I am going to look at the techniques available for making white light viewable
transmission holograms. I will go step by step, starting with a straightforward laser
transmission hologram, and look at the causes of image blur when we view this in
white light, and from there go on to ways of fixing this blur. I will then
look at image plane (full aperture) and rainbow holography, and finally
examine the little used method of dispersion compensation. There is, of course,
reflection holography for white light viewing, but I will not discuss that
here.
I find that simulated animations convey the best intuitive picture of a physical
process. So I have used animations throughout this article.
Laser transmission holograms
Let’s start by looking at the simplest off-axis hologram. We’ll use a collimated
reference beam, and a wavelength of 550 nm. This is a convenient wavelength to
choose, as it is roughly in the centre of the visible spectrum, i.e. midway between 400
and 700 nm. We’ll bring in the reference beam from an angle of 45∘ to the
normal to the plate. The object is centred on the plate, i.e. object angle is 0∘.
We have chosen an object made up of a series of small spheres on a 3D
grid. This helps us later in looking at distortions and aberrations in the
image.
The ‘perfect’ image
Let’s reconstruct the image of the hologram we have just made, using a
reconstruction beam identical in geometry and wavelength to the original reference
beam. As we would expect, we get an image that is geometrically identical to the
object, i.e. it is not distorted. Moreover, no matter what angle we look at it
from, the position of the image remains identical to that of the original
object. In other words, there are no aberrations in the image. The undistorted
laser-reconstructed image, almost indistinguishable from the original object, is
technically the most impressive image. We can call this the perfect holographic
image.
But the reconstruction beam is not always identical to the reference beam. It may
have a different geometry or wavelength. Now we can take a detailed look at the
effects of such changes on the resultant image.
Chromatic blurring
A major cause of image blur is the use of light that is not monochromatic, i.e. is
made up of more than one wavelength. The extreme case is, of course, white light,
which contains the complete range of visible wavelengths. We can start by using just
one wavelength, which is different to that of recording, look at the effect of that, then
see what happens with white light.
Changing the wavelength
Let’s look at what happens when we change the wavelength of the reconstruction
beam, leaving the geometry as before. Suppose we now use a red laser beam, of
wavelength 700 nm. This wavelength is around the limit of the eye’s sensitivity, i.e. it
is the longest wavelength that the eye can see, so you would not use it in practice, as
the image would appear very dim, but it is a nice round figure to work with, and
convenient for when we come to look at the dispersion of the spectrum by the
hologram. Well, a rule of thumb in (transmission) holography is that red bends more.
So, say for the centre of the hologram, whereas with the original green light the light
was diffracted through 45∘, now it bends through a greater angle. You can see that
the shape of the object is definitely ‘distorted’. It is somewhat sheared, and
‘squashed’ longitudinally.
Let’s now move our viewing position to the left and right a bit. We notice
that the image position depends on where we are looking at it from. This is
what is known as ‘aberrations’. It is what causes ‘swing’ in the image in
a lot of display holograms. If the image is highly aberrated, i.e. it moves
quickly with respect to observer movement, then it can be uncomfortable to
view from any position, as each eye will see the image in a slightly different
position, and the brain is confused with the signals it is not used to. In
severe cases, it can cause a headache, just like when viewing some stereo
images.
Going the other way in the spectrum, we can now try illuminating the hologram with
a deep blue laser beam, namely 400 nm. Again, this is on the edge of the
visible spectrum. As we might guess, the image is distorted and aberrated
again. This time the magnification and shift are in the opposite sense to
the case of red light. As before, we can see the aberrations in the image by
noting that the apparent image position shifts, depending on the observer
position.
Depth of the image
Here is a very important point. Looking at each image reconstructed, we can see that
the shift in image points is greater for image points located further from the
hologram plate. This is a general rule for holographic images: the further the image
point from the hologram, the more prone it is to blurring.
Illuminating with white light
We have seen what happens when we reconstruct the image with a single
wavelength that is different to the original. Now lets use white light, which is a
continuum of all visible wavelengths. As expected, the deep red wavelengths
diffract most, the deep blue least, and all other spectral colours form images in
between. What we get is a highly blurred image. If the image size is small,
or it is a long way from the hologram, it may be indistinguishable as an
image.
Whenever we use broadband (e.g. white light) illumination, we will have
some blurring. So we can’t eliminate it entirely, but we can minimize it.
Image plane hologram
Remember that in general, all blurring is proportional to the distance of the image
from the hologram. So the first thing we should do is to minimize this distance. But
in a transmission hologram, there is a limit to how close the object can be to the
hologram plate, as the reference beam must not be impeded. So how can we get the
image even closer to the final hologram?
