Description

This example seeks to optimize the position of a ball lens for the purpose of maximizing the power delivered to a fiber core. The system layout is shown below and the accompanying FRED file, exampleOptimizingABallLensCoupler.frd, can be found in the <install dir>\Resources\Samples\Tutorials & Examples\ directory.

Implementation

Before we begin our optimization, we must create and attach an Analysis Surface to the surface of interest, the fiber entrance face.  Right mouse click on the Analysis Surface(s)  folder in the object tree and select "New Analysis Surface" from the list menu.  To attach the analysis surface, drag and drop the analysis surface in the object tree onto surface "Geometry.collect fiber.ent face".   These steps are shown below.

Optimization Setup

Setting up an optimization requires defining variables, choosing a merit function and selecting the optimization method. Begin by opening the Define... dialog box from the Main menu topic Optimize:

Clicking in the Entity column exposes the list of entities that can be used in your optimization.  Here, we select the Custom Element "Geometry.Ball lens" in order to move both the front surface and back surface as a unit. Note that the Active box appears and is checked when this selection is made. We also add a descriptive name to our variable for easy identification.

Since the intent is to optimize the position of the ball, the variable Type must be the Position/Orientation parameter. Click in the Type column and select this option:

Note that an operation entry will be required, so shift values can be entered to move the ball. We add an operation to the Custom Element "Geometry.Ball lens" for this purpose.

We now return to the Optimize > Define... dialog. The next entries on the Variables Tab are Index # and Subindex #. For the operation entered above, the Index # is 1 as shown in the far left column. The Subindex is 2 since the Z-shift value is in the third position (all indicies in FRED are zero-based).  NOTE: In this example, the Fraction Var # entry is not used since there is only one variable.

The nominal position of our ball lens is at z = 0. Thus, zero is entered for both the Current and Initial Values. We make an educated guess as to the range in which the optimum value should be found. The Initial value MUST satisfy Lower Limit < Initial < Upper Limit. If the Initial value matches one of these limits, the optimization routine may not find a good answer.

We now move to the Merit Function Tab to set up our merit function.

Right-click in the Aberration Definition column to expose the list of definitions. Note that the Active box now appears checked:

We select Total power on the surface since that is what our objective is; to maximize the power on a surface:
 

Move to the Merit Function Tab and right-click in the Analysis Surface To Evaluate column. We find only one entry in this list; the Analysis Surface we created and attached to the fiber entrance face at the beginning of this example. With only one variable, the Weight value can be left at its default of 1:

Finally, we move to the Optimization Method Tab. Since only one variable is involved, the 1D minimization using variable option is selected and the variable name appears. The appropriate Stopping/Convergence Criteria selection in this particular example is When all variables change less than and this value is left at its default value of 0.001. We also allow FRED to try up to 100 iterations. The Variable Limit Enforcement option is left at its default setting. FRED is also instructed to write boith the merit function and varaible values to the Output Window as the Optimization progresses. After these selections are made, the OK button is pressed to accept the settings and dismiss the Optimization dialog box.

Source Properties

One thing that can lead to poor convergence is Poisson noise. We must therefore make sure that our source has enough rays to minimize this statistical noise. To that end, we increase the number of rays in our source from 11x11 to 51x51:

Running the Optimization

The system is now ready for Optimization. To proceed, select the Optimize option from the Main Menu Optimize drop down and allow FRED to do its job:

The optimum value achieved for this example is in the neighborhood of z = -0.17.

Related Topics

Optimize - Define / Edit

Example - LED Color Optimization