help me figure out refraction equation, please! its easy!

[unxzst]

This is my function, it calculates the normal reflectivity (%) of a non-absorbing multi-layer film on a substrate.

Function Rpc(Lambda As Single, SubstIndex As Single, n As Single, FilmProperty As Variant)
'FilmProperty(2N) made of R(1), T(1), R(2), T(2), ..., R(N), T(N).
'R(I) = FilmIndex
'T(I) = FilmThickness
'The layers are numbered starting from the one most away from the substrate.
'MEDIUM INDEX = R(0)
ReDim R(1 To n), T(1 To n), X(1 To n), C(1 To n), S(1 To n) As Variant
    AA = 1 / SubstIndex
    BB = 1
    CC = 1 / SubstIndex
For i = 1 To n
        R(i) = FilmProperty(2 * i - 1)
        T(i) = FilmProperty(2 * i)
    X(i) = (2 * 3.141592654 * R(i) * T(i)) / Lambda
'CALCULATE SINE AND COSINE TERMS FOR MATRIX ELEMENTS
    C(i) = Cos(X(i))
    S(i) = Sin(X(i))
Next i
'SETUP MATRIX ELEMENTS
    B11 = C(1)
    B12 = S(1) / R(1)
    B21 = S(1) * R(1)
    B22 = B11
'CHECK FOR ONE FILM
If n = 1 Then GoTo 500
For i = 1 To n
    C11 = C(i)
    C12 = S(i) / R(i)
    C21 = S(i) * R(i)
    C22 = C11
    A11 = B11 * C11 - B12 * C21 'C11
    A12 = B11 * C12 + B12 * C22 'C12
    A21 = B21 * C11 + B22 * C21 'C21
    A22 = -B21 * C12 + B22 * C22 'C22
    B11 = A11
    B12 = A12
    B21 = A21
    B22 = A22
Next i
500 CA = (AA * B11 - B22) ^ 2 + (BB * B12 - CC * B21) ^ 2
    CB = (AA * B11 + B22) ^ 2 + (BB * B12 + CC * B21) ^ 2
    Rpc = (CA / CB)
End Function

i will also have data being gathered from an instrument, which is monitoring the deposition of each thin film, by mearusing the transmission of light through quartz. trasferring between transmission and reflection is easy:

T=(1 - R) * 100

what I'm having trouble with is the crux of my program. I need to figure out at what thickness I am, and adjust that as deposition progresses.
I found some code online that will do what Solver does in Excel, plug in variables, get an answer, and iterate until the answer matches prediction, outputting the neccesary thickness values.
here, the example, uses a simple equation p1+p2*cx+p3*cx^2+p4*cx^3+p5*sin(p6*cx)

Private Function Fitter_OnGetLMFunction(ByVal X As Variant, ByVal Parameters As Variant) As Double
  Fitter_OnGetLMFunction = Parameters(0) + Parameters(1) * X + _
    Parameters(2) * X ^ 2 + Parameters(3) * X ^ 3 + _
    Parameters(4) * Sin(Parameters(5) * X)
End Function
Sub Fitter_OnProgress()
Dim I, X, Parameters
  Workbooks(1).Worksheets(1).Cells(39, 7) = Fitter.Iterations
  For I = 1 To NumPoints
    X = Workbooks(1).Worksheets(2).Cells(I, 1) ' X in 1st column
    Parameters = Fitter.Parameters
    Workbooks(1).Worksheets(2).Cells(I, 3) = Fitter_OnGetLMFunction(X, Parameters)
  Next
  DoEvents ' refresh chart
End Sub

Private Sub FitCommandButton_Click()
Dim I, datasheet, X, Y, Parameters
  Set datasheet = Workbooks(1).Worksheets(2)
  ReDim X(1000)
  ReDim Y(1000)
  I = 1
  While datasheet.Cells(I, 1) <> ""
    X(I - 1) = datasheet.Cells(I, 1)
    Y(I - 1) = datasheet.Cells(I, 2)
    I = I + 1
  Wend
  ReDim Preserve X(I - 2)
  ReDim Preserve Y(I - 2)
  NumPoints = UBound(X) + 1 ' save to use in Fitter_OnProgress
  
  ReDim Parameters(5)
  For I = 0 To UBound(Parameters)
    If Workbooks(1).Worksheets(1).Cells(34 + I, 4) <> "" Then
      Parameters(I) = Workbooks(1).Worksheets(1).Cells(34 + I, 4)
    Else
      Parameters(I) = 1
    End If
  Next
  
  Set Fitter = CreateObject("Fitter.DMFitter")
  Fitter.X = X
  Fitter.Y = Y
  Fitter.Expression = -2    ' perform differentiation numerically
  Fitter.ParamCount = 6
  '  Fitter.Parameters = Array(1, -1, -0.1, 0, 50, 0.192)
  Fitter.Parameters = Parameters
  Fitter.Sigmas = Array(0, 0, 0, 0, 0, 0)
  Fitter.WeightType = 0
  Fitter.Options = Array(0, 0.0000001, 0)
  Fitter.Iterations = 60
  If Fitter.LMFit Then
    Workbooks(1).Worksheets(1).Cells(33, 4) = Fitter.Deviation
    Parameters = Fitter.Parameters
    For I = 0 To UBound(Parameters)
      Workbooks(1).Worksheets(1).Cells(34 + I, 4) = Parameters(I)
    Next
  Else
    MsgBox "Fitter error " & Fitter.ResultCode
  End If
End Sub

but i need to adapt it to use my matrix equation. I am doing this in VB6, and I have no idea how I can begin to adopt this Levenberg-Marquardt least-squares fitter (ActiveX from http://fitting.datamaster2003.com/index.htm )to use my matrix function...but if anybody could help point me in the right direction for curve-fitting, it'll be greatly appreciated.


I found this Levenberg-Marquardt algorithm for multivariate optimization, sadly this is not something covered in school (or maybe i was sleeping?)
I cannot make head or tail of this example http://www.alglib.net/optimization/l...gmarquardt.php
maybe someone can point me to whatever is being optimized? I THINK i have to extrace a Jacobian determinant from the function in form of a matrix, and then plug it in...but where are the dependant variables??