The Equivalent of Fourier Holography at the Nanoscale

The paper deals with optical holographic interferometry at the nanometric scale. The observed objects are sodium chloride nanocrystals. The object illumination is done through the use of evanescent wavefronts. The observed crystals become self-luminous objects producing pseudo-non-diffracting wavefronts. The wavefronts emerging from the crystals are the result of electromagnetic resonances of the crystals. A microscope is utilized to register the wavefronts generated by the crystals. A 6 μm spherical particle made of polystyrene acts as a relay lens to collect the wavefronts that are recorded by a monochromatic CCD and a color camera attached to the microscope. The structure of the recorded images is determined through Fourier transform analysis. It is shown that the recorded images are lens holograms formed by the interference of the wavefronts generated by the crystals. Fourier transform algorithms and edge detection algorithms are utilized to obtain the dimensions of the crystals. The power of Gabor’s idea when he invented holography is again proven in this study. If the problem of super-resolution is viewed from the point of view of the Theory of Communications, the fact that one can register both amplitude and phase of a signal of a self-luminous object provides the means of reaching spatial resolutions with average standard deviation of ±3 nm using helium–neon laser illumination of λ = 632.8 nm. The resolution that can be achieved depends on the structure of the observed material, in the present case ±5d, where d is the distance of the atomic planes of the NaCl. With improvements in the hardware and software higher resolutions may be feasible.