Stellar Interferometry Research Articles

Stellar intensity interferometry of Vega in photon counting mode

ABSTRACT Stellar intensity interferometry is a technique based on the measurement of the second-order spatial correlation of the light emitted from a star. The physical information provided by these measurements is the angular size and structure of the emitting source. A worldwide effort is presently underway to implement stellar intensity interferometry on telescopes separated by long baselines and on future arrays of Cherenkov telescopes. We describe an experiment of this type, realized at the Asiago Observatory (Italy), in which we performed for the first time measurements of the correlation counting photon coincidences in post-processing by means of a single photon software correlator and exploiting entirely the quantum properties of the light emitted from a star. We successfully detected the temporal correlation of Vega at zero baseline and performed a measurement of the correlation on a projected baseline of ∼2 km. The average discrete degree of coherence at zero baseline for Vega is $\lt g^{(2)} \gt \, = 1.0034 \pm 0.0008$, providing a detection with a signal-to-noise ratio S/N ≳ 4. No correlation is detected over the km baseline. The measurements are consistent with the expected degree of spatial coherence for a source with the 3.3 mas angular diameter of Vega. The experience gained with the Asiago experiment will serve for future implementations of stellar intensity interferometry on long-baseline arrays of Cherenkov telescopes.

Stellar Speckle and Correlation Derived From Classical Wave Expansions for Spherical Antennas

Michelson phase and Hanbury Brown-Twiss intensity stellar interferometry require expressions for the first-and second-order correlation functions, respectively, of the fields radiated by stars in terms of their diameters and measured quasi-monochromatic wavelengths. Although our sun and most other stars are spherical in shape at optical wavelengths, previous determinations of speckle and correlation functions have modeled stars as circular disks rather than spheres because of the mathematical tools available for partially coherent fields on planar surfaces. However, with the incentive that most stars are indeed shaped like spheres and not disks, this article models a star as a spherical antenna composed of a random distribution of uncorrelated volume sources within a thin surface layer (photosphere). Working directly with the time-domain fields, a self-contained, straightforward, detailed derivation of speckle patterns and correlation functions is given based on a novel, angularly symmetric, spherical mode expansion with coefficients determined by the assumed Lambertian nature of the star's radiation and the uniform asymptotic behavior of the spherical Hankel functions. First-order spatially averaged and temporally averaged correlation functions are proven to be identical, and the normalized second-order correlation function is shown to equal one plus the square of the first-order correlation function. The direct time-domain approach reveals explicit expressions for the quasi-monochromatic wave-packet fields of stellar radiation as well as new criteria for the validity of the far-field approximation for the fields of incoherent sources that are much less restrictive than the Rayleigh-distance criterion for coherent sources.

Chromatic response of a four-telescope integrated-optics discrete beam combiner at the astronomical L band.

We show the results of simulation and experimental study of a 4-telescope zig-zag discrete beam combiner (DBC) for long-baseline stellar interferometry working at the astronomical L band (3 - 4 µm) under the influence of a narrow bandwidth light source. Following Saviauk et al. (2013), we used a quasi-monochromatic visibility-to-pixel matrix (V2PM) for retrieving the complex coherence functions from simulated and experimentally measured power at the output of the device. Simulation and coefficient of determination (R2) measurements show that we are able to retrieve the visibility amplitudes with >95 % accuracy of our chromatic model source up to a bandwidth of 100 nm centred at 3.5 µm. We characterized a DBC manufactured by 3D ultra-fast laser inscription (ULI) written on gallium lanthanum sulphate (GLS). Experimental results showed retrieval of visibility amplitude with an accuracy of 80-90 % at 69 nm bandwidth, validating our simulation. The standard deviation of experimental phase residuals are between 0.1-0.4 rad, which shows that the retrieval procedure is sufficient to get good quality images, where phase perturbations of less than 1 rad are expected under good seeing conditions for astronomical applications.

ASIIP: a stellar intensity interferometry target planner

Over recent years, several independent groups have pursued the realization of a modern stellar intensity interferometry (SII) system to perform high angular resolution observations at optical wavelengths. Here, we present a general purpose SII observation planner (ASIIP) that can be used to aid in SII observational efforts. ASIIP can be used to coordinate and prioritize SII observations based on observational and instrumental parameters. ASIIP constructs a master catalog by gathering information from several stellar catalogs, and targets within the master catalog are ranked based on the ability to make stellar diameter estimates using a Monte Carlo analysis. The Monte Carlo analysis takes into account the estimated angular diameter, apparent brightness, a target’s uv-plane baseline coverage for a given observation, and instrumental sensitivity.

