Explanation of the various effects of light is a very elusive task. Although light has captured the imagination of human beings since the dawn of civilization, science has yet to deliver a single, comprehensive explanation of all its effects. The advanced theories that now exist create many new questions along with new answers. Part of the confusion can be blamed on our tendency to explain physical phenomena using the perception of our senses. Unfortunately, our senses do not tell the full story. Although we can see light, and even distinguish among some of its colors, we cannot see most of the radiation emitted by the sun. Even our ability to visually determine the brightness of light sources is limited by the rapid saturation of the eye retina. Our senses tell us that light propagates in straight lines, yet careful experiments have demonstrated that the trajectories of light can be bent by gravitation. We cannot even capture and store light.

Holographic interferometry is an extension of interferometric measurement techniques in which at least one of the waves that interfere is reconstructed by a hologram.

The unique capabilities of holographic interferometry are due to the fact that holography permits storing a wavefront for reconstruction at a later time. Wavefronts which were originally separated in time or space or even wavefronts of different wavelengths can be compared by holographic interferometry. As a result, changes in the shape of objects with rough surfaces can be studied with interferometric precision.

One of the most important applications of holographic interferometry is in nondestructive testing (see Erf [1974], Vest [1981], and Rastogi [1994]). It can be used wherever the presence of a structural weakness results in a localized deformation of the surface when the specimen is stressed, either by the application of a load or by a change in pressure or temperature. Crack detection and the location of areas of poor bonding in composite structures are fields where holographic interferometry has been found very useful. An allied area of applications has been in medical and dental research, where it has been used to study the deformations of anatomical structures under stress, as well as for nondestructive tests on prostheses [Greguss, 1975, 1976; von Bally, 1979]; see also, Podbielska [1991, 1992].

Holographic interferometry has also proved its utility in aerodynamics, heat transfer, and plasma diagnostics.

The past ten years have seen an upsurge of interest in optical holography because of several major advances in its technology. Holography is now firmly established as a display medium as well as a tool for scientific and engineering studies, and it has found a remarkably wide range of applications for which it is uniquely suited.

My aim in writing this book is to present a self-contained treatment of the principles, techniques, and applications of optical holography, with particular emphasis on recent developments. After a brief historical introduction, three chapters outline the theory of holographic imaging, the characteristics of the reconstructed image, and the different types of holograms. Five chapters then deal with the practical aspects of holography – optical systems, light sources and recording media – as well as the production of holograms for displays and colour holography. The next two chapters discuss computer-generated holograms and some specialized techniques such as polarization recording, holography with incoherent light, and hologram copying. These are followed by four chapters describing the more important applications of holography. Particle-size analysis, high-resolution imaging, multiple imaging, holographic optical elements, and information storage and processing are covered in two of these, and the other two are devoted to holographic interferometry and its use in stress analysis, vibration studies, and contouring.

To make the best use of the available space, the scope of the book has been limited to optical holography.

Introduction

Previous discussions (see Section 10.4) suggested that stimulated emission can be used to generate optical gain, that is, to amplify radiation. The reader certainly has experience in the amplification of electronic signal. For example, radio receivers capture faint radio waves and turn them into a signal that is powerful enough to drive large speakers. This electronic amplification increases the amplitude of the signal while faithfully preserving its acoustic frequencies and modulation characteristics. Similarly, optical amplification is expected to increase the amplitude of an optical signal while preserving its frequency, its modulation characteristics, and its coherence. The latter requirement is of particular significance for optical radiation, where the coherence of naturally occurring radiation rarely exceeds one micrometer. Lasers are the primary source for coherent radiation. They depend on stimulated emission for amplification and for the generation of coherent radiation (the word laser is the acronym of Light Amplification by Stimulated Emission of Radiation). For amplification, an atomic system that is part of the laser medium must be prepared with a sufficiently large number of particles in the excited state. (The term atomic system is used here to describe all microscopic systems including molecules and free electrons.) Radiation passing through that excited medium encounters multiple events of stimulated emission, each event contributing one photon that is added coherently to the propagating beam. When the number of events of stimulated emission exceed all losses by absorption or scattering, the incident radiation is amplified.

