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Chapter 11

Lenses, Optics & NBTV
by Grant Dixon

Lenses play an important role in the field of NBTV, first of all to form an image which can be scanned and secondly to concentrate all the available light in the right place. Image formation is quite easy to understand as if the lens is not in the right place a fuzzy image is obtained, but the use of a lens in concentrating light is not always clearly understood.

A simple convex lens is a piece of glass, or plastic, with spherical surface on one or both sides. More complex lenses are made with two or more convex lenses but the same principles apply to these also. Take a lens and a piece of white card and using a distant object focus a clear image on the card and measure the distance from the card to the centre of the lens. This distance is called the FOCAL LENGTH (f) of that particular lens . (fig. 1).
Now if (u) is the distance of the object from the lens and (v) is the distance of the resulting image from the lens then these are all related by the 'lens formula'.....

You have just made the object distance (u) very large and so the reciprocal is negligible and (v) is equal to (f). So the image is formed at the focus of the lens.

Fig. 2 is a ray diagram for a typical point on the object; the diverging rays from the point are all converged by the lens on to a point on the image. This occurs for all points on the object thus giving an extended image which, in this case, is smaller than the object. As the object is brought nearer to the lens the image recedes from the lens and gets larger. At a distance of twice the focal length the image is the same size as the object and is at the same distance. Bringing the object still closer causes the image to recede from the lens and become much larger than the original object.
By considering similar triangles in fig. 2 one can define the magnification (m) as follows:

The f-number
The lens is essentially a gatherer of light and its efficiency is often measured in terms of the diameter of the lens compared to its focal length. If the diameter is equal to f/4 then this is often quoted as an 'f 4' lens.the lower the f-number the greater is the diameter of the lens and the greater its efficiency as a gatherer of light.
A lens used to create the image for scanning should have an f-number no higher than about 4, i.e. the diameter should be at least a quarter of the focal length.
When a lens forms an image of a distant object it does so in the 'focal plane', but this is an ideal situation and in practice, with a simple lens, the image is distorted at the edges due to 'spherical aberration', so try and check that your lens is producing a good image over the whole of the scanned area.

The condenser lens
Let us assume that we are using a scanning disc in an NBTV camera; this should be placed in the focal plane of the lens for distant objects and the lens is then moved away from the disc to produce clear images of nearer objects. From fig1 it is obvious that the light getting through the scanning holes is diverging and if a small photoelectric cell such as a photo-transistor is placed behind the disc then most of the light will not reach it.

A second 'condenser lens' is therefore placed behind the disc to concentrate the light. It is the placement and action of this lens which is often not clearly understood. We want all the light which comes through the imaging lens to reach the photocell so it is usual to have a 'condenser lens' which treats the imaging lens as an object and produces an image of it on the photocell. See fig4. (Yes, I know that the disc will block out a lot of the light but the general principle still holds).

But this is not the whole story, the size of the image on the photocell compared with the diameter of the imaging lens is in the same ratio as the image and object distances in fig3. So if our imaging lens is about 50mm diameter and our photocell is only 5mm in diameter we must have the object distance equal to ten times the value of the image distance. This implies a 'condenser lens' of very short focal length and also having a diameter large enough to cover the scanned area of the disc. This is usually achieved by using a pair of plano-convex lenses as shown in figs 3 & 4.

An old slide projector
Notice that the arrangement is very similar to the optics used in a slide projector which operates in reverse, the lamp being in the same position as the photocell. Here the requirement is that the maximum amount of light shall go forward through the projection lens and a small concave mirror is placed behind the lamp to increase its intensity in the forward direction. If you can manage to pick up an old slide projector you have got a ready-made optical system which is almost ideal for NBTV.
Just remove the rear mirror and put the photocell where the lamp was previously located. The only snag is the question of whether the 'condenser lens' is concentrating all the light on the required area. To check this, cut out a hole in a piece of cardboard with the same diameter as the imaging lens, place a piece of thin white paper over the hole and illuminate it with a torch. Remove the imaging lens and place this illuminated 'object' in its place. Remove the scanning disc and put a small piece of white card in the place where the photocell is going to go and examine the image of the circle. How large is it? Will it fit on the photocell you are going to use?

An extra condenser lens?
If the image is too large then an extra lens behind the condenser could be used; the image will now be in a different place and the white card must be moved until the image is clear. Putting in an extra lens in this way may raise other problems as each component of the optical system absorbs some light and there is the remote possibility that the extra efficiency gained will be offset by the loss of light due to absorption in the extra lens. In general, it is much easier if one uses a photocell with an active area of reasonable size rather than a photo-transistor whose active area is very small.
Note that the condenser lens must have a diameter at least as great as the diagonal of the scanned area.

A drum instead of a disc
In the case of a drum camera the same rules apply but the optical axis is turned through a right angle by reflection.

There are three ways of reflecting a beam of light :

1. Using a surface silvered mirror.....

2. Using a rear silvered mirror........

3. Using a prism...........................

Methods 1 and 3 are to be preferred . With a rear silvered mirror there is a possibility that reflection can also take place from the front surface and multiple images can be formed. This is especially true for bright objects such as a lamp or a candle flame. It is not often a serious problem with the sort of scenes which are found in front of the NBTV camera.

Spherical aberration ..... some notes by Klaas Robers.

One defect that affects correct focusing of lenses is called spherical aberration. This is caused by the different focus point of the centre part and the edges of the lens, see fig. 8. This spherical aberration can be minimised by curving the lens, i.e. moving the edge in respect to the centre part of the lens. In the case of fig. 8 you might see that we have to move the edges to the right. We now obtain a lens with one spherical surface (convex) and one almost flat surface (planar), fig. 9.
The minimum of the spherical aberration depends on the way light is entering and leaving the lens. When light is a parallel beam at one side of the lens, then the minimal spherical aberration occurs when the other surface is flat.

Between the two lenses of a condenser system, see fig. 4, the beam is parallel so the condenser system is flat on both sides. Yes indeed, in fig. 4 the left lens should have been less curved, thus thinner than the right one.
When the beam enters the lens in a diverging way and leaves in a converging way, both surfaces should be convex. For reasons of symmetry both surfaces must have the same curvature if object and image have the same distance from the lens, see fig. 10.

When light enters the lens in a converging way and is even more focussed by the lens, then we need a convex-concave lens. This is done in the better photo cameras to minimise spherical aberration even more by using several lenses in stead of just one. Glasses always have convex-concave lenses, so they are not at all optimised for spherical aberration. It looks as if this is done just to prevent your lashes touching the glass.
As a general conclusion, lenses should be used in such a way that both glass surfaces contribute more or less the same amount of focusing action. The bend in the rays of light should be almost equal on both sides of the lens.

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