fit_tscan

fit tscan: fitting experimental time trace spectrum data with the convolution of the sum of exponential decay and irf function There are three types of irf function (gaussian, cauchy, pseudo voigt) It uses lmfit python package to fitting time trace data and estimates error bound of irf parameter and lifetime constants. To calculate the contribution of each life time component, it solve least linear square problem via scipy linalg lstsq module.

Note

  • The number of time zero parameter should be same as the number of scan to fit.

  • If you set shape of irf to pseudo voigt (pv), then you should provide two full width at half maximum value for gaussian and cauchy parts, respectively.

  • If you did not set tau then it assume you finds the timezero of this scan. So, –no_base option is discouraged.

  • usage: fit_tscan.py [-h] [–irf {g,c,pv}] [–fwhm_G FWHM_G] [–fwhm_L FWHM_L] [-t0 TIME_ZEROS [TIME_ZEROS …]] [-t0f TIME_ZEROS_FILE] [–tau [TAU [TAU …]]] [–no_base] [–fix_irf] [–slow] [-o OUT] prefix

  • positional arguments:

    • prefix prefix for tscan files It will read prefix_i.txt

  • optional arguments:

    • -h, –help show this help message and exit

    • –irf {g,c,pv} shape of instrument response function

    1. g: gaussian distribution

    2. c: cauchy distribution

    3. pv: pseudo voigt profile, linear combination of gaussian distribution and cauchy distribution pv = eta*c+(1-eta)*g the mixing parameter is fixed according to Journal of Applied Crystallography. 33 (6): 1311–1316.

    • –fwhm_G FWHM_G full width at half maximum for gaussian shape It should not used when you set cauchy irf function

    • –fwhm_L FWHM_L full width at half maximum for cauchy shape It should not used when you did not set irf or use gaussian irf function

    • -t0 TIME_ZEROS [TIME_ZEROS …], –time_zeros TIME_ZEROS [TIME_ZEROS …] time zeros for each tscan

    • -t0f TIME_ZEROS_FILE, –time_zeros_file TIME_ZEROS_FILE filename for time zeros of each tscan

    • –tau [TAU [TAU …]] lifetime of each component

    • –no_base exclude baseline for fitting

    • –fix_irf fix irf parameter (fwhm_G, fwhm_L) during fitting process

    • –slow use slower but robust global optimization algorithm

    • -o OUT, –out OUT prefix for output files

Parameter bound scheme

  • fwhm: temporal width of x-ray pulse

    • lower bound: 0.5*fwhm_init

    • upper bound: 2*fwhm_init

  • t_0: timezero for each scan

    • lower bound: t_0 - 2*fwhm_init

    • upper bound: t_0 + 2*fwhm_init

  • tau: life_time of each component

    • if tau < 0.1

      • lower bound: tau/2

      • upper bound: 1

    • if 0.1 < tau < 10

      • lower bound: 0.05

      • upper bound: 100

    • if 10 < tau < 100

      • lower bound: 5

      • upper bound: 500

    • if 100 < tau < 1000

      • lower bound: 50

      • upper bound: 2000

    • if 1000 < tau < 5000 then

      • lower bound: 500

      • upper bound: 10000

    • if 5000 < tau < 50000 then

      • lower bound: 2500

      • upper bound: 100000

    • if 50000 < tau < 500000 then

      • lower bound: 25000

      • upper bound: 1000000

    • if 500000 < tau < 1000000 then

      • lower bound: 250000

      • upper bound: 2000000

    • if 1000000 < tau then

      • lower bound: tau/4

      • upper bound: 4*tau

Mixing parameter eta

For pseudo voigt IRF function, mixing parameter eta is guessed to

\[\begin{equation*} \eta = 1.36603({fwhm}_L/f)-0.47719({fwhm}_L/f)^2+0.11116({fwhm}_L/f)^3 \end{equation*}\]

where

\[\begin{align*} f &= ({fwhm}_G^5+2.69269{fwhm}_G^4{fwhm}_L+2.42843{fwhm}_G^3{fwhm}_L^2 \\ &+ 4.47163{fwhm}_G^2{fwhm}_L^3+0.07842{fwhm}_G{fwhm}_L^4 \\ &+ {fwhm}_L^5)^{1/5} \end{align*}\]

This guess is according to J. Appl. Cryst. (2000). 33, 1311-1316