Simplex
Simplex refinement is very fast. A family of designs, the simplex, is set up by perturbing the layers and/or the packing densities of the starting design. Usually the total number of designs will be one more than the number of layers and packing densities with a minimum of five for very small numbers of layers. The refinement technique then consists of a process of exchanging the poorest design for a better one at each iteration.
The better design is generated by reflecting the worst one in the center of gravity of the simplex, or, if that is not successful, by moving towards the center of gravity.
Simplex Parameters
Simplex parameters are set in a parameters dialog box (see next page).
Either or both Refine Thicknesses and Refine Index may be selected. In order that dispersive materials may be accommodated, the model used for the variation of refractive index is that of variable packing density. The model is detailed in the subsection Packing Density in the Essential Macleod Structure earlier in the manual. The starting thickness increment is the amount by which each layer is perturbed to set up the original simplex of designs. The packing density increment is likewise shown but there is an additional check box, Common Scaling. If this box is checked then the packing densities of all layers of the same material move together. This is useful in reverse engineering where deposition conditions may have caused all the layers of a particular material to vary in the same way from ideal. In reverse engineering the packing density range will be quite restricted. In index refinement the range can be made large. Inhomogeneity can be simulated by
splitting each possibly affected layer into at least two parts each with its own packing density. The number of iterations determines the absolute limit to the refinement process.
It should be set fairly large.
Simplex is very fast and each iteration is quickly over so a large number, several thousand, is recommended. It is always possible for the user to terminate the process earlier. For more complicated designs, the convergence can often be improved by recycling the simplex during refinement. The Recycle Interval parameter specifies the number of iterations between each automatic recycle. If this parameter is set to zero, then automatic recycling does not happen.
Progress of the refinement is automatically displayed as a plot of performance. The plots will be produced each time the performance is improved by the amount in Minimum Merit Function Improvement To Update Plot since the last plot.
Use Custom Merit Function, Source File, and Browse… only apply to Designs and are only available when the Function enhancement is licensed. Information on the use of custom merit functions is included in the Scripting Language manual that is installed on your computer.
Optimac
Optimac has many facets. It possesses some aspects of a direction set technique but with a large number of different ways of constructing the conjugate search sets which are constantly changing in response to the progress of the refinement. As soon as one construction technique appears to be giving diminishing returns, another takes over. The
method is appropriate for both synthesis and refinement. In synthesis there are rules for altering the design at the end of each refinement cycle by splitting layers, inserting layers, adding layers and even periodic random perturbation. The changes, however, are only provisional until proved to be useful by the subsequent progress of the process. If the promised improvements are not maintained then the current changes are dropped and a different way of introducing the changes adopted. The process, therefore, is constantly altering itself in response to progress.
Optimac Parameters
Optimac has no limits on layer thickness, except that they may not become negative, although thicker layers are more likely to be subdivided in the course of the synthesis.
The parameters editor determines whether or not refinement or synthesis is involved by the value set for Number of Synthesis Cycles. If this is zero then only refinement will be performed. If synthesis is to be carried out then the value to insert depends very much on whether or not there is a good starting design. With virtually no starting design then a value of 50 or so is reasonable. With a good starting design, a lower figure can be used.
The Synthesis Step represents the thickness of layers that are inserted in the synthesis process. This should normally be set quite large and 0.1 to 0.3 are good values. The Synthesis Parameter determines whether the changes will be retained in the synthesis operation. When a design is changed by adding or perturbing layers, the merit figure usually rises. A short process of adjustment then begins and continues as long as the improvement in the merit function continues to be satisfactory as defined by certain conditions on the relative improvement. If the resulting figure of merit is poorer than the old nevertheless the new design will be accepted provided the fractional increase in the figure of merit is not greater than the synthesis parameter. A value of around 0.2 or so is
quite a good starting value. The Initial Search Step is the search interval for the first quick scan of the search direction. The initial search takes place over a width that is given by the current value ± the Initial Search Width. If convergence is good, this value can be set equal to the initial search step. If convergence is slow and performance improves only slowly then the search region can be greatly extended. During refinement, however, the interval is constantly adjusted on the basis of progress. The Number Of Iterations refers to the refinement between each synthesis operation. This should be set to 40 or 50. The Maximum Number of Layers should not be set too large if the process is to be
completely automatic, otherwise there may be a tendency to continue to add thin layers.
If the process is to be monitored and stopped manually at an appropriate point then this can be large. Progress of the refinement is automatically displayed as a plot of
performance. The plots will be produced each time the performance is improved by the amount in Minimum Merit Function Improvement To Update Plot since the last plot.
Use Custom Merit Function, Source File, and Browse… only apply to Designs and are only available when the Function enhancement is licensed. Information on the use of custom merit functions is included in the Scripting Language manual that is installed on your computer.
Click on the Synthesis Materials tab to control the materials that will be used by Optimac when inserting new layers.
Initially, all the materials in the design will be used for synthesis. Some of these materials may be removed or others not in the starting design may be added to the list.
Clicking on OK will save the parameters for future use. Clicking on Refine will start synthesis.