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Most optical holograms are produced using laser light. A wide laser beam is split into two parts. One part is directed unperturbed onto a photographic plate, the other part is reflected off (or shone through) the object being imaged. The reflected light interferes with the non-reflected portion at the surface of the photographic plate that records the resulting interference pattern. This pattern can only form if the light scattered from the object is coherent with the light falling directly on the photographic plate. This is why a laser is used as lasers have a coherence length greater that the difference of the two optical paths. This process was first described by Gabor1,2 in 1948.

Reconstruction of the optical hologram is achieved by illuminating the developed photographic plate with a planer laser light of the same frequency used to record the hologram.

A hologram of a very small point-like object produces a very simple looking interference pattern, it is a series of concentric circles. When reconstructed, this simple hologram will of course reconstruct the image of the point object. The pattern of concentric circles is exactly the same as a Gabor Zone plate, a device than can be used as a lens.

Incoherent radiation, such as white light or gamma radiation, cannot be used to form a hologram using the method described above. The interference pattern will not form because the radiation is incoherent. A type of hologram can, however, still be made.

Imagine a single point source of white light that is shining on to a screen. Any object placed between the light and the screen will cast a shadow on the screen. We define the x and y axes to lie in the plane of the screen and the z axis to be normal to the screen and passing through the light source.

```                                      |\
| \              y
|  \         x
|   \         \  |
|    |         \ |
/\                |    |          \|
*--------------(- )---------------+--  |----       O---- z
\/                |    |
Light                               |    |
Object               \   |
\  |
\ |
\|
Screen
```

If the object is in a fixed position relative to the screen then the position of the shadow will depend only on the position of the light source. If the light is moved in the xy plane, then the shadow will be cast in a different place on the screen. If the light is moved nearer to or further from the object then the shadow will become larger or smaller respectively. All pretty obvious so far.

The cunning bit is the next step. If we use a Gabor zone plate as our shadow-casting object, then the shadow cast will be a Gabor zone plate. So if we replaced the screen with a photographic plate, developed the image and then illuminated the result with laser light we would end up with a reconstruction of the original point! If you had two points of light to start with you would end up with two shadows and the reconstruction would show the two points again. The same holds for as many points as you care to add, so must be true for the image of any object.

This technique is known as zone plate encoded holography and was first proposed by Mertz and Young in 19613, and because it works with incoherent radiation it is also known as incoherent holography.

There are other types of zone plates apart from the Gabor zone plate. The Fresnel zone plates are similar but simpler. The opacity of a Gabor plate varies continuously and smoothly, whereas the Fresnel plates are either opaque or transparent, there is no in between. This makes them far easier to manufacture, especially when you have to make the plate opaque to gamma radiation. (It is far easier to punch gaps in a tungsten plate than it is to make it have an accurately graduated thickness, especially as absorption varies with thickness exponentially.)

The holograms, or shadowgrams, produced using this method can be reproduced computationally rather than by physical illumination. This can be done using a variety of methods, including deconvolution of the produced image. This essentially means hunting through the two dimensional image for the shape and size of the shadow expected for a source at a certain point. By hunting for many, many shadows the full three dimensional image can be reconstructed. This method has the advantage that any old plate can be used as the shadow but the Gabor plate still wins out, as any point in 3D space produces a uniquely shaped shadow on the recording surface.

## Practical Uses

One of the most interesting uses for this imaging is currently being investigated at the University of Birmingham by Beynon et. al. They are using it to monitor the size of deeply embedded brain tumours whilst the patient undergoes therapy. The particular type of treatment, BNCT (Boron-Neutron Capture Therapy) makes the tumour emit gamma radiation as a by product, these relatively harmless gamma rays can be caught by the above technique and thus the tumour's shape and size can be accurately monitored without the need for further examination of any kind. They use a specially designed Binary Gabor Zone Plate which as the name implies has the ease of construction of a Fresnel plate because it is only fully transmissive of fully opaque, not continuously variable like a true Gabor plate. However, it also has the advantage over the Fresnel plates in that it does not produce multiple foci like the Fresnel plates do.

1. Gabor, D. Nature. 161(4098), 777-778. May 1948
2. Gabor, D. Proceedings of the Royal Society of London. A197, 454-487. 1949
3. Mertz, L. Proceedings of the international Conference on Optical Instruments and Techniques. 305-312 (Chapman and Hall, London 1961).

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