sourcefinder.deconv#

Gaussian deconvolution.

Functions#

`J_S_from_stddevs_and_pa`(sigma_maj, sigma_min, theta)	Jacobian `d(sxx, syy, sxy) / d(sigma_maj, sigma_min, theta)`.
`cov_S_to_cov_r`(S_dec, C_S_dec)	Convert covariance on S = [sxx, syy, sxy] to covariance on
`cov_p_to_cov_S`(C_p, sigma_maj, sigma_min, theta)	Propagate covariance C_p (3x3) on parameters p=(sigma_maj, sigma_min,
`covariance_matrix`(sigma_maj, sigma_min, theta)	Build covariance matrix for an anisotropic Gaussian.
`deconv`(fmaj, fmin, fpa, cmaj, cmin, cpa)	Deconvolve a Gaussian "beam" from a Gaussian component.
`sigma_to_stddevs_pa_and_jacobian`(sxx, syy, sxy)	From covariance elements sxx, syy, sxy return (sigma_maj, sigma_min, theta,

Module Contents#

sourcefinder.deconv.J_S_from_stddevs_and_pa(sigma_maj, sigma_min, theta)[source]#

Jacobian d(sxx, syy, sxy) / d(sigma_maj, sigma_min, theta).

Parameters:

sigma_majfloat: Standard deviation along the major axis of the ellipse.
sigma_minfloat: Standard deviation along the minor axis of the ellipse.
thetafloat: Major axis position angle in radians, counter-clockwise from the +Y axis.

Returns:

Jndarray of shape (3, 3): Jacobian matrix. Rows correspond to [dsxx/d*, dsyy/d*, dsxy/d*] and columns to [sigma_maj, sigma_min, theta].

sourcefinder.deconv.cov_S_to_cov_r(S_dec, C_S_dec)[source]#

Convert covariance on S = [sxx, syy, sxy] to covariance on r = [a_dec, b_dec, phi_dec] using analytic Jacobian.

Parameters:

S_decarray_like, shape (3,): [sxx, syy, sxy] of the deconvolved covariance matrix (pixels^2)
C_S_decndarray, shape (3,3): Covariance matrix of S_dec (units pixels^4)

Returns:

rndarray shape (3,): (a_dec, b_dec, phi_dec) where phi_dec is radians (CCW from +x)
C_rndarray shape (3,3): Covariance matrix on (a_dec, b_dec, phi_dec)
okbool: True if conversion succeeded (Sigma_dec positive definite), else False.

sourcefinder.deconv.cov_p_to_cov_S(C_p, sigma_maj, sigma_min, theta)[source]#

Propagate covariance C_p (3x3) on parameters p=(sigma_maj, sigma_min, theta) to covariance on S = (sxx, syy, sxy) using analytic Jacobian.

Parameters:

C_p(3,3) ndarray (covariance in order [sigma_maj, sigma_min, theta])
sigma_maj, sigma_min: float
theta: float (radians)

Returns:

C_S(3,3) ndarray (covariance on [sxx, syy, sxy])

sourcefinder.deconv.covariance_matrix(sigma_maj, sigma_min, theta)[source]#

Build covariance matrix for an anisotropic Gaussian.

Parameters:

sigma_maj, sigma_minfloat: Standard deviations along major and minor axes (same units as x, y grid).
thetafloat: Position angle in radians, measured CCW from +Y toward -X (north through east).

Returns:

Sigma(2,2) ndarray: Covariance matrix.

sourcefinder.deconv.deconv(fmaj, fmin, fpa, cmaj, cmin, cpa)[source]#

Deconvolve a Gaussian “beam” from a Gaussian component.

When we fit an elliptical Gaussian to a point in our image, we are actually fitting to a convolution of the physical shape of the source with the beam pattern of our instrument. This results in the fmaj/fmin/fpa arguments to this function.

Since the shape of the (clean) beam (arguments cmaj/cmin/cpa) is known, we can deconvolve it from the fitted parameters to get the “real” underlying physical source shape, which is what this function returns.

Parameters:

fmajfloat: Fitted major axis (pixels).
fminfloat: Fitted minor axis (pixels).
fpafloat: Fitted position angle of the major axis (degrees).
cmajfloat: Clean beam major axis (pixels).
cminfloat: Clean beam minor axis (pixels).
cpafloat: Clean beam position angle of the major axis (degrees).

Returns:

rmajfloat: real major axis in pixels
rminfloat: real minor axis in pixels
rpafloat: real position angle of the major axis in degress
ierrint: number of components which failed to deconvolve

Notes

Instead of fmaj, fmin, cmaj and cmin all in pixels, one could use any arbitrary unit of sky angular distance, such as arcseconds or radians. The first two elements of the returned tuple would then have that same unit, while the third element (the position angle) would still be in degrees.

sourcefinder.deconv.sigma_to_stddevs_pa_and_jacobian(sxx, syy, sxy)[source]#

From covariance elements sxx, syy, sxy return (sigma_maj, sigma_min, theta, J, ok) where sigma_maj>=sigma_min are stddevs along the elliptical axes and theta is angle (radians) CCW from +y. J is the 3x3 Jacobian d[a,b,theta]/d[sxx,syy,sxy] (rows outputs, cols inputs).

Parameters:

sxx, syy, sxyfloat

Covariance matrix elements: if sigma_maj is major axis stddev, sigma_min is minor axis stddev, and theta the position angle (CCW from +Y), then:

S = [[sxx, sxy],
     [sxy, syy]] = R @ [[sigma_maj^2, 0],
                        [0, sigma_min^2]] @ R.T

where R = [[-sin(theta), -cos(theta)],
           [ cos(theta), -sin(theta)]]

i.e. sxx = sigma_maj^2 sin^2(theta) + sigma_min^2 cos^2(theta)
     syy = sigma_maj^2 cos^2(theta) + sigma_min^2 sin^2(theta)
     sxy = -(sigma_maj^2 - sigma_min^2) sin(theta) cos(theta)

Returns:

sigma_majfloat: Major axis standard deviation (pixels)
sigma_minfloat: Minor axis standard deviation (pixels)
thetafloat: Position angle in radians, CCW from +Y axis
Jndarray, shape (3,3): Jacobian d[a,b,phi]/d[sxx,syy,sxy]
okbool: True if conversion succeeded (Sigma positive definite), else False.

sourcefinder.deconv#

Functions#

Module Contents#

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