Hi YoungDae,

That is exactly why I asked. When you make the assumption that the spot is aligned with X and Y, it is easier to calculate the FWHM.

If we make another assumption: The Spot has a Gaussian shape. Then it becomes even easier, to the point where I actually programmed a User-Operand for you.

I will not copy the source code here for visibility, but you can find it on my GitHub here. This is what the code does in short:

1. Retrieve detector half-widht and pixel #
2. Retrieve the centroid location (using NSDD and Data equal to -6 and -7, like in your screenshot)
3. Calculate the row and column indexes based on the centroid location and detector size
4. Calculate the standard deviation of the centroid row and index (in pixel size)
5. Multiply the standard deviation by the pixel size to have it in lens unit
6. Multiply the standard deviation by 2.355 to obtain the FWHM (assuming the spot is Gaussian-shaped)

The User-Defined operand is UDOC03.exe (UDOC01 and UDOC02 were already used in my case, feel free to change it to whatever number suits you).

This operand has a single input parameter: the Detector Number (note that I have only tested with Detector Rectangle so far).

This operand returns up to 6 parameters:

1. X-FWHM [lens unit]
2. Y-FWHM [lens unit]
3. X-sigma [lens unit]
4. Y-sigma [lens unit]
5. X centroid location [lens unit]
6. y centroid location [lens unit]

I have made a dummy example with a Source Gaussian (Beam Size = 0.2 mm in radius at 1/e^2) for demonstration purposes:

This is the result in the Merit Function:

Notice that Hx is 2 for the first UDOC operand (it is the detector number). Also remember that the UDOC is only computed once in this instance despite the presence of five additional UDOC operands (that are only here to display the other results calculated in the UDOC executable).

The first two UDOC operands are the X/Y FWHM. The UDOC operands with Data = 2/3 are the X/Y sigma, and remember that 2 * sigma gives you the 1/e^2. So, it is relatively accurate (0.101 instead of 0.100). The last two UDOC operands have the X/Y centroid locations that match the Source Gaussian X and Y Position.

We made two big assumptions that are important to keep in mind, and also all my interpolations are to the neirest neighbor. Despite all that, it should give you a good idea of the FWHM.

Please let me know if you try it. Take care,

PS: Please also double-check the results of the code yourself, I might have made a mistake in writting it, this is just a draft to illustrate how you could calculate the FWHM from your Detector Rectangle.

PSPS: if more people find it useful perhaps we can refine the code and have it in the Code Exchange at a later stage, what do you think @Sandrine Auriol?

David