Introduction

In the previous chapter we saw that, when electric dipoles are forced to oscillate, they induce an electric field that oscillates at the same frequency. In addition, owing to the motion of the oscillating charges, a magnetic field oscillating at the same frequency is also induced. These simultaneous oscillating fields are the basis for all known modes of electromagnetic radiation. Thus, Xrays, UV radiation, visible light, and infrared and microwave radiation are all part of the same physical phenomenon. Although each radiating mode is significantly different from the others, all modes of electromagnetic radiation can be described by the same equations because they all obey the same basic laws.

Oscillation alone is insufficient to account for electromagnetic radiation. The other important observation is that radiation propagates. It is broadcast by a source and, if uninterrupted, can propagate indefinitely in both time and space. An example of the boundless propagation of electromagnetic waves – whether X-ray, visible, or microwave – is the radiation emitted by remote galaxies. Some of this radiation, generated at primordial times and at remote reaches of the universe, can be detected on earth billions of years later. Evidently, radiation is not limited to the immediate vicinity of the source. Although we know that certain media can block radiation, we find it more astonishing that electromagnetic waves can propagate through free space; unlike electrical currents or sound, conductors are not necessary for the transmission of radiation.

Holographic microscopy

As mentioned in Chapter 1, holographic imaging was originally developed in an attempt to obtain higher resolution in microscopy. Equations (3.20) and (3.21) show that it is possible to obtain a magnified image if different wavelengths are used to record a hologram and reconstruct the image, or if the hologram is illuminated with a wave having a different curvature from the reference wave used to record it. However, neither of these techniques has found much use, in the first instance because of the limited range of coherent laser wavelengths available, and, in the second, because of problems with image aberrations [Leith & Upatnieks, 1965; Leith, Upatnieks & Haines, 1965].

The most successful applications of holography to microscopy have been with systems in which holography is combined with conventional microscopy. In one approach, a hologram is recorded of the magnified real image of the specimen formed by the objective of a microscope, and the reconstructed image is viewed through the eyepiece [van Ligten & Osterberg, 1966]. While this technique offers no advantages for ordinary subjects, it is extremely useful for phase and interference microscopy [Snow & Vandewarker, 1968]. In another, a hologram is recorded of the object, and the reconstructed real image is examined with a conventional microscope. This technique is particularly well adapted to the study of dynamic three-dimensional particle fields, as described in the next section.

Introduction

Of the three phenomena that result from the wavelike nature of light – polarization, interference, and diffraction – the third is the most puzzling. It does not render itself to intuitive explanation, since intuition suggests that light propagates in straight lines. Diffraction, however, allows for light under certain conditions to travel “around corners.” Because of this effect, light may be detected at points that could not be reached by straight rays. This effect also prevents indefinite propagation of collimated beams; invariably, after a certain distance, collimated beams appear to diverge. Similarly, when a focusing lens designed using considerations of geometrical optics is employed to focus radiation, the spot size at the focus cannot be reduced below a defined limit. In these examples, diffraction is seen to pose limitations on the application range of many optical devices. Thus, imaging resolution is reduced by the diffraction limits of lenses, power delivery by collimated laser beams is limited by their divergence, and the application of masks for processing semiconductor chips with photolithographic techniques is limited by diffraction induced by the minute pattern of the masks.

However, there exist numerous applications where diffraction presents an advantage. One example is the diffraction grating used for spectral separation of radiation (see Section 7.3). Another example is the advent of Fourier optics. This relatively new technology is based on the diffraction-limited imaging properties of lenses.

When confronted with a hologram for the first time, most people react with disbelief. They look through an almost clear piece of film to see what looks like a solid object floating in space. Sometimes, they even reach out to touch it and find their fingers meet only thin air.

A hologram is a two-dimensional recording but produces a three-dimensional image. In addition, making a hologram does not involve recording an image in the usual sense. To resolve these apparent contradictions and understand how a hologram works, we have to start from first principles.

