Technical Issues - FilmStar News 2013

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February 8    Reverse Engineering by Color Matching

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.

March 12    Organizing Data Directories

Users often need flexibility in dealing with data locations. A user might want to save AR designs in one directory and beamsplitters in another. Another possibility is to organize by customer, especially useful when confidentiality is paramount.

To that end, DESIGN has included two BASIC programs since 2004: SetPath.bas and SetPathMulti.bas. SetPath replaces entries in File.. Configuration.. Directories with a single path; SetPathMulti.bas generates multiple paths. You might find these assigned to Macro Button 6 (Tools.. Macro Commands.. File.. Open PopUpMenus.mcr).



n,k Tables  


New versions of these programs add a Browse For Folder dialog. When prompted for subdirectory name, typing '?' activates the browser.

Macro Button 6

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.

March 26    Importing Illuminants

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.

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.

'IllumImport.bas For FilmStar Design, MEASURE
'Copyright 2013 FTG Software Associates

Option Explicit
Option Base 1
Const Interval = 1 '1 or 5 nm interval

Sub Main
    Dim yDat!(), n%, i%, f$
    f$ = GetFilePath(, "csv", "C:\Winfilm\Data", "Open Digitized Spectrum")
    If f$ = "" Then End
    FileOpen f$, 1
    DataConvert 380, 780, Interval 'CIE range
    f$ = GetFilePath( , "csv", "C:\Winfilm", "Save CIE Illuminant",2)
    If f$ = "" Then End
    yDat = Spectrum_Y
    Open f$ For Output As #1
    If Interval = 1 Then n = 401 Else n = 81
    For i = 1 To n
        If PgmExe$ = "Design1" Then
            Print #1, CStr(yDat(i, 1))  'DESIGN
            Print #1, CStr(yDat(i))     'MEASURE
        End If
    Next i
    Close #1
End Sub

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.

[CIE Color]
Window32=0 3225 6420 7605 6495 0 0
Illum1=White LED;LED-White-1nm.csv

April 1    Correcting Coating Thickness Errors

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.

' ReOptimize.bas for FilmStar DESIGN
' Copyright 2013 FTG Software Associates
' Re-optimize to correct a layer thickness error

Option Explicit
Option Base 1
Const qErr = 150 ' +50% error
Const Title$ = "Laser Output Coupler" ' Laser-O.faw

Sub Main
    Dim i%, Legend%, nLayers%, q0!, q!(), qt$(), qd$()
    PlotTitle = Title$ & ", Error = " & Format$(qErr-100, "0.0") & "%"
    PlotLegendOn True
    Legend = 1: PlotLegend(1) = "Original": PlotNext
    GetLayers nLayers, q(), qt$(), qd$()
    For i = 3 To nLayers Step 3
        q0 = q(i): q(i) = .01 * qErr * q0
        If i < nLayers Then
            Legend = Legend + 1
            SetLayers q(), qt$()
            SetOptiVars i+1, nLayers: Optimize
            PlotLegend(Legend) = "Layer " & CStr(i)
            q(i) = q0: SetLayers q(), qt$() 'restore original design
        End If
    Next i
    OptiVars "" 'set all opti variables
End Sub

Sub SetOptiVars(kLay, nLay)
    Dim i%, v$
    For i = kLay To nLay
        v$ = v$ & CStr(i)
        If i < nLay Then v$ = v$ & ","
    Next i
    OptiVars v$
End Sub

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:

Additional layers may save the coating. In the graph shown below (50% error in layer 24) we added 2 new quarter wave layers to our 26 layer design and then re-optimized layers 25 through 28.

As shown in the image at the right, the Interactor can be used to manually modify layer thickness. The Adjust Design dialog is another possibility.

May 15    Excel (as Client) Reliability

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.

Dim dBasic As FtgDesign1.clsBasic
Option Explicit

Sub GetCieVals()
    On Error Resume Next
    Dim x As Single, y As Single, yy As Single, a As String
    a$ = Application.GetOpenFilename("FILM Archive (*.faw), *.faw")
    Set dBasic = New FtgDesign1.clsBasic
    Debug.Print dBasic.Angle  ' triggers DESIGN
    pause 0.5                 ' may need to increase
    dBasic.FileOpen a$
    dBasic.GetCie x, y, yy
    With Sheet1
        .Cells(1, 1) = dBasic.CieParams
        .Cells(1, 2) = x
        .Cells(1, 3) = y
        .Cells(1, 4) = yy
    End With
    Set dBasic = Nothing
End Sub

Sub pause(ByVal delay As Variant)
    Dim t0, t1
    If delay > 0 Then
        t0 = Timer ' start time
        t1 = t0 + delay ' end time
            If t0 > Timer Then t1 = t1 - 86400 ' adjust for midnight
        Loop Until Timer >= t1
    End If
End Sub

August 1    MONITOR Wavelength Calibration

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
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.

