Digital pyramid wavefront sensor with tunable modulation

The pyramid wavefront sensor is used in astronomical imaging systems to estimate the wavefront induced by the time-varying atmosphere. We have demonstrated that a spatial light modulator can be used to digitally generate a prism (pyramid) WFS and for the first time, we have created the digital 3-sided and digital cone wavefront sensors (WFS). The digital prism WFS is built in the University of Canterbury Electrical and Computer Engineering Optics lab. The 3-sided and cone WFS are first designed in simulation and then converted to a format suitable for the digital WFS. We show the resulting WFS images captured for the digitally generated WFS agree well with the simulated images for a planar and defocused wavefront. We have shown that using a spatial light modulator it is feasible to implement a digital 3-sided and cone WFS.

We report on a test bed to compare the performance of three different wavefront sensors, the Shack-Hartmann Wavefront Sensor (SHWFS), the Pyramid Wavefront Sensor (PWFS), and the non-linear Curvature Wavefront Sensor (nlCWFS). No single wavefront sensor easily allows for sensing all aspects of atmospheric turbulence. For instance the SHWFS has a large dynamic range and a linear response to input phase aberrations but is not sensitive to low order modes. The PWFS uses the full spatial resolution of the pupil which gives it increased sensitivity to low order modes, however it still treads the line between achieving high dynamic range and high sensitivity. The nlCWFS is the only wavefront sensor designed to sense low and high, spatial frequencies, however this leads to a complex algorithm. We discuss the reconstruction algorithm for each WFS along with simulated comparisons, we present the optical design for the WFS comparison tes tbed, and outline the adaptive optics controls system.

The next generation of giant ground and space telescopes will have the light-collecting power to detect and characterize potentially habitable terrestrial exoplanets using high-contrast imaging for the first time. This will only be achievable if the performance of the Giant Segment Mirror Telescopes (GSMTs) extreme adaptive optics (ExAO) systems are optimized to their full potential. A key component of an ExAO system is the wavefront sensor (WFS), which measures aberrations from atmospheric turbulence. A common choice in current and next-generation instruments is the pyramid wavefront sensor (PWFS). ExAO systems require high spatial and temporal sampling of wavefronts to optimize performance and, as a result, require large detectors for the WFS. We present a closed-loop testbed demonstration of a three-sided pyramid wavefront sensor (3PWFS) as an alternative to the conventional four-sided pyramid wavefront (4PWFS) sensor for GSMT-ExAO applications on the innovative comprehensive adaptive optics and coronagraph test instrument (CACTI). The 3PWFS is less sensitive to read noise than the 4PWFS because it uses fewer detector pixels. The 3PWFS has further benefits: a high-quality three-sided pyramid optic is easier to manufacture than a four-sided pyramid. We describe the design of the two components of the CACTI system, the adaptive optics simulator and the PWFS testbed that includes both a 3PWFS and 4PWFS. We detail the error budget of the CACTI system, review its operation and calibration procedures, and discuss its current status. A preliminary experiment was performed on CACTI to study the performance of the 3PWFS to the 4PWFS in varying strengths of turbulence using both the raw intensity and slopes map signal processing methods. This experiment was repeated for a modulation radius of 1.6 and 3.25 λ / D. We found that the performance of the two wavefront sensors is comparable if modal loop gains are tuned.

We present a reference-free computational wavefront sensor based on binary amplitude modulation and phase retrieval. The method employs a Digital Micromirror Device as a programmable amplitude modulator and reconstructs the complex optical field from multiple far-field intensity measurements using the Reweighted Amplitude Flow algorithm with Optimal Spectral Initialization. Unlike classical pupil-plane wavefront sensors, the proposed architecture contains no wavelength-specific optical elements, enabling straightforward adaptation across a broad spectral range. The achievable spatial resolution of the reconstructed wavefront scales directly with the modulator resolution. We experimentally demonstrate wavefront reconstruction at 650 nm and at 2116 nm, a wavelength regime where commercial wavefront sensors are scarce. At 650 nm, the reconstructed wavefront is validated against a commercial lateral shearing interferometer, and the sensor is further integrated into a closed-loop adaptive optics system using a deformable mirror. The proposed approach is particularly suited for applications requiring high spatial resolution and large dynamic range in slowly varying or quasi-static laser fields, where computational reconstruction speed is not a primary concern.

