Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy

Abstract

We report on the introduction of active optical elements into confocal and multiphoton microscopes in order to reduce the sample-induced aberration. Using a flexible membrane mirror as the active element, the beam entering the rear of the microscope objective is altered to produce the smallest point spread function once it is brought to a focus inside the sample. The conventional approach to adaptive optics, commonly used in astronomy, is to utilise a wavefront sensor to determine the required mirror shape. We have developed a technique that uses optimisation algorithms to improve the returned signal without the use of a wavefront sensor. We have investigated a number of possible optimisation methods, covering hill climbing, genetic algorithms, and more random search methods. The system has demonstrated a significant enhancement in the axial resolution of a confocal microscope when imaging at depth within a sample. We discuss the trade-offs of the various approaches adopted, comparing speed with resolution enhancement.

Semidefinite programming for model-based sensorless adaptive optics

“…Optimization (13) belongs to the realm of semidefinite programming [45]. A convenient tool for formulating Eq.…”

“…This latter is related to D in Eq. (13). A QR factorization can be used in order to compress the second-order cone constraint implicit in the cost function of Eq.…”

“…These include hill-climbing algorithms [12,13], genetic algorithms [13][14][15][16][17], image-based algorithms [18,19], conjugate gradient methods [20], stochastic parallel gradient descent methods [21], and the Nelder-Mead simplex algorithm [11,22,23]. Such general methodologies require a large number of measurements of the metric [2,24,25] and may not converge to the global optimum [23,26].…”

“…Such general methodologies require a large number of measurements of the metric [2,24,25] and may not converge to the global optimum [23,26]. Reducing the number of necessary measurements is a critical factor for the overall image acquisition time [12,13] and for inhibiting side effects, such as phototoxicity and photobleaching [2].…”

Dynamic closed-loop system for focus tracking using a spatial light modulator and a deformable membrane mirror

“…In the past this has been achieved either by measuring the aberrations present in the sample [9] or by using an optimization algorithm that rapidly alters the mirror shape to improve a particular property of the image [8,11]. Both approaches can be implemented using DMMs and SLMs separately as the adaptive optical element, each having its own advantages and drawbacks.…”