Biomedical Engineering Reference
In-Depth Information
(a)
k
o
Θ
k
r
y
x
Φ
z
N
x
(b)
B
k
0,
y
or
*
Φ
N
y
2
B
k
0,
x
oo
* +
rr
*
B
ro
*
FIgurE 9.6
Digital holography in an off-axis configuration. The off-axis angle θ determines the carrier fre-
quency modulation, and hence the separation of the zero-order and image terms, in the spatial frequency domain.
(a) Angle definition and (b) Fourier spectrum.
Very often, the azimuth angle is chosen as π/4, 3π/4, and so on, so that the carrier frequency modu-
lates the signal equally in the
k
x
and
k
y
direction. It does not have to be so, but it is more elegant and more
effective for spectral separation of zero-order terms. The ideal off-axis angle is that for which complete
separation of the imaging and zero-order terms is achieved. However, this only occurs when the object
wave as a diffraction-limited discrete bandwidth
B
that satisfies
NA
n
N x
M
∆
≤
N
x
x
B
=
2
2
,
(9.11)
λ
2
+
3 2
where
NA
and
M
are the numerical aperture and magnification of the microscope objective and where,
the sake of simplicity, we have assumed the hologram to be square:
N
x
thus represents the number of
pixels of the hologram in each direction.
In Equation 9.11, (
NA
/
n
λ) represents the physical cutoff frequency of the microscope objective. When
complete separation is possible, a simple binary mask can be designed to eliminate all spatial frequency
content but that of the desired imaging term. If complete separation is not possible, one can still use this
