Ghost projection via focal-field diffraction catastrophes

Ghost projection is the reversed process of computational classical ghost imaging that allows any desired image to be synthesized using a linear combination of illuminating patterns. Typically, physical attenuating masks are used to produce these illuminating patterns. A mask-free alternative form of ghost projection is explored here, where the illuminations are a set of caustic-laden diffraction patterns known as diffraction catastrophes. These are generated by focusing a coherent beam with a spatially modulated phase having random Zernike-polynomial aberrations. We demonstrate, via simulation, that a suitable linear combination of such random focal-field intensity patterns can be used as a basis to synthesize arbitrary images. In our proof-of-concept ghost-projection synthesis, the positive weighting coefficients in the decomposition are proportional to exposure times for each focal-field diffraction catastrophe. Potential applications include dynamic on-demand beam shaping of focused fields, aberration correction, and lithography.