The Performance menu controls the calculation of performance figures by the package. Access to the menu items is possible only when a design window is active and the calculation initiated by the choice of one of the items will refer to the design in the active window. There are two principal ways in which the results of a calculation may be presented. They may be plotted or tabulated and either may be chosen from the menu.
Another aspect of performance of a design is its susceptibility to errors, also available from this menu.
Plot
Plot initiates the plotting of performance in a plot window. The aspects of
performance and the range over which they are to be plotted have already been chosen under the item Performance in the Parameters menu.
The Plot window is now the active one and so the menu bar changes to reflect that.
The principal changes are that the Performance and Parameters menus disappear and the choices under the others are limited.
Many aspects of the plot can be modified. The section on the Plot Window later in this manual describes how plots may be modified. Note that the performance data do not change when the plot parameters are altered. If a change is made to the wavelength region outside the range of the original calculations then the altered plot will simply be blank over the new part of the region. To extend the wavelength region outside the original limits it is necessary to return to the design window and select Performance in the Parameters menu. The dependent variable is not limited in this way.
Plot Over
Plot Over permits the plotting of a second curve to be made over a first. The first curve must have been made using the current design. Once the first curve has been produced, then an adjustment to the design or a change in the calculation parameters, such as angle of incidence, may be made and then the performance of the new arrangement plotted over the first.
Plot Over will be grayed out if the design file is changed. To plot the results of a different design over those of a first, the Add command in the File menu should be used.
Plot the results of the first design. Save the plot as a plot file using the Save As...
command (the short cut key <F12> is the quickest and most convenient way of doing this). Change to the alternative design. Plot the results. While the plot window is active,
choose Add Line... from the File menu (<Alt><f> followed by <d>) and select the plot just saved. The plots will be combined.
Table
Table produces a table of results according to the options selected in the Performance menu item in the Parameters menu for the design window.
The table has the usual cells with individual results but as it is produced the table has the attribute read only and so is protected from change. This is a safety feature to guard the integrity of the data.
There may be occasions when some editing of the data is necessary. The legend against Design right at the top of the table is a good place to put a very short note, for example. For this reason the read only nature of the file can be changed. With the table window active select the Edit menu. There are two active items, Copy Table and Read Only. The read only status will be indicated by a tick to the left of the menu item. Select Read Only to toggle the status. When the tick is not visible, the table may be edited. It is good practice to return the status to read only after editing and immediately save the table.
Copy allows the table to be copied to the clipboard and pasted subsequently into any other suitable application, especially a word processor.
More information about the table menus will be found in a later section.
Errors...
One of the most difficult areas in the design of optical coatings is the assessment of the sensitivity of the coating to errors. The errors in manufacture are generally rather larger than the first order approximations that can be readily handled by analytical techniques and so the most successful ones involve Monte Carlo modeling of the deposition process. Random errors drawn from suitable infinite populations are introduced and their effects over a large number of simulations are assessed. This is the technique on which the Errors... menu item is based.
Errors calculates successive performance curves for the design with thickness errors and refractive index errors drawn from a normal population. The parameters dialog box appears first.
Errors may be specified for both thickness and refractive index for each material in the design. For thickness errors, there are three parameters: Thickness Mean Error, Thickness Standard Deviation and Minimum Thickness. The Thickness Mean Error and Thickness Standard Deviation specify the statistical properties of the normal population from which the random numbers for thickness errors will be drawn. For layers that are thicker than the Minimum Thickness, the error will be applied as a proportion of the layer thickness. For example, to apply a thickness error where the standard deviation is 2% of layer thickness and there are no systematic thickness errors, the following parameters are used:
Thickness Mean Error: 0
Thickness Standard Deviation: 0.02 Minimum Thickness: 0
In this case the thickness including error will be calculated as
ErrorThickness = LayerThickness + LayerThickness * RandomNumber
Another case is to apply an absolute error to the layer thickness that does not depend upon the thickness of the layer. For example, to apply a thickness error where the standard deviation is 2nm the following parameters can be used (providing no layer is thicker than 1000nm):
Thickness Mean Error: 0
Thickness Standard Deviation: 0.002 Minimum Thickness: 1000
In this case, the thickness including error will be calculated as:
ErrorThickness = LayerThickness + MinimumThickness * RandomNumber With the values above, the standard deviation of the amount added to the layer thickness will be 1000 * 0.002 = 2 nm.
A combination of proportional and absolute errors can be achieved by correct setting of the minimum thickness. For example, to specify 2% thickness errors with a minimum thickness error standard deviation of 2nm, the following parameters would be used:
Thickness Mean Error: 0
Thickness Standard Deviation: 0.02 Minimum Thickness: 100
For layers thicker than 100nm, the thickness error will be calculated as ErrorThickness = LayerThickness + LayerThickness * RandomNumber For layers thinner than 100nm, the thickness error will be calculated as:
ErrorThickness = LayerThickness + MinimumThickness * RandomNumber
For layers thinner than 100nm, the standard deviation of the amount added to the layer thickness will be 100 * 0.02 = 2 nm
For refractive index errors, there are two parameters: Index Mean and Index Standard Deviation. The Index Mean Error and Index Standard Deviation specify the statistical properties of the normal population from which the random numbers for index errors will be drawn. For refractive index errors, the random number is added to the packing density of the layer to generate the perturbed refractive index for the layer, i.e.
ErrorPackingDensity = Packing Density + RandomNumber
Two checkboxes control the application of thickness and index errors. If Include Thickness Errors is checked, then thickness errors will be calculated. If Include Index Errors is checked, then refractive index errors will be calculated. Both types of error can included at the same time.
