Diffractive Pupil Research Articles

Phase retrieval and design with automatic differentiation: tutorial

The principal limitation in many areas of astronomy, especially for directly imaging exoplanets, arises from instability in the point spread function (PSF) delivered by the telescope and instrument. To understand the transfer function, it is often necessary to infer a set of optical aberrations given only the intensity distribution on the sensor—the problem of phase retrieval. This can be important for post-processing of existing data, or for the design of optical phase masks to engineer PSFs optimized to achieve high-contrast, angular resolution, or astrometric stability. By exploiting newly efficient and flexible technology for automatic differentiation, which in recent years has undergone rapid development driven by machine learning, we can perform both phase retrieval and design in a way that is systematic, user-friendly, fast, and effective. By using modern gradient descent techniques, this converges efficiently and is easily extended to incorporate constraints and regularization. We illustrate the wide-ranging potential for this approach using our new package, Morphine. Challenging applications performed with this code include precise phase retrieval for both discrete and continuous phase distributions, even where information has been censored such as heavily saturated sensor data. We also show that the same algorithms can optimize continuous or binary phase masks that are competitive with existing best solutions for two example problems: an apodizing phase plate coronagraph for exoplanet direct imaging, and a diffractive pupil for narrow-angle astrometry. The Morphine source code and examples are available open-source, with an interface similar to the popular physical optics package Poppy.

Laboratory Demonstration of Astrometric Compensation Using a Diffractive Pupil

Astrometry is a promising exoplanet detection and characterization technique that can detect earth-size exoplanets if submicroarcsecond precision is achieved. However, instrumentation available today can only reach in the order of 102 microarcseconds, mainly limited by long-term dynamic distortions on wide-field observations. To overcome this problem, we propose the implementation of a diffractive pupil, which has an array of microscopic dots imprinted on the primary mirror coating. The dots create diffractive spikes on the focal plane that are used to calibrate image plane distortions that degrade the astrometric measurement precision. This astrometry technique can be utilized simultaneously with coronagraphy for exhaustive characterization of exoplanets (mass, spectra, orbit). We designed and built an astrometry laboratory to validate the diffractive pupil ability to calibrate distortions and stabilize wide-field astrometric measurements over time. We achieved a precision of 0.0123 px, which represents 42% of the 0.0288 px stability measured for this setup before the calibration. On sky units, this result is equivalent to 3.42 × 10-3λ/D that corresponds to 150 μas for a 2.4 m telescope at 500 nm wavelength. Also, at large field angles the distortion error was reduced by a factor of 5 when the calibration was used, proving its effectiveness for large field of view. We present an astrometry error budget here to explain the source of the residual error observed when the diffractive pupil calibration is used.

SIMULTANEOUS EXOPLANET CHARACTERIZATION AND DEEP WIDE-FIELD IMAGING WITH A DIFFRACTIVE PUPIL TELESCOPE

High-precision astrometry can identify exoplanets and measure their orbits and masses, while coronagraphic imaging enables detailed characterization of their physical properties and atmospheric compositions through spectroscopy. In a previous paper, we showed that a diffractive pupil telescope (DPT) in space can enable sub-microarcsecond accuracy astrometric measurements from wide-field images by creating faint but sharp diffraction spikes around the bright target star. The DPT allows simultaneous astrometric measurement and coronagraphic imaging, and we discuss and quantify in this paper the scientific benefits of this combination for exoplanet science investigations: identification of exoplanets with increased sensitivity and robustness, and ability to measure planetary masses to high accuracy. We show how using both measurements to identify planets and measure their masses offers greater sensitivity and provides more reliable measurements than possible with separate missions, and therefore results in a large gain in mission efficiency. The combined measurements reliably identify potentially habitable planets in multiple systems with a few observations, while astrometry or imaging alone would require many measurements over a long time baseline. In addition, the combined measurement allows direct determination of stellar masses to percent-level accuracy, using planets as test particles. We also show that the DPT maintains the full sensitivity of the telescope for deep wide-field imaging, and is therefore compatible with simultaneous scientific observations unrelated to exoplanets. We conclude that astrometry, coronagraphy, and deep wide-field imaging can be performed simultaneously on a single telescope without significant negative impact on the performance of any of the three techniques.