Demonstration of stellar intensity interferometry with the four VERITAS telescopes

High angular resolution observations at optical wavelengths provide valuable insights in stellar astrophysics, directly measuring fundamental stellar parameters, and probing stellar atmospheres, circumstellar disks, elongation of rapidly rotating stars, and pulsations of Cepheid variable stars. The angular size of most stars are of order one milli-arcsecond or less, and to spatially resolve stellar disks and features at this scale requires an optical interferometer using an array of telescopes with baselines on the order of hundreds of meters. We report on the successful implementation of a stellar intensity interferometry system developed for the four VERITAS imaging atmospheric-Cherenkov telescopes. The system was used to measure the angular diameter of the two sub-mas stars $\beta$ Canis Majoris and $\epsilon$ Orionis with a precision better than 5%. The system utilizes an off-line approach where starlight intensity fluctuations recorded at each telescope are correlated post-observation. The technique can be readily scaled onto tens to hundreds of telescopes, providing a capability that has proven technically challenging to current generation optical amplitude interferometry observatories. This work demonstrates the feasibility of performing astrophysical measurements with imaging atmospheric-Cherenkov telescope arrays as intensity interferometers and the promise for integrating an intensity interferometry system within future observatories such as the Cherenkov Telescope Array.

Quantum Limits to Incoherent Imaging are Achieved by Linear Interferometry.

We solve the general problem of determining, through imaging, the three-dimensional positions of N weak incoherent pointlike emitters in an arbitrary spatial configuration. We show that a structured measurement strategy in which a passive linear interferometer feeds into an array of photodetectors is always optimal for this estimation problem, in the sense that it saturates the quantum Cramér-Rao bound. We provide a method for the explicit construction of the optimal interferometer. Further explicit results for the quantum Fisher information and the optimal interferometer design that attains it are obtained for the special case of one and two incoherent emitters in the paraxial regime. This work provides insights into the phenomenon of superresolution through incoherent imaging that has attracted much attention recently. Our results will find a wide range of applications over a broad spectrum of frequencies, from fluorescence microscopy to stellar interferometry.

Simulation and Analysis of Telescopic Photonic Beam Combiner for Stellar Interferometry in Labview

The optical methods are the sensitive and subtle techniques of conducting optical investigations without any physical contact. They are both accurate and fast at the same time which provides an ease of having multiple observations. The need of optical interferometry has been increased at a very quick pace due to its high range of applications, from surface testing to locating of extra-solar planets in the universe. Optical Interferometry is a process or technique of combining light from various telescopes for calculating the angular resolution. The technique of optical interferometry helps astronomers for achieving a high angular resolution, that is not possible with the conventional telescopes. Optical approaches are the best approaches for non-contact evaluations, and these are accurate and fast. Due to optical nature of the interferometry, this process is used in various fields, and today it has become one of the important areas of research. Integrated Optics (IO) beam combiners are an efficient and compact technology to combine light interferometrically collected by multiple telescopes. IO beam combiner is based on the modal filtering properties of waveguides or fibers, and it improves thermo-mechanical stability, because of the characteristic rigidity of IO component substrate. Other advantages of this technology are miniaturization and non-existence of alignment needs. Several IO beam combiners are being proposed and tested nowadays. The purpose of this paper is to investigate different techniques used to develop interferometric instrument from previous researches and to simulate the technique suggested by Ermann in Labview.

Progress towards instrument miniaturisation for mid-IR long-baseline interferometry

We report recent results on passive mid-infrared integrated optics from the project “Advanced Laser-writing for Stellar Interferometry” and shortly describe the perspectives of their hybridisation with active components for the benefit of the spectro-interferometry technique.

Wide field fluorescence epi-microscopy behind a scattering medium enabled by speckle correlations.

Fluorescence microscopy is widely used in biological imaging, however scattering from tissues strongly limits its applicability to a shallow depth. In this work we adapt a methodology inspired from stellar speckle interferometry, and exploit the optical memory effect to enable fluorescence microscopy through a turbid layer. We demonstrate efficient reconstruction of micrometer-size fluorescent objects behind a scattering medium in epi-microscopy, and study the specificities of this imaging modality (magnification, field of view, resolution) as compared to traditional microscopy. Using a modified phase retrieval algorithm to reconstruct fluorescent objects from speckle images, we demonstrate robust reconstructions even in relatively low signal to noise conditions. This modality is particularly appropriate for imaging in biological media, which are known to exhibit relatively large optical memory ranges compatible with tens of micrometers size field of views, and large spectral bandwidths compatible with emission fluorescence spectra of tens of nanometers widths.

