Adjust Bessel function to data

[M_U]

Hi,

I need to adjust a Bessel function to this data. I was unable to make it and I can't discover the error. Can someone help me?

[Werner_E]

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I can't discover the error.

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Which error?

Post your Mathcad or Prime sheet!

[M_U]

I'm trying to use the QuickSheet of Fitting nonlinear functions to data. But my problem starts when I have to define the bessel function J0. I don't have the analytic expression for the function, so I can't use the genfit.

[Werner_E]

The Bessel function J0 does not have any parameters you may twist to fit to some data.

Why do you think that you must fit with a Bessel and what modified version of Bessel do you have in mind?

Where does the problem stem from?

[M_U]

Hello,

These data are of intensity depending on the distance of a diffraction pattern. From the aspect of the curve, I think it's a zero-order Bessel function because it doesn't cancel out at the origin. I even saw an example on the forum but I didn't quite understand it because I'm a Mathcad beginner

[Werner_E]

You may of course scale the Bessel in x and y direction and/or shift it, but the result sure is not satisfactory as you can see:

Maybe a damping factor of some kind is needed, but a first try with exp(-c*|x|) made it even worse:

So, unless you know a bit more about the type of function to fit, ...

[AlanStevens]

I think it might be better to fit a more standard diffraction function:

I = I0*sinc(k*x)^2

where I is your first column of data, x is your second column and sinc(x) = sin(x)/x

Having fitted I0 and k to your data you could see how k compares with the theoretical value (it’s a function of slit width, distance from slit to plane and wavelength of light),

Alan

[Werner_E]

Here's the result of Alans suggestion. I had to add a parameter c for vertical displacement

[M_U]

Thnak you Werner_E for the help. Using your tip and LucMeekes 1'm able to fit the function

[LucMeekes · Accepted solution]

The Bessel function will not work, note that J0 does not have a flat lower bound, like your data shows.

It may help to square the Bessel function, like this:

Success!
Luc