Optical holography is a technique which enables an optical wavefront to be recorded and later re-constructed. Holography is best known as a method of generating three-dimensional images but it also has a wide range of other applications. A hologram is made by superimposing a second wavefront (normally called the reference beam) on the wavefront of interest, thereby generating an interference pattern which is recorded on a physical medium. When only the second wavefront illuminates the interference pattern, it is diffracted to recreate the original wavefront. Holograms can also be computer-generated by modelling the two wavefronts and adding them together digitally. The resulting digital image is then printed onto a suitable mask or film and illuminated by a suitable source to reconstruct the wavefront of interest.
Basic physics To understand the process, it is helpful to understand interference and diffraction. Interference occurs when one or more wavefronts are superimposed. Diffraction occurs when a wavefront encounters an object. The process of producing a holographic reconstruction is explained below purely in terms of interference and diffraction. It is somewhat simplified but is accurate enough to give an understanding of how the holographic process works. For those unfamiliar with these concepts, it is worthwhile to read those articles before reading further in this article. A simple hologram can be made by superimposing two plane waves from the same light source on a light recording medium such as a photographic emulsion. The two waves interfere, giving a straight-line fringe pattern whose intensity varies sinusoidally across the medium. The spacing of the fringe pattern is determined by the angle between the two waves, and by the wavelength of the light. The recorded light pattern is a diffraction grating, which is a structure with a repeating pattern. A simple example is a metal plate with slits cut at regular intervals. A light wave that is incident on a grating is split into several waves; the direction of these diffracted waves is determined by the grating spacing and the wavelength of the light. When the recorded light pattern is illuminated by only one of the plane waves used to create it, it can be shown that one of the diffracted waves is a re-construction of the other plane wave.
When a plane wave is added to a point source and the resulting interference pattern recorded, a point source hologram is produced. This is effectively a Fresnel zone plate which acts as a lens. If the plane wave is normally incident on the recording plate, three waves are diffracted by the plate the original plane wave a wave which appears to diverge from the point source - this is a reconstruction of the original point source wave a wave which is focused to a point on the other side of the plate at the same distance as the original point source This is known as an in-line hologram. Its usefulness is limited by the fact that all three waves are superimposed. If the plane wave illuminates the recording plate at non-normal incidence, then the three diffracted waves are now as follows:
the original plane wave a wave which appears to diverge from the original point source - this is the re-constructed wave a wave which converges to a point which is deflected from the normal by twice the angle of incidence of the plane wave - this is known as the conjugate wave. The three waves are now separated in space. This is known as an off-axis hologram. It was first developed by Leith and Upatnieks and was a vital step in enabling 3-d images to be produced with holography.
Theory underlying the holographic process
General form The complex amplitude of a monochromatic electromagnetic wave can be represented by
U ( r ) = A exp i [ φ ( r ) ] {\displaystyle \mathbf {U} (\mathbf {r} )=A\exp {i[\varphi (\mathbf {r} )]}}
where A represents the amplitude of the vector, and φ ( r ) {\displaystyle \varphi (\mathbf {r} )} its phase. To make a hologram, two waves are added together to give a total complex amplitude which can be represented as
U T = U R + U O = A R exp i ( φ R ) + A O exp i ( φ O ) {\displaystyle \mathbf {U} _{\text{T}}=\mathbf {U} _{\text{R}}+\mathbf {U} _{\text{O}}=A_{\text{R}}\exp {i(\varphi _{\text{R}})}+A_{\text{O}}\exp {i(\varphi _{\text{O}})}}
where R refers to the recording wavefront, known as the reference wavefront, and O refer to the wavefront being recorded. The dependence on r has been omitted for clarity. The intensity of the combined beams is the average value of the complex amplitude times its complex conjugate:
… excerpt ends here. Continue reading the full article.
