stetson	O
and	O
Powell	O
obtained	O
real-time	O
interference	O
patterns	O
between	O
a	O
real	O
object	O
and	O
its	O
holographic	B-Algorithm
reconstruction	O
.	O
</s>
<s>
Since	O
its	O
introduction	O
,	O
vibrometry	O
by	O
holographic	B-Algorithm
interferometry	I-Algorithm
has	O
become	O
commonplace	O
.	O
</s>
<s>
Powell	O
and	O
Stetson	O
have	O
shown	O
that	O
the	O
fringes	O
of	O
the	O
time-averaged	O
hologram	B-Algorithm
of	O
a	O
vibrating	O
object	O
correspond	O
to	O
the	O
zeros	O
of	O
the	O
Bessel	O
function	O
,	O
where	O
is	O
the	O
modulation	O
depth	O
of	O
the	O
phase	O
modulation	O
of	O
the	O
optical	O
field	O
at	O
on	O
the	O
object	O
.	O
</s>
<s>
In	O
off-axis	O
configuration	O
,	O
with	O
a	O
slow	O
camera	O
and	O
a	O
laser	O
diode	O
,	O
holographic	B-Algorithm
interferometry	I-Algorithm
is	O
sensitive	O
enough	O
to	O
enable	O
wide-field	O
,	O
laser	O
Doppler	O
imaging	O
of	O
optical	O
fluctuations	O
in	O
amplitude	O
and	O
phase	O
,	O
either	O
with	O
a	O
slow	O
or	O
a	O
fast	O
camera	O
.	O
</s>
<s>
video	O
rate	O
)	O
camera	O
will	O
record	O
time-averaged	O
holographic	B-Algorithm
interferograms	O
which	O
will	O
result	O
in	O
lowpass	O
filtering	O
of	O
the	O
optical	O
fluctuation	O
signal	O
.	O
</s>
