Fundamental limit of resolving two point sources limited by an arbitrary point spread function

Context. As is common for infrared spectrometers, the constructive and destructive interference in different layers of the James Webb Space Telescope (JWST) Mid-Infrared Instrument (MIRI) detector arrays modulate the detected signal as a function of wavelength. The resulting “fringing” in the Medium-Resolution Spectrometer (MRS) spectra varies in amplitude between 10% and 30% of the spectral baseline. A common method for correcting for fringes relies on dividing the data by a fringe flat. In the case of MIRI MRS, the fringe flat is derived from measurements of an extended, spatially homogeneous source acquired during the thermal-vacuum ground verification of the instrument. While this approach reduces fringe amplitudes of extended sources below the percent level, at the detector level, point source fringe residuals vary in a systematic way across the point spread function. The effect could hamper the scientific interpretation of MRS observations of unresolved sources, semi-extended sources, and point sources in crowded fields. Aims. We find MIRI MRS point source fringes to be reproducible under similar observing conditions. We want to investigate whether a generic and accurate correction can be determined. Therefore, we want to identify the variables, if they exist, that would allow for a parametrization of the signal variations induced by point source fringe modulations. Methods. We determine the point source fringe properties by analyzing MRS detector plane images acquired on the ground. We extracted the fringe profile of multiple point source observations and studied the amplitude and phase of the fringes as a function of field position and pixel sampling of the point spread function of the optical chain. Results. A systematic variation in the amplitude and phase of the point source fringes is found over the wavelength range covered by the test sources (4.9 − 5.8 μm). The variation depends on the fraction of the point spread function seen by the detector pixel. We identify the non-uniform pixel illumination as the root cause of the reported systematic variation. This new finding allows us to reconcile the point source and extended source fringe patterns observed in test data during ground verification. We report an improvement after correction of 50% on the 1σ standard deviation of the spectral continuum. A 50% improvement is also reported in line sensitivity for a benchmark test with a spectral continuum of 100 mJy. The improvement in the shape of weak lines is illustrated using a T Tauri model spectrum. Consequently, we verify that fringes of extended sources and potentially semi-extended sources and crowded fields can be simulated by combining multiple point source fringe transmissions. Furthermore, we discuss the applicability of this novel fringe-correction method to the MRS data (and the data of other instruments).

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Hyperspectral resolution enhancement with an arbitrary point spread function

10.1117/12.553237 ◽

2004 ◽

Author(s):

Michael T. Eismann ◽

Russell C. Hardie

Keyword(s):

Point Spread Function ◽

Resolution Enhancement ◽

Arbitrary Point ◽

Point Spread ◽

Spread Function

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Metasurface integrated with double-helix point spread function and metalens for three-dimensional imaging

Nanophotonics ◽

10.1515/nanoph-2018-0216 ◽

2019 ◽

Vol 8 (3) ◽

pp. 451-458 ◽

Cited By ~ 1

Author(s):

Chunqi Jin ◽

Jihua Zhang ◽

Chunlei Guo

Keyword(s):

Particle Tracking ◽

Point Spread Function ◽

Double Helix ◽

Three Dimensional ◽

Super Resolution ◽

Single Particle Tracking ◽

Point Sources ◽

Phase Mask ◽

Point Spread ◽

Spread Function

AbstractMetasurfaces are two-dimensional arrangements of antennas that control the propagation of electromagnetic waves with a subwavelength thickness and resolution. Previously, metasurfaces have been mostly used to obtain the function of a single optical element. Here, we demonstrate a plasmonic metasurface that represents the combination of a phase mask generating a double-helix point spread function (DH-PSF) and a metalens for imaging. DH-PSF has been widely studied in three-dimensional (3D) super-resolution imaging, biomedical imaging, and particle tracking, but the current DH-PSFs are inefficient, bulky, and difficult to integrate. The multielement metasurface, which we label as DH-metalens, enables a DH-PSF with transfer efficiency up to 70.3% and an ultrahigh level of optical system integration, three orders of magnitude smaller than those realized by conventional phase elements. Moreover, the demonstrated DH-metalens can work in broadband visible wavelengths and in multiple incident polarization states. Finally, we demonstrate the application of the DH-metalens in 3D imaging of point sources. These results pave ways for realizing integrated DH-PSFs, which have applications in 3D super-resolution microscopy, single particle tracking/imaging, and machine vision.