Context. Direct detection of exoplanets around nearby stars requires advanced adaptive optics (AO) systems. High-order systems are needed to reach a high Strehl ratio (SR) in near-infrared and optical wavelengths on future giant segmented-mirror telescopes (GSMTs). Direct detection of faint exoplanets with the European Southern Observatory (ESO) Extremely Large Telescope (ELT) will require some tens of thousands of correction modes. The resolution and sensitivity of the wavefront sensor (WFS) are key requirements for this science case. We present a new class of WFSs, the bi-orthogonal Foucault knife-edge sensors (or Bi–O edge), that is directly inspired by the Foucault knife-edge test. The idea consists of using a beam-splitter producing two foci, each of which is sensed by an edge with a direction orthogonal to the other focus.Aims. We describe two implementation concepts: The Bi–O edge sensor can be realised with a sharp edge and a tip-tilt modulation device (sharp Bi–O edge) or with a smooth gradual transmission over a grey edge (grey Bi–O edge). A comparison of the Bi–O edge concepts and the four-sided classical pyramid wavefront sensor (PWS) gives some important insights into the nature of the measurements.Methods. We analytically computed the photon noise error propagation, and we compared the results to end-to-end simulations of a closed-loop AO system.Results. Our analysis shows that the sensitivity gain of the Bi–O edge with respect to the PWS depends on the system configuration. The gain is a function of the number of control modes and the modulation angle. We found that for the sharp Bi–O edge, the gain in reduction of propagated photon noise variance approaches a theoretical factor of 2 for a large number of control modes and small modulation angle, meaning that the sharp Bi–O edge only needs half of the photons of the PWS to reach similar measurement accuracy. In contrast, the PWS is twice more sensitive than the Bi–O edge in the case of very low order correction and/or large modulation angles. Preliminary end-to-end simulations illustrate some of the results. The grey version of the Bi–O edge opens the door to advanced amplitude filtering, which replaces the need for a tip-tilt modulator while keeping the same dynamic range. We show that an additional factor of 2 in reduction of propagated photon noise variance can be obtained for high orders, such that the theoretical maximum gain of a factor of 4 in photon efficiency can be obtained. A diffractive Fourier model that accurately includes the effect of modulation and control modes shows that for the extreme AO (XAO) system configuration of the ELT, the overall gain will well exceed one magnitude in guide-star brightness when compared to the modulated PWS.Conclusions. We conclude that the Bi–O edge is an excellent candidate sensor for future very high order Adaptive Optics systems, in particular on GSMTs.

Theoretical and experimental investigations of the imaging technique referred to as speckle holography have shown that wave-front information can be used in the postprocessing of astronomical data to improve the quality of images. In a closed-loop adaptive-optics system the wave-front sensor is continuously measuring the residual wave-front error. Thus wave-front information is continuously available for use in image reconstruction. We show here that wave-front information in a closed-loop adaptive-optics system, used in a postprocessing scheme, can improve the phase of the compensated optical-transfer function in systems with finite delays between wave-front sensing and phase correction. This technique is closely related to speckle holography and is referred to here as compensated speckle holography. This method requires good spatial sampling of the residual phase error and degrades gracefully as the wave-front sensor signal-to-noise ratio decreases. Also, the technique can be used to reduce the required closed-loop bandwidth of an imaging system, permitting longer integration times in the wave-front sensor, and thus allowing dimmer objects to be imaged without the use of an artificial guide star.

