## Shaped pupil coronagraph mask 1

Internship research project for the Terrestrial Planet Finder (TPF) lab of Mechanical and Aerospace Engineering (MAE) department, at Princeton University. Advisor Dr. R. Belikov.

The abstract.

Terrestrial Planet Finder (TPF) is a project with the objective of finding earthlike planets in the vicinity of other stars. Such planets cannot be detected using simple telescopes, because for the planet to be earthlike, it has to orbit the star close enough. Planets at such a close radius cannot be seen through a telescope because once the starlight gets to the telescope lens, it diffracts, and this diffracted light is much brighter than the light reaching the telescope from the planet. To see the planet, the physicists at Princeton designed, through various optimization techniques, a telescope mask which creates a dark region very close to the star image, in which the weak light from the planet can be detected.

The contrast of 10^10 must be achieved in this dark region, because this is how much dimmer the planet is than the star. A way of achieving this contrast is by designing telescope masks to diffract the light in such a way as to cancel it out at certain regions of the image. These dark regions have to be where we expect to find the earthlike planets.

The first summer of my internship my job was to analyze how manufacturing errors in the mask affect its performance. The goal was to simulate the mask imperfections and calculate how it affects the contrast. The shape of the mask is defined by a set of functions which determine the outlines of the regions on the mask. From these functions I make a matrix representation of the mask. The diffraction pattern of the mask, the point spread function (PSF), is defined by the two-dimensional Fourier Transform of the matrix representation of the mask. First I used the fast Fourier transform routine in Matlab, but I discovered that it was inadequate, so I made my own.

To simulate errors in the mask I added random disturbance of different means and standard deviations, to the functions that define the mask. I defined criteria for the performance of the mask as the total area of the dark regions in its PSF and performed the number of random numerical experiments. By averaging results, I made plots of how the performance criteria depend on the mean and standard deviation of the errors added to the mask design.

To see the complete project, click the link: Internship Project 2