Point Spread Function Estimation for Wide Field Small Aperture Telescopes with Deep Neural Networks and Calibration Data
Taiyuan University of Technology（太原理工大学）；Durham University（杜伦大学）；Nanjing Institute of Astronomical Optics and Technology CAS（中国科学院南京天文光学技术研究所）；Silesian University of Technology（西里西亚工业大学）
Peng Jia, Xuebo Wu, Zhengyang Li, Bo Li, Weihua Wang, Qiang Liu, Adam Popowicz
The point spread function (PSF) reflects states of a telescope and plays an important role in development of data processing methods, such as PSF based astrometry, photometry and image restoration. However, for wide field small aperture telescopes (WFSATs), estimating PSF in any position of the whole field of view is hard, because aberrations induced by the optical system are quite complex and the signal to noise ratio of star images is often too low for PSF estimation. In this paper, we further develop our deep neural network (DNN) based PSF modelling method and show its applications in PSF estimation. During the telescope alignment and testing stage, our method collects system calibration data through modification of optical elements within engineering tolerances (tilting and decentering). Then we use these data to train a DNN (Tel--Net). After training, the Tel--Net can estimate PSF in any field of view from several discretely sampled star images. We use both simulated and experimental data to test performance of our method. The results show that the Tel--Net can successfully reconstruct PSFs of WFSATs of any states and in any positions of the FoV. Its results are significantly more precise than results obtained by the compared classic method - Inverse Distance Weight (IDW) interpolation. Our method provides foundations for developing of deep neural network based data processing methods for WFSATs, which require strong prior information of PSFs.
Taiyuan University of Technology（太原理工大学）；Durham University（杜伦大学）；Wuxi Internet of Innovation Center Company Limited（无锡物联网创新中心有限公司）
The point spread function reflects the state of an optical telescope and it is important for data post-processing methods design. For wide field small aperture telescopes, the point spread function is hard to model, because it is affected by many different effects and has strong temporal and spatial variations. In this paper, we propose to use the denoising autoencoder, a type of deep neural network, to model the point spread function of wide field small aperture telescopes. The denoising autoencoder is a pure data based point spread function modelling method, which uses calibration data from …
The AKARI Infrared Astronomical Satellite produced the all-sky survey (AFASS) maps in the far-IR at roughly arc-minute spatial resolution, enabling us to investigate the whole sky in the far-IR for objects having surface brightnesses greater than a few to a couple of dozen MJy/sr. While the AFASS maps are absolutely calibrated against large-scale diffuse emission, it was uncertain whether or not an additional flux correction for point sources was necessary. Here, we verify that calibration for point-source photometry in the AFASS maps is proper. With the aperture correction method based on the…
Kernel-phase is a data analysis method based on a generalization of the notion of closure-phase invented in the context of interferometry, but that applies to well corrected diffraction dominated images produced by an arbitrary aperture. The linear model upon which it relies theoretically leads to the formation of observable quantities robust against residual aberrations. In practice, detection limits reported thus far seem to be dominated by systematic errors induced by calibration biases not sufficiently filtered out by the kernel projection operator. This paper focuses on the impact the ini…
This paper is concerned with algorithms for calibration of direction dependent effects (DDE) in aperture synthesis radio telescopes (ASRT). After correction of Direction Independent Effects (DIE) using self-calibration, imaging performance can be limited by the imprecise knowledge of the forward gain of the elements in the array. In general, the forward gain pattern is directionally dependent and varies with time due to a number of reasons. Some factors, such as rotation of the primary beam with Parallactic Angle for Azimuth-Elevation mount antennas are known a priori. Some, such as antenna po…
The Balloon-borne Large Aperture Submillimeter Telescope (BLAST) operated successfully during a 250-hour flight over Antarctica in December 2006 (BLAST06). As part of the calibration and pointing procedures, the red hypergiant star VY CMa was observed and used as the primary calibrator. Details of the overall BLAST06 calibration procedure are discussed. The 1-sigma absolute calibration is accurate to 10, 12, and 13% at the 250, 350, and 500 micron bands, respectively. The errors are highly correlated between bands resulting in much lower error for the derived shape of the 250-500 micron contin…