The paper deals with with the on-sky performance of the pyramid wavefront sensor-based Adaptive Optics (AO) systems. These wavefront sensors are of great importance, being used in all first light AO systems of the ELTs (E-ELT, GMT, and TMT), currently in design phase. In particular, non-common path aberrations (NCPAs) are a critical issue encountered when using an AO system to produce corrected images in an associated astronomical instrument. The AO wavefront sensor (WFS) and the supported scientific instrument typically use a series of different optical elements, thus experiencing different aberrations. The usual way to correct for such NCPAs is to introduce a static offset in the WFS signals. In this way, when the AO loop is closed the sensor offsets are zeroed and the deformable mirror converges to the shape required to null the NCPA. The method assumes that the WFS operation is linear and completely described by some pre-calibrated interaction matrix. This is not the case for some frequently used wavefront sensors like the Pyramid sensor or a quad-cell Shack-Hartmann sensor. Here we present a method to work in closed-loop with a pyramid wavefront sensor, or more generally a non-linear WFS, introducing a wavefront offset that remains stable when AO correction quality changes due to variations in external conditions like star brightness, seeing, and wind speed. The paper details the methods with analytical and numerical considerations. Then we present results of tests executed at the LBT telescope, in daytime and on sky, using the FLAO system and LUCI2 facility instrument. The on-sky results clearly show the successful operation of the method that completely nulls NCPA, recovering diffraction-limited images with about 70% Strehl ratio in H band in variable seeing conditions. The proposed method is suitable for application to the above-mentioned ELT AO systems.

Several telescopes include large Deformable Mirrors (DM) located directly inside the telescope. These adaptive telescopes trigger new constraints for the calibration of the Adaptive Optics (AO) systems as they usually offer no access to an artificial calibration source for the interaction matrix measurement. Moreover, the optical propagation between the DM and the Wave-Front Sensor (WFS) may evolve during the operation, resulting in mis-registrations that highly affect the AO performance and thus the scientific observation. They have to be measured and compensated, for instance by updating the calibration. A new strategy consists of estimating the mis-registrations and injecting them into synthetic models to generate noise-free interaction matrices. This pseudo-synthetic approach is the baseline for the Adaptive Optics Facility working with a Shack-Hartmann WFS and seems particularly suited for the future Extremely Large Telescope as the calibration will have to be regularly updated, for a large numbers of actuators. In this paper, the feasibility of a pseudo synthetic calibration with Pyramid WFS at the Large Binocular Telescope (LBT) is investigated. A synthetic model of the LBT AO systems is developed, and the procedure to adjust the mis-registrations parameters is introduced, extracting them from an experimental interaction matrix. We successfully tested an interaction matrix generated from the model on the real system in high-order AO mode. We recorded a slightly better performance with respect to the experimental one. This work demonstrates that a high accuracy calibration can be obtained using the pseudo synthetic approach with pyramid WFS.

The European Extremely Large Telescope (ELT) is a 39m large, ground-based optical and near- to mid-infrared telescope under construction in the Chilean Atacama desert. Operation is planned to start around the middle of the next decade. All first light instruments will come with wavefront sensing devices that allow control of the ELT’s intrinsic M4 and M5 wavefront correction units, thus building an adaptive optics (AO) system. To take advantage of the ELT’s optical performance, full diffraction-limited operation is required and only a high performance AO system can deliver this. Further technically challenging requirements for the AO come from the exoplanet research field, where the task to resolve the very small angular separations between host star and planet, has also to take into account the high-contrast ratio between the two objects. We present in detail the results of our simulations and their impact on high-contrast imaging in order to find the optimal wavefront sensing device for the METIS instrument. METIS is the mid-infrared imager and spectrograph for the ELT with specialised high-contrast, coronagraphic imaging capabilities, whose performance strongly depends on the AO residual wavefront errors. We examined the sky and target sample coverage of a generic wavefront sensor in two spectral regimes, visible and near-infrared, to pre-select the spectral range for the more detailed wavefront sensor type analysis. We find that the near-infrared regime is the most suitable for METIS. We then analysed the performance of Shack-Hartmann and pyramid wavefront sensors under realistic conditions at the ELT, did a balancing with our scientific requirements, and concluded that a pyramid wavefront sensor is the best choice for METIS. For this choice we additionally examined the impact of non-common path aberrations, of vibrations, and the long-term stability of the SCAO system including high-contrast imaging performance.

