<s>
In	O
signal	O
processing	O
,	O
apodization	B-Algorithm
(	O
from	O
Greek	O
"	O
removing	O
the	O
foot	O
"	O
)	O
is	O
the	O
modification	O
of	O
the	O
shape	O
of	O
a	O
mathematical	O
function	O
.	O
</s>
<s>
In	O
optics	B-Algorithm
,	O
it	O
is	O
primarily	O
used	O
to	O
remove	O
Airy	O
disks	O
caused	O
by	O
diffraction	O
around	O
an	O
intensity	O
peak	O
,	O
improving	O
the	O
focus	O
.	O
</s>
<s>
The	O
term	O
apodization	B-Algorithm
is	O
used	O
frequently	O
in	O
publications	O
on	O
Fourier-transform	O
infrared	O
(	O
FTIR	O
)	O
signal	O
processing	O
.	O
</s>
<s>
An	O
example	O
of	O
apodization	B-Algorithm
is	O
the	O
use	O
of	O
the	O
Hann	B-Algorithm
window	I-Algorithm
in	O
the	O
fast	O
Fourier	B-Algorithm
transform	I-Algorithm
analyzer	O
to	O
smooth	O
the	O
discontinuities	O
at	O
the	O
beginning	O
and	O
end	O
of	O
the	O
sampled	O
time	O
record	O
.	O
</s>
<s>
An	O
apodizing	B-Algorithm
filter	O
can	O
be	O
used	O
in	O
digital	O
audio	O
processing	O
instead	O
of	O
the	O
more	O
common	O
brick-wall	O
filters	O
,	O
in	O
order	O
to	O
avoid	O
the	O
pre-ringing	B-Algorithm
that	O
the	O
latter	O
introduces	O
.	O
</s>
<s>
This	O
presents	O
a	O
problem	O
for	O
the	O
Fourier	B-Algorithm
transformation	I-Algorithm
,	O
as	O
it	O
averages	O
the	O
oscillatory	O
signal	O
across	O
the	O
length	O
of	O
the	O
time-domain	O
measurement	O
.	O
</s>
<s>
The	O
software	O
allows	O
“	O
apodization	B-Algorithm
”	O
,	O
the	O
removal	O
of	O
the	O
front	O
and	O
back	O
section	O
of	O
the	O
transient	O
signal	O
from	O
consideration	O
in	O
the	O
FT	O
calculation	O
.	O
</s>
<s>
Thus	O
,	O
apodization	B-Algorithm
improves	O
the	O
resolution	O
of	O
the	O
resulting	O
mass	O
spectrum	O
.	O
</s>
<s>
Apodization	B-Algorithm
is	O
applied	O
to	O
NMR	O
signals	O
before	O
discrete	O
Fourier	B-Algorithm
Transformation	I-Algorithm
.	O
</s>
<s>
In	O
order	O
to	O
reduce	O
truncation	O
artifacts	O
,	O
the	O
signals	O
are	O
subjected	O
to	O
apodization	B-Algorithm
with	O
different	O
types	O
of	O
window	B-Language
functions	I-Language
.	O
</s>
<s>
In	O
optical	O
design	O
jargon	O
,	O
an	O
apodization	B-Algorithm
function	O
is	O
used	O
to	O
purposely	O
change	O
the	O
input	O
intensity	O
profile	O
of	O
an	O
optical	O
system	O
,	O
and	O
it	O
may	O
be	O
a	O
complicated	O
function	O
to	O
tailor	O
the	O
system	O
to	O
certain	O
properties	O
.	O
</s>
<s>
In	O
medical	B-Application
ultrasonography	I-Application
,	O
the	O
effect	O
of	O
grating	O
lobes	O
can	O
be	O
reduced	O
by	O
activating	O
ultrasonic	B-Algorithm
transducer	I-Algorithm
elements	O
using	O
variable	O
voltages	O
in	O
apodization	B-Algorithm
process	O
.	O
</s>
<s>
These	O
are	O
not	O
strictly	O
an	O
example	O
of	O
apodization	B-Algorithm
,	O
since	O
the	O
diaphragm	O
does	O
not	O
produce	O
a	O
smooth	O
transition	O
to	O
zero	O
intensity	O
,	O
nor	O
does	O
it	O
provide	O
shaping	O
of	O
the	O
intensity	O
profile	O
(	O
beyond	O
the	O
obvious	O
all-or-nothing	O
,	O
"	O
top	O
hat	O
"	O
transmission	O
of	O
its	O
aperture	O
)	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
Minolta/Sony	B-Algorithm
STF	I-Algorithm
135mm	I-Algorithm
f/2.8	I-Algorithm
T4.5	I-Algorithm
lens	I-Algorithm
however	O
,	O
has	O
a	O
special	O
design	O
introduced	O
in	O
1999	O
,	O
which	O
accomplishes	O
this	O
by	O
utilizing	O
a	O
concave	O
neutral-gray	O
tinted	O
lens	O
element	O
as	O
an	O
apodization	B-Algorithm
filter	I-Algorithm
,	O
thereby	O
producing	O
a	O
pleasant	O
bokeh	O
.	O
</s>
<s>
The	O
same	O
optical	O
effect	O
can	O
be	O
achieved	O
by	O
combining	O
depth-of-field	O
bracketing	O
with	O
multi	O
exposure	O
,	O
as	O
implemented	O
in	O
the	O
Minolta	B-Algorithm
Maxxum	I-Algorithm
7	I-Algorithm
's	O
STF	B-Algorithm
function	O
.	O
</s>
<s>
In	O
2014	O
,	O
Fujifilm	O
announced	O
a	O
lens	O
utilizing	O
a	O
similar	O
apodization	B-Algorithm
filter	I-Algorithm
in	O
the	O
Fujinon	O
XF	O
56mm	O
F1.2	O
R	O
APD	O
lens	O
.	O
</s>
<s>
In	O
2017	O
,	O
Sony	O
introduced	O
the	O
E-mount	B-Algorithm
full-frame	O
lens	O
Sony	B-Algorithm
FE	I-Algorithm
100mm	I-Algorithm
F2.8	I-Algorithm
STF	I-Algorithm
GM	I-Algorithm
OSS	I-Algorithm
(	O
SEL-100F28GM	O
)	O
based	O
on	O
the	O
same	O
optical	O
Smooth	B-Algorithm
Trans	I-Algorithm
Focus	I-Algorithm
principle	O
.	O
</s>
<s>
Simulation	O
of	O
a	O
Gaussian	O
laser	O
beam	O
input	O
profile	O
is	O
also	O
an	O
example	O
of	O
apodization	B-Algorithm
.	O
</s>
<s>
Photon	O
sieves	O
provide	O
a	O
relatively	O
easy	O
way	O
to	O
achieve	O
tailored	O
optical	O
apodization	B-Algorithm
.	O
</s>
<s>
Apodization	B-Algorithm
is	O
used	O
in	O
telescope	O
optics	B-Algorithm
in	O
order	O
to	O
improve	O
the	O
dynamic	O
range	O
of	O
the	O
image	O
.	O
</s>
<s>
Generally	O
,	O
apodization	B-Algorithm
reduces	O
the	O
resolution	O
of	O
an	O
optical	O
image	O
;	O
however	O
because	O
it	O
reduces	O
diffraction	O
edge	O
effects	O
,	O
it	O
can	O
actually	O
enhance	O
certain	O
small	O
details	O
.	O
</s>