We compared several techniques for calibrating angular separation between wide (>1 arcsec) pairs. These techniques are (i) reference pair calibration using α Cen AB orbital parameters, (ii) the video drift method, and (iii) the utilisation of an aperture diffraction grating with red filters of different passbands. Separations of 62 pairs were determined using these 3 calibration techniques and compared. It was found that α Cen AB and video drift methods are in good agreement. The use of the grating and filter (by measuring fringe spacing) proved unsatisfactory for the broad-band filters, and t…
The NIRSpec instrument for the James Webb Space Telescope (JWST) is a highly versatile near-infrared spectrograph that can be operated in various observing modes, slit apertures, and spectral resolutions. Obtaining dedicated calibration data for all possible combinations of aperture and disperser is an intractable task. We have therefore developed a procedure to derive a highly realistic model of the instrument's optical geometry across the entire field of view, using calibration data acquired through only a subset of NIRSpec apertures, which nevertheless allows the light paths within the spec…
High contrast imaging using coronagraphy is one of the main avenues to enable the search for life on extrasolar Earth analogs. The HiCAT testbed aims to demonstrate coronagraphy and wavefront control for segmented on-axis space telescopes as envisioned for a future large UV optical IR mission (LUVOIR). Our software infrastructure enables 24/7 automated operation of high-contrast imaging experiments while monitoring for safe operating parameters, along with graceful shutdown processes for unsafe conditions or unexpected errors. The infrastructure also includes a calibration suite that can run n…
The Simons Observatory: Detector Polarization Angle Calibration using Sparse Wire Grid with Initial Data Sets of the Small Aperture Telescope
Kyoto University（京都大学）；Okayama University（冈山大学）；Princeton University（普林斯顿大学）；University of California San Diego（加州大学圣迭戈分校）；KEK（高能加速器研究机构）；The University of Tokyo（东京大学）；University of Milano-Bicocca（米兰比可卡大学）
This paper deals with the calibration of the analogue chains of a Square Kilometre Array (SKA) phased aperture array station, using embedded element patterns (one per antenna in the array, thus accounting for the full effects of mutual coupling) or average element patterns to generate model visibilities. The array is composed of 256 log-periodic dipole array antennas. A simulator capable of generating such per-baseline model visibility correlation matrices was implemented, which allowed for a direct comparison of calibration results using StEFCal (Statistically Efficient and Fast Calibration) …
In the future, optical stellar interferometers will provide true images thanks to larger number of telescopes and to advanced cophasing subsystems. These conditions are required to have sufficient resolution elements (resel) in the image and to provide direct images in the hypertelescope mode. It has already been shown that hypertelescopes provide snapshot images with a significant gain in sensitivity without inducing any loss of the useful field of view for direct imaging applications. This paper aims at studying the properties of the point spread functions of future large arrays using the hy…
As the precision frontier of astrophysics advances towards the one millimagnitude level, flux calibration of photometric instrumentation remains an ongoing challenge. We present the results of a lab-bench assessment of the viability of monocrystalline silicon solar cells to serve as large-aperture (up to 125mm diameter), high-precision photodetectors. We measure the electrical properties, spatial response uniformity, quantum efficiency (QE), and frequency response of 3$^{rd}$ generation C60 solar cells, manufactured by Sunpower. Our new results, combined with our previous study of these cells'…
We make the in-orbit calibration to the point-spread functions (PSFs) of the collimators of the Hard X-ray Modulation Telescope with the scanning observation of the Crab. We construct the empirical adjustments to the theoretically calculated geometrical PSFs. The adjustments contain two parts: a rotating matrix to adjust the directional deviation of the collimators and a paraboloidal function to correct the inhomogeneity of the real PSFs. The parameters of the adjusting matrices and paraboloidal functions are determined by fitting the scanning data with lower scanning speed and smaller interva…
Small aperture telescopes provide the opportunity to conduct high frequency, targeted observations of near-Earth Asteroids that are not feasible with larger facilities due to highly competitive time allocation requirements. Observations of asteroids with these types of facilities often focus on rotational brightness variations rather than longer-term phase angle dependent variations (phase curves) due to the difficulty of achieving high precision photometric calibration. We have developed an automated asteroid light curve extraction and calibration pipeline for images of moving objects from th…
