Jacopo Antonello

Semidefinite programming for model-based sensorless adaptive optics

Wavefront sensorless adaptive optics methodologies are widely considered in scanning fluorescence microscopy where direct wavefront sensing is challenging. In these methodologies, aberration correction is performed by sequentially changing the settings of the adaptive element until a predetermined image quality metric is optimized. An efficient aberration correction can be achieved by modeling the image quality metric with a quadratic polynomial. We propose a new method to compute the parameters of the polynomial from experimental data. This method guarantees that the quadratic form in the polynomial is semidefinite, resulting in a more robust computation of the parameters with respect to existing methods. In addition, we propose an algorithm to perform aberration correction requiring a minimum of N+1 measurements, where N is the number of considered aberration modes. This algorithm is based on a closed-form expression for the exact optimization of the quadratic polynomial. Our arguments are corroborated by experimental validation in a laboratory environment.

Modal-based phase retrieval for adaptive optics.

We consider using phase retrieval (PR) to correct phase aberrations in an optical system. Three measurements of the point-spread function (PSF) are collected to estimate an aberration. For each measurement, a different defocus aberration is applied with a deformable mirror (DM). Once the aberration is estimated using a PR algorithm, we apply the aberration correction with the DM, and measure the residual aberration using a Shack-Hartmann wavefront sensor. The extended Nijboer-Zernike theory is used for modelling the PSF. The PR problem is solved using both an algorithm called PhaseLift, which is based on matrix rank minimization, and another algorithm based on alternating projections. For comparison, we include the results achieved using a classical PR algorithm, which is based on alternating projections and uses the fast Fourier transform.

Optimization-based wavefront sensorless adaptive optics for multiphoton microscopy

Optical aberrations have detrimental effects in multiphoton microscopy. These effects can be curtailed by implementing model-based wavefront sensorless adaptive optics, which only requires the addition of a wavefront shaping device, such as a deformable mirror (DM) to an existing microscope. The aberration correction is achieved by maximizing a suitable image quality metric. We implement a model-based aberration correction algorithm in a second-harmonic microscope. The tip, tilt, and defocus aberrations are removed from the basis functions used for the control of the DM, as these aberrations induce distortions in the acquired images. We compute the parameters of a quadratic polynomial that is used to model the image quality metric directly from experimental input-output measurements. Finally, we apply the aberration correction by maximizing the image quality metric using the least-squares estimate of the unknown aberration.

Coma aberrations in combined two- and three-dimensional STED nanoscopy.

Stimulated emission depletion (STED) microscopes, like all super-resolution methods, are sensitive to aberrations. Of particular importance are aberrations that affect the quality of the depletion focus, which requires a point of near-zero intensity surrounded by strong illumination. We present analysis, modeling, and experimental measurements that show the effects of coma aberrations on depletion patterns of two-dimensional (2D) and three-dimensional (3D) STED configurations. Specifically, we find that identical coma aberrations create focal shifts in opposite directions in 2D and 3D STED. This phenomenon could affect the precision of microscopic measurements and has ramifications for the efficacy of combined 2D/3D STED systems.

Snapshot coherence-gated direct wavefront sensing for multi-photon microscopy

Deep imaging in turbid media such as biological tissue is challenging due to scattering and optical aberrations. Adaptive optics has the potential to compensate the tissue aberrations. We present a wavefront sensing scheme for multi-photon scanning microscopes using the pulsed, near-infrared light reflected back from the sample utilising coherence gating and a confocal pinhole to isolate the light from a layer of interest. By interfering the back-reflected light with a tilted reference beam, we create a fringe pattern with a known spatial carrier frequency in an image of the back-aperture plane of the microscope objective. The wavefront aberrations distort this fringe pattern and thereby imprint themselves at the carrier frequency, which allows us to separate the aberrations in the Fourier domain from low spatial frequency noise. A Fourier analysis of the modulated fringes combined with a virtual Shack-Hartmann sensor for smoothing yields a modal representation of the wavefront suitable for correction. We show results with this method correcting both DM-induced and sample-induced aberrations in rat tail collagen fibres as well as a Hoechst-stained MCF-7 spheroid of cancer cells.

