Here we will shortly explain how to Furier transform the S(Q,ω) to I(Q,t) by the Fast Fourier Transformation algorithm implemented in FRIDA1. Please do take into account a couple of things:

- The space between points in frequency space gives an upper limit in the time space, i.e., the upper limit of times will be given roughly by t
_{max}=2*pi/Δt_{min}

- On the other hand the difference between the last and first frequencies will give you the lower limit in time space, given again by the same formula than before t
_{min}=2*pi/Δt_{max}.

Therefore do not cut your S(Q,ω) and try to rebin your data with the lowest spacing (in w) between points (be reasonable however!!!! do not bin the data in a grid smaller than that of the experiment. That will not help at all ).

We will explain, therefore, first how to “cut” the S(Q,ω) to retain only the “gain” (positive) part of the S(Q,ω) spectra, then we will explain how to “deconvolve” with the resolution function, which in time domain reduces to a division by the I(Q,t) of the resolution function, and at last to normalize by the I(Q,t=0) value.

The notion is as follows:

Nsqt | the number of the file(s) having your I(Q,t) data |

Nvan | the number of the file(s) having your vanadium data |

Nsqtv | the number of the file(s) having your I(Q,t) divided by vanadium |

Nnorm | the number of the file(s) having your normalization constant |

mcd | To delete the loss part |

3 | to select by x value |

0-100 | to keep only the positive values. Now we can do the fft… |

tff | Fourier Transform in cosinus (we want the real part!) |

t | Output coordinate is time |

ps | the output unit is generally in the ps scale for TOF measurements |

1e-12 | a picosecond is 10^{-12} s |

S(Q,t) | the output coordinate is S(Q,t) |

that is its unit: none |

glx | to put x axis of graphics in a log scale |

p Nsqt | You can plot your nice s(q,t). Now we are ready to divide by the resolution |

oy | to recalculate y |

/ | to divide by |

y2 | to catch a value per channel |

Nvan | the number of the file with your vanadium data. |

Nsqt | we go to the number of file you have your S(q,t) (already divided by vanadium!) |

oi | I will keep a file with only one point per spectrum (the first) which is most similar to S(Q,t=0) |

3 | one y value |

1 | from the first channel of each spectrum. Now we get a file with a point for every spectrum. |

Nsqtv | now we select the file where our data are |

oy | we will divide by the points in the file we have just created with one point per spectra |

/ | divide |

i | one point of file Nnorm per spectra |

Nnorm | the file with your normalization constants (that we have calculated as the first point of our S(Q,t) |

That's all folks!