In
two-photon microscopy,
the excitation beam (red solid lines) consists of light from
a pulsed laser that is focused inside the specimen.
Because of
two-photon absorption,
most of the fluorescence emission (blue solid lines)
is coming from the focal spot.
By scanning the focal spot within a volume and collecting the emitted fluorescence
with a
PMT,
a 3D reconstruction of the specimen can be made.

Since the distribution of the
index of refraction
is not homogeneous inside the specimen,
optical aberrations
(\( \Phi_a \))
affect both the
resolution
and the maximum depth that can be reached.

To suppress these side effects,
a
DM
can be used to introduce an appropriate aberration
(\( \Phi_d \))
in the excitation beam,
so that it cancels out
with the specimen-induced aberration,
\(\Phi_a - \Phi_d = 0\).

Direct measurement of the aberration \(\Phi_a\)
is a non trivial task and
a
wavefront sensor cannot be easily implemented in this imaging
device. For this
reason, wavefront sensorless adaptive optics is considered.

Research challenge

The challenge of wavefront sensorless adaptive optics
is to determine the unknown aberration \( \Phi_a \)
by taking as few measurements as
possible of the signal \( y \), which is collected with the
PMT.

Development of a solution & experimental validation

A model-based solution
(10.1364/JOSAA.29.002428,
pdf)
was developed. The solution was experimentally validated using the
following optical setup. Here an unknown optical aberration
\( \Phi_a \) is estimated by examining a few measurements
of the signal \(y\). The signal \(y\) is collected with a photodiode that is
covered by a pinhole. The unknown aberration is expressed in
Zernike modes, \(\Phi_a = \sum_i \mathcal{Z}_i x_i\),
with the coefficients \(x_i\) collected into a vector \(\mathbf{x}\).

A Shack-Hartmann
wavefront sensor and a camera measuring the
point-spread function are used to monitor the performance of the
aberration correction. Nevertheless, \(\mathbf{x}\) is determined
using only the measurements of \(y\).