The concept of holographic imaging

In all conventional imaging techniques, such as photography, a picture of a three-dimensional scene is recorded on a light-sensitive surface by a lens or, more simply, by a pinhole in an opaque screen. What is recorded is merely the intensity distribution in the original scene. As a result, all information on the relative phases of the light waves from different points or, in other words, information about the relative optical paths to different parts of the scene is lost.

The unique characteristic of holography is the idea of recording the complete wave field, that is to say, both the phase and the amplitude of the light waves scattered by an object. Since all recording media respond only to the intensity, it is necessary to convert the phase information into variations of intensity.

A typical optical system for recording transmission holograms of a diffusely reflecting object is shown in fig. 5.1; one for recording a reflection hologram is shown in fig. 5.2.

A simpler system for making reflection holograms is shown in fig. 5.3. This arrangement is essentially the same as that described originally by Denisyuk [1965] in which, instead of using separate object and reference beams, the portion of the reference beam transmitted by the photographic plate is used to illuminate the object. It gives good results with specular reflecting objects and with a recording medium, such as dichromated gelatin, which scatters very little light.

Making a hologram involves recording a two-beam interference pattern. The principal factors that must be taken into account in a practical setup to obtain good results are discussed in the next few sections.

Stability requirements

Any change in the phase difference between the two beams during the exposure will result in a movement of the fringes and reduce modulation in the hologram [Neumann, 1968].

In some situations, the effects of object movement can be minimized by means of an optical system in which the reference beam is reflected from a mirror mounted on the object [Mottier, 1969]. Alternatively, if the consequent loss in resolution can be tolerated, a portion of the laser beam can be focused to a spot on the object, producing a diffuse reference beam [Waters, 1972].

Introduction

The emission and absorption of radiation, as well as the conversion of radiation into other modes of energy such as heat or electricity, all involve interaction between electromagnetic waves and atoms, molecules, or free electrons. Such daily phenomena as the radiative emission by the sun, the shielding of earth from harmful UV radiation by the ozone layer, the blue color of the sky, and red sunsets are all – despite their celestial magnitude – generated by microscopic particles. Most lasers depend on emission by excited atoms (e.g. the He-Ne laser), ionized atoms (the Ar+ laser), molecules (CO or CO2 lasers), impurities trapped in crystal structures (Nd: YAG or Ti:sapphire lasers), or semiconductors (GaAs diode lasers). Similarly, many scattering processes of interest (e.g., Rayleigh or Mie scattering) result from the exchange of energy and momentum between incident radiation and atomic or molecular species. In the previous chapter we saw that the energy of microscopic particles is quantized: their energy can be acquired, stored, or released only in fixed lumps called quanta. The example of the “particle in the box” (eqn. 8.19) illustrated that these energy quanta are specific not only to the particle itself but to the system to which it belongs. Thus, in the box, the energy of the particle is specified by its own mass and by the dimension of the box; in a different box, the same particle will have an entirely different system of energy levels and the quanta will have different magnitudes.

Introduction

Until now, our discussion of the interaction between radiation and matter has concentrated only on the spectral aspects of radiation. The results could determine the wavelengths for absorption and emission or the selection rules for such transitions, but could not be used to determine the actual extent of emission or absorption. These too are important considerations which are needed to fully quantify radiative energy transfer. Unfortunately, none of the classical theories can predict the extent of emission from an excited medium, or even the extent of absorption. Although the discussion in Section 4.9 (on the propagation of electromagnetic waves through lossy media) touched briefly on the concept of attenuation by absorption, it failed to show the reasons for the spectral properties of the absorption or to accurately predict its extent. We will see later that the classical results are useful only as a benchmark against which the actual absorber is compared. The objective of this chapter is therefore to present an introduction to quantum mechanical processes that control the emission and absorption by microscopic systems consisting of atoms and molecules. The results will then be used to predict the extent of emission by media when excited by an external energy source and to evaluate the absorption of incident radiation.

It is now well recognized that all emission or absorption processes are the result of transitions between quantum mechanical energy levels.