Pyramid vs Shack-Hartmann Wavefront Sensors: Sensitivity Gain

Adaptive optics systems use wavefront sensors (specifically Shack-Hartmann sensors) to analyze incoming starlight. These sensors consist of arrays of small lenses that form images of a reference star. The computer analyzes these images to determine how the wavefront has been distorted by atmospheric turbulence. Based on this analysis, the system adjusts the mirror shape several times per second to compensate for atmospheric distortions, effectively 'subtracting' atmospheric effects from the observed image.

Adaptive optics compensates for atmospheric distortions by deforming a mirror under computer control, producing images nearly as sharp as space-based observatories. The system requires reference stars, with eight lasers creating artificial stars by exciting sodium atoms in the upper atmosphere. Wavefront cameras (ELVIS, LISA, FReD) continuously monitor distortions and transmit data for real-time correction. The MORFEO module uses two additional deformable mirrors to build 3D atmospheric distortion maps across three height slices, enabling correction at multiple atmospheric layers simultaneously.

Extreme adaptive optics (XAO) pushes AO to deliver diffraction-limited performance over narrow fields for exoplanet imaging. Unlike conventional AO targeting wide fields, XAO sacrifices coverage for ultimate correction quality. The Subaru XAO system demonstrates this: an 8-meter telescope beam compressed to ~1 cm, featuring a 20mm deformable mirror with 2000 actuators at 10 kHz, gold-coated infrared optics, and multiple optical wheels for coronagraph selection. Three key requirements define XAO: operation above 2 kHz to track rapidly changing turbulence, large numbers of control modes requiring many actuators and sensor pixels, and high measurement accuracy. Mathematical foundations rely on linear relationships between sensor measurements and mirror commands, with control matrices derived via Singular Value Decomposition. Pyramid wavefront sensors split light into four images using a glass pyramid, measuring aberrations by analyzing intensity distributions. Wavelength selection balances measurement sensitivity against photon availability for different star types. The system achieves diffraction-limited performance shown by Airy rings around star images, demonstrating the power of XAO combined with coronagraphy for exoplanet detection.

GPI 2.0 replaces the Shack-Hartmann wavefront sensor with a pyramid wavefront sensor based on designs from NEAT/TMT. This upgrade increases operating speed from 1 kHz to 2 kHz and uses a zero-read-noise EMCCD (CCD 220) from Newwood Cameras instead of the original First Light CCD. Simulations show this should enable operation to 13th magnitude while gracefully degrading to 14th magnitude, with potential operation to 15th magnitude under good conditions.

The pyramid wavefront sensor measures optical aberrations by splitting focused starlight into four beams using a transmissive pyramid located at the diffraction spot. The distribution of light between these four beams reveals information about wavefront errors. This sensor operates at kilohertz speeds (up to 3.5 kHz) and can correct over 1,200 optical modes simultaneously, enabling real-time adaptive optics correction that maintains diffraction-limited performance even in visible wavelengths.

This session presents two complementary approaches to wavefront reconstruction in adaptive optics. The first approach, moving horizon estimation, addresses the phase retrieval ambiguity problem by incorporating temporal information from multiple wavefront sensor images and deformable mirror shapes. Using higher-order Taylor expansions and maximum likelihood estimation, this non-linear method successfully identified segment piston errors in the Giant Magellan Telescope, improving Strehl ratio from 30-50% to 60%+. The second approach presents a universal non-linear reconstruction method using Landweber iteration that works across all Fourier-type sensors (pyramids, Shack-Hartmann, Zernike) by simply changing the optical transfer function input. This method automatically compensates for optical gain approximations inherent in linear methods. Both approaches represent significant advances over traditional linear reconstruction methods, though they require substantial computational resources and careful mathematical formulation.

The pyramid wavefront sensor works by pushing light across all four facets of an optical pyramid, creating four images. The non-linearity comes from the fact that if light is only in one facet, you have no information about changes in other facets. To mitigate this, modulation is used - rotating the pyramid rapidly around each face so light is always in all four facets. This makes it linear but less sensitive, requiring a larger tip to achieve circular illumination. Earth's atmosphere has a known turbulence profile that follows a specific pattern. The atmosphere can be thought of as a bunch of tiny lenses stacked on top of each other with different sizes. Most turbulence is large-scale, with the predominant effect being 'tip and tilt' (which moves the spot on the camera plane). For the lowest-order aberrations (tip and tilt, focus), you don't need a fancy wavefront sensor. Tip and tilt can be corrected by watching star position and using a control loop to keep the star centered.

