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.

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 $$y$$.

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 model-free algorithm

 Summary of the experiment