The basic outline of a pupil plane WaveFront Sensor is reviewed taking into account that the source to be sensed could be different from an unresolved source, i.e. it is extended, and that it could deploy also in a 3D fashion, enough to exceed the field's depth of the observing telescope. Under these conditions it is pointed out that the features of the reference are not invariant for different position on the pupil and it is shown that the INGOT WFS is the equivalent of the Pyramid for a Laser Guide Star. Under these conditions one can imagine to use a Dark WFS approach to improve the SNR of such a WFS, or to use a corrected upward beam in order to achieve a better use of the LGS photons with respect to an ideal Shack-Hartmann WFS.
This paper introduces a novel wavefront sensing approach that relies on the Fourier analysis of a single conventional direct image. In the high Strehl ratio regime, the relation between the phase measured in the Fourier plane and the wavefront errors in the pupil can be linearized, as was shown in a previous work that introduced the notion of generalized closure-phase, or kernel-phase. The technique, to be usable as presented requires two conditions to be met: (1) the wavefront errors must be kept small (of the order of one radian or less) and (2) the pupil must include some asymmetry, that ca…
A pupil plane wavefront reconstruction procedure is proposed based on analysis of a sequence of focal plane images corresponding to a sequence of random pupil plane phase probes. The developed method provides the unique nontrivial solution of wavefront retrieval problem and shows global convergence to this solution demonstrated using a Gerchberg-Saxton implementation. The method is general and can be used in any optical system that includes deformable mirrors for active/adaptive wavefront correction. The presented numerical simulation and lab experimental results show low noise sensitivity, hi…
The ingot wavefront sensor (I-WFS) has been proposed, for ELT-like apertures, as a possible pupil plane WFS, to cope with the geometrical characteristics of a laser guide star (LGS). Within the study and development of such a WFS, on-going in the framework of the MAORY project, the final purpose of the I-WFS simulation is to estimate its performance in terms of wavefront aberration measurement capability. The first step of this analysis is to translate incoming wavefronts into the three pupil images, produced by the optical system. The intrinsic geometrical characteristics of the ingot optical…
Wavefront estimation using in-focus image data is critical to many applications. This data is invariant to a sign flip with complex conjugation of the complex amplitude in the pupil, making for a non-unique solution. Information from an in-focus image taken through a non-redundant pupil mask (NRM) can break this ambiguity, enabling the true aberration to be determined. We demonstrate this by priming a full pupil Gerchberg-Saxton phase retrieval with NRM fringe phase information. We apply our method to measure simulated aberrations on the segmented James Webb Space Telescope (JWST) mirror using…
The next generation of Extremely Large Telescope (24 to 39m diameter) will suffer from the so-called "pupil fragmentation" problem. Due to their pupil shape complexity (segmentation, large spiders ...), some differential pistons may appear between some isolated part of the full pupil during the observations. Although classical AO system will be able to correct for turbulence effects, they will be blind to this specific telescope induced perturbations. Hence, such differential piston, a.k.a petal modes, will prevent to reach the diffraction limit of the telescope and ultimately will represent t…
The differential Optical Transfer Function (dOTF) is a focal plane wavefront sensing method that uses a diversity in the pupil plane to generate two different focal plane images. The difference of their Fourier transforms recovers the complex amplitude of the pupil down to the spatial scale of the diversity. We produce two simultaneous PSF images with diversity using a polarizing filter at the edge of the telescope pupil, and a polarization camera to simultaneously record the two images. Here we present the first on-sky demonstration of polarization dOTF at the 1.0m South African Astronomical …
