Are CIE color coordinates such as L*a*b* useful in correcting color shifts? This is an issue in ophthalmic coatings where AR cosmetic appearance is critical. BASIC Sub SetCieAxes (2.61.3141) in conjunction with Sub CieOptimize helps us reverse-engineer by matching L*a*b* values.

We performed Gedankenspektrum calculations using our 4 layer optimized BBAR design and a modification of FilmSolve1.bas based on L*a*b* color matching. We considered two cases: 1. All layers vary independently, 2. Tooling factors vary so that L and H variations are linked. We also ran the original FilmSolve1.bas and found that solutions based on normal incidence spectral matching (380-780 nm) gave 100% confidence. In both cases it is assumed that refractive index variations are negligible.

Case 1 (independent variation): Color matching was insufficient for reliable reverse-engineering. When setting Tolerancing Values SD = 3%/6% and 3% Verification Level we typically attained a Confidence Level in the range 40-50%. As shown here (RGB Boost = 30), different spectra give indistinguishable colors, and if the eye cannot distinguish, neither can a computer algorithm.

Case 2 (linked variation): Under the same tolerancing and verification conditions, Confidence Level = 100% when L and H layers vary in tandem as in tooling factor shifts. This is physically verified by reference to the Excel Color Grid published last year (updated Feb 21, 2013).

Engineers dealing with AR color shifts will need to include any additional materials as well as refractive index variations in their Gedankenspektrum analyses.

These programs are easily modified as required. BASIC experts: Note that Browse For Folder is a Windows shell command, not a BASIC dialog. Reviewing the code may be helpful in your other applications.

With the popularity of LED light sources, it is important to be able to utilize published illuminant data. Such spectra, however, are often presented graphically as shown below.

Fortunately there are programs which digitize spectral curves. We have tried two: Dagra and DigitizeIt. DigitizeIt is, in some cases, easier to use as it can automatically digitize entire spectra. It fit the above spectrum perfectly with one click. Dagra utilizes Bezier curves and is recommended for noisy data or any situation where smoothing is required. An example utilizing Dagra can be found here. You may want to try the free Engauge Digitizer.

Both programs generate CSV files (Wavelength, Intensity). The BASIC program below opens digitized data in c:\Winfilm\Data and converts it to an illuminant file in c:\Winfilm. A FilmStar illuminant is a list of intensities from 380 to 780 nm. There are either 81 or 401 values corresponding to 5 nm and 1 nm intervals. There is no need to normalize the intensity scale.

Excel .xls, .xlsx files are internationally invariant, but CSV is problematic when exchanging data files between English (decimal point '.') and European (decimal point ',') notation. One possibility is conversion in Notepad. European to English: 1. Replace All "," by ".", 2. Replace All ";" by ",".

The final task is to make the illuminant available in FilmStar's CIE Setup Parameters. This is accomplished by adding Illum lines to the CIE Color section in ..\Winfilm\Config\Design1.ini (Measure.ini). Illum lines are added in numerical order starting with Illum1. Edit with Notepad or even better Notepad++. A path under Winfilm is optional (e.g. Illuminants\LED-White-1nm). Use the link below to download the LED illuminant.

Consider a known thickness error during deposition, perhaps caused by a dozing operator or a monitor glitch. Can the coating be saved by redesigning it? We can get an idea with a Gedankenspektrum calculation where we assign an error to each layer and re-optimize the remaining stack.

Running the BASIC code gives us the following for our 26 layer Laser Output Coupler design. This helps us determine whether the coating can be repaired or should be abandoned. As expected, errors in initial layers are more easily corrected than errors in final layers.

What happens if the layers are not re-optimized? After commenting-out (disabling) the line starting with SetOptiVars we obtain the following:

We recently observed that Excel (client) running FilmStar DESIGN (server) did not always operate as expected. As shown in this example (displays CIE values), the fix is simple. We cannot, however, explain just why it is necessary. The extra steps shown in blue cannot be deleted. It seems necessary to execute some spurious command such as Debug.Print dBasic.Angle or dBasic.Angle = 0 and follow that with a small time delay before proceeding with required commands.

Upon executing the following Design1.exe is removed from the Windows Task Manager. Single stepping through the code is instructive. Note that Set dBasic = Nothing is not required if Dim dBasic... is placed within Sub GetCieVals.

Optical monitor settings may not accurately indicate actual wavelengths. Calibration is often required. In addition, it is possible to utilize different wavelength ranges by replacing gratings. A monochromator setting of 500 nm might correspond to an evaluation wavelength of 2000 nm. This feature was previously available in FilmStar MONITOR but not fully implemented.

