Automated PSF modelling of telescopic images blurred with optic and atmospheric noise

Abstract

Man's model of the world and the universe has evolved over time from what could be seen and touched to what can be inferred. As this model became more sophisticated it began to show that the directly observable universe is only a very small component of all matter and energy in existence. It is thought that a large amount, about 953, of matter in the universe is not directly visible. This is believed to be a combination of Dark Matter and Dark Energy. Techniques like Gravitational Lensing are used to infer the presence of Dark Matter. This technique is based on an effect that causes distant objects like galaxies, to appear distorted to observers. The mass in between the observer and the source causes this warping effect. The distortion of an observed image is proportional to the amount of mass that caused it. The mass of observable matter is subtracted from the determined using this technique to obtain an accurate measurement of the quantity of Dark Matter. In order to measure this distortion or shear of galaxies within the images taken from Earth using telescopes, the images must be first ("cleaned" from) secondary effects. The images used in Gravitational Lensing surveys are subject to further degradation such as blurring due to imperfections in telescope optics, light diffraction in the atmosphere, pixilation and noise. The primary goal of this project is to model the way the image degrades, due to these effects. The secondary goal is to show that a common pattern exists in the way the image blurs across many observations by finding high correlations across these models. A blur can be used to categorised know as a Point Spread Function (PSF). The PSF describes how a pixel's intensity is dispersed across an area causing a blurring effect. This project makes use of stellar images to model the blur variation throughout an image. An accepted technique when dealing with blur variation is that the PSF does not vary within small areas. The image is segmented into small windows and a technique called independent component analysis (ICA) is used to extract the averaged PSF from each window. A simple interpolation is carried out between each window to fit a surface that correctly depicts the PSF variation. Once the PSF is modelled on different images a property of the PSF, in this case the orientation is extracted. Using the calculated orientation we can determine correlations between similar blurring patterns across images. In order to reduce the PSF into a comparable metric, its shape is analysed and orientation determined. Using this derived orientation correlations were determined between blurring patterns across images. The results produced by this project have shown, that within each image lies a correlated PSF pattern showing high area to orientation similarities. This result means that the images do in-fact have a very visible underlying pattern. The analysis across multiple models yielded results showing high matches. The variations found in separate images where found to match to a very high degree.