Holograms

A photograph is a store of information.  Unfortunately the word "information" has at least two different usages.  One refers to the data which are stored in bytes and pixels.  The quantity of information can be precisely specified in terms of bits.  Another usage refers to the meaning of the set of data for a user.  For example a JPEG file conveys no useful information to a program that can only read GIFs.  A photograph may carry a lot of meaning if the viewer is prepared by knowing something about the subject.  

A photograph, or a TV image, of a familiar subject, however clear, is seldom recognized by a pet animal.  Yet a robin may attack a crude model or its own reflection in a mirror, and a stickleback during the breeding season will respond aggressively to a red blob.  A cartoon contains much less information than a photograph, yet the subject may be instantly recognizable.

We interpret a photograph in terms of three dimensional space, yet both the photograph and the image of a scene on the retina carry only indirect clues about spatial position.  That is one reason why "impossible objects" and optical illusions can be so fascinating.

Only the first sense of information will be used here.  A photograph. like an eye, throws away vast amounts of information.  This is inevitable in representing a three dimensional scene on a flat surface.  Colours, too, are ruthlessly simplified, often being encoded in the responses of only three types of receptor.  We don’t know how much interpretation the eye-brain system does in looking at a photograph. Sometimes it adds unwanted information.  For example, because we are used light from above, if we see a photograph of some side-lit object with deep relief, and the photograph is lit from below, we may find it difficult not to see the valleys and ridges of the subject inverted.

A well known illusion uses a mask which is is hollow instead of bulging.  It is so difficult to see it as it really is, that when we move, we see the mask as rotating, even though we know it is fixed.

To retain some information about the third dimension of a subject we need to store some information about the direction from which light falls on the storage medium.  And the medium must recreate those directions afterwards.  Photographs don’t do that.  A hologram does.  In order to get this extra spatial information, we actually need some timing information about the light.  This may seem strange, but effects in space and time often get interwoven where waves and oscillations are concerned.

How can we get some timing information about the light?  Think of a lone soldier on the parade ground.  No matter how well he has been drilled, and how well he has learned, we cannot attach meaning to the phrase "being in step".  A second soldier is needed in order to talk about that.  And that is what we need with light, a second source for comparison.  In practice it ought to be the same source that illuminates the subject, because otherwise there will be no relationship between the two sets of light rays.  Unrelated light sources would be like a film of marching soldiers, with a sound-track made on another occasion by a different band with a different squad.  

Many holograms are made by illuminating the film in two ways – whit light straight from the source, and with light that has been reflected from the subject.  The phrase "straight from the source" may conceal a number of mirrors and prisms, but these have no significant effect on the light.  On the film these two light sources interact in a way which leaves a record of their relative phases. ( See Interference )  The light does not even have to be focussed on the film – it can spread all over it.   So even a part of the hologram can reconstruct the image.

What happens at the storage medium is that the addition of light waves is strictly according to the size and polarity of the two incoming waves at any point.  They may add or subtract.  A photograph consists of areas whose brightness is related to the brightness of the corresponding parts of the object.  A hologram is encoded quite differently.  There is no one-to-one correspondence of the the parts of the medium and the parts of the message.

A vaguely analogous example might be the chord of C major on a piano.  On the score it just looks like four blobs.  A spectrum analyzer would show four peaks.  But a microphone and oscilloscope would show a complicated oscillation.  But although the spectrum and the oscillation both describe the system exactly, you can’t say that any part of one corresponds to any part of the other.  If you were to record the chord on a tape you could do two things.  You could erase a short section, leaving a gap in time, but the four peaks would still be present, though smaller.  Or you could do a processing trick and cut out one peak, and then play the recording.  There would be no gap in the sound, but one note would be missing.  In the same way, you can cut a piece off a hologram, yet the picture doesn’t have a missing piece – the lost information is from all over the picture.  In this respect a hologram behaves like the mirror in "The Snow Queen".

Here are three views of a hologram.

Between the first picture and the second two the horizontal angle of the camera was changed slightly,  resulting in a different picture.  Between the second and third pictures the vertical angle of the camera was changed, resulting in two different views of the same picture.  To obtain a good beam of light, the sun was used, indoors to reduce background light.  The angular diameter of the sun is about 0.5 degree, giving a root-mean-square width of about 0.3 degree, about 5 milliradians.

These pictures have lost the properties of the hologram, because information that was in the hologram has been thrown away.  The magic has gone.  The camera can lie.  It always lies – it makes a flat picture from a three dimensional scene.  It is we who reconstruct what we think the picture represents.  Even the images on our retinas convey no 3-D information, and it is quite easy to fool the system with optical illusions.

This is a picture of a part of a bag, which has a thin coating of metal.  The metal is covered in fine regular grooves which act as diffraction gratings.  Different parts of the surface have the grooves in different orientations, leading to the brilliantly coloured effects that such an object displays in bright directional light.

A grating is not a hologram in that it has not been made by photography.  But a simple grating is in a sense the hologram of a line or point of light.  That line is in a slightly different position for each colour, because of the relationship between the pitch of the grating and the wavelengths of light and the direction of diffraction.

In principle it ought to be possible to compute the hologram of a simple object and put it on a photographic film or a metal plate, without ever having photographed the object.