High-Resolution Astronomical Imaging By Triple Correlation Processing

The atmosphere of the earth restricts the resolution of conventional astrophotography to about 1". We will discuss various high-resolution speckle methods which can overcome image degradation caused by the atmosphere and telescope aberrations. All methods yield diffraction-limited resolution, for example 0.03" for a 3.6m telescope. We will show various astronomical applications of speckle interferometry, observations of asteroids, Pluto/Charon, double stars and the gravitational-lens triple quasar. Speckle interferometry can yield a true diffraction-limited image if there is a point source (reference star) in the isoplanatic neighbourhood of the object (holographic speckle interferometry). We show an application of holographic speckle interferometry to the central object R136a of the 30 Doradus nebula in the Large Magellanic Cloud. A true diffraction-limited image of R136a has been reconstructed. The image shows that R136a consists of 8 stars. Speckle masking is a triple correlation method which yields diffraction-limited images of general astronomical objects. A point source near the object is not required. We will describe an application of speckle masking to the central object in the giant H II region NGC 3603. The reconstructed image shows that this central object is a star cluster of 4 stars with magnitudes 11m, 12m, 13m and 13m. The signal-to-noise ratio of the speckle masking image is about the same as the signal-to-noise ratio of the speckle interferometry autocorrelation. Speckle spectroscopy is a speckle method which yields diffraction-limited objective prism spectra. It is also possible to apply speckle masking to multiple-mirror interferometers or long-baseline interferometers on the ground or in space. True images of very high angular resolution can be obtained by these techniques. We will show computer simulations which illustrate the dependence of the signal-to-noise ratio on photon noise.

The turbulent atmosphere of the earth restricts the resolution of large ground-based telescopes to about 1 arc second. Much higher resolution can be obtained by various speckle methods 1-11. These methods yield exactly diffraction-limited resolution, for example 0.03 arc second in the case of a 3.6m telescope and for λ = 500nm. Many of these speckle methods can also be used to improve the resolution of large space telescopes if the resolution is limited by telescope aberrations. In the following text three examples of high-resolution speckle imaging are shown.

To obtain spatial information about an arbitrary atomic distribution in x-ray structure analysis, e.g. in molecules or proteins, the standard method is to measure the intensity in the far field, i.e. the first-order photon correlation function of the coherently scattered x-ray photons (coherent diffractive imaging). Recently, it was suggested to record alternatively the incoherently scattered photons and measure the second-order photon correlation function to reconstruct the geometry of the unknown atomic distribution (incoherent diffractive imaging). Yet, besides various advantages of the latter method, both techniques suffer from the so-called phase retrieval problem. Lately, an ab-initio phase retrieval algorithm to reconstruct the phase of the so-called structure factor of the scattering objects based on the third-order photon correlation function was reported. The algorithm makes use of the closure phase, which contains important, yet incomplete phase information, well-known from triple correlations and their bispectrum in speckle masking and astronomy applications. Here, we provide a detailed analysis of the underlying scheme and quantities in the context of x-ray structure analysis. In particular, we explicitly calculate for the first time the third-order photon correlation function for single photon emitters in a full quantum mechanical treatment and discuss the uniqueness of the closure phase equations constructed from. In this context, we recapitulate the sign problem of the closure phase and how it can be lifted using redundant information. We further show how the algorithm can be improved using even higher-order photon correlation functions produced by single photon emitters, e.g. the fourth-order correlation function, delivering new phase relations appearing in the four-point correlations.

Speckle illumination microscopy offers resolution beyond the diffraction limit but typically requires capturing hundreds of speckle frames to reconstruct a single super-resolution image, which significantly reduces imaging speed. To address this, we propose a spatiotemporal optimization method for speckle illumination that improves imaging speed. This method jointly optimizes the temporal uniformity of the speckle pattern, the spatial frequency spectrum of the phase modulation field, and the spatial contrast of the speckle pattern, enabling fast and uniform excitation of the sample’s fluorescence while maintaining the fine granular distribution and high contrast of the speckle patterns. Using only five speckle frames, our method achieves the super-resolution image, resulting in a nearly 20-fold increase in imaging speed compared to conventional speckle super-resolution methods. Simulations with resolution targets and experimental measurements of cycad leaves and potato tubers show a resolution approximately 1.7 times higher than the diffraction limit. Additionally, compared to the most advanced fast speckle illumination super-resolution methods (pseudo-random illumination and USRNN), our method exhibits superior robustness against aberration-induced illumination distortions, showcasing its robust, high-speed, and super-resolution capabilities.

