Introduction

The simulations discussed in Chapter 1.2.2 provided a very simple model for the the effect of the atmosphere at a single instant in time. In order to determine the best observational approach for the Lucky Exposures technique, it is important to develop more realistic simulations which also address the time evolution and spatial distribution of atmospheric perturbations above the telescope. The principle model atmospheres investigated here consist of a number of thin moving layers above the telescope, each introducing perturbations following the Kolmogorov model described in Chapter 1.2.1. Each layer is blown at a characteristic wind velocity. These layers introduce position-dependent path length variations into the incoming wavefronts, and are intended to simulate turbulent atmospheric layers with variable refractive index.

In order to apply the Lucky Exposures method to an astronomical target which is too faint or too resolved for accurate measurement of the Strehl ratio of the PSF, an unresolved source must be found which is sufficiently bright to allow Strehl ratio measurements, and which lies within the isoplanatic patch surrounding the target of interest (the isoplanatic patch is the area of sky enclosed by a circle of radius equal to the isoplanatic angle, and will be discussed in more detail in the chapter). The size of the isoplanatic patch which prevails at the times of the selected exposures thus affects the range of astronomical targets for which a suitable reference star can be found for the Lucky Exposures approach. In this chapter the size of the isoplanatic patch around a reference star is calculated for the layered models under different atmospheric conditions. The timescales for changes in the speckle pattern and the isoplanatic angle are found to be determined by similar geometrical effects for these models, which helps to simplify the analysis.

In the last part of the chapter, Monte Carlo simulations of the atmosphere are used to investigate the range of short exposure Strehl ratios which are obtained with a variety of different telescope diameters and atmospheric conditions. This will be important in determining the applicability of the Lucky Exposures technique at various observatory sites.

I start this chapter with an introduction to measurements of the timescale for changes to speckle patterns in the image plane of a telescope. This will be useful in comparing results from my own simulations with previous observational results.