Kai-Erik Peiponen

Theory of Reflectance

The accurate measurement of the refractive index of transparent liquids is possible using conventional devices such as Abbe-refractometer or an interferometer. The problems of estimation of the real refractive index arise when the liquid is optically very thick i.e. absorbing but non-scattering, or the liquid is turbid which usually means relatively strong scattering of light and sometimes simultaneous absorption of light. Fortunately, reflection spectroscopy can be applied to such difficult tasks that require the estimation of the complex refractive index of turbid liquids. In addition reflection spectroscopy can provide means for adsorption studies [50] such as for example contamination of probe window. There are sources that describe thoroughly the exploitation of reflection spectroscopy in material research [51, 52] and industrial measurement applications [53]. However, there has been recent progress both in technology for reflection spectroscopy and spectra analysis, which give new light to the physical phenomena behind the measured data related to reflection measurements. In this chapter we will describe the theory of the oblique incidence light reflection from absorbing or turbid liquids.

Demands on Measurement of Optical Constants of Liquids in Science and Industry

The optical properties of liquids have been investigated for a long time in science. Such investigations have provided much information related to the material properties of pure liquids. With the aid of optical spectroscopy the intrinsic optical properties of many liquids have been measured and calculated. Since the optical properties depend on the thermodynamic state of the liquid, refractive index and absorption of light has been investigated for liquids at different temperature and pressure. Such studies are usually related to basic studies in material sciences. Different optical measurement methods and theories for assessment of the optical constants (refractive index and extinction coefficient) have been well documented in literature. As an example of the richness of the methods and theory we mention the classical book written by Partington [1]. Nowadays, due to the progress in technology, such as machine vision, and in theory development, new measurement methods and theories have arisen, which may complement the older ones. One typical feature in modern optics is the demand on one hand that the optical constants are required with an increasing accuracy, and on the other hand smaller changes of the optical constants should be measured. Recently, the investigation of bio-optical liquids has become an important field of research in science and optical spectroscopy plays a big role in that field see e.g. [2]. As concern reflection spectroscopy in bio-optical research we mention for instance the utilization of surface plasmon resonance as a sensitive method for detection of dynamic biological interactions [3].

Exploring the Insides of a Spectrophotometer

The functioning of optical measurement devices is based on the observation of changes and effects produced by the interaction of electromagnetic radiation and matter. From a technical viewpoint this requires the generation of electromagnetic radiation, the modification of its characteristics and the control of its propagation through a given space. Similarly, the “fingerprints” which the material leaves on the radiation need to be producible in an easily understood form. In this often complicated process use is made of optics, optoelectronics, electronics and mechanics. In this chapter we shall examine the nature and application of the main components used in spectroscopic instruments. These include light sources, components and devices for selecting the desired wavelength, polarizers and detectors.

Understanding Your Signal

Manmade devices intended for performing measurements of even the slightest complexity operate to a greater or lesser extent non-ideally. The final result includes an error component, the origin of which may be traced to inadequate calibration, noise, stray light, incorrect data processing or user error. In addition, careless sampling and sample processing cause problems. In this chapter we will look at indicators of measuring device performance, sources of error and methods for eliminating noise.

From Theory to Measurement

In this final chapter we shall present results obtained from the application of methods and theories described in Part I of this book. Actual measurements were performed using a reflectometer constructed for the measurement of liquids. Our main aim was to seek and develop effective measurement and calculation techniques for determining the optical properties of various types of liquids. By optical properties we mean those quantities which describe the progress of an electromagnetic wave through a homogenous liquid — in other words, the refractive index and the extinction coefficient. Our choice of samples also included diffusing liquids such as milk and paper coating suspension. Our interest lay chiefly with reflection measurements because, in terms of measurement geometry, these are well suited to e.g. problematic industrial process measurements.

Definitions of Optical Instrumentation and Measurement

In this chapter we turn our attention to the definitions, terms, quantities and units most commonly employed in optical instrumentation and measurements. For example, in the planning and construction of experimental arrangements and, in particular, in the application of light sources and detectors there is a need for a basic understanding of radiometry and photometry. We will also define some basic concepts such as absorptance, transmittance and reflectance. There is still a plethora of terms in use in this field of science. Indeed, terminology developed for use in one discipline is sometimes carelessly applied in another. Our treatment of this subject follows the thorough expositions by Zalewski [178] and Palmer [179].

Theory of Optical Constants

In the UV—VIS spectral range the interaction of electric field with a liquid phase is important and the interaction of magnetic field with liquid can usually be neglected in most cases of practical optical metrology. The electric charges of molecules in liquids experience the coulombian interaction. In addition to mutual interaction of the molecules, external electric field, such as light can disturb the charge distribution of the electrons. Liquids belong to materials, which are called dielectrics. Dielectrics are non-conducting but polarizable media, which can be either permanently polar or nonpolar. Molecules, which have a center of symmetry i.e. they are arranged in a symmetric manner are nonpolar, whereas asymmetric molecules are polar. However, light can disturb the electron charge cloud of a polar or nonpolar medium and, hence, to induce a polarization. Next we consider in details the interaction of light with the electronic system of a liquid.

Probe Window Contamination and Reflectance

In practical metrology, especially in industrial environments, the measurement conditions are usually hostile. If we consider for instance the quality assessment of process liquids in process industry such as paper mill the contamination of the probing face of prism reflectometer is a drawback. In other words different constituents of the liquid can be adsorbed on the probe face. This in turn causes change in the reflectance signal either because of the change of the complex refractive index or because of light scattering in the vicinity of interface between the liquid and the probe face. In this chapter we briefly describe simple models that may be used for evaluation of the growth of contamination on the probe window. Then we are talking about adsorption. In addition we consider a totally contaminated layer and related depth profiling.

Wavelength Spectra Analysis

A great deal of our knowledge related to spectroscopic properties, such as dispersion and absorption of light, of media is based on the exploitation of Kramers-Kronig (K-K) dispersion relations [120–122]. The idea of KramersKronig relations for complex electric field reflectance is that the phase of the electric field can be calculated, as a function of wavelength, with the aid of the intensity reflectance, which is measured. Then the complex refractive index is obtained e.g. from (4.1) or (4.2). Probably the most common situation is where the dispersion relations are applied for normal reflectance i.e. reflectance that is measured at normal incidence. Unfortunately, the rigorous derivation of K-K relations is usually neglected in the literature of the field, probably due to some mathematics, which usually involves complex analysis. However, in the derivation some crucial assumptions are made and one has to be convinced that these assumptions are fulfilled in order to apply K-K relations. Therefore we will spend some time in dealing with the assumptions and derivations of the K-K relations. We will also point out that especially in nonlinear optics the K-K relations can be invalid. As an alternative method, which has been pointed out to be more powerful than K-K relations, we deal with maximum entropy model in phase retrieval problems of spectroscopy. We begin the presentation, due to historical reasons, by derivation of the K-K relations of the complex refractive index. Such relations have importance especially in transmission spectroscopy. The results for the complex refractive index are helpful when we derive the K-K relations for the complex reflectance.

Nonlinear spectral properties of layered nanocomposite materials

We present here predictions for a nonlinear optical response of nanocomposites having a layered structure. In particular, we have studied nanocomposites with alternating thin layers of titanium dioxide and nonlinear optical polymers (PT10 and PDHS). It is demonstrated that both enhancement in magnitude and change in spectral properties of the degenerate third-order nonlinear susceptibility can be tailored in such composites.