Spectral line polarimetry with a channeled polarimeter.

Channeled spectropolarimetry or spectral polarization modulation is an accurate technique for measuring the continuum polarization in one shot with no moving parts. We show how a dual-beam implementation also enables spectral line polarimetry at the intrinsic resolution, as in a classic beam-splitting polarimeter. Recording redundant polarization information in the two spectrally modulated beams of a polarizing beam-splitter even provides the possibility to perform a postfacto differential transmission correction that improves the accuracy of the spectral line polarimetry. We perform an error analysis to compare the accuracy of spectral line polarimetry to continuum polarimetry, degraded by a residual dark signal and differential transmission, as well as to quantify the impact of the transmission correction. We demonstrate the new techniques with a blue sky polarization measurement around the oxygen A absorption band using the groundSPEX instrument, yielding a polarization in the deepest part of the band of 0.160±0.010, significantly different from the polarization in the continuum of 0.2284±0.0004. The presented methods are applicable to any dual-beam channeled polarimeter, including implementations for snapshot imaging polarimetry.

Fast & Furious focal-plane wavefront sensing.

We present two complementary algorithms suitable for using focal-plane measurements to control a wavefront corrector with an extremely high-spatial resolution. The algorithms use linear approximations to iteratively minimize the aberrations seen by the focal-plane camera. The first algorithm, Fast & Furious (FF), uses a weak-aberration assumption and pupil symmetries to achieve fast wavefront reconstruction. The second algorithm, an extension to FF, can deal with an arbitrary pupil shape; it uses a Gerchberg-Saxton (GS)-style error reduction to determine the pupil amplitudes. Simulations and experimental results are shown for a spatial-light modulator controlling the wavefront with a resolution of 170×170 pixels. The algorithms increase the Strehl ratio from ∼0.75 to 0.98-0.99, and the intensity of the scattered light is reduced throughout the whole recorded image of 320×320 pixels. The remaining wavefront rms error is estimated to be ∼0.15 rad with FF and ∼0.10 rad with FF-GS.

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.

Calibrating a high-resolution wavefront corrector with a static focal-plane camera.

We present a method to calibrate a high-resolution wavefront (WF)-correcting device with a single, static camera, located in the focal-plane; no moving of any component is needed. The method is based on a localized diversity and differential optical transfer functions to compute both the phase and amplitude in the pupil plane located upstream of the last imaging optics. An experiment with a spatial light modulator shows that the calibration is sufficient to robustly operate a focal-plane WF sensing algorithm controlling a WF corrector with 40,000 degrees of freedom. We estimate that the locations of identical WF corrector elements are determined with a spatial resolution of 0.3% compared to the pupil diameter.

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.

Joint optimization of phase diversity and adaptive optics: demonstration of potential.

We study different possibilities to use adaptive optics (AO) and phase diversity (PD) together in a jointly optimized system. The potential of the joint system is demonstrated through numerical simulations. We find that the most significant benefits are obtained from the improved deconvolution of AO-corrected wavefronts and the additional wavefront sensor (WFS) information that reduces the computational demands of PD algorithms. When applied together, it is seen that the image error can be reduced by 20% compared to traditional PD, working with one focused and one defocused camera image, and the computational load is reduced by a factor of 20 compared to a more reliable PD algorithm requiring more camera images. In addition, we find that the system performance can be optimized by adjusting the magnitude of the applied diversity wavefronts.

Spectral modulation for full linear polarimetry.

Linear (spectro) polarimetry is usually performed using separate photon flux measurements after spatial or temporal polarization modulation. Such classical polarimeters are limited in sensitivity and accuracy by systematic effects and noise. We describe a spectral modulation principle that is based on encoding the full linear polarization properties of light in its spectrum. Such spectral modulation is obtained with an optical train of an achromatic quarter-wave retarder, an athermal multiple-order retarder, and a polarizer. The emergent spectral modulation is sinusoidal with its amplitude scaling with the degree of linear polarization and its phase scaling with the angle of linear polarization. The large advantage of this passive setup is that all polarization information is, in principle, contained in a single spectral measurement, thereby eliminating all differential effects that potentially create spurious polarization signals. Since the polarization properties are obtained through curve fitting, the susceptibility to noise is relatively low. We provide general design options for a spectral modulator and describe the design of a prototype modulator. Currently, the setup in combination with a dedicated retrieval algorithm can be used to measure linear polarization signals with a relative accuracy of 5%.

Evaluation of seeing-induced cross talk in tip-tilt-corrected solar polarimetry.

We reanalyze the effects of atmosphere-induced image motions on the measurement of solar polarized light using a formalism developed by Lites. Our reanalysis is prompted by the advent of adaptive optics (AO) systems that reduce image motion and higher-order aberrations, by the availability of liquid crystals as modulation devices, and by the need to understand how best to design polarimeters for future telescopes such as the Advanced Technology Solar Telescope. In this first attempt to understand the major issues, we analyze the influence of residual image motion (tip-tilt) corrections of operational AO systems on the cross talk between Stokes parameters and present results for several polarization analysis schemes. Higher-order wave-front corrections are left for future research. We also restrict our discussion to the solar photosphere, which limits several important parameters of interest, using some recent magnetoconvection simulations.