Model-based wavefront sensorless aberration correction

Motivation

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.

two-photon microscope with adaptive optics

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 \(y\).

optical breadboard   plant schema
Example: correction of a 1.1 rms rad aberration

The same unknown aberration \(\Phi_a\) is corrected using a model-free algorithm (top row) and the model-based algorithm (bottom row). The residual aberration \(\Phi_a - \Phi_d = 0\) is measured with a Shack-Hartmann wavefront sensor (left column). The point-spread function is measured with a camera (right column).

  \(\Phi_a - \Phi_d\), measured with the SHWS PSF, measured with a camera

 

Summary of the experiment
summary