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Use regularized inverse Laplace transform to recover the distribution of T2 or ln(T2) in NMR.

Screen Shot and Video:

This app can be used to solve inverse Laplace transform in NMR. It can recover the distribution of T2 or ln(T2) from the NMR relaxometry signal. It can also help estimate time constants for exponential decay functions in curve fit.


  1. This App requires contin-windows.exe file. Please download it from the page and copy it to the App folder first. To open the App folder, right click on the Inverse Laplace Transform in NMR icon in the Apps Gallery window, and choose Show in Folder from the short-cut menu.
  2. This App calls Python script. You should make sure to check Embedded Python check box in Select Features (it is checked by default) when you install Origin.

Download RILT.opx file, and then drag-and-drop onto the Origin workspace. An icon will appear in the Apps Gallery window.
NOTE: This tool requires OriginPro.


  1. Highlight XY data in a worksheet or make a graph active. Click the Inverse Laplace Transform in NMR icon in the Apps Gallery window.
  2. In the opened dialog, choose Distribution type: T2 or ln(T2). If you have multiple peaks in the result, ln(T2) distribution can produce a sharper peak at the larger T2.
  3. In Specify T2 Range group, you can define Number of PointsT2 Minimum and T2 Maximum for output result's X. Origin provides default values if you check Auto check box. If there is only one peak in the result, 31 for Number of Points is enough.
  4. In Output branch, you can click on the Right button and choose <new> on the right of Range 1Y Error box. And it will create Y error for the distribution result.
  5. Click Preview button, a graph with two layers is shown in the Preview window on the right of the dialog. The black curve represents the input data and the red curve indicates the inverse Laplace transform result.
  6. Click OK button, the distribution result will be created in a worksheet.

Sample OPJU File
This app provides a sample OPJU file.  Right click on the Inverse Laplace Transform in NMR icon in the Apps Gallery window, and choose Show Samples Folder from the short-cut menu. A folder will open. Drag-and-drop the project file ILTSample.opju from the folder onto Origin. The Notes window in the project shows detailed steps.
Note: If you wish to save the OPJU after changing, it is recommended that you save to a different folder location (e.g. User Files Folder).


v1.2 7/10/2020 Updated sample opju file.
v1.1 4/11/2019 Updated code for writing data.

Reviews and Comments:
06/30/2021saguiar800Any chance of this app fitting increasing exponentials?

02/26/2021yukiOriginlabHi janicke,
We called CONTIN package:
Its document said alpha is often used with peak constrained analysis. This app didn't provide this option.
Regards, OriginLab Technical support

02/25/2021janickeIs there a way to adjust the alpha value for the regularization. I would like to try and minimize this number to see what minimal distribution for the decay constant can be


You should use the peak area of the result to compare with your exp decay function's coefficient. I tested they are close.

07/09/2020gor.alexIt works, but it doesn't give out weight coefficients correctly. I modeled an exponential decay with this function: exp(-wcol(1)/0,1)/15+7,3*exp(-wcol(1)/1)/15+43*exp(-wcol(1)/10)/15+320*exp(-wcol(1)/100)/15+2500*exp(-wcol(1)/1000)/1500. And only with such weight coefficients does this Inverse Laplace transform produce approximately equal weight coefficients.