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Point spread function reconstruction of adaptive-optics imaging: meeting the astrometric requirements for time-delay cosmography

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab2587 ◽

2021 ◽

Vol 508 (1) ◽

pp. 755-761

Author(s):

Geoff C-F Chen ◽

Tommaso Treu ◽

Christopher D Fassnacht ◽

Sam Ragland ◽

Thomas Schmidt ◽

...

Keyword(s):

Time Delay ◽

Adaptive Optics ◽

Point Spread Function ◽

Cosmological Parameters ◽

Hubble Constant ◽

Point Sources ◽

Multiple Point ◽

Point Spread ◽

Wide Range ◽

Spread Function

ABSTRACT Astrometric precision and knowledge of the point spread function are key ingredients for a wide range of astrophysical studies including time-delay cosmography in which strongly lensed quasar systems are used to determine the Hubble constant and other cosmological parameters. Astrometric uncertainty on the positions of the multiply-imaged point sources contributes to the overall uncertainty in inferred distances and therefore the Hubble constant. Similarly, knowledge of the wings of the point spread function is necessary to disentangle light from the background sources and the foreground deflector. We analyse adaptive optics (AO) images of the strong lens system J 0659+1629 obtained with the W. M. Keck Observatory using the laser guide star AO system. We show that by using a reconstructed point spread function we can (i) obtain astrometric precision of <1 mas, which is more than sufficient for time-delay cosmography; and (ii) subtract all point-like images resulting in residuals consistent with the noise level. The method we have developed is not limited to strong lensing, and is generally applicable to a wide range of scientific cases that have multiple point sources nearby.

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A modified algorithm for Cleaning wide-field maps with extended structures

International Astronomical Union Colloquium ◽

10.1017/s0252921100013397 ◽

1991 ◽

Vol 131 ◽

pp. 242-242

Author(s):

K. S. Dwarakanath ◽

A. A. Deshpande ◽

N. Udaya Shankar

Keyword(s):

Point Spread Function ◽

Dynamic Range ◽

Computing Time ◽

Point Sources ◽

Aperture Synthesis ◽

Wide Field ◽

Point Spread ◽

Sky Survey ◽

Spread Function ◽

Modified Algorithm

AbstractA simple but effective modification to the conventional CLEAN algorithm is suggested. This modification ensures both stability and speed when CLEAN is applied to maps containing a mixture of point sources and extended structures. The method has been successfully applied to the recently-completed sky survey at 34.5 MHz. This survey was made using the Gauribidanur T array (GEETEE) in 1-D aperture synthesis mode. Since in this case the ‘dirty beam’ (point spread function) cannot be directly computed, a method to obtain this is discussed in detail. The results of this deconvolution procedure have been encouraging in terms of reduced computing time and improved dynamic range in our maps. This algorithm should find wider application in deconvolving maps which have both extended structures and point sources.

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Stable super-resolution of images: theoretical study

Information and Inference A Journal of the IMA ◽

10.1093/imaiai/iaaa029 ◽

2020 ◽

Author(s):

Armin Eftekhari ◽

Tamir Bendory ◽

Gongguo Tang

Keyword(s):

Point Spread Function ◽

Super Resolution ◽

Continuous Functions ◽

Point Sources ◽

Chebyshev System ◽

Imaging Device ◽

Point Spread ◽

Convex Feasibility ◽

Spread Function ◽

Resolution Problem

Abstract We study the ubiquitous super-resolution problem, in which one aims at localizing positive point sources in an image, blurred by the point spread function of the imaging device. To recover the point sources, we propose to solve a convex feasibility program, which simply finds a non-negative Borel measure that agrees with the observations collected by the imaging device. In the absence of imaging noise, we show that solving this convex program uniquely retrieves the point sources, provided that the imaging device collects enough observations. This result holds true if the point spread function of the imaging device can be decomposed into horizontal and vertical components and if the translations of these components form a Chebyshev system, i.e., a system of continuous functions that loosely behave like algebraic polynomials. Building upon the recent results for one-dimensional signals, we prove that this super-resolution algorithm is stable, in the generalized Wasserstein metric, to model mismatch (i.e., when the image is not sparse) and to additive imaging noise. In particular, the recovery error depends on the noise level and how well the image can be approximated with well-separated point sources. As an example, we verify these claims for the important case of a Gaussian point spread function. The proofs rely on the construction of novel interpolating polynomials—which are the main technical contribution of this paper—and partially resolve the question raised in Schiebinger et al. (2017, Inf. Inference, 7, 1–30) about the extension of the standard machinery to higher dimensions.

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