The occulter, whose screen may take one or more of a myriad number of shapes, will act as an opaque apodizing screen, redistributing the energy over the telescope aperture. There are many sources that describe diffraction phenomena related to this basic problem (Born and Wolf 1980, Hecht and Zajac 1987, etc ...) Only a brief description of the problem is given here.
Diffraction is used to describe the phenomenon of light bending around the edges of an object and converging on the opposite side. This phenomenon is due to the wave like nature of light.
If we consider a square occulter 45 m on a side at a distance of 16,000 km from the telescope, it has a width of 0.58 arcsec. A pattern of light from a blocked star will be visible within the shadow of the occulter. The diffraction pattern within the shadow area will be surrounded by a series of bright and dark (null) fringes with bright diffraction spikes due to straight edges of the occulter.
To the left is the PSF (point spread function) of a star as seen through a conventional telescope. The PSF is the resultant image of the light from a very distant, point-like source of light--such as a star. The four spikes leading off the star are produced by diffraction of the starlight around support arms (spider) for the secondary mirror in this newtonian/reflector design. The spider in Newtonians gets in the way of part of the light and produces these features in the image plane. The role of the occulter is to:
The physical size of the occulter and its distance from the telescope are the deciding factors in the resulting on-axis intensity of light and the average intensity over the aperture. The larger the physical size of the occulter (occulter subtends larger angle), the greater the reduction in the on-axis and average intensities of the light in the image plane.
But, a larger subtended angle defeats the goal of looking for planets near their parent stars. Therefore, placing the occulter further away (occulter subtends smaller angle) is required.