It is now twenty years since the pioneering work of Antoine Labeyrie gave the technique of stellar speckle interferometry to the astronomical community. Subsequently, the field has exploded with many new insights, ideas and innovations. This paper reflects upon and discusses these developments. In particular, the extremely powerful speckle imaging techniques such as triple correlation analysis or speckle masking are reviewed. Image reconstruction algorithm developments are considered. The recent developments in the area of imaging using pupil masking, aperture synthesis and phase-closure techniques are also discussed.

This paper applied the zero-crossings of laser speckle (ZCLS) method, utilizing the diffraction of a focused Gaussian beam, to obtain the dynamics of lymph flow on the rat mesentery in vivo. Two experiments were designed in this study: one was the intralipid model experiment; and the other was the lymph flow under the influence of isoprenaline. In the former, the temporal dynamics of intralipid flow were acquired indicating the validity of the ZCLS method. In the latter, the speckle interferometry results manifested no significant changes in the average velocities of lymph flow, which was consistent with the result obtained by the conventional physiological method of frame by frame analysis. However, the speckle results also manifested that the lymph flow dynamics changed under the drug's influence, which could not be gained by the conventional physiological methods. These indicated that the speckle interferometry technique was promising to determine lymph-flow diagnostics.© (2002) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Video-based speckle interferometric methods such as electronic speckle pattern interferometry (ESPI) allow us to measure full-field surface deformation of a diffuse object. In this paper we show, in a first step, that the susceptibility of ESPI to noise can be substantially reduced [1] by synchronizing the optical interferometer and the object stressing system with the CCD image acquisition and processing system, and by performing what amounts to a repetitive sequence of rapid ESPI tests. In this manner, a stable fringe pattern can be obtained as long as the ambient noise is of sufficiently lower frequency than the video acquisition rate (typically 30 Hz). This scheme will be referred in this paper as reference-updating subtractive correlated ESPI to distinguish it from classical ESPI. We then take this issue further with a hybrid additive-subtractive decollated ESPI technique that will freeze out unwanted environmental noise of frequencies much higher than video rates [2], The basic principle of this proposed technique can be summed up as follows: (i) acquire speckle images containing information about the same two deformed object states in every frame of the image acquisition sequence, (ii) decorrelate the speckles between every frame, and (iii) compare every consecutive pair of speckle images to extract visible fringes corresponding to the two deformed states of the test object.

Since the invention in 1970 by Labeyrie1 of the technique of stellar speckle interferometry, there have been many attempts to extend it to produce diffraction-limited images through turbulence. In speckle interferometry, short exposure (≈10ms) images i(x) are recorded through a narrowband filter (≈10nm) and an estimate is made of the average energy spectrum <|I(u)|2> of the image, where I(u) is the Fourier transform of i(x).

Single-emitter microscopy has emerged as a promising method of imaging nanostructures with nanoscale resolution. This technique uses the centroid position of an emitter's far-field radiation pattern to infer its position to a precision that is far below the diffraction limit. However, nanostructures composed of high-dielectric materials such as noble metals can distort the far-field radiation pattern. Previous work has shown that these distortions can significantly degrade the imaging of the local density of states in metallic nanowires using polarization-resolved imaging. But unlike nanowires, nanoparticles do not have a well-defined axis of symmetry, which makes polarization-resolved imaging difficult to apply. Nanoparticles also exhibit a more complex range of distortions, because in addition to introducing a high dielectric surface, they also act as efficient scatterers. Thus, the distortion effects of nanoparticles in single-emitter microscopy remains poorly understood. Here we demonstrate that metallic nanoparticles can significantly distort the accuracy of single-emitter imaging at distances exceeding 300 nm. We use a single quantum dot to probe both the magnitude and the direction of the metallic nanoparticle-induced imaging distortion and show that the diffraction spot of the quantum dot can shift by more than 35 nm. The centroid position of the emitter generally shifts away from the nanoparticle position, which is in contradiction to the conventional wisdom that the nanoparticle is a scattering object that will pull in the diffraction spot of the emitter toward its center. These results suggest that dielectric distortion of the emission pattern dominates over scattering. We also show that by monitoring the distortion of the quantum dot diffraction spot we can obtain high-resolution spatial images of the nanoparticle, providing a new method for performing highly precise, subdiffraction spatial imaging. These results provide a better understanding of the complex near-field coupling between emitters and nanostructures and open up new opportunities to perform super-resolution microscopy with higher accuracy.