MONITOR 2.53 upgrades this capability by adding a separate Mono wavelength column when either a Correction Function or non-unity Grating Factor is specified.

Correction Function or non-unity Grating Factor triggers dual wavelength mode.

Changing Mono or Wave automatically updates the other column.

Specify Monochromator or Evaluation in Edit...Wavelength Type to select
the column incremented by F4-F5 or Increase/Decrease toolbar icons. Only one
wavelength column is shown when Correction Function off and Grating Factor=1.

Notes: 1. If you use Evaluate.. Copy Worksheet, there are now two wavelength columns (identical when Correction Function off and Grating Factor=1). This requires a modification of any procedures (typically in Excel) based on the copied sheet. 2. The Run-Sheet template adds field code 'Eval' for accessing the second (evaluation) wavelength column. Use 'Wave' or new 'Mono' for the first (monochromator) column. 3. Files saved in 2.53 will not open in previous versions.

There may be occasions when a time plot at a single wavelength is required. This can be accomplished in Mpe983.exe, Mpe19AX.exe, mCary5.exe and mH3410.exe with the BASIC program shown below. The X-axis label was changed with Property PlotXAxisLabel introduced in revision 2.51.1369. The graph shown below illustrates Test Mode on.

August 27    Rugate Analysis with Stack Mode

September 12    Thickness-Modulated Minus Filter Designs

Option Base 1
Option Explicit
Const PI = 3.14159

Sub Main
    Dim iLay%, kLay%, nLay%, q!(), qt$(), qd$()
    FileOpen "Modulate1.faw"
    GetLayers nLay, q(), qt$(), qd$()
    kLay = nLay - 1
    For iLay = 1 To kLay
        If qt$(iLay) = "H" Then
            q(iLay) = 1 + .22 * Sin(PI*(iLay-1)/kLay)
        Else
            q(iLay) = 1 - .22 * Sin(PI*(iLay-1)/kLay)
        End If
    Next iLay
    SetLayers q(), qt$()
    AxesDraw
    CalcPlot
End Sub

Results are shown below. In the Modulated design, the Interactor was used to tweak the last layer and center the stack at 525 nm. Starting with the Modulated design, the Optimized design was obtained by adding and optimizing matching layers (T=100% targets: 400-495 nm, 505-750 nm).

Excel Layer-Thickness Profile (added September 19)

A user requested that the Interactor include plotting vs layer thickness. This has been implemented in DESIGN 2.61.3171. As shown here, Zoom Mode is supported.

Font size, background and grid colors are the same as the Interactor; bar colors are the same as FSPlot line colors. Up to 12 materials can be utilized, but may become hard to distinguish, especially with monochrome settings (Setup.. Colors). All layers (except massive) must be in optical OR physical thickness and designs with parentheses are not allowed. Massive layers are not to scale and indicated by a diamond instead of square graphic legend.

Scanning just after FTIR initialization suggests
that at least 10 minutes warm-up is required.

Subsequent scans appear stable over ~50 minutes.

This test (30 min interval) suggests that the
reference be measured at least every hour.

A µm wavelength axis provides a different perspective.

One possibility for eliminating the 15 µm CO2 line is a nitrogen purge. Another possibility, assuming there are no important spectral features at 15 µm is to skip over it with a wavelength list.

How were these graphs saved and recalled? We took advantage of FSPlot Data..Copy and Data..Paste which support multiple spectra with up to 12 line legends. Copying is very Excel-friendly with the option of assigning graph legends to row headers. MEASURE 2.51.1373 and DESIGN 2.61.3185 fix a bug preventing Data..Paste & Data..Save As from working properly when wavelength axes are inverted.

The code listed below is easily adapted to Ocean Optics, StellarNet and similar single-beam instruments. More than 12 scans are possible if the PlotLegend statement is deleted.

BasExec automatically adds Sub Main and End Sub and, in this case, is equivalent to...

BasExec is best suited to simple BASIC programs contained within Sub Main and End Sub. Complex BASIC programs should be saved to disk and executed with macro command BasRun.

Tolerancing with thickness variations is straightforward via DESIGN Evaluate.. Tolerancing. What users might not realize is that this capability is also in FSPlot. In addition to superior graphs (especially the ability to zoom), FSPlot includes means to copy or save (.csv) multiple spectra. In the graph below we set L errors to 0 and H errors to 0.24%. DESIGN 2.61.3189 improves matters by automatically switching legends off and assigning a single line color as specified in Graph Details.