Compatibility of a Diffractive Pupil and Coronagraphic Imaging

ABSTRACTDetection and characterization of exo-Earths require direct imaging techniques that can deliver contrast ratios of 1010 at 100 mas or smaller angular separation. At the same time, astrometric data is required to measure planet masses and to help detect planets and constrain their orbital parameters. To minimize costs, a single space mission can be designed using a high-efficiency coronagraph to perform direct imaging and a diffractive pupil to calibrate wide field distortions to enable high-precision astrometric measurements. This article reports the testing of a diffractive pupil on the high-contrast test bed at the NASA Ames Research Center to assess the compatibility of using a diffractive pupil with coronagraphic imaging systems. No diffractive contamination was found within our detectability limit of 2 × 10-7 contrast outside a region of 12 λ/D and 2.5 × 10-6 within a region spanning from 2 to 12 λ/D. Morphology of the image features suggests that no contamination exists even beyond the detectability limit specified or at smaller working angles. In the case that diffractive contamination is found beyond these stated levels, active wavefront control would be able to mitigate its intensity to 10-7 or better contrast.

Microarcsecond Astrometry with MCAO Using a Diffractive Mask

AbstractWe present a new ground-based technique to detect or follow-up long-period, potentially habitable exoplanets via precise relative astrometry of host stars using Multi-Conjugate Adaptive Optics (MCAO) on 8 meter telescopes equipped with diffractive masks. MCAO improves relative astrometry both by cancellation of high-altitude atmospheric layers, which induce dynamic focal-plane distortions, and the improvement of centroiding precision with sharper PSFs. However, mass determination of habitable exoplanets requires multi-year reference grid stability of ~1–10 μas or nanometer-level stability on the long-term average of out-of-pupil phase errors, which is difficult to achieve with MCAO (e.g., Meyer et al. 2011). The diffractive pupil technique calibrates dynamic distortion via extended diffraction spikes generated by a dotted primary mirror, which are referenced against a grid of background stars (Guyon et al. 2012). The diffractive grid provides three benefits to relative astrometry: (1) increased dynamic range, permitting observation of V < 10 stars without saturation; (2) calibration of dynamic distortion; and (3) a spectrum of the target star, which can be used to calibrate the magnitude of differential atmospheric refraction to the microarcsecond level. A diffractive 8-meter telescope with diffraction-limited MCAO in K-band reaches < 3–5 μas relative astrometric error per coordinate perpendicular to the zenith vector in one hour on a bright target star in fields of moderate stellar density (~10–40 stars arcmin−2). We present preliminary on-sky results of a test of the diffractive mask on the Nickel telescope at Lick Observatory.

HIGH-PRECISION ASTROMETRY WITH A DIFFRACTIVE PUPIL TELESCOPE

Astrometric detection and mass determination of Earth-mass exoplanets requires sub-microarcsec accuracy, which is theoretically possible with an imaging space telescope using field stars as an astrometric reference. The measurement must however overcome astrometric distortions which are much larger than the photon noise limit. To address this issue, we propose to generate faint stellar diffraction spikes using a two-dimensional grid of regularly spaced small dark spots added to the surface of the primary mirror (PM). Accurate astrometric motion of the host star is obtained by comparing the position of the spikes to the background field stars. The spikes do not contribute to scattered light in the central part of the field and therefore allow unperturbed coronagraphic observation of the star's immediate surrounding. Because the diffraction spikes are created on the PM and imaged on the same focal plane detector as the background stars, astrometric distortions affect equally the diffraction spikes and the background stars, and are therefore calibrated. We describe the technique, detail how the data collected by the wide-field camera are used to derive astrometric motion, and identify the main sources of astrometric error using numerical simulations and analytical derivations. We find that the 1.4 m diameter telescope, 0.3 sq.deg field we adopt as a baseline design achieves 0.2 microarcsec single measurement astrometric accuracy. The diffractive pupil concept thus enables sub-microarcsec astrometry without relying on the accurate pointing, external metrology or high stability hardware required with previously proposed high precision astrometry concepts.

Nondiffracting array generation using an N-wave interferometer

A particular class of nondiffracting beams is discussed called the nondiffracting arrays (NDA’s). Such beams are useful for applications that require the projection of arrays of achromatic narrow light spots with a long depth of field. Regarding their general expression, NDA’s can be seen as three-dimensional interference fields whose narrow fringes are parallel to the propagation axis. We propose to use a compact and achromatic N-wave interferometer to generate them. This original solution, based on the use of a spider’s-web-shaped diffractive pupil, is studied experimentally.