Photometry of moving sources typically suffers from reduced signal-to-noise (SNR) or flux measurements biased to incorrect low values through the use of circular apertures. To address this issue we present the software package, TRIPPy: TRailed Image Photometry in Python. TRIPPy introduces the pill aperture, which is the natural extension of the circular aperture appropriate for linearly trailed sources. The pill shape is a rectangle with two semicircular end-caps, and is described by three parameters, the trail length and angle, and the radius. The TRIPPy software package also includes a new t…
Low-resolution spectroscopy is a frequently used technique. Aperture prism spectroscopy in particular is an important tool for large-scale survey observations. The ongoing ESA space mission Gaia is the currently most relevant example. In this work we analyse the fundamental limitations of the calibration of low-resolution spectrophotometric observations and introduce a calibration method that avoids simplifying assumptions on the smearing effects of the line spread functions. To this aim, we developed a functional analytic mathematical formulation of the problem of spectrophotometric calibrati…
We present results of inflight calibration of the point spread function (PSF) of the Soft X-ray Telescope (SXT-S) that focuses X-ray onto the pixel array of the Soft X-ray Spectrometer system (SXS). We make a full array image of a point-like source by extracting a pulsed component of the Crab nebula emission. Within the limited statistics afforded by an exposure time of only 6.9~ksec and the limited knowledge of the systematic uncetainties, we find that the raytracing model of 1'.2 half-power-diameter (HPD) is consistent with an image of the observed event distributions across pixels. The rati…
A method of absolute calibration for large aperture optical systems is presented, using the example of the Pierre Auger Observatory fluorescence detectors. A 2.5 m diameter light source illuminated by an ultra--violet light emitting diode is calibrated with an overall uncertainty of 2.1 % at a wavelength of 365 nm.
Context: The unprecedented astrometric precision of the Gaia mission relies on accurate estimates of the locations of sources in the Gaia data stream. This is ultimately performed by point spread function (PSF) fitting, which in turn requires an accurate reconstruction of the PSF. Gaia Early Data Release 3 (EDR3) will, for the first time, use a PSF calibration that models several of the strongest dependences, leading to signficantly reduced systematic errors. Aims: We describe the PSF model and calibration pipeline implemented for Gaia EDR3, including an analysis of the calibration results ove…
A New Method for Aperture Masking Interferometric Imaging: Demonstration with the JWST
National Radio Astronomy Observatory（国家射电天文台）；Astrophysics Group, Cavendish Laboratory, Univ. of Cambridge（剑桥大学卡文迪许实验室天体物理组）；ALBA - CELLS Synchrotron Radiation Facility（阿尔巴-CELLS同步辐射设施）；Commonwealth Scientific and Industrial Research Organisation (CSIRO), Space & Astronomy（联邦科学与工业研究组织（CSIRO）空间与天文部门）
We characterize the variation in photometric response of the Dark Energy Camera (DECam) across its 520~Mpix science array during 4 years of operation. These variations are measured using high signal-to-noise aperture photometry of $>10^7$ stellar images in thousands of exposures of a few selected fields, with the telescope dithered to move the sources around the array. A calibration procedure based on these results brings the RMS variation in aperture magnitudes of bright stars on cloudless nights down to 2--3 mmag, with <1 mmag of correlated photometric errors for stars separated by $\ge20$".…
PHOTOMETRYPIPELINE (PP) is an automated pipeline that produces calibrated photometry from imaging data through image registration, aperture photometry, photometric calibration, and target identification with only minimal human interaction. PP utilizes the widely used Source Extractor software for source identification and aperture photometry; SCAMP is used for image registration. Both image registration and photometric calibration are based on matching field stars with star catalogs, requiring catalog coverage of the respective field. A number of different astrometric and photometric catalogs …
We develop a general framework for quantifying the many different contributions to the noise budget of an image made with an array of dishes or aperture array stations. Each noise contribution to the visibility data is associated with a relevant correlation timescale and frequency bandwidth so that the net impact on a complete observation can be assessed. All quantities are parameterised as function of observing frequency and the visibility baseline length. We apply the resulting noise budget analysis to a wide range of existing and planned telescope systems that will operate between about 100…
Sparse Aperture Masking (SAM) allows for high-contrast imaging at small inner working angles, however the performance is limited by the small throughput and the number of baselines. We present the concept and first lab results of Holographic Aperture Masking (HAM) with extreme liquid-crystal geometric phase patterns. We multiplex subapertures using holographic techniques to combine the same subaperture in multiple non-redundant PSFs in combination with a non-interferometric reference spot. This way arbitrary subaperture combinations and PSF configurations can be realized, giving HAM more uv-co…