Context.Adaptive optics (AO) is a technique allowing for ground-based telescopes’ angular resolution to be improved drastically. The wavefront sensor (WFS) is one of the key components of such systems, driving the fundamental performance limitations.Aims.In this paper, we focus on a specific class of WFS: the Fourier-filtering wavefront sensors (FFWFSs). This class is known for its extremely high sensitivity. However, a clear and comprehensive noise propagation model for any kind of FFWFS is lacking.Methods.Considering read-out noise and photon noise, we derived a simple and comprehensive model allowing us to understand how these noises propagate in the phase reconstruction in the linear framework.Results.This new noise propagation model works for any kind of FFWFS, and it allows one to revisit the fundamental sensitivity limit of these sensors. Furthermore, a new comparison between widely used FFWFSs is held. We focus on the two main FFWFS classes used: the Zernike WFS (ZWFS) and the pyramid WFS (PWFS), bringing new understanding of their behavior.

A pyramid wavefront sensor (PWFS) bench has been setup at NRC-Herzberg (Victoria, Canada) to investigate, first, the feasibility of a double roof prism PWFS, and second, test the proposed pyramid wavefront sensing methodology to be used in NFIRAOS for the Thirty Meter Telescope. Traditional PWFS require shallow angles and strict apex tolerances, making them difficult to manufacture. Roof prisms, on the other hand, are common optical components and can easily be made to the desired specifications. Understanding the differences between a double roof prism PWFS and traditional PWFS will allow for the double roof prism PWFS to become more widely used as an alternative to the standard pyramid, especially in a laboratory setting. In this work, the response of the double roof prism PWFS as the amount of modulation is changed, is compared to an ideal PWFS modelled using the adaptive optics toolbox, OOMAO in MATLAB. The object oriented toolbox uses physical optics to model complete AO systems. Fast modulation and dithering using a PI mirror has been implemented using a micro-controller to drive the mirror and trigger the camera. The various trade offs of this scheme, in a controlled laboratory environment, are studied and reported.

The pyramid wavefront sensor (PWFS) is a novel sensor, equipped with superiorities in many aspects comparing with Shack-Hartmann wavefront sensor. The optical system of PWFS is more complicated, and relationships among different elements affect the static aberration of the system, which coupling with the turbulence would impact the sensing accuracy of the sensor. Aiming at improving the sensing accuracy, we analyzed the precise calibration of the system and verified the theory through experiments, which enhanced the closed-loop system's ability to correct the static turbulence.

We introduce in this article a general formalism for Fourier based wave front sensing. To do so, we consider the filtering mask as a free parameter. Such an approach allows to unify sensors like the Pyramid Wave Front Sensor (PWFS) and the Zernike Wave Front Sensor (ZWFS). In particular, we take the opportunity to generalize this two sensors in terms of sensors' class where optical quantities as, for instance, the apex angle for the PWFS or the depth of the Zernike mask for the ZWFS become free parameters. In order to compare all the generated sensors of this two classes thanks to common performance criteria, we firstly define a general phase-linear quantity that we call meta-intensity. Analytical developments allow then to split the perfectly phase-linear behavior of a WFS from the non-linear contributions making robust and analytic definitions of the sensitivity and the linearity range possible. Moreover, we define a new quantity called the SD factor which characterizes the trade-off between these two antagonist quantities. These developments are generalized for modulation device and polychromatic light. A non-exhaustive study is finally led on the two classes allowing to retrieve the usual results and also make explicit the influence of the optical parameters introduced above.

Light-induced material organization extends over a broad area of research, from photon momentum transfer to atoms, molecules and particles, serving the basis for optical trapping, and expands into the laser-induced changes of material properties through photopolymerization, photodarkening, and materials ablation. Relevant phenomena are observed over many orders of magnitude of light intensity, from a few kW cm-2 for the optical trapping of living cells to 1014 W cm-2 encountered in femtosecond laser micromachining and micro-explosion. Relevant interactions reveal a rich palette of novel phenomena in the solid state, from subtle excitations and material organization to phase transformations, non-equilibrium and transient states. The laser-induced material modifications relate to changes in the crystal structure and the molecular bonding, phase transitions in liquid state, ablation and plasma production associated with extreme pressure and temperature conditions towards entirely new states of matter.

Computational approaches in 3D quantitative phase Imaging: Current and future trends in cellular imaging.