If Include Locking is checked, then only the layers that are not locked will have their thicknesses altered. If Include Links is checked, then the thickness of one of the layers in each set of linked layers will be randomly altered and then the other layers in the link set will have their thicknesses adjusted so that they have the same ratio of thicknesses to the randomly altered layer as in the original unperturbed design. For example, if layer 1 is 15nm thick and layer 2 is 30nm thick, and these layers are linked, then during Errors, layer 1 will be randomly altered and layer 2 will be set to be twice as thick as layer 1
If Independent Index Errors is not checked, then all layers of the material will have the same packing density error applied to them. If Independent Index Errors is checked, then different refractive index errors will be applied to each layer.
The Number of Cases is just the number of different curves with different random errors drawn from the specified populations.
Sometimes it is useful to look at the worst designs generated where “worst” means has the largest merit figure. To keep the worst designs, check Keep Worst Designs and enter the maximum number of designs to be kept in Number to Keep. When the process is started a window will appear with a list merit figures. These are the worst designs generated. Double-click on a merit figure to open the design that has that merit figure.
When the list of merit figures window is closed, the worst designs that are not open or have not been saved will be discarded.
Once the correct parameters have been entered click the Plot button. The program will draw a series of curves each of which represents the performance of the coating with a different set of errors all drawn at random from the specified infinite populations with the parameters that have just been entered. By varying the error parameters and replotting an assessment of manufacturing tolerances can readily be made.
To see a table of statistics, click on the Statistics Table button.
A new set of errors will be generated and the statistics of the resulting performance data will be calculated and displayed as shown in the table above. The statistics calculated are Mean, Standard Deviation, Median, Maximum and Minimum. If a filename is entered in the Statistics Table spectra stored in box, the calculated performance data will be stored in the file in CSV format. This data can then be manipulated by any program that reads csv files. The Choose button next to the box displays a file chooser for easier entry of the filename. If a filename is entered in the Statistics Table color data stored in box, the color parameters selected in the Table list of the color dialog (see below) will be stored in the file in CSV format. This data can then be manipulated by any program that reads csv files. The Choose button next to the box displays a file chooser for easier entry of the filename.
For convenience, the Errors dialog also has a Color button. Clicking on this button will display the Color dialog (see below) with the error parameter part also displayed.
Color
The following color parameters are available: Tristimulus, Chromaticity, CIE L*a*b*, CIE L*u*v*, CIE L*u’v’, Hunter LAB, CIE1960 u,v, Correlated Color Temperature (CCT), Reciprocal Correlated Color Temperature (RCCT), Dominant Wavelength (Wd), Complementary Wavelength (Wc), Excitation Purity (Pe) and Colorimetric Purity (Pc).
For the CIE L*a*b* color space, the hue and chroma correlates are also calculated. For the CIE L*u*v* color space, the hue, chroma and saturation correlates are also
calculated. The Coloring Rendering Index for a coating combined with a light source can also be calculated.
The dialog box that appears has several fields for completion.
Source lists the sources. The standard sources are CIE A, B, C, D55, D65, D75 and equal energy. Black body and other sources can readily be added especially if the Function Enhancement is present. Instructions are in the earlier section on Color.
Observer lists the sets of tristimulus values that are to be used. As supplied, these are CIE 1931 and CIE 1964. Again other observer definitions can be added if required.
Mode specifies whether the transmitted or reflected color will be calculated.
Polarization specifies the polarization to be used for oblique incidence calculations.
Context specifies the coating context to be used for the calculations.
Incident Angle contains a set of three parameters that specify the range of incident angles and interval to be used in the calculation.
Show White Point places a symbol on the plot or creates a table entry that shows the coordinates of the source.
Show Color Patch creates a window that displays a visual impression of the color(s) of the coating.
The Plot tab allows you to choose a standard plot or select two color parameters to plot. The standard plots available are: Tristimulus XY, Chromaticity xy, CIE 1976 UCS, CIE 1976 h*c*(ab), CIE 1976 h*c*(uv). The Chromaticity xy plot is plotted on a
chromaticity diagram. The CIE 1976 UCS plot is plotted on a UCS diagram. The CIE 1976 h*c*(ab) and CIE 1976 h*c*(uv) plots are plotted on a polar diagram. If a Custom plot is selected, then the X Axis Parameter and Y Axis Parameter specify the color parameters to use in the plot. Clicking on the Plot button causes the selected parameters to be plotted. Clicking on the Active Plot button causes the parameters to be plotted in an Active Plot window. If Show Color Patch is checked, the color patch will also be active. See the Active Plot chapter (page 133) for more information on Active Plots.
The Table tab allows you to choose the color parameters to be included in the table output. Parameters are selected by clicking on them. Each selected parameter is highlighted in the list. In the figure below, the table will contain three parameters:
Tristimulus X with Chromaticity x and y.
Errors >> drops down an extra part of the form that allows you to see the effects of random thickness errors on the color of a coating in the same manner as the Errors command.
Please see the Errors command described earlier in this chapter for information on the error parameters.
If you do not wish to include the error variation in the color output, click on the Errors << button to close the error parameters part of the form. Plotting or generating a table with the errors part closed will calculate the color of the coating design without random variation.
Active Plot
This command starts an Active Plot using the current plot parameters. For more information on active plots, see the active plot chapter (page 133).
3D Plot
3D Plot initiates the plotting of performance in a 3D plot window. The aspects of performance and the range over which they are to be plotted have already been chosen under the item 3D Performance in the Parameters menu.
The 3D Plot window is now the active one and so the menu bar changes to reflect that.
The principal changes are that the Performance and Parameters menus disappear and the choices under the others are limited.
Many aspects of the plot can be modified. The section on the 3D Plot Window later in this manual describes how 3D plots may be modified. Note that the performance data do not change when the 3D plot parameters are altered.