August 22    MEASURE/Scantraq Time Plot

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.

Option Base 1
Option Explicit
Const nRead% = 21   ' number of readings
Const Wave! = 550   ' wavelength

Sub Main
    Dim i%, t0!, s$
    t0 = Timer
    ReDim xDat(nRead), yDat(nRead)
    comPortOpen       ' ignored in TestMode
    For i = 1 To nRead
        xDat(i) = Timer - t0  ' current time
        yDat(i) = Reading(Wave)
        ' randomize Test Mode (otherwise just straight line)
        If TestMode Then yDat(i) = yDat(i) * (1 + .05*Rnd)
        Pause 1       ' time between readings in seconds
        StatusLabel "Iteration " & CStr(i) & "/" & CStr(nRead)
    Next i
    Spectrum_X = xDat
    Spectrum_Y = yDat
    PlotXaxisLabel = "Time (seconds)"  ' assign X-axis label
    PlotXAxisLabel = ""   ' restore default X-axis label
End Sub

Sub Pause(ByVal delay!)
    Dim t0!, t1!
    If delay > 0 Then
        t0 = Timer      ' start time
        t1 = t0 + delay ' end time
            If t0 > Timer Then t1 = t1 - 86400  ' adjust for midnight
        Loop Until Timer >= t1
    End If
End Sub

The spectrum can be saved via the Plotting Module Data menu. IMPORTANT: To simplify matters we have assumed that no correction to Reading is required. This is not usually the case. Please refer to BASIC help under Function Reading. The actual time between readings will depend on Filter Response and Delay Factor.

August 27    Rugate Analysis with Stack Mode

Stack Mode provides a convenient way to evaluate rugate designs. Here we utilize a formula for sinusoidal rugate index profile given by Southwell and Hall, Applied Optics 28, 2949-2651 (1989). The apodization functions given by Southwell in Applied Optics 28, 5091-5094 (1989) can easily be generated with a VBA macro. By combining Excel and FilmStar, rugate designs are not limited to pre-programmed functions.

Copy columns A-H and paste into the Stack Mode editor.

The structure is pasted into the Stack Mode Editor and matching layers are added. Note that the 41 layer sinusoid structure is repeated 50 times: Num specifies the number of layers to be repeated, Rpt gives the repeat factor. This is equivalent to using parentheses in Groups Mode designs.

The Stack Mode editor eliminates index symbols (L, H, M etc), thereby supporting up
to 32K materials. Use the left/right arrow button to observe changes in the Interactor.

To illustrate optimization in Stack Mode (variables specified in the Sel column), we refine matching layers.

Users wishing to try the above for themselves should update FilmStar to add the following files

Rugate-Matching.faw    Rugate-Matching.dmw (Film Stack)     Rugate.xlsx

Open Rugate-Matching.faw. Then click Design..Stack Editor and open the Film Stack. Click on the main screen and note that Film Indices, Groups Editor and Layers Editor are no longer available. Activate the Interactor and observe that the design grid has disappeared, being replaced by the Stack Editor. In the case of nondispersive films, there is no need (DESIGN 2.61.3157) to increase Film Indices capacity.

September 12    Thickness-Modulated Minus Filter Designs

A recent article by Z Wang et al, Applied Optics 52, 5788-5793 (2013) caught our attention. We thought that DESIGN BASIC macros would be useful in generating thickness-modulated designs. Starting with FILM Archive Modulate1, the following BASIC program provides an example (see Figure 5a):

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$(iLay) = "H" Then
            q(iLay) = 1 + .22 * Sin(PI*(iLay-1)/kLay)
            q(iLay) = 1 - .22 * Sin(PI*(iLay-1)/kLay)
        End If
    Next iLay
    SetLayers q(), qt$()
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)

The referenced article includes layer-thickness profile graphs. FilmStar users can create graphs of this type with Excel workbook LayersPlot.xlsm to be found in c:\Winfilm\Excel 2007. Note: Designs are converted to physical thickness and groups are expanded to separate layers! Please be careful about resaving designs which may have been altered.

Recognizing the limitations of Excel graphics, thickness profile plots were added to DESIGN 2.61.3180 (scroll down to Sep 25). Excel enthusiasts will find that the Excel workbook is quite instructive.

September 17    Interactor Update - Thickness Plot

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.

September 25   Layer-Thickness Profile

Our previous Thickness Profile Excel graph (scroll up to Sep 19) has limitations. A superior and easier-to-use capability has been added to DESIGN 2.61.3182. Click Design.. Thickness Profile.

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.