An image-based technique for measuring the complex field in the pupil of an imaging system is presented. Two point source images, one with a small modification introduced in the pupil, are combined using a simple and non-iterative algorithm. The non-interferometric method is based on the change in the optical transfer function (OTF), giving a differential OTF (dOTF). The dOTF includes two images of the complex pupil field, conjugated and reflected about the position of the pupil modification, leaving an overlap that obscures some the the pupil. The overlap can be minimized by introducing the m…
The Low Wind Effect (LWE) refers to a phenomenon that occurs when the wind speed inside a telescope dome drops below $3$m/s creating a temperature gradient near the telescope spider. This produces phase discontinuities in the pupil plane that are not detected by traditional Adaptive Optics (AO) systems such as the pyramid wavefront sensor or the Shack-Hartmann. Considering the pupil as divided in 4 quadrants by regular spiders, the phase discontinuities correspond to piston, tip and tilt aberrations in each quadrant of the pupil. Uncorrected, it strongly decreases the ability of high contrast …
In an effort to transcend the limitations of differential imaging of exoplanets in the era of extremely large telescopes (ELTs), the first paper in this series established a rigorous, fully polarimetric framework for determining the science camera (SC) image given a turbulent wavefront and unknown aberrations in multiple planes the optical system. This article builds on the structure developed in Paper I in order to rigorously express the polarimetric SC image in terms of the field impinging on the wavefront sensor (WFS), thereby providing a direct connection between the measurements made in b…
The Ingot wavefront sensor is a novel pupil-plane wavefront sensor, specifically designed to cope with the elongation typical of the extended nature of the Laser Guide Star (LGS). In the framework of the ELT, we propose an optical solution suitable for a Laser launch telescope, located outside the telescope pupil. In this paper, we present the current optical design, based on a reflective roof-shaped prism, which, at the level of the focal plane, splits the light from an LGS producing three beams. The three images of the telescope pupils can be then used for the retrieval of the first derivati…
Stellar coronagraph performance is highly sensitive to optical aberrations. In order to effectively suppress starlight for exoplanet imaging applications, low-order wavefront aberrations entering a coronagraph such as tip-tilt, defocus and coma must be determined and compensated. Previous authors have established the utility of pupil-plane masks (both non-redundant/sparse-aperture and generally asymmetric aperture masks) for wavefront sensing. Here we show how a sparse aperture mask (SAM) can be integrated with a coronagraph to measure low-order, differential phase aberrations. Starlight rejec…
A new concept of using focus-diverse point spread functions (PSFs) for modal wavefront sensing (WFS) is explored. This is based on relatively straightforward image moment analysis of measured PSFs, which differentiates it from other focal-plane wavefront sensing techniques (FPWFS). The presented geometric analysis shows that the image moments are non-linear functions of wave aberration coefficients, but notes that focus-diversity (FD) essentially decouples the coefficients of interest from others, resulting in a set of linear equations whose solution corresponds to modal coefficient estimates.…
HiCAT is a high-contrast imaging testbed designed to provide complete solutions in wavefront sensing, control and starlight suppression with complex aperture telescopes. The pupil geometry of such observatories includes primary mirror segmentation, central obstruction, and spider vanes, which make the direct imaging of habitable worlds very challenging. The testbed alignment was completed in the summer of 2014, exceeding specifications with a total wavefront error of 12nm rms over a 18mm pupil. The installation of two deformable mirrors for wavefront control is to be completed in the winter of…