The Mingantu Spectral Radioheliograph (MUSER), a new generation of solar dedicated radio imaging-spectroscopic telescope, has realized high-time, high-angular, and high-frequency resolution imaging of the sun over an ultra-broadband frequency range. Each pair of MUSER antennas measures the complex visibility in the aperture plane for each integration time and frequency channel. The corresponding radio image for each integration time and frequency channel is then obtained by inverse Fourier transformation of the visibility data. In general, the phase of the complex visibility is severely corrup…
AstroSat is India's first space-based astronomical observatory, launched on September 28, 2015. One of the payloads aboard AstroSat is the Cadmium Zinc Telluride Imager (CZTI), operating at hard X-rays. CZTI employs a two-dimensional coded aperture mask for the purpose of imaging. In this paper, we discuss various image reconstruction algorithms adopted for the test and calibration of the imaging capability of CZTI and present results from CZTI on-ground as well as in-orbit image calibration.
In this paper, we describe the principle of a multi-aperture interferometer that uses a phase-shifting technique and is suitable for quick, snapshot imaging of astrophysical objects at extreme angular resolution through Fourier inversion. A few advantages of the proposed design are highlighted, among which are radiometric efficiency, Field of View equivalent to those of Fizeau interferometers, and a preliminary calibration procedure allowing characterization of instrumental errors. For large telescope numbers, the proposed design also results in considerable simplification of the optical and m…
The design and development process for the Square Kilometre Array (SKA) radio telescope, the Low Frequency Aperture Array component, was progressed during the SKA pre-construction phase by an international consortium, with the goal of meeting requirements for a critical design review. As part of the development process a full-sized prototype SKA Low station was deployed, the Aperture Array Verification System 1 (AAVS1). We provide a system overview and describe the commissioning results of AAVS1, which is a low frequency radio telescope with 256 dual-polarisation log-periodic dipole antennas w…
In this communication are presented rigorous and approximate analytical expressions of the Point Spread Function (PSF) and Field of View (FoV) achievable by multi-aperture Fizeau interferometers, either of the imaging or nulling types. The described formalism can be helpful for dimensioning future space missions in search of habitable extra-solar planets. Herein the characteristics of PSF and FoV are derived from simple analytical expressions that are further computed numerically in order to evidence the critical role of pupil re-imaging along the interferometer arms. The formalism is also wel…
Dense aperture arrays provide key benefits in modern astrophysical research. They are flexible, employing cheap receivers, while relying on the ever more sophisticated compute back-end to deal with the complexities of signal processing required for optimal use. Their advantage is that they offer very large fields of view and are readily scalable to any size, all other things being equal. Since they represent "software telescopes", the science cases these arrays can be applied to are quite broad. Here, we describe the calibration and performance of the AARTFAAC-12 instrument, which is composed …
Most telescope designs have a circular-shape aperture. We demonstrate that telescopes with an elongated pupil have better contrast, at lower separations, between a bright central star and a faint companion. We simulate images for an elongated-pupil telescope and for a circular-pupil telescope of equal aperture area and integration time, investigating specifically what is the maximal contrast for finding faint companions around bright stars as a function of angular separation. We show that this design gives better contrast at lower separation from a bright star. This is shown for diffraction-li…
We investigate the Sloan Digital Sky Survey (SDSS) photometry from Data Release 8 (DR8) in the search for systematic trends that still exist after the calibration effort of Padmanabhan et al. We consider both the aperture and point-spread function (PSF) magnitudes in DR8. Using the objects with repeat observations, we find that a large proportion of the aperture magnitudes suffer a ~0.2-2% systematic trend as a function of PSF full-width half-maximum (FWHM), the amplitude of which increases for fainter objects. Analysis of the PSF magnitudes reveals more complicated systematic trends of simila…
