**1. Introduction**

Fourier transform (FT) represents one of the oldest and the most powerful analytical tools in many fields such as applied mathematics, physical sciences, and engineering. Because FT helps to describe the physical mechanism of collecting and reconstructing data, it also becomes a priceless image-processing instrument in other areas which are related to biomedicine. The development of FT techniques pushed the utilization of the spectroscopic methods dramatically. So, FT methods have long been proved to be extremely useful in all fields of science and technology, such as radio-astronomy, seismology, spectroscopy crystallography, medical image processing, and signal analysis techniques.

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© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Particularly, Fourier transform spectroscopy (FTS) has become an innovative, powerful, and extra sensitive method to study biologically important systems, varying from simple molecules to highly complex samples such as living cells and tissues. These enhanced spectroscopic methods in their modern form represent an important area of research with various applications in diverse fields of science and industry.

The main purpose of this chapter is to provide a modern review about the recent advances on FTS technique with a wide range of medical, biological, and biomedical applications. This chapter begins with a short history about FTS, followed by a description of the theoretical background of FTS with emphasis of some remarkable new results of the research of the quantum dots (QDs) based on Fourier transform visible spectroscopy (FTVS).

After a short historical presentation of the evolution of the important discoveries in the field of the Fourier transforms, the basic ideas of the FT theory are briefly reviewed. In what follows, the power of the Fourier transforms is illustrated through new spectral applications in medicine, biological, and biomedical areas.

In this present chapter, the Fourier transform spectroscopic techniques discussed in the chapter and their important physical principles will be described, that is, Fourier transform spectroscopy, such as Fourier transform visible spectroscopy, Fourier transform infraredattenuated total reflectance (FTIR-ATR), Fourier transform infrared-photoacoustic spectroscopy (FTIR-PAS), Fourier transform infrared imaging spectroscopy (FTIR imaging), and Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS).

This review is focused on presenting new developments in FTS technique sample preparation methods, experimental conditions used in these investigations, and its useful applications in various fields of biomedical and biological research, including examples of recent advances in the area of nanobiotechnology. Among many other various products of nanotechnology, semiconductor nanocrystals or quantum dots are useful for biomedical research and applications.

Nanobiology, as an area of study, represents the fusion of the biological research with the nanotechnologies such as nanodevices and nanoparticles. This combination of nanotechnology with biology has resulted in the development of diagnostic tools, contrast agents, physical therapy applications, and targeted drug delivery vehicles [1].

Nanomedicine is the medical application of nanotechnology and involves the programs for the application of newly emerging nanotechnologies to molecular processes at the cellular level. The applications of this area of nanoscience include drug delivery, both *in vitro* and *in vivo* diagnostics, nutraceuticals, and production of biocompatible materials. An important device to achieve a series of applications is the engineered nanoparticles [2].

By grouping the study into these areas of research, the general modalities in which the nanotechnology, biology, medicine, and FTS methods are brought together for common research purposes can be noticed.

In this sense, an FTS system able to evaluate optical properties of the CdSe/ZnS core-shell QDs, produced by Evident Technologies, is presented. So, by the use of ARCspectroHT-HR Fourier transform spectrometer (ARCOPTIX S.A. Switzerland), the fluorescence spectra of QDs for two excitation sources (a UV laser and a blue LED) are discussed [3]. This study reveals that the FTVS of commercial quantum dots is used to show that CdSe/ZnS core-shell QDs are an example of nanomaterial that is useful such as an alternative to classical fluorochromes in order to label microbial cells.

In another research work, the FTVS is presented like a novel, rapid, and efficient technique to provide quantitative information about the QDs, including their sizes. The use of FTVS methodology for the size determination of CdSe/ZnS core-shell QDs can be easily extended to other types of QDs. Some relationships between the QD size and its corresponding fluorescence average wavelength, calculated from each emission peak of the Fourier transform spectrum, are discussed in this study [4]. The characterization of QD dimension with the help of the FTVS is important in their preparation procedures and their applications.

The reference list contains both historical and extensive analysis works together with the articles that describe several key breakthroughs in the mentioned areas of interest.