Aberrations in 4Pi Microscopy

The combination of two opposing objective lenses in 4Pi fluorescence microscopy significantly improves the axial resolution and increases the collection efficiency. Combining 4Pi microscopy with other super-resolution techniques has resulted in the highest three-dimensional (3D) resolution in fluorescence microscopy to date. It has previously been shown that the performance of 4Pi microscopy is significantly affected by aberrations. However, a comprehensive description of 4Pi microscope aberrations has been missing. In this paper, we introduce an approach to describe aberrations in a 4Pi cavity through a new functional representation. We discuss the focusing properties of 4Pi systems affected by aberrations and discuss the implications for adaptive optics schemes for 4Pi microscopes based on this new insight.

Coherence-gated wavefront sensing for microscopy using fringe analysis

We have implemented a coherence-gated wavefront sensor on a two-photon excitation microscope. We used the backscattered near-infrared light from the sample to interfere with an optically flat reference beam. By applying a known waverfront tilt in the reference beam, a fringe pattern emerged on the camera. The deformmation of the wavefront due to the turbid media under study warps the fring pattern, similar to frequency modulation. Through Fourier transform analysis of the modulated fringe pattern we were able to determine the wave fornt aberrations induced by synthetic and biological samples. By defocussing the microscope objective and measuring the wavefront deformation we established that the errors are reproduceible to within λ/227 for the defocus mode.

Data driven identification and aberration correction for model-based sensorless adaptive optics

Wavefront sensorless adaptive optics methodologies are considered in many applications where the deployment of a dedicated wavefront sensor is inconvenient, such as in fluorescence microscopy. In these methodologies, aberration correction is achieved by sequentially changing the settings of the adaptive optical element until a predetermined imaging quality metric is optimised. Reducing the time required for this optimisation is a challenge. In this paper, a two stage data driven optimisation procedure is presented and validated in a laboratory environment. In the first stage, known aberrations are introduced by a deformable mirror and the corresponding intensities are measured by a photodiode masked by a pinhole. A generic quadratic metric is fitted to this collection of aberrations and intensity measurements. In the second stage, this quadratic metric is used in order to estimate and correct for optical aberrations. A closed form expression for the optimisation of the quadratic metric is derived by solving a linear system of equations. This requires a minimum of N +1 pairs of deformable mirror settings and intensity measurements, where N is the number of modes of the aberrations.

Sensorless adaptive optics for isoSTED nanoscopy

The presence of aberrations is a major concern when using fluorescence microscopy to image deep inside tissue. Aberrations due to refractive index mismatch and heterogeneity of the specimen under investigation cause severe reduction in the amount of fluorescence emission that is collected by the microscope. Furthermore, aberrations adversely affect the resolution, leading to loss of fine detail in the acquired images. These phenomena are particularly troublesome for super-resolution microscopy techniques such as isotropic stimulated-emission-depletion microscopy (isoSTED), which relies on accurate control of the shape and co-alignment of multiple excitation and depletion foci to operate as expected and to achieve the super-resolution effect. Aberrations can be suppressed by implementing sensorless adaptive optics techniques, whereby aberration correction is achieved by maximising a certain image quality metric. In confocal microscopy for example, one can employ the total image brightness as an image quality metric. Aberration correction is subsequently achieved by iteratively changing the settings of a wavefront corrector device until the metric is maximised. This simplistic approach has limited applicability to isoSTED microscopy where, due to the complex interplay between the excitation and depletion foci, maximising the total image brightness can lead to introducing aberrations in the depletion foci. In this work we first consider the effects that different aberration modes have on isoSTED microscopes. We then propose an iterative, wavelet-based aberration correction algorithm and evaluate its benefits.

Aberrations in stimulated emission depletion (STED) microscopy.

Like all methods of super-resolution microscopy, stimulated emission depletion (STED) microscopy can suffer from the effects of aberrations. The most important aspect of a STED microscope is that the depletion focus maintains a minimum, ideally zero, intensity point that is surrounded by a region of higher intensity. It follows that aberrations that cause a non-zero value of this minimum intensity are the most detrimental, as they inhibit fluorescence emission even at the centre of the depletion focus. We present analysis that elucidates the nature of these effects in terms of the different polarisation components at the focus for two-dimensional and three-dimensional STED resolution enhancement. It is found that only certain low-order aberration modes can affect the minimum intensity at the Gaussian focus. This has important consequences for the design of adaptive optics aberration correction systems.