Investigation of the Cauchy–Riemann equations for one-dimensional image recovery in intensity interferometry

Holmes, Richard B.; Belen'kii, Mikhail S.

doi:10.1364/josaa.21.000697

Cited by 38 publications

(47 citation statements)

References 16 publications

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“…Methods specifically for intensity interferometry were worked out by Holmes et al (2004; for one and two dimensions, respectively. Once a sufficient coverage of the Fourier plane is available, phase recovery and imaging indeed become possible.…”

Section: Image Reconstruction From Second-order Coherencementioning

confidence: 99%

“…Some strategies that specialize in analyzing intensity interferometry data have been developed; e.g., Holmes & Belen'kii (2004); Nuñez et al (2012a), and consist in estimating Fourier phases from Fourier magnitudes. Since the Fourier transform of a finite object is an analytic function, the Cauchy-Riemann equations can be used to find derivatives of the phase from derivatives of the magnitude, producing images that are unique except for translation and reflection.…”

Section: Image Reconstructionmentioning

confidence: 99%

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Long-baseline optical intensity interferometry

Dravins

Lagadec

Nuñez

2015

A&A

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Context. A long-held vision has been to realize diffraction-limited optical aperture synthesis over kilometer baselines. This will enable imaging of stellar surfaces and their environments, and reveal interacting gas flows in binary systems. An opportunity is now opening up with the large telescope arrays primarily erected for measuring Cherenkov light in air induced by gamma rays. With suitable software, such telescopes could be electronically connected and also used for intensity interferometry. Second-order spatial coherence of light is obtained by cross correlating intensity fluctuations measured in different pairs of telescopes. With no optical links between them, the error budget is set by the electronic time resolution of a few nanoseconds. Corresponding light-travel distances are approximately one meter, making the method practically immune to atmospheric turbulence or optical imperfections, permitting both very long baselines and observing at short optical wavelengths. Aims. Previous theoretical modeling has shown that full images should be possible to retrieve from observations with such telescope arrays. This project aims at verifying diffraction-limited imaging experimentally with groups of detached and independent optical telescopes. Methods. In a large optics laboratory, artificial stars (single and double, round and elliptic) were observed by an array of small telescopes. Using high-speed photon-counting solid-state detectors and real-time electronics, intensity fluctuations were cross-correlated over up to 180 baselines between pairs of telescopes, producing coherence maps across the interferometric Fourier-transform plane. Results. These interferometric measurements were used to extract parameters about the simulated stars, and to reconstruct their twodimensional images. As far as we are aware, these are the first diffraction-limited images obtained from an optical array only linked by electronic software, with no optical connections between the telescopes. Conclusions. These experiments serve to verify the concepts for long-baseline aperture synthesis in the optical (somewhat analogous to radio interferometry) and to optimize the instrumentation and observing procedures for future observations with large arrays of Cherenkov telescopes, aiming at order-of-magnitude improvements of the angular resolution in optical astronomy.

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Section: Image Reconstruction From Second-order Coherencementioning

confidence: 99%

Section: Image Reconstructionmentioning

confidence: 99%

Long-baseline optical intensity interferometry

Dravins

Lagadec

Nuñez

2015

A&A

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“…To recover the phase information, we can still use the amplitude itself thanks to the analycity of the discrete FT (see for instance Holmes & Belen'kii 2004, although an image flip degeneracy remains) or the high-order correlations (see for instance Zhilyaev 2008), but with the issue of even lower sensitivity. The correlator of an intensity interferometer is designed to measure the quantity…”

Section: The Second-order Correlation Functionmentioning

confidence: 99%

Intensity interferometry and the second-order correlation function $g^{(2)}$ in astrophysics

