The Equivalent of Fourier Holography at the Nanoscale

Abstract

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 l=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.

Optical Holography Reconstruction of Nano-objects

“…18c. These patterns are similar to those observed for the prismatic nanocrystals (Sciammarella et al, 2009). The gray level intensity decays from 255 to 20 within 75 nm: this quantity corresponds to the radius of the nanosphere.…”

“…Successive shifted luminous images of the prism are then recorded. The largest fraction of energy is concentrated in the zero order and the first order (Sciammarella et al, 2009). These orders overlap in an area that depends on the process of formation of the image (see Fig.…”

“…Through this analysis and using the Fourier Transform it is possible to compute the thickness t of the prism in an alternative way to the procedure that will be described in the following. These developments are a verification of the mechanism of the formation of the images as well as of the methods to determine prism thickness (Sciammarella et al, 2009). Let us now consider the quasi-monochromatic coherent wave emitted by a nano-sized prismatic crystal.…”

“…New methods recently developed by C.A. Sciammarella and his collaborators (see, for example, Sciammarella, 2008;Sciammarella et al, 2009) rely on the emission of coherent light by the objects that are under analysis. This is done through the phenomenon of light generation produced by electromagnetic resonance.…”

Holography at the Nano Level With Visible Light Wavelengths

“…The second terms of the equations (18,19) are the Maxwell-Neumann equations that relate the absolute retardations to the principal stresses σ 1 and σ 2 . In the current case, since residual stresses are both compressive, it holds σ 1 < σ 2 .…”