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I was trying calculating Fourier transform of some rings. as follow:

enter image description here

By directly calculating of model as several rings, the result showed different from the the experimental ones. So I tried to get a curve from the image and planed to calculate Fourier transform by the fitting curve..

Following is the data of the curve..

data = {{0,0.815686},{5/21,0.51634},{10/21,0.207843},{5/7,0.0529412},{20/21,0.0363922},{25/21,0.117766},{10/7,0.189434},{5/3,0.132985},{40/21,0.0463529},{15/7,0.0222948},{50/21,0.0502674},{55/21,0.0873281},{20/7,0.0840623},{65/21,0.042402},{10/3,0.0102884},{25/7,0.00596238},{80/21,0.0145603},{85/21,0.0231629},{30/7,0.0190779},{95/21,0.00710383},{100/21,0.00200784},{5,0.0046875},{110/21,0.00948855},{115/21,0.0113505},{40/7,0.00738178},{125/21,0.00252279},{130/21,0.00134028},{45/7,0.00285617},{20/3,0.00439216},{145/21,0.00396351},{50/7,0.00247457},{155/21,0.00115583},{160/21,0.00149211},{55/7,0.00257593},{170/21,0.00304012},{25/3,0.00233126},{60/7,0.00126775},{185/21,0.0015069},{190/21,0.00200769},{65/7,0.00241613},{200/21,0.00249372},{205/21,0.00165757},{10,0.00157282},{215/21,0.00201617},{220/21,0.00255754},{75/7,0.00303752},{230/21,0.00316325},{235/21,0.00289558},{80/7,0.0033218},{35/3,0.00349822},{250/21,0.004},{85/7,0.00339083},{260/21,0.00370167},{265/21,0.00411765},{90/7,0.00484144},{275/21,0.00461993},{40/3,0.00455182},{95/7,0.00447059},{290/21,0.00593018},{295/21,0.00518659},{100/7,0.00410831},{305/21,0.00241327},{310/21,0.00280112},{15,0.}}
ListLinePlot[data, PlotRange -> All]

enter image description here

Then I did the fitting by

fit = NonlinearModelFit[data,0.8 Exp[-t*r] Sin[4.5 (r + b)] + d, {t, b, d}, r];

If it fits well I will continue the Fourier transform from the fitting functions.. Anyway the result always not well fitted:

enter image description here

Not very good. Should I modify the model or something? How can I solve the problem?

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    $\begingroup$ Graph your data on log-linear axes: that will show this functional form can only be a terrible fit. A close look also shows that it's not exactly periodic, either. This site could serve you better if, instead of showing us what is going wrong, you were to ask a question about what you really want to achieve: explain what your data mean and what you would like to learn about them, then ask us ways to accomplish that. $\endgroup$
    – whuber ♦
    Commented Jan 16, 2015 at 15:42
  • $\begingroup$ What are your rings? Fresnel rings? $\endgroup$
    – Aksakal
    Commented Jan 16, 2015 at 16:31
  • $\begingroup$ Actually the rings are CorrelationFunction of a image.It usually are one inner dots and 2 rings outside.sometimes changes slightly,depends on the original images..not the fresnel rings. $\endgroup$
    – Cici
    Commented Jan 16, 2015 at 16:35
  • $\begingroup$ Can you explain what is correlation f-n of image? Is there a theoretical equation for this curve? $\endgroup$
    – Aksakal
    Commented Jan 16, 2015 at 16:56
  • $\begingroup$ The reason I'm asking is because the curve you're trying to fit will not fit at all. It can take negative values, while your data is all positive. That's why I asked if it's Fresnel rings' radial intensity $\endgroup$
    – Aksakal
    Commented Jan 16, 2015 at 17:00

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