Foellmi¹

2009

A&A

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Most observational techniques in astronomy can be understood as exploiting the various forms of the first-order correlation function g (1) . As demonstrated by the Narrabri stellar intensity interferometer back in the 1960s by Hanbury Brown & Twiss, the first experiment to measure the second-order correlation function g (2) , light can carry more information than simply its intensity, spectrum, and polarization. Since this experiment, theoretical and laboratory studies of non-classical properties of light have become a very active field of research, called quantum optics. Despite the variety of results in this field, astrophysics remained focused essentially on first-order coherence. In this paper, we study the possibility that quantum properties of light could be observed in cosmic sources. We provide the basic mathematical ingredients about the first and the second order correlation functions, applied to the modern context of astronomical observations. We aim at replacing the Hanbury Brown & Twiss experiment in this context, and present two fundamental limitations of an intensity interferometer: the requirement of a chaotic light source and the rapid decrease of the amount of correlated fluctuations with the surface temperature. The first of these limitations paradoxically emphasizes that the exploitation of g (2) is richer than what a modern intensity interferometer could bring and is particularly interesting for sources of nonthermal light. We also discuss new photon-counting avalanche photodiodes currently being developed in Grenoble, and their impact on limiting magnitudes of an intensity interferometer. We conclude by briefly presenting why microquasars in our galaxy and their extragalactic parents can represent an excellent first target in the optical/near-infrared where to observe nonthermal light and to test the use of g (2) in astrophysical sources.

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“…The many (tens and up) baselines will create a dense Fourier plane coverage in a single run, without the need to fit a model to the data. Phases could be recovered by one of the already known and somewhat redundant algorithms [7][8][9][10][11][12]. Imaging will be possible by having sufficient (u, v) coverage (see also §2.2).…”

Section: Off-line Multi-detector Intensity Interferometersmentioning

confidence: 99%

“…Since then, many other algorithms were proposed for the full reconstruction of the complex degree of coherence from amplitude-only measurements [7][8][9][10][11][12]. Classical two-detector intensity interferometry [1] was abandoned in the mid seventies due to its low sensitivity, and indeed higher-order correlations were never observed for astronomical sources.…”

Section: Introductionmentioning

confidence: 99%

Offline, multidetector intensity interferometers - II. Implications and applications

Ribak¹

2006

Monthly Notices of the Royal Astronomical Society

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Intensity interferometry removes the stringent requirements on mechanical precision and atmospheric corrections that plague all amplitude interferometry techniques at the cost of severely limited sensitivity. A new idea we recently introduced, very high redundancy, alleviates this problem. It enables the relatively simple construction (~1cm mechanical precision) of a ground-based astronomical facility able to transform a two-dimensional field of point-like sources to a three-dimensional distribution of micro-arcsec resolved systems, each imaged in several optical bands. Each system will also have its high resolution residual timing, high quality (inside each band) spectra and light curve, emergent flux, effective temperature, polarization effects and perhaps some thermodynamic properties, all directly measured. All the above attributes can be measured in a single observation run of such a dedicated facility. We conclude that after three decades of abandonment optical intensity interferometry deserves another review, also as a ground-based alternative to the science goals of space interferometers.Subject Heading: instrumentation: interferometers -instrumentation: high angular resolution -techniques: interferometric 1. INTRODUCTION Amplitude interferometry is today's mainstream technique for high angular resolution astronomy, mainly in the infrared regime. In principle, amplitude interferometers combine the electromagnetic waves from two or more separate locations to produce a high-resolution brightness distribution, or image, of the source. Intensity interferometry, on the other hand, combines the intensities of the electromagnetic wave via the correlation of the electrical currents generated by the detectors of the already-detected intensities. For astronomical purposes, the main advantage of intensity interferometry is its mechanical robustness: the required mechanical accuracy depends on the electrical bandwidth of the detectors, and not on the wavelength of the light. This opto-mechanical robustness also means that the atmosphere does not influence the performance of the instrument. The main disadvantages of intensity interferometry are its very low intrinsic sensitivity and the fact that the classical, two-detector intensity interferometer cannot reconstruct the phase of the complex degree of coherence, and thus can't be used to produce true images [1].

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Investigation of the Cauchy–Riemann equations for one-dimensional image recovery in intensity interferometry

Cited by 38 publications

References 16 publications

Long-baseline optical intensity interferometry

Long-baseline optical intensity interferometry

Intensity interferometry and the second-order correlation function $g^{(2)}$ in astrophysics

Offline, multidetector intensity interferometers - II. Implications and applications

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