The crossed-sine wavefront sensor (WFS) is a pupil plane wavefront sensor that measures the first derivatives of the wavefront. It is made by three main components: a gradient transmission filter (GTF) built from a product of sine functions rotated by 45 degrees around the optical axis, a 2x2 mini-lens array (MLA) at the focus of the tested optical system and a detector array located on a plane conjugated to the pupil. The basic principle consists in acquiring four pupil images simultaneously, each image being observed from different points located behind the GTF. After the simulation work whi…
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 style error reduction to determine the pupil amplitudes. Simulations and experi…
The use of Adaptive Optics in Extremely Large Telescopes brings new challenges, one of which is the treatment of Shack-Hartmann Wavefront sensors images. When using this type of sensors in conjunction with laser guide stars for sampling the pupil of telescopes with 30+ m in diameter, it is necessary to compute the centroid of elongated spots, whose elongation angle and aspect ratio are changing across the telescope pupil. Existing techniques such as Matched Filter have been considered as the best technique to compute the centroid of elongated spots, however they are not good at coping with the…
We present a method to calibrate a high-resolution wavefront-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 (dOTF) 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 wavefront sensing algorithm controlling a wavefront corrector with ~40 000 degrees of freedom. We estimat…
This article describes the implementation of a focal plane based wavefront control loop on the high-contrast imaging instrument SCExAO (Subaru Coronagraphic Extreme Adaptive Optics). The sensor relies on the Fourier analysis of conventional focal-plane images acquired after an asymmetric mask is introduced in the pupil of the instrument. This absolute sensor is used here in a closed-loop to compensate the non-common path errors that normally affects any imaging system relying on an upstream adaptive optics system.This specific implementation was used to control low order modes corresponding to…
The direct detection and imaging of exoplanets requires the use of high-contrast adaptive optics (AO). In these systems quasi-static aberrations need to be highly corrected and calibrated. In order to achieve this, the pupil-modulated point-diffraction interferometer (m-PDI), was presented in an earlier paper. This present paper focuses on m-PDI concept validation through three experiments. First, the instrument's accuracy and dynamic range are characterised by measuring the spatial transfer function at all spatial frequencies and at different amplitudes. Then, using visible monochromatic ligh…
Multiconjugate adaptive optics (MCAO) systems have the potential to deliver diffraction-limited images over much larger fields of view than traditional single conjugate adaptive optics systems. In MCAO, the high altitude deformable mirrors (DMs) cause a distortion of the pupil plane and lead to a dynamic misregistration between the DM actuators and the wavefront sensors (WFSs). The problem is much more acute for solar astronomy than for night-time observations due to the higher spatial sampling of the WFSs and DMs, and the fact that the science observations are often made through stronger turb…
Laser guide stars (LGS) are used in many adaptive optics systems to extend sky coverage. The most common wavefront sensor used in combination with a LGS is a Shack-Hartmann wavefront sensor (SHWFS). The Shack-Hartmann has a major disadvantage for extended source wavefront sensing because it directly samples the image. In this proceeding we propose to use the generalized-Optical Differentation Wavefront Sensor (g-ODWFS) a wavefront sensor for wavefront sensing of LGS. The g-ODWFS uses only 4 pixels per sub-aperture, has little to no aliasing noise and therefore no spurious low-order errors and …
A new wavefront sensing approach, derived from the successful curvature wavefront sensing concept but using a non-linear phase retrieval wavefront reconstruction scheme, is described. The non-linear curvature wavefront sensor (nlCWFS) approaches the theoretical sensitivity limit imposed by fundamental physics by taking full advantage of wavefront spatial coherence in the pupil plane. Interference speckles formed by natural starlight encode wavefront aberrations with the sensitivity set by the telescope's diffraction limit lambda/D rather than the seeing limit of more conventional linear WFSs. …
