<s>
For	O
digital	B-Algorithm
image	I-Algorithm
processing	I-Algorithm
,	O
the	O
Focus	B-Algorithm
recovery	I-Algorithm
from	O
a	O
defocused	O
image	O
is	O
an	O
ill-posed	O
problem	O
since	O
it	O
loses	O
the	O
component	O
of	O
high	O
frequency	O
.	O
</s>
<s>
Most	O
of	O
the	O
methods	O
for	O
focus	B-Algorithm
recovery	I-Algorithm
are	O
based	O
on	O
depth	O
estimation	O
theory	O
.	O
</s>
<s>
The	O
Linear	B-Algorithm
canonical	I-Algorithm
transform	I-Algorithm
(	O
LCT	O
)	O
gives	O
a	O
scalable	O
kernel	O
to	O
fit	O
many	O
well-known	O
optical	O
effects	O
.	O
</s>
<s>
In	O
photography	O
,	O
depth	O
of	O
field	O
(	O
DOF	O
)	O
means	O
an	O
effective	O
focal	B-Algorithm
length	I-Algorithm
.	O
</s>
<s>
The	O
important	O
measure	O
related	O
to	O
DOF	O
is	O
the	O
lens	O
aperture	B-General_Concept
.	O
</s>
<s>
Decreasing	O
the	O
diameter	O
of	O
aperture	B-General_Concept
increases	O
focus	O
and	O
lowers	O
resolution	O
and	O
vice	O
versa	O
.	O
</s>
<s>
The	O
disturbance	O
of	O
diffraction	O
depends	O
on	O
two	O
circumstance	O
parameters	O
,	O
the	O
size	O
of	O
aperture	B-General_Concept
and	O
the	O
interfiled	O
distance	O
.	O
</s>
<s>
The	O
further	O
distance	O
z	O
or	O
the	O
smaller	O
aperture	B-General_Concept
(	O
x1	O
,	O
y1	O
)	O
causes	O
a	O
greater	O
diffraction	O
.	O
</s>
<s>
In	O
a	O
real	O
imaging	O
environment	O
,	O
the	O
depths	O
of	O
objects	O
comparing	O
to	O
the	O
aperture	B-General_Concept
are	O
usually	O
not	O
enough	O
to	O
lead	O
to	O
serious	O
diffraction	O
.	O
</s>
<s>
Small	O
aperture	B-General_Concept
,	O
small	O
blurring	O
radius	O
,	O
few	O
wave	O
information	O
.	O
</s>
<s>
Loses	O
details	O
in	O
comparing	O
to	O
a	O
large	O
aperture	B-General_Concept
.	O
</s>
<s>
Both	O
of	O
them	O
are	O
related	O
to	O
aperture	B-General_Concept
size	O
.	O
</s>
<s>
As	O
the	O
meaning	O
of	O
"	O
canonical	O
"	O
,	O
the	O
linear	B-Algorithm
canonical	I-Algorithm
transform	I-Algorithm
(	O
LCT	O
)	O
is	O
a	O
scalable	O
transform	O
that	O
connects	O
to	O
many	O
important	O
kernels	O
such	O
as	O
the	O
Fresnel	O
transform	O
,	O
Fraunhofer	O
transform	O
and	O
the	O
fractional	O
Fourier	O
transform	O
.	O
</s>
<s>
Consider	O
a	O
general	O
imaging	O
system	O
with	O
object	O
distance	O
z0	O
,	O
focal	B-Algorithm
length	I-Algorithm
of	O
the	O
thin	O
lens	O
f	O
and	O
an	O
imaging	O
distance	O
z1	O
.	O
</s>
<s>
The	O
effect	O
of	O
the	O
propagation	O
in	O
freespace	O
acts	O
as	O
nearly	O
a	O
chirp	B-Application
convolution	B-Language
,	O
that	O
is	O
,	O
the	O
formula	O
of	O
diffraction	O
.	O
</s>
<s>
Besides	O
,	O
the	O
effect	O
of	O
the	O
propagation	O
in	O
thin	O
lens	O
acts	O
as	O
a	O
chirp	B-Application
multiplication	O
.	O
</s>
<s>
It	O
does	O
not	O
consider	O
aperture	B-General_Concept
size	O
.	O
</s>
