Nano-Holographic Interferometry for In-Vivo Observations - Biomedical Optical Phase Microscopy and Nanoscopy - page 340

CHAPTER 17
Nano-Holographic Interferometry for
In-Vivo Observations

Federico M. Sciammarella 1 , Cesar A. Sciammarella 2 , Luciano Lamberti 2

1

College of Engineering and Engineering Technology, Northern Illinois University, DeKalb, IL
2

Dipartimento di Ingegneria Meccanica e Gestionale, Politecnico di Bari, Bari, Italy

Editor: Natan T. Shaked

17.1 Introduction: Theoretical Basis of Nano Fourier
Transform Holography

With the introduction of holographic recording in the Fourier transform (FT) space,
applications for reconstructing objects have gained considerably in spatial resolution [1 4] .

The utilization of Fourier transform holography (FTH) is well documented both in the
visible light realm [5,6] and in other frequencies of the electromagnetic spectrum [7,8] .

The work presented in this chapter is a variant of FTH that utilizes evanescent illumination
to increase the spatial bandwidth of the recorded holograms and includes Fourier transform
holographic interferometry (FTHI). Following the principle of reverse interference postulated
by Toraldo di Francia [9] and using numerical procedures based on Fourier image analysis,
image components can be analyzed in different regions of the spatial frequency spectrum.

In the scheme of plane-wave solutions of the Maxwell equations available in classical
optics, monochromatic waves with definite frequencies and wave numbers are usually
considered. However, this idealized condition does not apply in the present case. One of the
foundations of this new method is the observation of objects that are self-luminous. The
objects themselves will generate electromagnetic waves that are related to the object's
material properties and depend on the geometry of the object: hence, these waves carry
information on the object configuration. The object is excited by an evanescent
electromagnetic field and under conditions of resonance will emit light. A superposition
of waves will be generated and it will be distributed over the frequency bandwidth Δ thus

producing a sequence of wave packets of length 2 π / Δ .