A set of pupil apodization functions for use with a vortex coronagraph on telescopes with obscured apertures is presented. We show analytically that pupil amplitudes given by real-valued Zernike polynomials offer ideal on-axis starlight cancellation when applied to unobscured circular apertures. The charge of the vortex phase element must be a nonzero even integer, greater than the sum of the degree and the absolute value of its azimuthal order of the Zernike polynomial. Zero-valued lines and points of Zernike polynomials, or linear combinations thereof, can be matched to obstructions in the p…
As part of a study funded by NASA Headquarters, we are developing a Probe-class mission concept called the Cosmic Evolution Through UV Spectroscopy (CETUS). CETUS includes a 1.5-m aperture diameter telescope with a large field-of-view (FOV). CETUS includes three scientific instruments: a Far Ultraviolet (FUV) and Near Ultraviolet (NUV) imaging camera (CAM); a NUV Multi-Object Spectrograph (MOS); and a dual-channel Point Source Spectrograph (PSS) in the Lyman Ultraviolet (LUV), FUV, and NUV spectral regions. The large FOV Three Mirror Anastigmatic (TMA) Optical Telescope Assembly (OTA) simultan…
We develop a new process of image plane self-calibration for interferometric imaging data. The process is based on Shape-Orientation-Size (SOS) conservation for the principal triangle in an image generated from the three fringes made from a triad of receiving elements, in situations where interferometric phase errors can be factorized into element-based terms. The basis of the SOS conservation principle is that, for a 3-element array, the only possible image corruption due to an element-based phase screen is a tilt of the aperture plane, leading to a shift in the image plane. Thus, an image ma…
Muon ring images observed with Imaging Atmospheric Cherenkov Telescopes (IACTs) provide a powerful means to calibrate the optical throughput of IACTs and monitor their optical point spread function. We investigate whether muons ring images can be used as the primary optical throughput calibration method for the telescopes of the future Cherenkov Telescope Array (CTA) and find several additional systematic effects in comparison to previous works. To ensure that the method achieves the accuracy required by CTA, these systematic effects need to be taken into account and minor modifications to the…
The study of ring images generated from high-energy muons is a very useful tool for the performance monitoring and calibration of any Imaging Atmosphere Cherenkov Telescope. Isolated muons travelling towards the telescope light collector system produce characteristic Cherenkov ring images in the focal plane camera. Since the geometry and the distribution of light deployed onto the camera can be easily reconstructed analytically for a muon of given energy and direction, muon rings are a powerful tool for monitoring the behaviour of crucial properties of an imaging telescope such as the point-sp…
MSE is an 11.25m telescope with a 1.5 sq.deg. field of view. It can simultaneously obtain 3249 spectra at R=3000 from 360-1800nm, and 1083 spectra at R=40000 in the optical. The large field of view, large number of targets, as well as the use of more than 4000 optical fibres to transport the light from the focal plane to the spectrographs, means that precise and accurate science calibration is difficult but essential to obtaining the science goals. As a large aperture telescope focusing on the faint Universe, precision sky subtraction and spectrophotometry are especially important. Here, we di…
Phased array feeds (PAFs) for reflector antennas offer the potential for increased reflector field of view and faster survey speeds. To address some of the development challenges that remain for scientifically useful PAFs, including calibration and beamforming algorithms, sensitivity optimization, and demonstration of wide field of view imaging, we report experimental results from a 19 element room temperature L-band PAF mounted on the Green Bank 20-Meter Telescope. Formed beams achieved an aperture efficiency of 69% and system noise temperature of 66 K. Radio camera images of several sky regi…
Next generation radio telescopes will be much larger, more sensitive, have much larger observation bandwidth and will be capable of pointing multiple beams simultaneously. Obtaining the sensitivity, resolution and dynamic range supported by the receivers requires the development of new signal processing techniques for array and atmospheric calibration as well as new imaging techniques that are both more accurate and computationally efficient since data volumes will be much larger. This paper provides a tutorial overview of existing image formation techniques and outlines some of the future dir…
With telescope apertures becoming larger and larger, the deployment of large-field telescopes is becoming increasingly popular. However, optical path calibration is necessary to ensure the image quality of large-field and large-diameter telescopes. In particular, focal plane attitude calibration is an essential optical path calibration technique that has a direct impact on image quality. In this paper, a focal plane attitude detection method using eight acquisition cameras is proposed based on the calibration requirements of the wide-field telescope, LAMOST. Comparison of simulation and experi…
