Chapter 10 : Holographic multi-stereogram

10.1 Holographic stereogram

Holographic stereograms are hybrids of holography and photography. They have some of the qualities of both media, but each add something of their own. Holographic stereograms are a series of holograms, stripes of maybe hundreds, which are multiplexed into a single hologram.

This can be done if we take several photographs of an object from different angles. Each of these pictures are then to be exposed onto a little area of the holographic filmplate.

Figure 10-1 Principle of holographic multi-stereogram

The figure 10-1 shows us the principle of a multi-stereogram with 3 pictures which are multiplexed into one hologram. 3 pictures have been used to show the reader the method in an easy way. However, this hologram will have a low resolution. Therefore is it important to use as many pictures as is needed to obtain a good resolution in the hologram. It is common to expose about 1 to 2 mm of the holographic filmplate for each picture.

The figure 10-2 shows us a method to expose a hologram with horizontal parallax, and the filmplate will be exposed in vertical parts.²¹ ⁵¹

Figure 10-2 Holographic filmplate with horizontal parallax

In this method it is not possible to see the top or bottom of the object in 3 dimensions.

To reproduce the object completely in 3 dimensions, we also need vertical parallax. That means that in practice we have to also move the camera in a vertical direction, and we thus get full parallax.

Figure 10-3 Holographic filmplate with full parallax

We would like to make the hologram so good as possible in the shortest time. The solution to this problem is to make a hologram with the fewest possible number of exposures. This must be done without loss in quality or resolution. Besides, it is very important that the pictures which make up the multi-stereographic hologram form one image, and not a sequence of many images.

An other method for make multi-stereograms is to use a computer model instead of pictures of an object.¹² If we get a DAC picture drawn in perspective, we can turn this pictures through different angles over the screen.³² The exposure will made for each model position, in the same way as for photographic pictures. A perspective drawing is an image where the object which is closer will appear larger than a similar object which is far away.

Figure 10-4 Principe of holographic multi-stereogram

The width of each part hologram or exposure is determine of the size of the human eyes pupil. This size varies from 1 to 3 mm in diameter. This is also the ideal size of the exposure area, and under reconstruction of the picture, only one image is seen by each eye.

When the hologram is reconstructed, can we see a 3 dimensional image of the object. If the hologram is exposed in full parallax, the image is completely in 3 dimensions.

The figure 10-5 shows us the principle behind a holographic filmplate which is exposed with horizontal parallax. During the reconstruction only the observer will see the image in different perspectives when he moves his head in horizontal directions. If the observer moves his head in the vertical direction, the image will give no impression of being 3-dimensional.

During the reconstruction of a hologram with horizontal parallax, the observer sees the image of the object in two different perspectives.¹ When we look at a real object, we also see the object in two different perspectives, because there is a space between our eyes.

Figure 10-5 Reconstruction of holographic multi-stereogram

10.2 The choice of slit width in HMS ²

In order to obtain satisfactory holographic multi-stereograms (HMS) it is necessary to keep the slit width X between 1 mm and 3 mm. The lower limit is chosen such that the hologram does not become a limiting aperture in the optical system under normal viewing conditions. Decreasing the width of the strips increases the resolution in the reconstruction. If the pupil diameter of the eye is taken to be 3 mm, then the eye is the limiting aperture if

X 3D / (Dd) (10.1)

Calculation :

D = 250 mm
d = 400 mm

where D is the distance from the hologram to the image plane and d is the distance between the hologram and the observer. The upper limit is chosen to keep the hologram width smaller than the pupil diameter. If the upper limit is exceeded, the discontinuities in the image become noticeable as the hologram is scanned visually.

Figure 10-6 Determination of the slit width

10.3 Parallax ¹⁹ ²² ²³

The most important thing which helps us to see the world in three-dimensions is the phenomenon of parallax. When you look at an object, you see only the front side. When you move your head to one side you see the front and another side of the object. This is also very important in holography and constitutes the most common difference between photography and holography. When you are look at a hologram, you can see the image in different visual angles when you move your head to the side just as and when you are looking at a real object. This phenomenon is called parallax. When we look at an object we can see different details depending on whether the head is moved in a horizontal or vertically direction. This means that there is horizontal and vertical parallax.

Figure 10-7 Viewpoint of an object of different position

10.4 Exposure

Exposure of the photographic emulsion is defined as the incident intensity times the time of exposure for the recording material. If the intensity is constant during the whole exposure then

H = E^.t (10.2)

where

H = Exposure
E = Intensity
t = Exposure time

Radiation measured in radiometric units applies to electromagnetic radiation over the whole spectrum, and is independent of the human eye electron optic sensitive curve. The radiometric equivalent of illuminance is irradiance, and exposure is then defined.

Exposure = irradiance x time

The unit of irradiance is Watt per square meter and the exposure will then be expressed in joule/m². Holographic materials are usually characterised by radiometric units. The sensitivity of a holographic emulsion is most often expressed in J/cm². If we know the sensitivity of the material used and having measured the irradiance at the position of the holographic plate, the exposure time can be calculated using the formula

Exposure time = sensitivity / irradiance

10.4.1 Exposure of the holograms in HMS

The object beam from the He-Ne laser goes through the spatial filter which consists of a microscope lens and a pinhole. This spatial filter expands the laser beam, so the whole LCD is illuminated. The laser light illuminates the picture of the LCD and gets modulated. The information from the picture is then dispersed when the light passes through the screen of ground glass. The grain structure of the ground glass scatters the information from the image in all directions.

The light then passes through the slit of the printer and illuminates a small area of the holographic filmplate, shown in figure 10-8. The exposed area of the filmplate receives all the information from the image. The ground glass is essential, and without it the picture on the LCD will be exposed directly on the film, like a photograph (see section 7.2, image 4).

Figure 10-8 Principle of exposure of the film plate

During the processing of transmission hologram, the reference beam must illuminate the filmplate on the same side as the object beam.

For a reflection hologram the reference beam must illuminate the filmplate on the opposite side to the object beam.