Electrical Field Temporal Autocorrelation Function

Definition: The unnormalized Electric Field Temporal Autocorrelation function ( $G_1$ ) is the temporal autocorrelation function of the electric field traversing the scattering medium or (more typically) emitted/scattered from the medium. It is a key function used in the analysis of data from measurements implementing diffuse correlation spectroscopy (DCS) and related methods that utilize laser speckle statistics. $G_1$ is modeled by the correlation diffusion equation and its normalized form, $g_1$ , is used to fit the measured data.It can be written as $G_1(bf{r}, tau,t) = < E (bf{r},t) E^* (bf{r},tau+t)>$ . In a typical experiment, it is derived from the normalized intensity autocorrelation function ( $g_2$ ) that is often the main measured quantity in DCS by relying on the so-called “Siegert relation”. The Siegert relationship between intensity based autocorrelation function ( $g_2$ ) and electric field temporal autocorrelation $(g_1)$ is $g_2 (tau) = 1 + beta |g_1(tau)| 2$

Alternative definition:

Synonym: Normalized Electric Field Temporal Autocorrelation (g1)

References:

https://doi.org/10.1364/JOSAA.14.000192

https://doi.org/10.1103/PhysRevLett.75.1855

https://doi.org/10.1016/j.neuroimage.2013.06.017

https://doi.org/10.1088/0034-4885/73/7/076701

Related terms: Intensity Temporal Autocorrelation (G2), Diffuse Correlation Spectroscopy