In the previous post I wrote about the "starting point" – implying that this is the starting point of the optimization process, the process of changing and optimizing the system.
Optimization is an area that, in most engineering fields, requires very little effort and attention relatively to optical design. In optical design, the essence of the design process is optimization.
In my opinion, one of the root causes of the misunderstanding of the optical design field may be the mis-perception of the optimization process.
So, what is the big deal with the optimization? When considering the optimization with one variable, it's easy to understand what the optimization is about: you keep changing the variable until you reach the best performances. In order to better illustrate the complexity of optical system optimization, we will try to understand how many variables (dimensions) are there in the average system.
Suppose we have a system with 5 optical elements and a display or a sensor, as illustrated.
From a simple calculation we can see that there are:
12 optical surfaces each with a radius variable and 4 degrees of freedom of position (linear and angular), giving a total of 48 variables;
7 different materials
12 distances between the surfaces.
In rough calculation, this simple system has about 70 variables. As a result in this case, we have a 70-dimensional function of performances, which is a function of 70 independent variables. This entity is even impossible to imagine, and we are trying to find a global minimum point of this monstrous function.
This is similar to traveling on a road in a world of 70 dimensions and our goal is to find the lowest valley.
We want to explore this unique world of 70 dimensions using the following tools:
"The starting point", which is the starting collection of the system parameters – the place where we start our journey
The optical software algorithm – is the vehicle we travel with
The Merit function / Error function (MF) – is the vehicle's navigation tool
Value / Error – is a number calculated from the Merit function (it has no units) that gives us an indication of our height (altimeter)
Most of our effort is building the MF that will change and adapt to our journey as we drive.
Merit function / Error function may consist of:
System requirements, such as: focal length, field of view, image quality (MTF), wavelengths range, etc.
System variables, such as: lens radii, lens thickness, lens material, the distance between elements, etc.
System limitations or constrains, such as: overall system length, size, weight, price, etc.
Each parameter in the MF can be given a different weight and the value (or error) can be calculated in any given system state and in each step in the optimization process. The software algorithm combined with the "starting point" and the MF should drive the system to a minimum value (or error) – the Valley of Dreams (see the flowchart).
Therefore, because of the complexity of the multi-dimensional function, the diversity of the MF and the different choice of the "starting point", given the optical design task to 10 optical designers with the same requirements and the same software, the result will be 10 different designs, or actually, each will reach a different Valley of Dreams.
So how do you get to the lowest Valley of Dreams, the local minima?
Every optical designer has his own methods, his secret recipe.
I will share a simple flowchart that I sometimes use on my journey to find my Valley of Dreams. I hope it can be useful to others as well.