T. I. M. van Werkhoven

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.

High-order aberration compensation with multi-frame blind deconvolution and phase diversity image restoration techniques

Context. For accurately measuring intensities and determining magnetic field strengths of small-scale solar (magnetic) structure, knowledge of and compensation for the point spread function is crucial. For images recorded with the Swedish 1-meter Solar Telescope (SST), restoration with multi-frame blind deconvolution (MFBD) and joint phase diverse speckle (JPDS) methods lead to remarkable improvements in image quality but granulation contrasts that are too low, indicating additional stray light. Aims. We propose a method to compensate for stray light from high-order atmospheric aberrations not included in MFBD and JPDS processing. Methods. To compensate for uncorrected aberrations, a reformulation of the image restoration process is proposed that allows the average effect of hundreds of high-order modes to be compensated for by relying on Kolmogorov statistics for these modes. The applicability of the method requires simultaneous measurements of Frieds parameter r(0). The method is tested with simulations as well as real data and extended to include compensation for conventional stray light. Results. We find that only part of the reduction of granulation contrast in SST images is due to uncompensated high-order aberrations. The remainder is still unaccounted for and attributed to stray light from the atmosphere, the telescope with its re-imaging system and to various high-altitude seeing effects. Conclusions. We conclude that statistical compensation of high-order modes is a viable method to reduce the loss of contrast occurring when a limited number of aberrations is explicitly compensated for with MFBD and JPDS processing. We show that good such compensation is possible with only 10 recorded frames. The main limitation of the method is that already MFBD and JPDS processing introduces high-order compensation that, if not taken into account, can lead to over-compensation.

Analysis and interpretation of 15 quarters of Kepler data of the disintegrating planet KIC 12557548 b

The Kepler object KIC 12557548 shows irregular eclipsing behaviour with a constant 15.685 hr period, but strongly varying transit depth. In this paper we fit individual eclipses, in addition to fitting binned light curves, to learn more about the process underlying the eclipse depth variation. Additionally, we put forward observational constraints that any model of this planet-star system will have to match. We find two quiescent spells of ~30 orbital periods each where the transit depth is 0.5% deep transits are followed by apparently no transit at all. Apart from these isolated events we find neither significant correlation between consecutive transit depths nor a correlation between transit depth and stellar intensity. We find a three-sigma upper limit for the secondary eclipse of 4.9*10^-5, consistent with a planet candidate with a radius of less than 4600 km. Using the short cadence data we find that a 1-D exponential dust tail model is insufficient to explain the data. We improved our model to a 2-D, two-component dust model with an opaque core and an exponential tail. Using this model we fit individual eclipses observed in short cadence mode. We find an improved fit of the data, quantifying earlier suggestions by Budaj (2013) of the necessity of at least two components. We find that deep transits have most absorption in the tail, and not in a disk-shaped, opaque coma, but the transit depth and the total absorption show no correlation with the tail length.

S-DIMM+ height characterization of day-time seeing using solar granulation

Context. To evaluate site quality and to develop multi-conjugative adaptive optics systems for future large solar telescopes, characterization of contributions to seeing from heights up to at least ...

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.

Dusty tails of evaporating exoplanets. II. Physical modelling of the KIC 12557548b light curve

Evaporating rocky exoplanets, such as KIC 12557548b, eject large amounts of dust grains, which can trail the planet in a comet-like tail. When such objects occult their host star, the resulting transit signal contains information about the dust in the tail. We aim to use the detailed shape of the Kepler light curve of KIC 12557548b to constrain the size and composition of the dust grains that make up the tail, as well as the mass loss rate of the planet. Using a self-consistent numerical model of the dust dynamics and sublimation, we calculate the shape of the tail by following dust grains from their ejection from the planet to their destruction due to sublimation. From this dust cloud shape, we generate synthetic light curves (incorporating the effects of extinction and angle-dependent scattering), which are then compared with the phase-folded Kepler light curve. We explore the free-parameter space thoroughly using a Markov chain Monte Carlo method. Our physics-based model is capable of reproducing the observed light curve in detail. Good fits are found for initial grain sizes between 0.2 and 5.6 micron and dust mass loss rates of 0.6 to 15.6 M_earth/Gyr (2-sigma ranges). We find that only certain combinations of material parameters yield the correct tail length. These constraints are consistent with dust made of corundum (Al2O3), but do not agree with a range of carbonaceous, silicate, or iron compositions. Using a detailed, physically motivated model, it is possible to constrain the composition of the dust in the tails of evaporating rocky exoplanets. This provides a unique opportunity to probe to interior composition of the smallest known exoplanets.

Modeling the instrumental polarization of the VLT and E-ELT telescopes with the M&m's code

Polarimetry is a particularly powerful technique when imaging circumstellar environments. Currently most telescopes include more or less advanced polarimetric facilities and large telescopes count on it for their planet-finder instruments like SPHERE-ZIMPOL on the VLT or EPICS on the future E-ELT. One of the biggest limitations of this technique is the instrumental polarization (IP) generated in the telescope optical path, which can often be larger than the signal to be measured. In most cases this instrumental polarization changes over time and is dependent on the errors affecting the optical elements of the system. We have modeled the VLT and E-ELT telescope layouts to characterize the instrumental polarization generated on their optical paths using the M&ms code, an error budget and performance simulator for polarimetric systems. In this study we present the realistic Mueller matrices calculated with M&ms for both systems, with and without the setups to correct for the IP, showing that correction can be achieved, allowing for an accurate polarimetric performance.

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.

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.

FOAM: the modular adaptive optics framework

Control software for adaptive optics systems is mostly custom built and very specific in nature. We have developed FOAM, a modular adaptive optics framework for controlling and simulating adaptive optics systems in various environments. Portability is provided both for different control hardware and adaptive optics setups. To achieve this, FOAM is written in C++ and runs on standard CPUs. Furthermore we use standard Unix libraries and compilation procedures and implemented a hardware abstraction layer in FOAM. We have successfully implemented FOAM on the adaptive optics system of ExPo - a high-contrast imaging polarimeter developed at our institute - in the lab and will test it on-sky late June 2012. We also plan to implement FOAM on adaptive optics systems for microscopy and solar adaptive optics. FOAM is available* under the GNU GPL license and is free to be used by anyone.