A new refinement standard targets window contains only four columns, wavelength or frequency, operator, required value and type. Frequently these are all that is required.
Other attributes of the targets are set to default values. Incident angle is zero, weights are all unity and tolerances have their default values. Targets may be either equality targets or inequality targets. This is specified by the operator.
The other target attributes can be activated by the menu item, Display Setup > in the File menu. The sub-menu that appears has the following entries, Context, Incident Angle, Weight, Tolerance, Derivative, Link and Current Value. Note that Context only appears for Design Targets.
Selecting all of these gives a window similar to the following.
Context specifies the design context in which the target applies.
Incident Angle is measured in the current incident angle units and when the incident angle column is present the polarization column (Pol) is also automatically activated.
The Weight column controls the relative importance of each target. The larger the value of the weight of a target relative to others, the more the refinement will be driven by the performance at that target.
The Target Tolerance column indicates the relative acceptable error magnitude of each target. For each target, the difference between the required value and actual value is divided by the tolerance. When the Type of a target is changed, the default tolerance for the target type will be inserted in Target Tolerance column. The default tolerance values may be edited by selecting Tolerances from the Options menu.
The Derivative column lists the order of the derivative of the target type with respect to the independent variable that is either wavelength or frequency, whichever is listed in the first column. An order of zero indicates that no derivative is involved.
Link permits the assignment of relationships between targets. For example, it might be required that the reflectance at 525nm should be 4% greater than that at 550nm but that the absolute level of the reflectance be unimportant. To arrange this we first of all link the two targets together by giving each the identical link number, in this case unity. Note that as the link numbers are entered so the Required Value against the second linked target disappears and also that the number unity appears by default in the Link Multiplier column. Now we want the difference between the values to be 4% and so we set the multiplier for 550nm to -1 and the Required Value against 525nm to be 4%. By default the weight given to the combination is unity. It can be adjusted by forcing the appearance of the Weight column.
More than two values can be linked. The links are interpreted in this way.
πΏπππππ ππππ’π = οΏ½(πΏπππ ππ’ππ‘ππππππ Γ ππππ’π ππ πππ£ππ ππ¦ππ)
πΏπππ
πππππ‘ ππ’πππ‘πππ πππππππππ‘ = ππππβπ‘ Γ |π πππ’ππππ π£πππ’π β πΏπππππ ππππ’π|πππ€ππ
If all the types involved in a particular link are phases then the principal values of the phases will be used and the result will be expressed as the principal value. If only some of the values involved in a single link are phases (this may not make any physical sense) then the principal values of the individual phases will be derived but from then on the phases will be considered as simple numbers and the final result will be completely untreated.
As an example of a refinement operation that uses linking we can imagine that we want to derive a beam splitter coating with 50% reflectance at normal incidence over the region 400 to 700nm. We use ZnS and Na3AlF6 (cryolite) as materials on glass with air as incident medium. We use a starting design of nine layers of optical thickness 0.15 at 510nm with Na3AlF6 outermost.
We first set up a conventional set of targets, that is reflectance 50% from 400 to 700nm at intervals of 25nm. We use simplex with a starting thickness increment of 0.01.
The simplex during the refinement process eliminates two layers to yield a seven-layer design with Na3AlF6 outermost and a performance given by the thinner line (red) in the following plot.
Next we construct a set of targets that consist of absolute values of 50% at 400, 450, 500, 550, 600, 650 and 700nm, but we add separate links of 400 with 425nm, 525 with 575nm and 675 with 700nm each requiring zero difference between the values of
reflectance. The link multipliers, in other words, are set to 1 and -1. The weights are set at three, larger than the unity values for the individual targets, to emphasize the links. The arrangement is shown in the following table.
This maintains the nine layers of the design during the course of the simplex refinement with identical parameters and a much flatter performance is obtained. In the
plot below, the heavier line shows the performance of the design refined with linked targets.
Links give an added dimension to the refinement and synthesis specifications and increase greatly the power of the technique. However, a word of caution is appropriate. A performance specified with links can often be more difficult to achieve than one without, and so the convergence will take longer. It is also very easy to demand a completely unreasonable performance and in such a case the process will be very slow and the result disappointing.
The Current Value and Contribution columns provide data on the performance of the design for the current set of targets.
The Current Value column shows the actual design performance value for the target.
The Contribution column shows the % contribution of the target to the total merit figure.
The principal menu item that concerns us when the target window is active is the Edit menu. The other items are the usual general ones concerning the package as a whole.