This article provides detailed description on the fundamentals of aperture photometry analysis. The differential and all-sky aperture photometry techniques are described thoroughly to depict the difference between the two techniques and their selection for determining the stars' magnitudes and their respective magnitude errors. The crucial calibration parameters required for the all-sky photometry analysis such as atmospheric extinctioncoefficient, air-mass, zero point, color term and color index are discussed comprehensively with their extraction from the Sloan Digital Sky Survey (SDSS) archi…
Low wind and petaling effects, caused by the discontinuous apertures of telescopes, are poorly corrected -- if at all -- by commonly used workhorse wavefront sensors (WFSs). Wavefront petaling breaks the coherence of the point spread function core, splitting it into several side lobes, dramatically shutting off scientific throughput. We demonstrate the re-purposing of non-redundant sparse aperture masking (SAM) interferometers into low-order WFSs complementing the high-order pyramid WFS, on the SCExAO experimental platform at Subaru Telescope. The SAM far-field interferograms formed from a 7-h…
We present a new method to achieve high-contrast images using segmented and/or on-axis telescopes. Our approach relies on using two sequential Deformable Mirrors to compensate for the large amplitude excursions in the telescope aperture due to secondary support structures and/or segment gaps. In this configuration the parameter landscape of Deformable Mirror Surfaces that yield high contrast Point Spread Functions is not linear, and non-linear methods are needed to find the true minimum in the optimization topology. We solve the highly non-linear Monge-Ampere equation that is the fundamental e…
We present a new high-contrast imaging testbed designed to provide complete solutions in wavefront sensing, control and starlight suppression with complex aperture telescopes. The testbed was designed to enable a wide range of studies of the effects of such telescope geometries, with primary mirror segmentation, central obstruction, and spiders. The associated diffraction features in the point spread function make high-contrast imaging more challenging. In particular the testbed will be compatible with both AFTA-like and ATLAST-like aperture shapes, respectively on-axis monolithic, and on-axis…
In radio astronomy, holography is a commonly used technique to create an image of the electric field distribution in the aperture of a dish antenna. The image is used to detect imperfections in the reflector surface. Similarly, holography can be applied to phased array telescopes, in order to measure the complex gains of the receive paths of individual antennas. In this paper, a holographic technique is suggested to calibrate the digital beamformer of a phased array telescope. The effectiveness of the technique was demonstrated by applying it on data from the Engineering Development Array 2, o…
Segmented telescopes are a possibility to enable large-aperture space telescopes for the direct imaging and spectroscopy of habitable worlds. However, the complexity of their aperture geometry, due to the central obstruction, support structures and segment gaps, makes high-contrast imaging challenging. The High-contrast Imager for Complex Aperture Telescopes (HiCAT) testbed was designed to study and develop solutions for such telescope pupils using wavefront control and coronagraphic starlight suppression. The testbed design has the flexibility to enable studies with increasing complexity for …
The JWST Early Release Science Program for Direct Observations of Exoplanetary Systems IV: NIRISS Aperture Masking Interferometry Performance and Lessons Learned
The Japanese infrared astronomical satellite AKARI performed ~4000 pointed observations for 16 months until the end of 2007 August, when the telescope and instruments were cooled by liquid Helium. Observation targets include solar system objects, Galactic objects, local galaxies, and galaxies at cosmological distances. We describe recent updates on calibration processes of near- and mid-infrared images taken by the Infrared Camera (IRC), which has nine photometric filters covering 2-27 um continuously. Using the latest data reduction toolkit, we created calibrated and stacked images from each …
In this paper we present the electromagnetic modeling and beam pattern measurements of a 16-elements ultra wideband sparse random test array for the low frequency instrument of the Square Kilometer Array telescope. We discuss the importance of a small array test platform for the development of technologies and techniques towards the final telescope, highlighting the most relevant aspects of its design. We also describe the electromagnetic simulations and modeling work as well as the embedded-element and array pattern measurements using an Unmanned Aerial Vehicle system. The latter are helpful …