Future large space telescopes will be equipped with adaptive optics (AO) to overcome wavefront aberrations and achieve high contrast for imaging faint astronomical objects, such as earth-like exoplanets and debris disks. In contrast to AO that is widely used in ground telescopes, space-based AO systems will use focal plane wavefront sensing to measure the wavefront aberrations. Focal plane wavefront sensing is a class of techniques that reconstruct the light field based on multiple focal plane images distorted by deformable mirror (DM) probing perturbations. In this paper, we report an efficie…
The ingot WFS is a new kind of wavefront sensor specifically designed to deal with the elongation of LGS reference sources on ELT-class telescopes. Like the pyramid, it belongs to the family of pupil plane wavefront sensors and can be considered as a generalization of the pyramid WFS for extended, three-dimensional elongated sources. The current design uses a simple, reflective roof-shaped prism to split the light into three pupils that are used to retrieve the wavefront shape. A test-bench has been realized at the INAF-Padova laboratories to test the alignment and functioning of the ingot. Th…
For ExAO instruments for the Giant Segmented Mirror Telescopes (GSMTs), alternative architectures of WFS are under consideration because there is a tradeoff between detector size, speed, and noise that reduces the performance of GSMT-ExAO wavefront control. One option under consideration for a GSMT-ExAO wavefront sensor is a three-sided PWFS (3PWFS). The 3PWFS creates three copies of the telescope pupil for wavefront sensing, compared to the conventional four-sided PWFS (4PWFS) which uses four pupils. The 3PWFS uses fewer detector pixels than the 4PWFS and should therefore be less sensitive to…
We present early laboratory simulations and extensive on-sky tests validating of the performance of a shaped pupil coronagraph (SPC) behind an extreme-AO corrected beam of the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system. In tests with the SCExAO internal source/wavefront error simulator, the normalized intensity profile for the SPC degrades more slowly than for the Lyot coronagraph as low-order aberrations reduce the Strehl ratio from extremely high values (S.R. $\sim$ 0.93--0.99) to those characteristic of current ground-based extreme AO systems (S.R. $\sim$ 0.74--0.93) and t…
Reaching the fundamental sensitivity limit of wavefront sensing on arbitrary apertures with the Phase Induced Amplitude Apodized Zernike Wavefront Sensor (PIAA-ZWFS)
Commonly used wavefront sensors, the Shack Hartmann wavefront sensor and the pyramid wavefront sensor, for example, have large dynamic range or high sensitivity, trading one regime for the other. A new type of wavefront sensor is being developed and is currently undergoing testing at the University of Arizona's Center for Astronomical Adaptive Optics. This sensor builds on linear optical differentiation theory by using linear, spatially varying halfwave plates in an intermediate focal plane. These filters, along with the polarizing beam splitters, divide the beam into four pupil images, simila…
We describe the concept of splitting spatial frequency perturbations into some kind of pupil planes wavefront sensors. Further to the existing approach of dropping higher spatial frequency to suppress aliasing effects (the so-called spatial filtered Shack-Hartmann), we point out that spatial frequencies splitting and mixing of these in a proper manner, could be handled in order to exhibit some practical or fundamental advantages. In this framework we describe the idea behind such class of concepts and we derive the relationship useful to determine if, by which extent, and under what kind of me…
A NASA sounding rocket for high contrast imaging with a visible nulling coronagraph, the Planet Imaging Coronagraphic Technology Using a Reconfigurable Experimental Base (PICTURE-B) payload has made two suborbital attempts to observe the warm dust disk inferred around Epsilon Eridani. We present results from the November 2015 launch demonstrating active wavefront sensing in space with a piezoelectric mirror stage and a micromachine deformable mirror along with precision pointing and lightweight optics in space.