4th international symposium on liquid—solid flows

Antoine Labeyrie first pointed out in 1970 that short exposure pictures of astronomical objects can be analyzed in a simple way to recover information about the objects' structures down to the diffraction limit of a telescope. Labeyrie's method, which rather quickly came to be called speckle interferometry, takes advantage of the convolution theorem to separate the modulation transfer function of the telescope and atmosphere from the average squared-modulus of the two-dimensional Fourier transform of the object intensity. Alternatively and equivalently, the autocorrelations of speckle pictures can be produced and analyzed to study spatial structures in astronomical objects. Although speckle interferometry does not produce diffraction limited images, it has provided a wealth of new data in a wide variety of fields where the objects of interest have relatively simple morphologies usually characterized by combinations of point sources or only first order deviations from circular symmetry.

Y. M. HeHuazhong University of Science andTechnologyDepartment of MechanicsHuazhong 430074ChinaC. J. TayH. M. ShangNational University of SingaporeDepartment of Mechanical and ProductionEngineering10 Kent Ridge CrescentSingapore 119260E-mail: mpetaycj@nus.edu.sgAbstract. An electronic speckle shearing interferometry method for thefull field measurement of the slope of an object is presented. The objectunder study is placed on a rotating platform and illuminated by an ex-panded laser beam. Its image is recorded by a shearing CCD cameraand stored directly into a computer. By recording two images before andafter giving the object a small angle of rotation, the resulting correlationfringe pattern that represents the object surface slope can be obtained.The theory of the new method and some experimental results are pre-sented.

A novel interferometric method for contour mapping of optically rough surfaces

The Multi-Spectral Solar Telescope Array (MSSTA) is a sounding rocket-borne observatory composed of a set of normal-incidence multilayer-coated telescopes that obtained selected bandpass spectroheliograms of the Solar atmosphere. These spectroheliograms were recorded on specially fabricated XUV and FUV 70mm Kodak film. Rocket launches of this instrument payload took place in 1991 and 1994 at the White Sands Missile Test Range in New Mexico, sponsored by the NASA sounding rocket experiment program. Immediately prior to the 1994 launch, visible light focusing test of each telescope were performed in-situ using a 1951 Standard Air Force High Resolution Test-target, to measure optical resolution performance. We determined that the MSSTA II telescopes performed at diffraction-limited resolutions down to 0.70 arc-second at visible wavelengths. Based on these measurements, we calculated an upper-bound to the focusing errors that incorporate the sum of all uncorrelated system resolution errors that affect resolution performance. Coupling these upper-bound estimates with the in-band diffraction limits, surface scattering errors and payload pointing jitter, we demonstrate that eleven of nineteen MSSTA II telescopes - having negligible figures of focus errors in comparison to the corresponding visible diffraction limits - performed at sub arc-second resolution at their operation FUV/EUV/XUV wavelengths during flight. We estimate the in-band performance down to 0.14 +/- 0.08 second of arc.

In astronomical imaging techniques, the relative level of the zero-frequency component of an image is usually unknown relative to all other components. This problem arises because the overall object brightness cannot easily be separated from background when viewing small, faint objects. This affects image interpretability and therefore is a problem that is ubiquitous in high-resolution astronomical imaging. Potential solutions to this problem include various interpolation techniques and image-constraint techniques. These approaches are described, and performance is evaluated with an optimal interpolator that accounts for sample density, signal-to-noise ratio, and the object's overall shape. Novel analytic expressions are obtained which provide insight into the limitations of any restoration approach, and practical means for achieving those limits.