Biomedical Engineering Reference
In-Depth Information
ϕ
0
(a)
z
0
(b)
n
n
λ
0
λ
0
z
2
z
SHG
z
5
z
1
z
3
λ
=
λ
0
/2
z
4
λ
=
λ
0
/2
z
H
ϕ
1
ϕ
2
ϕ
3
ϕ
4
ϕ
5
ϕ
(
ϕ
0
,
n
,
z
0
)
z
FIgurE 9.14
Determination of axial position from direct SHG phase value. (a) Dependence of the detected SHG
phase on the phase of the fundamental-wavelength illumination at the position of SHG
z
SHG
, as well as on the opti-
cal path length (at SHG wavelength) from there to the plane of interest. (b) The SHG phase of different SHG scatter-
ers relates to their respective axial position.
in the axial direction. In fact, the precision of this method was evaluated at roughly 10-50 nm for
hologram-to-hologram comparison and 10 nm for comparison within the same hologram (Shaffer et
al
.
, 2010a). On the other hand, it also raises the problem of determining the position of two or more
particles located more than one fundamental wavelength apart in the axial direction. Even worst, for
discrete SHG scatterers, it is impossible to rely on unwrapping algorithms, because the wavefront is
discontinuous. Without a priori knowledge, recourse to the first method presented here is the only way
to lift the 2π phase ambiguity.
This method, unlike the first one, is not based on an imaging principle, but only on direct phase obser-
vation. Accordingly, there is, in principle, no need to numerically propagate the SHG field to form in
focus images. The SHG phase might very well be compared right in the hologram plane, which reduces
the required processing steps and considerably shortens the processing time. However, this method will
work only as long as the respective phase patterns of the SHG scatterers can be spatially (laterally or axi-
ally) resolved. At high nanoparticle densities, this could require numerical field propagation. Even then,
the hologram will most likely need to be reconstructed only once, which makes this method much faster
than the other one, enough to work in real time at video frame rates.
9.6.3 optical Phase conjugation imaging
Focusing or imaging through turbid media is actively sought for. However, the nature of turbid media
prevents from doing so efficiently. By definition, a turbid medium is a medium that has very inhomoge-
neous, possibly random optical properties. Light propagating through such medium has its wavefront
and polarization state seriously perturbed. Naive attempts to focus light or image a subject in a turbid
medium result in very blurry, deformed focal spots or unrecognizable images.
One solution to overcome this problem is to use optical phase conjugation to precompensate for the
effects of the turbid medium. Optical phase conjugation is a two-step technique that first requires to
fully characterize the wavefront distortion induced by the medium, and then engineer an illumination
that counterbalances it. In principle, this should allow focusing or imaging through turbid medium with
results comparable to those achievable in a nondispersive, nonscattering, uniform environment.
Hsieh et al
.
have recently demonstrated the efficiency of an optical phase conjugation microscope rely-
ing on holographic SHG characterization of the turbid medium (Hsieh et al
.
, 2010a,c). Their approach
