Not all projects start with a well understood specification that just needs to be turned into an optical design. Many clients approach us initially to discover whether an idea can actually work, or be made to work! Many of our projects are therefore genuine research projects where we need to invent the physics as we go along.

A typical example was the work that we did on solar concentrators.

A cheap solar boiler can be based on a simple concave spherical mirror, pointing roughly South. The image of the sun follows a path on a sphere which is concentric with the surface of the mirror. An absorber is then swung on a pendulum suspended from the centre of curvature of the mirror to follow the image of the sun. All of this is cheap, and deceptively simple!

The problem is that the spherical mirror has an optical design defect known as spherical-aberration which blurs the image so that only light from a limited amount of the mirror can actually hit a small absorber at any one time. The alternative is a parabolic mirror, but that has a very small field of view and needs to be mounted on an expensive guidance system to track the sun.

Radio-astronomers have traditionally been the physicists that solar energy engineers have turned to for advice, and some very large and ornate secondary concentrators have resulted. The reason for the size has been the astronomers natural desire to create a good image.

However if you abandon the idea of an image then it becomes clear that some of the light (that nearest the centre of the used area of the mirror) is already well enough imaged to not need a secondary concentrator. That light can be allowed to proceed directly to the absorber. The light from the surrounding mirror area now misses the absorber, but can be trapped by a secondary mirror and directed towards the absorber. In fact the light from an even larger zone of the main mirror can be captured if we aim the light towards a tertiary concentrator and finally arrive at the absorber. The two paths are shown in red and blue in the accompanying diagram.

In the concept we arrived at, there were two different paths to the absorber, depending on how difficult it was to cope with that part of the main mirror. This system created no image, each of the paths had a different focal length and from an astronomer's viewpoint each had a different path length through the system so that it was theoretically impossible to combine the information about a distant galaxy from information obtained by the two different routes. It was the realisation that we were not trying to create information or images that allowed a radically different approach, that led to exceptionally small concentrators whose next research stage was to be the problem of building them out of materials that were not melted by the sun at the levels of concentration that we had achieved in the optical design!

Another research field has been the modelling of the diffraction pattern created by an extremely complex obstruction placed in front of an optical aperture. Why? Well that's still covered by the confidentiality agreement! What was needed was a diffraction pattern modelling program, written in Visual Basic, that performed a finite element analysis on an aperture that had been divided into tens of millions of aperture elements, each of which was diffraction-scattering light towards about a thousand elements of the image. Even with the diffraction algorithm stripped to a bare minimum the software ran for thirty-six hours at a time. Fortunately the calculation only needed to be run a few times to establish the required answer, and it is by this type of technique that optical designers generate time for golf!

Over the years my personal passion has been research into the optical design theory that underlies the design of aspheric systems.  Aspheric?  Well, an aspheric surface is simply one that is not spherical. Since the thirteenth century lens makers have taken advantage of the fact that nature wants to make polished surfaces spherical. However Newton recognised that if the surface was parabolic instead of spherical then a much sharper image could be produced. Unfortunately it was much more expensive to make a non-spherical surface, because it takes time and skill to overcome nature's desire to make the surface spherical.

From the 1960's onwards, air-bearings, CNC and laser measurement permitted the development of increasingly successful machine tools. By the 1980's my team at British Aerospace were operating two of the largest such machine tools to single point diamond turn increasingly complex optical surfaces, a long way from the mediaeval monks and their spherical spectacles! Some of the things we made will live forever, because some of our optical surfaces are in satellites, and some are on the Cassini Mission to Saturn!

However, my personal interest was not just the engineering of the fabrication process, interesting as that was, particularly as it led to many visits to Japan to speak at meetings on nanotechnology. It even resulted in a seat on the UK Department of Trade and Industry's Nanotechnology Strategy committee, but fascinating as those ten years were, that too was not my passion!

My interest was in the abstruse mathematics that underlay the way in which aspheric surfaces affect the defects in an optical image, the aberrations.

Since the 1800's it has been known how individual surfaces affect the aberrations of a complex lens system, and since the 1960's it has been known how to calculate the aberrations as the sum of a series of quadratic equations, to arrive at aberration sums in terms of the shapes of the lenses. However that theory, which was elegant and should have been a theory of everything, instead simply resulted in a set of equations that were too complex to result in useful closed-solutions for anything more complex than a very simple two or at most three-element lens.

During the 1980's I realised that because aspheric surfaces and their fundamental design variables did not create quadratic equations, the equation being a straight line, the set of equations was much simpler, and could be solved. The systems were still simple, just two or three elements, but those elements could be aspheric increasing the number of design variables to a number equivalent to a much more complex spherical system. At the same time, the wavelength of interest had shifted to the Far-Infra-Red at 8 to 12 micrometres and at that wavelength the preferred material is Germanium which diamond machines to a beautiful optical surface. Germanium is expensive, so there is an imperative to reducing the number of lens elements, and the cost of material saved outweighs the cost of the machining.

Realising that what I was creating was a new field of research, and with the help and support of Prof Robin Smith, Assoc. Head of Physics at Imperial College, London, the research was submitted as a thesis to London University. The PhD degree was presented by the Chancellor of London University at a ceremony at Central Hall, Westminster on 19 March 2004, a memorable day because the Chancellor is Princess Anne, the Princess Royal.

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