residual

pyoof.residual(params, idx, N_K_coeff, beam_data_norm, u_data, v_data, d_z, wavel, illum_func, telgeo, resolution, box_factor, interp, config_params)

Wrapper for the residual_true function. The objective of this function is to fool the least_squares package by changing the number of parameters that will be used in the fit. The parameter array must be organized as follows, params = np.hstack([ I_coeff, K_coeff]). The parameter selection is done by default or by adding a config_params.yml file to the fit_beam function.

Parameters:

params : ndarray

Two stacked arrays, the illumination and Zernike circle polynomials coefficients. params = np.hstack([I_coeff, K_coeff]).

idx : list

List of the positions for the removed parameters for the least squares minimization in the params array. on.

N_K_coeff : int

Total number of Zernike circle polynomials coefficients to fit. It is obtained from the order to be fitted with the formula N_K_coeff = (n + 1) * (n + 2) // 2..

beam_data_norm : list

The beam_data_norm is a list with the three observed beam maps, \(P^\mathrm{obs}_\mathrm{norm}(u, v)\), minus, zero and plus out-of-focus. The data has to be initially normalized by its maximum.

u_data : ndarray

\(x\) axis value for the 3 beam maps in radians. The values have to be flatten, in one dimension, and stacked in the same order as the d_z = [d_z-, 0., d_z+] values from each beam map.

v_data : ndarray

\(y\) axis value for the 3 beam maps in radians. The values have to be flatten, one dimensional, and stacked in the same order as the d_z = [d_z-, 0., d_z+] values from each beam map.

d_z : list

Radial offset \(d_z\), added to the sub-reflector in meters. This characteristic measurement adds the classical interference pattern to the beam maps, normalized squared (field) radiation pattern, which is an out-of-focus property. The radial offset list must be as follows, d_z = [d_z-, 0., d_z+] all of them in meters.

wavel : float

Wavelength, \(\lambda\), of the observation in meters.

illum_func : function

Illumination function, \(E_\mathrm{a}(x, y)\), to be evaluated with the key I_coeff. The illumination functions available are illum_pedestal and illum_gauss.

telgeo : list

List that contains the blockage distribution, optical path difference (OPD) function, and the primary radius (float) in meters. The list must have the following order, telego = [block_dist, opd_func, pr].

resolution : int

Fast Fourier Transform resolution for a rectangular grid. The input value has to be greater or equal to the telescope resolution and with power of 2 for faster FFT processing. It is recommended a value higher than resolution = 2 ** 8.

box_factor : int

Related to the FFT resolution (resolution key), defines the image pixel size level. It depends on the primary radius, pr, of the telescope, e.g. a box_factor = 5 returns x = np.linspace(-5 * pr, 5 * pr, resolution), an array to be used in the FFT2 (fft2).

interp : bool

If True, it will process the correspondent interpolation between the observed grid (\(P^\mathrm{obs}_\mathrm{norm}(u, v)\)) and the computed grid (\(P_\mathrm{norm}(u, v)\)) for the FFT2 aperture distribution model (\(\underline{E_\mathrm{a}}(x, y)\)).

config_params : dict

Contains the values for the fixed parameters (excluded from the least squares minimization), by default four parameters are kept fixed, i_amp, x0, y0 and K(0, 0). See the config_params.yml file.

Returns:

_residual_true : ndarray

Same output from residual_true. One dimensional array of the residual between the observed data and the FFT aperture distribution model. It has been concatenated as minus, zero and plus radial offset (to do a multiple fit). It is required to have the residual in one dimension in order to use a least squares minimization least_squares package.

Notes

The idx key needs an indices list of the parameters to be removed. The structure of the parameters always follows, params = np.hstack([ I_coeff, K_coeff]), a list with idx = [0, 1, 2, 4] will remove from the least squares minimization, [i_amp, taper_dB, x0, y0, K(0, 0)].