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 element, designed to be coupled with the LGS elongated image, make the system conceptually different with respect to other pupil WFSs (like the Pyramid WFS, P-WFS) also in terms of the simulation technique to be selected, within the ones which can be found in literature. In this paper, we aim to report the considerations and derivations which led to the selection of a ray-tracing method for ingot pupil images simulation, and the geometrical assumptions and approach made to optimize the computing time.
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 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…
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…
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…
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 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 …
The Ingot WFS, a Pyramid-like WFS, has been proposed as a relief to the LGS spot elongation. Actually, the artificial sources are confined in an excited cigar-shaped region in the sodium layer and portions of the telescope aperture have a corresponding different perspective. This diversity generates a variation of the WFS response depending on the illuminated sub-aperture position. The feasibility study of the INGOT WFS is developing within the MAORY project. In this work we present the numerical simulator built in order to investigate the performance of the IngotWFS in terms of Strehl Ratio, …
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…
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…
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…
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.…
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 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…
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…
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…
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…
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…
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. …
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…
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…
The Shack-Hartman wavefront sensor designed for final acceptance of 2.5m SAI telescope allows to measure the shape of the wavefront on exit pupil of the telescope using a bright star. The reference laser source on wavelength 532 nm is used for measurements. During testing the device at different telescopes it was found out what it's probable to estimate some properties of air streams in the dome. Such estimations have been made for three domes: 1.5 m AZT-22 and 1.0 m Zeiss telescope of Maidanak Observatory, Uzbekistan and for 2.6 m telescope ZTSh of Crimean observatory, Ukraine. The following …
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 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…
In the present paper, we consider the optical design of a zoom system for the active refocusing in laser guide star wavefront sensors. The system is designed according to the specifications coming from the Extremely Large Telescope (ELT)-HARMONI instrument, the first-light, integral field spectrograph for the European (E)-ELT. The system must provide a refocusing of the laser guide as a function of telescope pointing and large decentring of the incoming beam. The system considers four moving lens groups, each of them being a doublet with one aspherical surface. The advantages and shortcomings …
The sensitivity of the the pyramid wavefront sensor (PyWFS) has made it a popular choice for astronomical adaptive optics (AAO) systems, and it is at its most sensitive when it is used without modulation of the input beam. In non-modulated mode, the device is highly nonlinear. Hence, all PyWFS implementations on current AAO systems employ modulation to make the device more linear. The upcoming era of 30-m class telescopes and the demand for ultra-precise wavefront control stemming from science objectives that include direct imaging of exoplanets make using the PyWFS without modulation desirabl…
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, …
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…
Laser guide star (LGS) wave-front sensing (LGSWFS) is a key element of tomographic adaptive optics system. However, when considering Extremely Large Telescope (ELT) scales, the LGS spot elongation becomes so large that it challenges the standard recipes to design LGSWFS. For classical Shack-Hartmann wave-front sensor (SHWFS), which is the current baseline for all ELT LGS-assisted instruments, a trade-off between the pupil spatial sampling [number of sub-apertures (SAs)], the SA field-of-view (FoV) and the pixel sampling within each SA is required. For ELT scales, this trade-off is also driven …
AOSAT is a python package for the analysis of single-conjugate adaptive optics (SCAO) simulation results. Python is widely used in the astronomical community these days, and AOSAT may be used stand-alone, integrated into a simulation environment, or can easily be extended according to a user's needs. Standalone operation requires the user to provide the residual wavefront frames provided by the SCAO simulation package used, the aperture mask (pupil) used for the simulation, and a custom setup file describing the simulation/analysis configuration. In its standard form, AOSAT's "tearsheet" funct…
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.…
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 …
The nonlinear curvature wavefront sensor (nlCWFS) has been shown to be a promising alternative to existing wavefront sensor designs. Theoretical studies indicate that the inherent sensitivity of this device could offer up to a factor of 10 times improvement compared to the widely-used Shack-Hartmann wavefront sensor (SHWFS). The nominal nlCWFS design assumes the use of four detector measurement planes in a symmetric configuration centered around an optical system pupil plane. However, the exact arrangement of these planes can potentially be optimized to improve aberration sensitivity, and mini…
In astronomy and microscopy, distortions in the wavefront affect the dynamic range of a high contrast imaging system. These aberrations are either imposed by a turbulent medium such as the atmosphere, by static or thermal aberrations in the optical path, or by imperfectly phased subapertures in a segmented mirror. Active and adaptive optics (AO), consisting of a wavefront sensor and a deformable mirror, are employed to address this problem. Nevertheless, the non-common-path between the wavefront sensor and the science camera leads to persistent quasi-static speckles that are difficult to calib…
The Multiconjugate Adaptive optics Demonstrator (MAD) for ESO-Very Large Telescopes (VLT) will demonstrate on sky the MultiConjugate Adaptive Optics (MCAO) technique. In this paper the laboratory tests relative to the first preliminary acceptance in Europe of the Layer Oriented (LO) Wavefront Sensor (WFS) for MAD will be described: the capabilities of the LO approach have been checked and the ability of the WFS to measure phase screens positioned at different altitudes has been experimented. The LO WFS was opto-mechanically integrated and aligned in INAF - Astrophysical Observatory of Arcetri …
The Multiconjugate adaptive Optic Relay For ELT Observations (MORFEO, formerly known as MAORY) is the adaptive optics (AO) module for the Extremely Large Telescope (ELT) aimed at providing a 1 arcmin corrected field to the Multi-AO Imaging CamerA for Deep Observations (MICADO) and to a future client instrument. It should provide resolution close to the diffraction limit on a large portion of the sky and in a wide range of atmospheric conditions. Its ability to provide a flat wavefront must face the known aspect of the atmospheric turbulence and telescope environment, but also the final charact…
