Driving Through a Rainbow: The Truth Behind This Phenomenon

[lookbehindu]

Hi - you have put me on the spot!

Remember that a hologram is just a diffraction pattern, made by combining the light reflected from an object with a reference beam. It is easiest to describe the early types of hologram which are 'transmission holograms'. This is arranged using half silvered mirrors which split laser light so that one part illuminates the object and the other acts as reference beam (there are loads of diagrams around which show this basic setup). This will produce a very complicated diffraction (interference) pattern between the two components of the laser light but any area of the pattern can be recorded on a piece of film placed there. In practice, of course, you use clever optics to get a bright enough image where you want to put the film so that you get adequate exposure. The interference pattern is very fine and you need a long exposure [Edit:and] to avoid getting a blurred image on your film (the hologram). When you shine light on the developed piece of film, you will see a diffraction pattern, caused by the hologram, which will be the same as the original object, as viewed from that direction. Different areas of the hologram contain information about the view from different directions - hence the 3D appearance. But you don't get something for nothing. The resolution of the hologram is limited so that limits the actual quantity of information that can be stored. It is totally magic, though.

The basic principle is much the same as the two slits experiment - one slit can be looked upon as the object and the other as the reference. The interference pattern can be recorded on film and, if you illuminate the film from behind and look through this pattern, you will actually see two slits. The simplest hologram you could imagine. Another simple precursor of the hologram is the zone plate, which is like a photograph of the Newton's rings you get with a convex surface resting against a plane surface. That zone plate will produce a 'focussed' point image when a wide beam of light falls on it - just like a convex lens will do.

The reason that holograms work is that the diffraction pattern is a Fourier transform of the object and the Fourier transform of the hologram looks like the original object. This wiki link discusses how holograms can be constructed without using light beams and it may help you.

Once the reference and object beam reach the plate haven't they undergone spreading (similar to incoherent light). Also when both beams reach the plate aren't they not in phase anymore? So what was the point of keeping them in phase until that point? Also I'm having a hard time understanding the divisibility principle (how can a tiny piece contain the entire image minus perspectives).

 

[sophiecentaur]

Once the reference and object beam reach the plate haven't they undergone spreading (similar to incoherent light). Also when both beams reach the plate aren't they not in phase anymore? So what was the point of keeping them in phase until that point? Also I'm having a hard time understanding the divisibility principle (how can a tiny piece contain the entire image minus perspectives).

That is the very same question I asked my lecturer at University in 1966! (Nothing is new under the Sun ) He was actually flummoxed by the question and I only came to terms with the problem years later, when I approached it again.

To answer your main question, the reason that you get a diffraction pattern is that the various light paths through the system are all different - their relative phases, where they are detected (the film) are different from place to place on the film. That's why you get the light / dark fringes of the hologram. For a simple two slits, the effect is easily explained (in wiki and all over) - at different angles, the phase relation between light from the two slits is different, which gives you the fringes. You can do the two slits with almost any old light source and get fringes over a limited range of angles. To work well, you need good coherence so that, even at large angles, the different wave trains that make up the light source are still long enough for self interference to occur. (For a pair of radio signals, for instance, the coherence is almost perfect and the interference is more or less textbook and a laser is about as good)

For a hologram to work, the requirement is even more strict because you need a broad, coherent wavefront for your reference and a broad, coherent wavefront hitting the object. The resultant (max / min / intermediate value) at any single point on the film is due to light reflected from every point on that side of the object, interfering with the reference beam and with itself (of course). To one side of that point, you will get the interference result from a slightly different direction from the scene. When the hologram is reconstructed, you are looking through the film, from one point of view, at light coming through the hologram through a small cone (iris width). That cone of light will have passed through a small disc (part of the whole hologram) and what gets into your eye will be another interference pattern (i.e. viewing light through the fine, complicated hologram pattern). This interference pattern is an approximate version of a picture of the whole original scene from that point of view. The resolution is limited (I think) by the aperture of your eye as well as the quality of the equipment.
Did you look at that wiki article on computer generated holograms? If you can understand the bit involving the Fourier transform it becomes clearer. If you aren't familiar with that then you may just have to accept the fact that 'it works'. (Btw, Fourier transforms work on spatial frequencies and variations in the same way that they work on sound frequency spectra and waveforms - same Maths involved with each)

 

[lookbehindu]

That is the very same question I asked my lecturer at University in 1966! (Nothing is new under the Sun ) He was actually flummoxed by the question and I only came to terms with the problem years later, when I approached it again.

To answer your main question, the reason that you get a diffraction pattern is that the various light paths through the system are all different - their relative phases, where they are detected (the film) are different from place to place on the film. That's why you get the light / dark fringes of the hologram. For a simple two slits, the effect is easily explained (in wiki and all over) - at different angles, the phase relation between light from the two slits is different, which gives you the fringes. You can do the two slits with almost any old light source and get fringes over a limited range of angles. To work well, you need good coherence so that, even at large angles, the different wave trains that make up the light source are still long enough for self interference to occur. (For a pair of radio signals, for instance, the coherence is almost perfect and the interference is more or less textbook and a laser is about as good)

For a hologram to work, the requirement is even more strict because you need a broad, coherent wavefront for your reference and a broad, coherent wavefront hitting the object. The resultant (max / min / intermediate value) at any single point on the film is due to light reflected from every point on that side of the object, interfering with the reference beam and with itself (of course). To one side of that point, you will get the interference result from a slightly different direction from the scene. When the hologram is reconstructed, you are looking through the film, from one point of view, at light coming through the hologram through a small cone (iris width). That cone of light will have passed through a small disc (part of the whole hologram) and what gets into your eye will be another interference pattern (i.e. viewing light through the fine, complicated hologram pattern). This interference pattern is an approximate version of a picture of the whole original scene from that point of view. The resolution is limited (I think) by the aperture of your eye as well as the quality of the equipment.
Did you look at that wiki article on computer generated holograms? If you can understand the bit involving the Fourier transform it becomes clearer. If you aren't familiar with that then you may just have to accept the fact that 'it works'. (Btw, Fourier transforms work on spatial frequencies and variations in the same way that they work on sound frequency spectra and waveforms - same Maths involved with each)

Thanks. I think I understand it a bit better. One more question...how does the hologram divisibility principle work. Is it a trick of the eye? If instead of cutting a piece off you placed a sheet over and cut a hole in the center of the sheet would the effect still occur and would you be able to see the entire image through that "peephole"?