November 6   PE Spectrum 10 Support

Note: Click here for related material

PerkinElmer's Spectrum Version 10 software imports/exports FTIR settings as XML files with .set extension (different from previous .set files). This upgrades the previous Spectrum Express which lacked the ability to export and import settings. Spectrum 10 works with all PE FTIR after Spectrum GX. (A minor point of confusion is that 'Spectrum' refers to instruments as well as software.) The most recent model is Spectrum Frontier (Optica) which supersedes Spectrum 100 which in turn replaced Spectrum One.

Spectrum 10 Server installation

Integration with FilmStar MEASURE (Scantraq) is through our new Spectrum 10 Server: Sp10.exe. While the server typically runs as a background task, it also runs standalone for testing purposes. Users export one or more .set files (typically one for transmission and another for reflectance) in Spectrum 10. These are then opened by Spectrum Server via File..Open. Click File..Review to verify. Note that Sp10.exe requires you to install Chilkat's free XML library. Use this version.

.set viewer displays instrument settings
updated by the Spectrum 10 Server;
other settings remain at default values.

Three settings are user-settable via Setup..Parameters or BASIC: number of scans and wavenumber min, max. Recommended practice: specify the entire instrument range in wavenumbers, say 500 to 10000 and rely on MEASURE to convert to the required Ám or nm range.

A Data Viewer dialog lets users review the spectrum. F9 toggles between Ám and 1/cm scales. The server can be run from other Windows applications as illustrated by Excel workbook Spectrum10.xlsm.

November 11   FTIR Stability

The accuracy of single-beam spectrometers, including diode-array and FTIR, depends on the reference (aka background) remaining constant. How often is a new reference required? Once a day? Once an hour? Before every sample scan? How much warm-up time? Such issues can be addressed with repeated T=100% scans over a period of time.
This is accomplished automatically with MEASURE BASIC program sp10Stability.bas for PerkinElmer FTIR instruments. The code is included in the FilmStar Spectrum 10 installer and listed below for users to modify for other instruments.

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 Ám wavelength axis provides a different perspective.

One possibility for eliminating the 15 Ám CO2 line is a nitrogen purge. Another possibility, assuming there are no important spectral features at 15 Ám 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.

Option Explicit
Option Base 1
Dim FTIR As FtgSp10.clsDAQ  ' connect to FTG Spectrum 10 Server
Const Delay! = 10   ' delay in minutes
Const Scans% = 6    ' number of scans (12 max)
Sub Main
    Dim xDat!(), yDat!(), i%, t0!
    PlotClose       ' clears previous FSPlot graphs
    Set FTIR = New FtgSp10.clsDAQ
    FTIR.Scan 1     ' BACKGROUND
    t0 = Timer
    For i = 1 To Scans
        PlotLegend(i) = Format$((Timer-t0)/60,"0.0") & " min"
        FTIR.Scan 0 ' SAMPLE
        FTIR.GetSample xDat(), yDat()
        Spectrum_X = xDat
        Spectrum_Y = yDat
        If i < Scans Then Wait 60*Delay!
    Next i
    Set FTIR = Nothing
End Sub

November 14   Workbook Optimization without Pasting Spectra

A user recently requested help in optimizing color-related quantities in the Workbook. Transferring calculated spectra and computing CIE quantities in the Workbook is possible, but complex and very slow compared with built-in BASIC Sub GetCie. It was not clear whether Workbook optimization could utilize GetCie.

When developing Workbook models, it is best to start with a simple case where the answer is well-known, say BBAR.faw. We make use of BASIC Property Merit which utilizes the Optimization Targets specified in DESIGN's main menu. This is the same merit function obtained with Evaluate.. Merit Function.

Macro (E2) function BasExec executes BASIC code setting the Objective (D4) to Merit. DataType (C1) = 16 suppresses pasting of spectra below the DataMarker (A2) cell. There needs to be a DataMarker cell even if not actually used. Before optimizing, test by clicking Evaluate.. Execute Macro <F8>.

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

Sub Main
   WbSetNum "$D$4", Merit ' compute merit, place in D4 (Objective)
End Sub

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.

November 26   Tolerancing with Index Variations

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.

FilmStar BASIC code

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

Excel VBA code

Sub DesignCopy()
    Calculate 'update index column
    Range(Selection, _ 
End Sub

Pseudo-normal distribution replaces H indices with randomized values.

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

Comparing this graph with the previous suggests that index errors are worse than thickness errors of the same relative magnitude. Note: Close Excel before closing DESIGN.

December 10   Edge Filter Measurement vs. Design

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
    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$()
    Design = des0$ '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)▓}. Now suppose that source depletion makes the path 1 cm longer. M/W = 1.5473 {(51/41)▓}. 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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