140 4.5 Light Microscopy of Deep or Thick Samples
the aberration due to optical inhomogeneity in thick samples, since corrections for the phase
variations can be made numerically in reciprocal space.
One potential problem is that the detected diffraction pattern consists of just intensity
data and does not contain information concerning the relative phase of a scattered beam
from a particular part of the sample. However, this phase information can be recovered since
the illuminated area moves over the sample to generate redundancy in the data since there
is always some overlap in the sampled regions, which can be used to retrieve the phase from
the scattered object using an algorithm called the “pytchographic iterative engine” (Faulkner
and Rodenburg, 2004).
The main issues with ptychography are the huge volumes of data captured (a gigapixel
image for each illuminated area on the sample) and a requirement for potentially very long
acquisition time scales. A typical single dataset from a static biological sample contains
hundreds of images to obtain sufficient information from different diffraction angles. The
LED array approach improves the time resolution issue to some extent; however, to monitor
any time-resolved process potentially involves datasets that would fill a normal computer
hard drive very quickly.
4.5.4 MULTIPHOTON EXCITATION
Multiphoton excitation (MPE) is a nonlinear optical effect. In MPE microscopy, the tran
sition energy required to excite a ground state electron to a higher level during fluores
cence excitation in a fluorophore can in principle be contributed from the summation of the
equivalent quantum energies of several photons, provided these photons are all absorbed
within a suitably narrow time window. In two-photon excitation microscopy (or 2PE micros
copy), the initial excitation of a ground state electron is made following the absorption of two
photons of the same wavelength λ during a time window of only ~10−18 s, since this is the
lifetime of a virtual state halfway between the excited and ground states (Figure 4.4a). This
means that λ is twice that of the required for the equivalent single-photon excitation process,
and so for visible light, two-photon excitation fluorescence detection near IR (NIR) incident
wavelengths (~ a micron) are typically used.
Two-photon absorption, also known as the Kerr effect, is described as a third-order non
linear effect because of the dependence of the complex polarization parameter of the optical
medium on the cubic term of the electrical susceptibility. Since two photons are required,
the rate of two-photon absorption at a depth z depends on the square of the incident photon
intensity I, whereas for one-photon absorption, the dependence is linear, such that the overall
rate has a quadratic dependence:
(4.20)
d
d
l
z
I
I
= −
+
(
)
α
β 2
where α and β are the one- and two-photon absorption coefficients, respectively.
The longer wavelengths required result is less scattering from biological tissue, for
example, Rayleigh scattering, for which the length scale of the scattering objects is much
smaller than the incident wavelength, has a very sensitive 1/λ4 dependence. Much of
the scattering in tissue is also due to Mie scattering, that is, from objects of size com
parable to or greater than λ, for which there is a less sensitive dependence of λ than for
Rayleigh scattering, but still a reduction at higher wavelengths. This is significant since
at depths greater than a few hundred microns, tissues are essentially opaque at visible
light wavelengths due to scattering, whereas they are still optically transparent at the NIR
wavelength used in two-photon microscopy. The geometrical scattering regime applies to
scattering objects whose effective radius r is at least an order of magnitude greater than the
wavelength of light.
The measure of the ability of an object to scatter can be characterized by its scattering cross-
section. The cross-section σ can be deduced from the Mie scattering model for any general