Multi-Element Systems - Design Method

Multi-element (ME from here on in, I'm sick of typing multi-elemtent out all the time) photo-optical systems exist for one very good reason; to eliminate image errors. Increasing the number of optical components within a system increases the number of controllable parameters that can be altered in order to reduce or eliminate image aberrations. To show what this means, I have written an example below comparing my first lens prototype to a hypothetical ME lens:

My first prototype lens features only 2 optical components; the PMMA singlet element and a stop down aperture ring placed directly behind it. In this system there are very few controllable parameters, including:

• Front and back surfaces of the PMMA element
• Element lens thickness
• Element material specification (RI, Abbe number)
• Aperture pupil size (diameter of the hole in the stop down rings). 

As you can see, there are 5 alterable parameters. Some of these, such as lens thickness and material spec cannot be changed due to manufacturing constraints, so we are only left with 3 parameters that are available to eliminate errors. During the initial prototyping, all these alterable parameters were tested. A version of the system using an aspherical back surface was made, which only made errors worse. The aperture pupil size was also altered continuously through testing, reducing the aperture value in steps down to F/16. There were visible reductions in image errors, but at severe cost of light collecting ability.

Now lets consider a ME lens. A Tessar lens (like the one shown above) contains 4 elements in a unique configuration designed specifically to reduce image errors such as SA and CA. Each element contains the same alterable parameters as shown above; front and back surfaces, material spec, and lens thickness. As well as this we can now alter the size of the air-space between each element. Therefore, for each element there are 5 parameters. Multiply this by the number of elements, and add consideration for the aperture stop, and we suddenly have 20+ alterable parameters that can be utilised to tackle image errors!

Knowing how many elements are needed within a design to achieve your primary specification comes with experience. There is no software or formula which can tell you this, which is why lens design is not something that can be automated by a computer program. A computer program can help refine and optimise, but a designer must have the initial insight to provide a close fit design in the first place to achieve what he or she wants. To design a ME lens, there is a basic design methodology which can be used. This is shown below:

1. Work out a primary specification for what you want your lens to do. This will include things like your desired focal length (considering sensor size and desires FOV), back focal distance (considering camera mount flange distance), aperture F/#, what aberrations you specifically want to eliminate.
2. Pick a reference design to use as a base to work from. There are hundreds of lens designs out there, it is likely that there is a design that has similar specification to yours.
3. Develop a paraxial thin lens and then a thick lens system. This will involve modifying the reference design to meet your specification and physical requirements.
4. Optimise the new design using ray tracing software such as ZeMAX. This stage removes the errors you want to eliminate by iteratively altering the design parameters to find a best solution. I will talk about this step in detail in another post.