Accessing High Spatial Resolution in Astronomy Using Interference Methods

In astronomy, methods such as direct imaging or interferometry-based techniques (Michelson stellar interferometry for example) are used for observations. A particular advantage of interferometry is that it permits greater spatial resolution compared to direct imaging with a single telescope, which is limited by diffraction owing to the aperture of the instrument as shown by Rueckner et al. in a lecture demonstration. The focus of this paper, addressed to teachers and/or students in high schools and universities, is to easily underline both an application of interferometry in astronomy and stress its interest for resolution. To this end very simple optical experiments are presented to explain all the concepts. We show how an interference pattern resulting from the combined signals of two telescopes allows us to measure the distance between two stars with a resolution beyond the diffraction limit. Finally this work emphasizes the breathtaking resolution obtained in state-of-the-art instruments such as the VLTi (Very Large Telescope interferometer).

Development of a digital astronomical intensity interferometer: laboratory results with thermal light

We present measurements of the second-order spatial coherence function of thermal light sources using Hanbury-Brown and Twiss interferometry with a digital correlator. We demonstrate that intensity fluctuations between orthogonal polarizations, or at detector separations greater than the spatial coherence length of the source, are uncorrelated but can be used to reduce systematic noise. The work performed here can readily be applied to existing and future Imaging Air-Cherenkov Telescopes used as star light collectors for stellar intensity interferometry to measure spatial properties of astronomical objects.

Development of low-loss mid-infrared ultrafast laser inscribed waveguides

The mid-infrared (mid-IR) is a spectral region (≈2 to 20 μm) that is of key importance in astronomy for applications such as exoplanet imaging and spectroscopic analysis. Long baseline stellar interferometry is the only imaging technique that offers the possibility to achieve milli-arcsecond angular resolution in the mid-IR. At the heart of such an interferometer is the beam combining instrument, which enables coherent beam combination of the signals from each baseline. In comparison to bulk-optic beam combiners, beam combiners that utilize photonic planar light wave circuits for interferometry provide a more scalable and stable platform. The current generation of beam combination circuits are fabricated using conventional fabrication technologies, using silica-based materials, and are thus not suitable for operation in the mid-IR. There is, therefore, a need to explore more unconventional waveguide fabrication technologies, capable of enabling the fabrication of low-loss mid-IR waveguides and photonic beam combining circuits. We report on the development of low-loss single-mode waveguides in a gallium lanthanum sulfide glass using ultrafast laser inscription. The optimum waveguides are found to exhibit a propagation loss of 0.25±0.05 dB cm−1.

Light incoherence due to background space fluctuations

Working by analogy, we use the description of light fluctuations due to random collisions of the radiating atoms to figure out why the reduction of the coherence for light propagating a cosmological distance in the fluctuating background space is negligibly small to be observed by the stellar interferometry.

Application of shift-and-add algorithms for imaging objects within biological media

The Shift-and-Add (SAA) technique is a simple mathematical operation developed to reconstruct, at high spatial resolution, atmospherically degraded solar images obtained from stellar speckle interferometry systems. This method shifts and assembles individual degraded short-exposure images into a single average image with significantly improved contrast and detail. Since the inhomogeneous refractive indices of biological tissue causes light scattering similar to that induced by optical turbulence in the atmospheric layers, we assume that SAA methods can be successfully implemented to reconstruct the image of an object within a scattering biological medium. To test this hypothesis, five SAA algorithms were evaluated for reconstructing images acquired from multiple viewpoints. After successfully retrieving the hidden object's shape, quantitative image quality metrics were derived, enabling comparison of imaging error across a spectrum of layer thicknesses, demonstrating the relative efficacy of each SAA algorithm for biological imaging.

