Direct imaging of extra-solar planets in the visible and infrared region has generated great interest among scientists and the general public as well. However, this is a challenging problem. Difficulties of detecting a planet (faint source) are caused, mostly, by two factors: sidelobes caused by starlight diffraction from the edge of the pupil and the randomly scattered starlight caused by the phase errors from the imperfections in the optical system. While the latter difficulty can be corrected by high density active deformable mirrors with advanced phase sensing and control technology, the optimized strategy for suppressing the diffraction sidelobes is still an open question.; In this thesis, I present a new approach to the sidelobe reduction problem: pupil phase apodization. It is based on a discovery that an anti-symmetric spatial phase modulation pattern imposed over a pupil or a relay plane causes diffracted starlight suppression sufficient for imaging of extra-solar planets. Numerical simulations with specific square pupil (side D) phase functions, such as fx,y=a&sqbl0;ln &parl0;1+3+ 2x/D1+3-2x /D˙1+3 +2y/D1+3 -2y/D&parr0;&sqbr0; demonstrate annulling in at least one quadrant of the diffraction plane to the contrast level of better than 10-12 with an inner working angle down to 3.5lambda/D (with a = 3 and 3 = 10-3). Furthermore, our computer experiments show that phase apodization remains effective throughout a broad spectrum (60% of the central wavelength) covering the entire visible light range.; In addition to the specific phase functions that can yield deep sidelobe reduction on one quadrant; we also found that a modified Gerchberg-Saxton algorithm can help to find small sized (101 x 101 element) discrete phase functions if regional sidelobe reduction is desired. Our simulation shows that a 101 x 101 segmented but gapless active mirror can also generate a dark region with Inner Working Distance about 2.8lambda/D in one quadrant.; Phase-only modulation has the additional appeal of potential implementation via active segmented or deformable mirrors, thereby combining compensation of random phase aberrations and diffraction halo removal in a single optical element.
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