ecpi.common.num.gaussian_tools module

Section author: ECLAIRs GP team

Generic functions to generate and fit gaussians based on ‘CodedMaskImage.py’ python program of Cyril Lachaud modfied from http://scipy-cookbook.readthedocs.io/items/FittingData.html

Summary

Functions:

fit_gaussian_2d	fit the 2D distribution with 2D gaussian function
gaussian_1d	Returns a gaussian function + offset with the given parameters
gaussian_2d_1width	Returns a gaussian function with the given parameters
gaussian_2d_1width_offset	Returns a gaussian function + offset with the given parameters
gaussian_2d_2width	Returns a gaussian function with the given parameters
gaussian_2d_2width_offset	Returns a gaussian function + offset with the given parameters
gaussian_2d_fixedwidth	Returns a gaussian function with the given parameters
gaussian_2d_fixedwidth_offset	Returns a gaussian function + offset with the given parameters
gaussian_2d_moments	Guess the gaussian parameters of a distribution

Reference

fit_gaussian_2d(data, fit_method, fit_sigma, verbose=False)

fit the 2D distribution with 2D gaussian function

The fit success parameter is the parameter returned by the optimize.leastsq function.

Returns (height, x, y, sigma_x, sigma_y), the gaussian parameters of a 2D distribution found by a fit.

error is computed based on the covariance matrix.

Parameters

• data (2D array) – 2D distribution to fit

• fit_method (string) – fit method to be used: ‘gaussian_2d_fixedwidth’, ‘gaussian_2d_1width’ or ‘gaussian_2d_2width’

• fit_sigma (float>0) – standard deviation of the gaussian fit_function. Default is 1.555.

• verbose (bool) – verbosity parameter. Default=False

Returns

success_flag, fitparameters (height, x, y, sigma_x, sigma_y), error (=0 if success=0)

Return type

bool, (floats), float

gaussian_1d(height, center, sigma)

Returns a gaussian function + offset with the given parameters

Parameters

• height (float) – height of the gaussian function

• center (float) – center of the gaussian function

• sigma (float) – sigma of the gaussian function

gaussian_2d_1width(height, center_x, center_y, sigma)

Returns a gaussian function with the given parameters

sigma is the same for x and y direction.

Parameters

• height (float) – height of the gaussian function

• center_x (float) – center in x of the gaussian function

• center_y (float) – center in y of the gaussian function

• sigma (float) – sigma of the gaussian function

Returns

gaussian function with the given parameters

Return type

lambda function

gaussian_2d_1width_offset(height, center_x, center_y, sigma, offset)

Returns a gaussian function + offset with the given parameters

sigma is the same for x and y direction.

Parameters

• height (float) – height of the gaussian function

• center_x (float) – center in x of the gaussian function

• center_y (float) – center in y of the gaussian function

• sigma (float) – sigma of the gaussian function

• offset – offset of the gaussian function

:type offset float

Returns

gaussian function with the given parameters

Return type

lambda function

gaussian_2d_2width(height, center_x, center_y, sigma_x, sigma_y)

Returns a gaussian function with the given parameters

Parameters

• height (float) – height of the gaussian function

• center_x (float) – center in x of the gaussian function

• center_y (float) – center in y of the gaussian function

• sigma_x (float) – sigma in x of the gaussian function

• sigma_x – sigma in y of the gaussian function

Returns

gaussian function with the given parameters

Return type

lambda function

gaussian_2d_2width_offset(height, center_x, center_y, sigma_x, sigma_y, offset)

Returns a gaussian function + offset with the given parameters

Parameters

• height (float) – height of the gaussian function

• center_x (float) – center in x of the gaussian function

• center_y (float) – center in y of the gaussian function

• sigma_x (float) – sigma in x of the gaussian function

• sigma_x – sigma in y of the gaussian function

• offset – offset of the gaussian function

:type offset float

Returns

gaussian function with the given parameters

Return type

lambda function

gaussian_2d_fixedwidth(height, center_x, center_y)

Returns a gaussian function with the given parameters

sigma is unique and fixed.

FWHM_fit = FWHM_PSF = sqrt(m**2+d**2) (=sqrt(m**2+1) en pixel) m = mask element d = detector pitch sigma = sqrt(m**2+1)/2.3548 (with m=2.53) sigma = 1.155 pixel

Parameters

• height (float) – height of the gaussian function

• center_x (float) – center in x of the gaussian function

• center_y (float) – center in y of the gaussian function

Returns

gaussian function with the given parameters

Return type

lambda function

gaussian_2d_fixedwidth_offset(height, center_x, center_y, offset)

Returns a gaussian function + offset with the given parameters

sigma is unique and fixed.

FWHM_fit = FWHM_PSF = sqrt(m**2+d**2) (=sqrt(m**2+1) en pixel) m = mask element d = detector pitch sigma = sqrt(m**2+1)/2.3548 (with m=2.53) sigma = 1.155 pixel

Parameters

• height (float) – height of the gaussian function

• center_x (float) – center in x of the gaussian function

• center_y (float) – center in y of the gaussian function

• offset – offset of the gaussian function

:type offset float

Returns

gaussian function with the given parameters

Return type

lambda function

gaussian_2d_moments(data, fit_method, fit_sigma)

Guess the gaussian parameters of a distribution

Use for initial fitting parameters

the gaussian parameters of a 2D distribution by calculating its moments

Modified from : http://scipy-cookbook.readthedocs.io/items/FittingData.html

Parameters

• data (float 2D-array) – 2D distribution to evaluate

• fit_method (string) – fit method that will be used: ‘gaussian_2d_fixedwidth’, ‘gaussian_2d_1width’ or ‘gaussian_2d_2width’

• fit_sigma (float>0) – standard deviation of the gaussian fit_function. Default is 1.555.

Returns

(height, x, y), (height, x, y, sigma_x, sigma_y) or (height, x, y, sigma) depending on fit_method

Return type

floats (number of which depend on the fit_method)