The Telescope: Its History, Technology, and Future

Preface 9 Chapter 1: The naked-eye universe 13 Chapter 2: The development of the telescope 25 Chapter 3: How a telescope works 37 Imaging Refracting telescopes Reflecting telescopes Chapter 4: The perfect telescope 44 Diffraction and the perfect image Resolution limit Chapter 5: When good telescopes go bad 53 Aberrations Field of view Air turbulence Chapter 6: Analysing the light 66 Imaging devices--the camera Spectroscopy Photometry Polarimetry Chapter 7: Interferometry 80 Interference--how light waves combine Michelson interferometer Michelson stellar interferometer Imaging interferometry Nulling interferometry Chapter 8: So you want to build an observatory? 95 Making a mirror Site selection Mechanical engineering Chapter 9: The Hubble Space Telescope 109 Chapter 10: Advanced telescope techniques 125 Lightweighting Active optics Segmented primaries Adaptive optics Laser guide stars Chapter 11: Laser communications and remote sensing 140 Laser communications Lidar Chapter 12: Surveillance 149 Airborne surveillance Space-based surveillance Other surveillance methods Laser weapons Chapter 13: Non-traditional observatories 162 Liquid mirror telescopes Solar telescopes Seeing the invisible Gravitational wave observatories Chapter 14: Key discoveries 181 The Solar System and Pluto Comet Halley The first exo-solar planet Milky Way black hole Hubble Ultra-Deep Field Hoag's Object Chapter 15: Future telescopes 197 Wide-field wonders Another pale blue dot The big boys One last word 217 Appendix A: Some mathematical basics 220 Appendix B: Electromagnetic radiation 226 Appendix C: Getting your own telescope 233 Notes 236 Bibliography 240 Index 243

Study of the inner disk of the Herbig star MWC480

The inner structure and properties (temperature, mass) of the circumstellar disk of Herbig star MWC480 are studied by stellar interferometry method used in the infrared and are interpreted using semi-analytical models. From these models, the SED (Spectral Energy Distribution) was fitted and multi- wavelength intensity map of the source were calculated. The intensity map provides the input for modeling the Keck Interferometer (KI) data in the near-infrared (near-IR) and the data of the Very Large Telescope Interferometer (VLTI) with the mid-infrared instrument MIDI. We conclude that with our limited set of data, we can fit the SED, the Keck visibilities and the MIDI visibilities using a two-components disk model. Furthermore, we suspect that MWC480 has a transitional dusty disk. However, we need more MIDI observations with different baseline orientations to confirm our modeling.

Ultrafast laser inscription of mid-IR directional couplers for stellar interferometry.

We report the ultrafast laser fabrication and mid-IR characterization (3.39 μm) of four-port evanescent field directional couplers. The couplers were fabricated in a commercial gallium lanthanum sulfide glass substrate using sub-picosecond laser pulses of 1030 nm light. Straight waveguides inscribed using optimal fabrication parameters were found to exhibit propagation losses of ∼0.8 dB·cm(-1). A series of couplers were inscribed with different interaction lengths, and we demonstrate power-splitting ratios of between 8% and 99% for mid-IR light with a wavelength of 3.39 μm. These results clearly demonstrate that ultrafast laser inscription can be used to fabricate high-quality evanescent field couplers for future applications in astronomical interferometry.

Higher order optical vortices and formation of speckles.

We have experimentally generated higher order optical vortices and scattered them through a ground glass plate that results in speckle formation. Intensity autocorrelation measurements of speckles show that their size decreases with an increase in the order of the vortex. It implies an increase in the angular diameter of the vortices with their order. The characterization of vortices in terms of their annular bright ring also helps us to understand these observations. The results may find applications in stellar intensity interferometry and thermal ghost imaging.

A daylight experiment for teaching stellar interferometry

We discuss the design of a simple experiment that reproduces the operation of the Michelson stellar interferometer. The emission of stellar sources has been simulated using light emerging from circular end-faces of step-index polymer optical fibers and from diffuse reflections of laser beams. Interference fringes have been acquired using a digital camera, coupled to a telescope obscured by a double aperture lid. The experiment is analogous to the classical determination of stellar sizes by Michelson and can be used during the day. Using this experimental set-up, we can determine the size of extended sources, located at a distance of about 75 m from our telescope, with errors less than 25%.

Stellar granulation and interferometry

Stars are not smooth. Their photosphere is covered by a granulation pattern associated with the heat transport by convection. The convection-related surface structures have different size, depth, and temporal variations with respect to the stellar type. The related activity (in addition to other phenomena such as magnetic spots, rotation, dust, etc.) potentially causes bias in stellar parameters determination, radial velocity, chemical abundances determinations, and exoplanet transit detections. The role of long-baseline interferometric observations in this astrophysical context is crucial to characterize the stellar surface dynamics and correct the potential biases. In this Chapter, we present how the granulation pattern is expected for different kind of stellar types ranging from main sequence to extremely evolved stars of different masses and how interferometric techniques help to study their photospheric dynamics.