Wavefront sensing reconstructs 3D wavefronts from distortion analysis. Outgoing systems use lasers on the retina with microlens arrays (Shack-Hartmann), limited by lens count and crossover errors. Entry systems project lasers onto the retina and photograph distortions, avoiding crossover but potentially missing points. Modern systems like iPro use pyramidal mirrors for 45,000 points, while iTrace uses sequential slit scanning. All use safe infrared or green lasers. Wavefronts decompose into Zernike polynomials like musical chords into notes, each with coefficients. The RMS (root mean square) quantifies total aberration. Low-order aberrations (≤2nd order) include defocus, astigmatism, and spherical aberration, correctable by glasses. High-order aberrations (3rd order+) affect peripheral wavefronts and are pupil-dependent. Physiological limits are <0.3-0.35 microns RMS, with asymmetric aberrations being most detrimental.

Two innovative wavefront sensing approaches are demonstrated. The Pupil Plane Tilt method uses a deformable mirror to create intentional local tilt shapes, producing characteristic PSF distortions. Alternating between tilted and flat mirror states with two captured images resolves phase ambiguities. This broadly applicable technique works for any PSF-imaging scenario including solar system science and laser guide stars. The Bright Pyramid sensor adds a λ/2 piston phase shift to the conventional four-sided pyramid, diffracting more light into pupil footprints. Laboratory testing confirms improved linearity in reconstructing known Zernike modes, demonstrating enhanced performance for second-stage correction applications.

Optical aberration describes deviations from ideal light focusing, causing light rays to spread across the retina instead of converging at a single point. A wavefront represents surfaces of constant optical phase, always perpendicular to light rays. Wavefront error quantifies the difference between actual and ideal wavefronts. The principle of light reversibility enables wavefront sensing by analyzing exit paths. The pyramidal sensor uses two conjugate planes: one imaging the retina and another imaging the pupil. Light exiting the eye creates four pupil images (sub-pupils) in the second plane. Rays with zero slope split energy equally among all four sub-pupils, while tilted rays create asymmetric intensity distributions. These intensity variations correlate directly with wavefront slope, enabling calculation of partial derivatives along x and y axes. Integration reconstructs the complete wavefront. This technology achieves 45,000 sampling points versus ~125-250 for Hartmann-Shack sensors, enabling real-time 30 fps reconstruction without complex fitting algorithms.

The curvature sensor measures wavefront aberrations by comparing intensity distributions in two different planes separated by a known distance. A beamsplitter directs light to two separate channels. Converging wavefront sections show reduced intensity in one channel compared to the other, while diverging sections show increased intensity. The difference between these intensity measurements reveals information about local wavefront curvature, enabling reconstruction of the overall wavefront shape.

Three major wavefront sensing technologies exist: Fizeau interferometry, Shack-Hartmann sensors, and quadri-wave lateral shearing interferometry. Key comparisons include: (1) Compactness - all wavefront sensors are camera-like devices, more compact than bulky interferometers; (2) Sampling capabilities - megapixel cameras provide excellent sampling, with quadri-wave offering superior capabilities compared to Shack-Hartmann; (3) Achromaticity - quadri-wave is the only truly intrinsically achromatic technology by design, unlike Shack-Hartmann which requires post-processing tricks and Fizeau which has built-in laser sources requiring separate interferometers per wavelength; (4) Vibration sensitivity - quadri-wave cameras are self-referenced and less sensitive to vibrations compared to phase-shifting interferometers; (5) Dynamic range - quadri-wave can measure up to 500 micron peak-to-valley wavefront distortions across UV to long-wave infrared wavelengths.

Different wavefront sensors offer varying resolution capabilities: Hartmann-Shack sensors provide 1-300 points over a 6mm pupil, while pyramid sensors like those in the OSIRIS T offer approximately 5,800 points across a 9mm pupil. The OPFA device provides even higher resolution with over 5,800 points in the central 3mm zone, nearly tripling the resolution of competing devices in the most critical area for vision. Higher resolution enables detection of finer corneal irregularities that lower-resolution systems miss.