Focal plane wavefront sensing is an elegant solution for wavefront sensing since near-focal images of any source taken by a detector show distortions in the presence of aberrations. Non-Common Path Aberrations and the Low Wind Effect both have the ability to limit the achievable contrast of the finest coronagraphs coupled with the best extreme adaptive optics systems. To correct for these aberrations, the Subaru Coronagraphic Extreme Adaptive Optics instrument hosts many focal plane wavefront sensors using detectors as close to the science detector as possible. We present seven of them and com…
This paper presents the basic principle and theoretical relationships of an original method allowing to retrieve the Wavefront Errors (WFE) of a ground or space-borne telescope when combining its main pupil with a second, decentered reference optical arm. The measurement accuracy of such a "telescope-interferometer" is then estimated by means of various numerical simulations, demonstrating a high performance excepted on limited areas near the telescope pupil rim. In particular, it allows direct phase evaluation (thus avoiding the use of first or second-order derivatives), which is of special i…
We present an enhanced version of the Zernike wavefront sensor, that simultaneously measures phase and amplitude aberrations. The 'vector-Zernike' wavefront sensor consists of a patterned liquid-crystal mask, which imposes $\pm π/2$ phase on the point spread function core through the achromatic geometric phase acting with opposite sign on opposite circular polarizations. After splitting circular polarization, the ensuing pupil intensity images are used to reconstruct the phase and the amplitude of the incoming wavefront. We demonstrate reconstruction of the complex wavefront with monochromatic…
The Magellan extreme adaptive optics (MagAO-X) instrument is a new extreme adaptive optics (ExAO) system designed for operation in the visible to near-IR which will deliver high contrast-imaging capabilities. The main AO system will be driven by a pyramid wavefront sensor (PyWFS); however, to mitigate the impact of quasi-static and non-common path (NCP) aberrations, focal plane wavefront sensing (FPWFS) in the form of low-order wavefront sensing (LOWFS) and spatial linear dark field control (LDFC) will be employed behind a vector apodizing phase plate (vAPP) coronagraph using rejected starligh…
A NASA sounding rocket for high-contrast imaging with a visible nulling coronagraph, the PICTURE payload, has made two suborbital attempts to observe the warm dust disk inferred around Epsilon Eridani. The first flight in 2011 demonstrated a 5 milliarcsecond fine pointing system in space. The reduced flight data from the second launch, on 25 November 2015, presented herein, demonstrate active sensing of wavefront phase in space. Despite several anomalies in flight, post-facto reduction phase stepping interferometer data provides insight into the wavefront sensing precision and the system stabi…
An adaptive optics system with a single deformable mirror is being implemented on the THEMIS 90cm solar telescope. This system is designed to operate in the visible and is required to be as robust as possible in order to deliver the best possible correction in any atmospheric conditions, even if wavefronts are sensed on some low-contrast solar granulation. In extreme conditions, the images given by the subapertures of the Shack-Hartmann wavefront sensor get randomly blurred in space, in the set of subapertures, and the distribution of blurred images is rapidly changing in time, some of them po…
The segmentation of the telescope pupil (by spiders & the segmented M4) create areas of phase isolated by the width of the spiders on the wavefront sensor (WFS), breaking the spatial continuity of the wavefront. The poor sensitivity of the Pyramid WFS (PWFS) to differential piston leads to badly seen and therefore uncontrollable differential pistons. In close loop operation, differential pistons between segments will settle around integer values of the average sensing wavelength. The differential pistons typically range from one to ten times the sensing wavelength and vary rapidly over time, l…
Focus anisoplanatism is a significant measurement error when using one single laser guide star (LGS) in an Adaptive Optics (AO) system, especially for the next generation of extremely large telescopes. An alternative LGS configuration, called Projected Pupil Plane Pattern (PPPP) solves this problem by launching a collimated laser beam across the full pupil of the telescope. If using a linear, modal reconstructor, the high laser power requirement ($\sim1000\,\mbox{W}$) renders PPPP uncompetitive with Laser Tomography AO. This work discusses easing the laser power requirements by using an artifi…
The future of space and ground based telescopes is intimately tied to technology and algorithm development surrounding wavefront sensing and control. Only with cutting edge developments and unusual ideas will we be able to build diffraction limited observatories on the ground that contend with earth-atmosphere, as well as space-based observatories that sense and control for optical aberrations and telescope jitter. There exist a variety of mathematical bases for decomposing wavefront images, including the zonal modal basis, Zernike polynomials, and Fourier modes. However, previous bases have n…