But what about index variations? This seems impossible because only one index value for each material is specified in the Film Indices dialog. Fortunately, Stack Mode automatically assigns individual index values to each layer. Since Stack Mode is Excel-compatible, we can copy the design, paste into Excel, vary indices and paste back into DESIGN. And, of course, with FilmStar BASIC we can automate the procedure.

Randomized indices are shown below. The original design on the left remains fixed while the design on the right is altered by the function shown. It is a simple extension to vary both thickness and index.

Note that FilmStar BASIC and Excel are both open. FilmStar BASIC statement xlApp.Run triggers Excel VBA code DesignCopy. Compare columns G and V to see how indices vary.

Option Explicit
Sub Main()
    Dim i%, xlApp As Excel.Application
    If StackRows = 0 Then End
    PlotClose
    PlotActivate
    For i = 1 To 100
        xlApp.Run "DesignCopy"
        DoEvents
        DesignPaste
        Macro "CALCULATE;"
        PlotNext
    Next i
    Set xlApp = Nothing
End Sub

Sub DesignCopy()
    Calculate 'update index column
    Range("P1:AC3").Select
    Range(Selection, _ 
       Selection.End(xlDown)).Select
    Selection.Copy
End Sub

=IF($G3=2.1, $G3*(1 + 0.0024*(RAND()
 + RAND() + RAND() + RAND() + RAND()
 + RAND() + RAND() + RAND() + RAND()
 + RAND() + RAND() + RAND() - 6))

A LinkedIn member reported discrepancy between edge filter design and measurement. While spectral shape appeared as designed, the transition was not as sharp. A possible explanation is non-zero monochromator bandwidth. This is easily estimated in the DESIGN Interactor.

As emphasized in the diabatic plot below, the wavelength span of the transition zone is greatly affected by monochromator bandwidth. The magnitude of the effect will, of course, depend on the number of layers, etc. Here we have used an extremely sharp edge filter for emphasis.

What if discrepancies cannot be (or are only partially) attributed to spectrometer errors? One might suspect random errors. Using the same 180 layer Ta2O5-SiO2 design as above (November 26) it appears that errors sufficient to broaden cutoff give awful spectral shapes, contradicting measured results.

In the various replies, one LI member proposed tooling factor shifts, as previously considered in our Layer Error Analyzer. Do systematic tooling variations give the optimized spectral shape except for slope? This can be tested with the BASIC program below for any design containing L and H layers. Testing index variation is somewhat more complex, requiring Stack Mode and an appropriate Excel model.

Option Base 1
Const PC_H = 1 'H layer % change
Const PC_L = 1 'L layer % change

Sub Main
    Dim iLay%, nLay%, q!(), qt$(), qd$(), des0$
    des0$ = Design 'save original design
    PlotActivate
    GetLayers nLay, q(), qt$(), qd$()
    For iLay = 1 To nLay 'Linear approximation for simplicity
        If qt$(iLay) = "L" And PC_L <> 0 Then
            q(iLay) = q(iLay) * (1+.01*PC_L*(iLay-1)/(nLay-1))
        ElseIf qt$(iLay) = "H" And PC_H <> 0 Then
            q(iLay) = q(iLay) * (1+.01*PC_H*(iLay-1)/(nLay-1))
        End If
    Next iLay
    SetLayers q(), qt$()
    Calculate
    PlotNext
    Design = des0$ 'restore original design
End Sub

Users who have no idea how to utilize the code should contact FTG for an online tutorial. As we see below, modest thickness errors have a marked effect on slope. While a coating engineer can easily move the edge to the correct 50% wavelength, there is no simple adjustment to correct slope.

Large deviations generally preserve the optimized shape.

Zooming the above graph indicates that +L compensates for -H even with large errors.

It appears that, except for slope, this highly optimized design withstands significant errors. Index variations give similar results and compensation by thickness adjustment is possible. Applying the above BASIC macro to a laser output coupler gives the following.

Whether coating errors become thinner or thicker during deposition depends on monitor layout. Consider a monitor witness at 40 cm and a substrate at 50 cm above the source. M/W (monitor to work ratio) = 1.5625 {(50/40)²}. Now suppose that source depletion makes the path 1 cm longer. M/W = 1.5473 {(51/41)²}. The final layers will be about ~1% too thick.

Ultimately our simple linear approximation should be replaced by a model which computes source depletion as layers are deposited. Depending on design and measurement capability, it may be possible to corroborate these ideas with inverse-synthesis as discussed in the Layer Error Analyzer. Disclaimer...This page does not imply that there are no other possibilities for edge broadening.

Users concerned with source depletion might find it useful to deposit a Tooling Factor Correction design before (with filled sources) and after (without refilling) an actual coating run.

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