Thanks Callie for this reply. This saved me a bunch of time trying to figure this out. Love the idea of using MFE operands for this rather than saveing the text file. 

Hi Paolo,

You’re absolute correct about both the MFE being correct and the GetOperandValue() being incorrect.  To get around this, you will have to manually build up the MFE.

As a little background, the Zernike algorithm is a regressive fitting algorithm where lower values are dependent on the maximum term defined (you can think of this as balancing low order terms with higher order terms if you define a higher order term with the maximum term number).  Zernike terms are similar to wavefront coefficients in that they are grouped around a rho^n term.  So, when you are looking at fitting a wavefront/surface to Zernikes, you need to make sure you use the appropriate rho^n maximum term.  Looking at the Zernike Standard Coefficients, the rho^n term always increases when moving to the next spherical term, namely:

• Z4 (2nd order)
• Z11 (4th order)
• Z22 (6th order)
• Z37 (8th order)
• Z56 (10th order)
• Z79 (12th order)
• Z106 (14th order)
• Z137 (16th order)

The maximum term should always be 1 less than the next highest order you want to investigate.  So, if you want to decompose a wavefront/surface to 3rd order wavefront coefficients, you will need to include all the terms of the rho^4 Zernikes meaning the maximum term should be Z21.

The Merit Function Editor recognizes the maximum term for adjacent ZERN operand, using the maximum term as described above.  So, to keep the fitting algorithm consistent while extracting different terms, you will need to insert (at least) 2 new operands in your MFE, the first operand will be the ZERN that you want to extract and the second operand will be the ZERN that will define the maximum fitting term.  I would suggest adding all your terms to the MFE so the Zernike fitting would only have to occur once.

The ZOS-API Sample Code Example 3 shows how to add new operands and change the type as a quick example if you need a starting point.

~Michael

Hey Brian,

It’s slightly different from both options you mention. 

3. Create entries in the MFE, update the MFE, and then GetOperandAt(#).Value

The (slow) psuedo code would look like:

int wave = 2;
int samp = 2;      // 2 ^ (samp + 4) is the grid density
int field = 2;
int zType = 1;     // 0 = fringe, 1 = standard

int numOfTerms = 37;


IMFERow op;
for (int i = 1; i <= numOfTerms; i++)
{
    // get a reference to the operand...add a new row if needed
    if (i == 1)
    {
        op = TheSystem.MFE.GetOperandAt(1);
    }
    else
    {
        op = TheSystem.MFE.InsertNewOperandAt(TheSystem.MFE.NumberOfOperands + 1);
    }

    // change the operand type and add column values
    op.ChangeType(MeritOperandType.ZERN);
    op.GetCellAt(1).IntegerValue = i;
    op.GetCellAt(2).IntegerValue = wave;
    op.GetCellAt(3).IntegerValue = samp;
    op.GetCellAt(4).IntegerValue = field;
    op.GetCellAt(5).IntegerValue = zType;
}

// update the merit function
TheSystem.MFE.CalculateMeritFunction();

// puposely add an extra term so zernikes[1] = Z1
double[] zernikes = new double[numOfTerms + 1];

// get all the zernikes
for (int i = 1; i <= numOfTerms; i++)
{
    zernikes[i] = TheSystem.MFE.GetOperandAt(i).Value;
}

For #2, if you get the merit function value itself, as you pointed out it will always be positive and you can only get a single value at a time.  

For #1, you cannot use the single line method GetOperandValue() since the Zernike will only consider terms lower than or equal to the term in question.  For example, if you look at the Double Gauss 28 degree field.zmx sample file (wave 2, field 2), you can see that the Zernike Standard Coefficient report will give the following for Z22, Z29, Z37:

• Z22 = -0.03632469
• Z29 = 0.00232182
• Z37 = -0.00119946

If you use the GetOperandValue(), this is equivalent to having a BLNK between different ZERN terms (in red below).  When you look at Z22 with this method, only Z1 through Z22 are used in the Zernike fitting.  Then when you look at the Z29, this looks at Z1 through Z29, but the Z22 will be different since the Zernike fitting is done to minimize the RMS error.  In order to get the proper Zernike fitting, you will need to place all ZERN operands one next to the other, only increase the Term column, calculate the MFE and then retrieve each operand’s value (in green below).