We revisit one class of z-invariant WaveFront sensor where the LGS is fired aside of the telescope aperture. In this way there is a spatial dependence on the focal plane with respect to the height where the resonant scattering occurs. We revise the basic parameters involving the geometry and we propose various merit functions to define how much improvement can be attained by a z-invariant approach. We show that refractive approaches are not viable and we discuss several solutions involving reflective ones in what has been nicknamed "ingot wavefront sensor" discussing the degrees of freedom req…
The Large Synoptic Survey Telescope (LSST) will use an active optics system (AOS) to maintain alignment and surface figure on its three large mirrors. Corrective actions fed to the LSST AOS are determined from information derived from 4 curvature wavefront sensors located at the corners of the focal plane. Each wavefront sensor is a split detector such that the halves are 1mm on either side of focus. In this paper we describe the extensions to published curvature wavefront sensing algorithms needed to address challenges presented by the LSST, namely the large central obscuration, the fast f/1.…
To reach the full potential of the new generation of ground based telescopes, an extremely fine adjustment of the phase is required. Wavefront control and correction before detection has therefore become one of the cornerstones of instruments to achieve targeted performance, especially for high-contrast imaging. A crucial feature of accurate wavefront control leans on the wavefront sensor (WFS). We present a strategy to design new Fourier-Filtering WFS that encode the phase close from the fundamental photon efficiency limit. This strategy seems promising as it generates highly sensitive sensor…
The ESA Gaia spacecraft has two Shack-Hartmann wavefront sensors (WFS) on its focal plane. They are required to refocus the telescope in-orbit due to launch settings and gravity release. They require bright stars to provide good signal to noise patterns. The centroiding precision achievable poses a limit on the minimum stellar brightness required and, ultimately, on the observing time required to reconstruct the wavefront. Maximum likelihood algorithms have been developed at the Gaia SOC. They provide optimum performance according to the Crámer-Rao lower bound. Detailed wavefront reconstructio…
Second-generation exoplanet imagers using extreme adaptive optics and coronagraphy have demonstrated their great potential for studying close circumstellar environments and for detecting new companions and helping to understand their physical properties. However, at very small angular separation, their performance in contrast is limited by several factors: diffraction by the complex telescope pupil not perfectly canceled by the coronagraph, residual dynamic wavefront errors, chromatic wavefront errors, and wavefront errors resulting from noncommon path aberrations (NCPAs). In a previous work, …
Island effect (IE) aberrations are induced by differential pistons, tips, and tilts between neighboring pupil segments on ground-based telescopes, which severely limit the observations of circumstellar environments on the recently deployed exoplanet imagers (e.g., VLT/SPHERE, Gemini/GPI, Subaru/SCExAO) during the best observing conditions. Caused by air temperature gradients at the level of the telescope spiders, these aberrations were recently diagnosed with success on VLT/SPHERE, but so far no complete calibration has been performed to overcome this issue. We propose closed-loop focal plane …
In this article we show that the vector-Apodizing Phase Plate (vAPP) coronagraph can be designed such that the coronagraphic point spread functions (PSFs) can act as a wavefront sensor to measure and correct the (quasi-)static aberrations, without dedicated wavefront sensing holograms nor modulation by the deformable mirror. The absolute wavefront retrieval is performed with a non-linear algorithm. The focal-plane wavefront sensing (FPWFS) performance of the vAPP and the algorithm are evaluated with numerical simulations, to test various photon and read noise levels, the sensitivity to the 100…
Wave-front sensing from focal plane multiple images is a promising technique for high-contrast imaging systems. However, the wave-front error of an optics system can be properly reconstructed only when it is very small. This paper presents an iterative optimization algorithm for the measurement of large static wave-front errors directly from only one focal plane image. We firstly measure the intensity of the pupil image to get the pupil function of the system and acquire the aberrated image on the focal plane with a phase error that is to be measured. Then we induce a dynamic phase to the test…
High quality, repeatable point-spread functions are important for science cases like direct exoplanet imaging, high-precision astrometry, and high-resolution spectroscopy of exoplanets. For such demanding applications, the initial on-sky point-spread function delivered by the adaptive optics system can require further optimization to correct unsensed static aberrations and calibration biases. We investigated using the Fast and Furious focal-plane wavefront sensing algorithm as a potential solution. This algorithm uses a simple model of the optical system and focal plane information to measure …
