Identification of the Response Function

Start and end point of the signal flow is the computer, where the excitation pattern is generated and the sample response collected. 

Because of the time scale separation of 3 to 4 decades between both modes, it is of advantage to convolute the heat mode gT(t) = T, 1 exp(-t/Tth) into the effective excitation  

the effective linear response function h(t) can be identified with g(t) as defined in Eqs. (25) and (29) h(t) = g(t). The primary sample response is the heterodyne diffraction efficiencyy (t) = Chet(t)- The instantaneous contribution of the temperature grating to the diffraction efficiency is expressed by the 5-function in g(t) [Eq. (25)]. After the sample, an unavoidable noise term e(t) is added. The continuous yff) is sampled by integrating with an ideal detector over time intervals At to finally obtain the time-discrete sequence y[n]. 

the TDFRS experiment converts an ideal time-discrete excitation x[n] into a time discrete signaly[n], and the task is to extract the response h(t) =g(t) from the measuredy[n] and the known x[n] according to Eq. (61). 

In Ref. [75], it is discussed in more detail why it is advantageous to convolute the response of the temperature grating into the excitation and how to treat systematic errors arising from this approximation and from imperfections of the components in the setup. Especially the switching properties of the Pockels cell require careful analysis, since the switching number increases from 2 in case of pulsed excitation to approximately N in case of pseudostochastic binary sequences. 

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