The answer is, of course, to use a two step method: first make a master hologram
(conventionally called H1), and use the projected image to make another hologram
(H2). Now the iamge can be place anywhere, even straddling the plane of the
hologram, partly in front and partly behind it. The average distance of the image is
now close to zero, and the image is as close as we can get it to the hologram
plane.
Now where the image coincides with the hologram plane, it is perfectly sharp. In
practice, display holograms up to around 2cm in depth can be accpetable in
such a hologram. This type of hologram is also called an ‘open-aperture’
hologram, to distinguish it from a rainbow hologram, which we’ll look at
later.
The open-aperture transmission hologram can have a very realistic look to it.
Because the entire visible spectrum is used in image reconstruction, the image viewed
is black and white, or achromatic. This seems to look more realistic than, say, a
reflection hologram, which has an overall spectral hue. The realism is especially true
with objects that we naturally assume to be achromatic, or nearly so, e.g. bone,
wood, metal.
We now look at different methods we can use to increase the depth of the white-light
reconstructed image.
Rainbow or Benton hologram
Now it’s time to look at the image plane hologram in a bit more detail. Remember
that that image plane hologram was made using an intermediate ‘H1’. I won’t go into
the details of the two-step process, but the result is that when we look at the final
hologram (the H2), we are effectively looking through a ‘porthole’ which is the image
of the H1, and which is projected into viewer space. The image is only visible when
we look through this porthole.
Now, just as the image is distorted when the recontstruction wavelength or geometry
are different to those of recording, so is the shape of the H1. So we should consider
the H1 to be part of the image. The result is that not only is the image distorted
and displaced, but for each wavelength it is visible only the ‘porthole’ for
that wavelength. For example, for a red image, the porthole is diffracted
through a greater angle, and only the top of the image might be visible to the
viewer.
When the image is shallow, the full aperture method works fine, and we
see a sufficiently sharp achromatic image. But we notice that as we move
our head towards the top and bottom extremities of the visible zone, the
image loses its ‘achromaticity’ and takes on a color tinge. At the top it looks
reddish, and looking from the bottom of the porthole it looks bluish. This is
because in those areas we are only picking up the image from a narrow band of
wavelengths, not the full spectrum. This last effect is the important one. If only
we could make the image as it appears at the very top and bottom, i.e.
color-cast, but sharper, we could would be able to view a deep image in white
light.
Well, welcome to rainbow holograms! This is precisely the important step that
Stephen Benton introduced. His solution was to reduce the height of the H1. What
happens is that the overlap of the H1’s in space is reduced, so at any time the
viewer can only see each part of the image in one wavelength or, to be more
precise, a small range of wavelengths. Hence the blurring is reduced. But
there is a price to pay. As the height of H1 is very limited, there is very
little vertical parallax. In other words, we can’t look above and below the
image. The image seems to distort and ‘follow us around’ as we move up and
down.
Dispersion compensation
Now we take another approach to reducing chromatic blur. Let’s go back to the case
where we changed the wavelength and watched the image distort and be displaced.
how can we bring the image back to be aligned with the original position of the
object? Well, the answer is to alter the angle of the reconstruction beam. Suppose
again we make a hologram with a reference angle of 45∘ and wavelength 550 nm,
and reconstucted with red light at 700 nm. When the reconstuction angle is the same
as that of recording, the red light ‘bends more’ and the image seems to
be lower than the original object position. As the reconstruction angle is
altered to hit the plate at a steeper angle, the image moves towards the object
position. At around 64∘, we find that the image is more or less aligned with
the object position. We can call this the ‘dispersion compensated’ angle
for that wavelength. For blue light at 400 nm, the angle turns out to be
31∘.
Another thing that we notice is that the distortion in the image is reduced, as is the
‘swing’ as we move around. This means that dispersion compensation not only
brings the image back to the original position, but reduces the aberrations
too.
But if we are using white light to view the image, we need each wavelength to hit the
plate at a different angle, namely the dispersion compensated angle for that
wavelength. There is a very convenient way of achieving this, and that is to use a
plain diffraction grating to disperse the beam first, before it hits the hologram. In
effect, we compensate for the normal ‘dispersion’ of the white light when it
diffracts from the hologram, but ‘predispersing’ it through a diffraction grating
first.
As we can see, dispersion compensation goes a long way to eliminating image
blur, but there is still residual blur present. Once again, the further the
image from the hologram, the greater the blur. By using an image-plane
hologram in conjunction with dispersion compensation, we can obtain very sharp
images.
