Maximum likelihood image restoration. III. Algorithm. One-dimensional test problems

Crimean Laboratory of the P. K. Shternberg State Astronomical Institute. Translated from Astrofizika, Vol. 33, No. 2, pp. 305–315, September–October, 1990.     

Maximum likelihood image restoration. II. Point and line spread functions

P. K. Shternberg State Astronomical Institute. Translated from Astrofizika, Vol. 33, No. 1, pp. 113–127, July–August, 1990.     

Maximum likelihood image restoration. VII. Wandering of image due to atmospheric turbulence and reconstruction in computerized tomography

Crimean Laboratory of the P. K. Shternberg State Astronomical Institute. Translated from Astrofizika, Vol. 34, No. 3, pp. 419–432, May–June, 1991.     

Small-Scale Angular Fluctuations of Cosmic Background Radiation. Basic relations

A statistical treatment is given of small-scale angular fluctuations of cosmic background radiation propagating in FRIEDMANN models with Λ= o. It is assumed that the fluctuations arise from

• i the discrete nature of radiation sources;
• ii density inhomogeneities in continuously distributed radiating matter or from
• iii variable absorption along different light paths towards the observer.

The observable angular correlation function of the intensity fluctuations is expressed in terms of statistical measures of the sources of fluctuations. The rather general formulae are reduced as far as possible without specifying the frequency region.     

Improved astrometry of space debris with image restoration

In order to implement an observing strategy,image degradation that occurs during optical observation of space debris is ineluctable and has distinct characteristics. Image restoration is presented as a way to remove the influence of degradation in CCD images of space debris,based on assumed PSF models with the same FWHM as images of the object. In the process of image restoration,the maximum entropy method is adopted. The results of reduction using observed raw CCD images indicate that the precision in estimating positions of objects is improved and the effects of degradation are reduced. Improving the astrometry of space debris using image restoration is effective and feasible.     

A direct restoration method for spectral and image analysis

Physical constraints to directly control the output restoration are introduced in each iteration of solving the spectral or image formation equation. For the purpose of increasing the restoration sensitivity and the capability of smoothing noises, the fitting technique is used to reform the resolved equation. Our reconstruction results for Monte Carlo samples and observation data from space high energy astronomy show that, in comparison with traditional restorations, the direct method has high sensitivity, high resolution ability and capability of effectively reducing the effect of statistical fluctuation in data and can be used in the case of poor statistics. This method is model independent and has the capability to simultaneously represent both the extended and discrete features in object.     

Period–luminosity relations for red supergiant variables – I.The calibration

We present CCD photometry of red supergiant long-period variables (LPVs) in the Per OB1 association, the Large Magellanic Cloud (LMC) and M33. The photometry was obtained in the Kron–Cousins R and I bandpasses and in a narrow bandpass ( λ ₀=8250 Å, FWHM=300 Å) chosen to avoid TiO bands in the spectral energy distribution of the LPVs. Because the strength of the TiO bands varies greatly with temperature, which varies with the phase of an LPV, avoiding TiO reduces the amplitude of the photometric variations seen in LPVs. The result is a lower dispersion and a well defined period–luminosity (PL) relation.
For the LMC sample we find an rms dispersion of 0.27 mag in the narrow-band PL relation and slightly larger dispersions for the LPVs in Per OB1 and M33. This dispersion is comparable to that of the Cepheid PL relation at similar wavelengths. Adopting a distance modulus of 18.5±0.1 mag for the LMC, we obtain distance moduli of 11.68±0.15 mag for Per OB1 and 24.85±0.13 mag for M33. These distances agree well with those based on main sequence fitting for Per OB1 and the Cepheid distance for M33. Since LPVs are ∼ 5 times more common than Cepheids and have a well defined PL relation, LPVs provide a promising method for estimating Galactic and extra galactic distances.     

Evaluation of the effect of equal power spectrum filtering in image restoration

The effectiveness of equal power spectrum filtering in image restoration is analyzed via digital simulation. We start with a gray-scale map of concentric rings with different grey values. To obtain a dirty image, the original image is first transformed via a linear space-invariant system. Then, white noise is mixed into the image. The equal power spectrum filter is then used for the image restoration. The signal to noise ratio (SNR) and a defined steepness of the steps, together with the visual impression, are accepted to characterize the performance of the image restoration. It is concluded that a satisfactory restoration can be realized when the SNR > 15. When SNR < 5, the image is completely un-restorable. The effect of system's transfer function on image restoration is also discussed. The effectiveness of the presented model of equal power spectrum filter is confirmed by applying it to the restoration of an actual astronomical image. Finally, a typical application of the equal power spectrum filter is given.     

Basic N-body modelling of the evolution of globular clusters – I. Time scaling

We consider the use of N -body simulations for studying the evolution of rich star clusters (i.e. globular clusters).The dynamical processes included in this study are restricted to gravitational (point-mass) interactions, the steady tidal field of a galaxy, and instantaneous mass loss resulting from stellar evolution. With evolution driven by these mechanisms, it is known that clusters fall roughly into two broad classes: those that dissipate promptly in the tidal field, as a result of mass loss; and those that survive long enough for their evolution to become dominated by two-body relaxation.
The time-scales of the processes we consider scale in different ways with the number of stars in the simulation, and the main aim of the paper is to suggest how the scaling of a simulation should be done so that the results are representative of the evolution of a 'real' cluster. We investigate three different ways of scaling time. One of these is appropriate to the first type of cluster, i.e. those that dissipate rapidly; similarly, a second scaling is appropriate only to the second (relaxation-dominated) type. We also develop a hybrid scaling, which is a satisfactory compromise for both types of cluster. Finally we present evidence that the widely used Fokker–Planck method produces models that are in good agreement with N -body models of those clusters that are relaxation-dominated, at least for N -body models with several thousand particles, but that the Fokker–Planck models evolve too fast for clusters that dissipate promptly.     

Shock metamorphism of quartz in nature and experiment: I. Basic observation and theory*

Abstract— Quartz, as a ubiquitous mineral constituent of the Earth's crust, displays the greatest variety of well-defined residual shock effects among all rock-forming minerals. It represents an important and most reliable shock barometer and thermometer for terrestrial impact formations. In this paper, the current status of knowledge about the nature, origin, and experimental pressure-temperature calibration of shock-induced deformations and phase transformations is reviewed for natural and experimental shock conditions.