Converting between Time (delay) Domain and Frequency (wavelength) Domain in OVA Measurements

When you take a FFT of the Jones Matrix data that is given in the optical frequency domain to get the Jones Matrix terms in the time delay domain, the inverse of the optical frequency range gives you the time delay increment in the time delay domain, and the number of points times the time delay increment gives you the time delay range.

Likewise, when you take an Inverse FFT of data in the time delay domain to get back to the optical frequency domain, the inverse of the total delay range gives you the optical frequency step size and the number of points time the optical frequency step size gives you the optical frequency range.

In both cases, however, the x-axis offset is lost.  When transforming from the optical frequency domain to the time delay domain, you would want to add back in the time delay offset, which is stored with the measurement file.  You can get the time delay offset from the DUT Length, which can be seen in the measurement details.  For example, if I click on the “Details” button for the data in Matrix A:

A window with the measurement details will pop up:

The time delay data x-axis should be centered at the delay associated with the Length of DUT:  time delay center = index of refraction  x  Length of DUT  /  speed of light .  By default the OVA will assume n=1.5 for the DUT Length determination.

Likewise, when transforming time delay data back to optical frequency, we would want to recenter the optical frequency x-axis to have the same center optical frequency of the laser sweep.  We can get the center optical frequency by converting the Start Wavelength and End Wavelength in the Measurement Details into optical frequency and take the mean, or we could save text file data and access the optical frequency range data from the “X Axis - Frequency (GHz)” column.