# FRET Correction Formulas¶

The fretmath module contains functions to compute corrected FRET efficiency from the proximity ratio and vice-versa.

For derivation see notebook: “Derivation of FRET and S correction formulas.ipynb” (link).

fretbursts.fretmath.correct_E_gamma_leak_dir(Eraw, gamma=1, leakage=0, dir_ex_t=0)

Compute corrected FRET efficiency from proximity ratio Eraw.

For the inverse function see uncorrect_E_gamma_leak_dir().

Parameters: Eraw (float or array) – proximity ratio (only background correction, no gamma, leakage or direct excitation) gamma (float) – gamma factor leakage (float) – leakage coefficient dir_ex_t (float) – coefficient expressing the direct excitation as n_dir = dir_ex_t * (na + gamma*nd). In terms of physical parameters it is the ratio of acceptor over donor absorption cross-sections at the donor-excitation wavelength.
Returns
Corrected FRET effciency
fretbursts.fretmath.correct_S(Eraw, Sraw, gamma, leakage, dir_ex_t)

Correct S values for gamma, leakage and direct excitation.

Parameters: Eraw (scalar or array) – uncorrected (“raw”) E after only background correction (no gamma, leakage or direct excitation). Sraw (scalar or array) – uncorrected (“raw”) S after only background correction (no gamma, leakage or direct excitation). gamma (float) – gamma factor. leakage (float) – donor emission leakage into the acceptor channel. dir_ex_t (float) – direct acceptor excitation by donor laser. Defined as n_dir = dir_ex_t * (na + g nd). The dir_ex_t coefficient is the ratio between D and A absorption cross-sections at the donor-excitation wavelength.
Returns
Corrected S (stoichiometry), same size as Sraw.
fretbursts.fretmath.dir_ex_correct_E(Eraw, dir_ex_t)

Apply direct excitation correction to the uncorrected FRET Eraw.

The coefficient dir_ex_t expresses the direct excitation as n_dir = dir_ex_t * (na + gamma*nd). In terms of physical parameters it is the ratio of acceptor over donor absorption cross-sections at the donor-excitation wavelength.

For the inverse see dir_ex_uncorrect_E().

fretbursts.fretmath.dir_ex_uncorrect_E(E, dir_ex_t)

Reverse direct excitation correction and return uncorrected FRET.

For the inverse see dir_ex_correct_E().

fretbursts.fretmath.gamma_correct_E(Eraw, gamma)

Apply gamma correction to the uncorrected FRET Eraw.

For the inverse see gamma_uncorrect_E().

fretbursts.fretmath.gamma_uncorrect_E(E, gamma)

Reverse gamma correction and return uncorrected FRET.

For the inverse see gamma_correct_E().

fretbursts.fretmath.leakage_correct_E(Eraw, leakage)

Apply leakage correction to the uncorrected FRET Eraw.

For the inverse see leakage_uncorrect_E().

fretbursts.fretmath.leakage_uncorrect_E(E, leakage)

Reverse leakage correction and return uncorrected FRET.

For the inverse see leakage_correct_E().

fretbursts.fretmath.test_fretmath()

Run a few consistency checks for the correction functions.

fretbursts.fretmath.uncorrect_E_gamma_leak_dir(E, gamma=1, leakage=0, dir_ex_t=0)

Compute proximity ratio from corrected FRET efficiency E.

This function is the inverse of correct_E_gamma_leak_dir().

Parameters: E (float or array) – corrected FRET efficiency gamma (float) – gamma factor leakage (float) – leakage coefficient dir_ex_t (float) – direct excitation coefficient expressed as n_dir = dir_ex_t * (na + gamma*nd). In terms of physical parameters it is the ratio of absorption cross-section at donor-excitation wavelengths of acceptor over donor.
Returns
Proximity ratio (reverses gamma, leakage and direct excitation)
fretbursts.fretmath.uncorrect_S(E_R, S, gamma, L_k, d_dirT)

Function used to test correct_S().