Gaussian2D¶

class sofia_redux.scan.source_models.beams.gaussian_2d.Gaussian2D(peak=1.0, x_mean=0.0, y_mean=0.0, x_fwhm=0.0, y_fwhm=0.0, theta=<Quantity 0. deg>, peak_unit=None, position_unit=None)[source]¶

Bases: ABC

Initializes a 2-D Gaussian beam model.

The Gaussian2D class is a wrapper around the functional_models.Gaussian2D class with additional functionality including convolution/deconvolution with another beam, and header parsing/editing.

Parameters:

peakfloat or units.Quantity, optional: The peak amplitude of the Gaussian.
x_meanfloat or units.Quantity, optional: The position of the peak along the x-axis.
y_meanfloat or units.Quantity, optional: The position of the peak along the y-axis.
x_fwhmfloat or units.Quantity, optional: The Full-Width-Half-Max beam width in the x-direction.
y_fwhmfloat or units.Quantity, optional: The Full-Width-Half-Max beam width in the y-direction.
thetafloat or units.Quantity, optional: The rotation of the beam pertaining to x_fwhm and y_fwhm in relation to the actual (x, y) coordinate axis. If a float value is supplied, it is assumed to be in degrees.
peak_unitunits.Unit or units.Quantity or str, optional: The physical units for the peak amplitude. The default is dimensionless.
position_unitunits.Unit or units.Quantity or str, optional: The physical units of all position based parameters (x_mean, y_mean, x_fwhm, y_fwhm)

Attributes Summary

`AREA_FACTOR`
`FWHM_TO_SIZE`
`QUARTER`
`area`	Return the area of the PSF.
`fwhm`	Return the average FWHM
`major_fwhm`	Return the major (maximum) FWHM value.
`minor_fwhm`	Return the minor (minimum) FWHM value.
`peak`	Return the peak amplitude of the Gaussian.
`position_angle`	Return the position angle of the Gaussian.
`referenced_attributes`	Return the names of attributes to be referenced rather than copied.
`theta`	Return the position angle of the Gaussian.
`x_fwhm`	Return the FWHM in the x-direction.
`x_mean`	Return the center of the Gaussian in x.
`x_stddev`	Return the standard deviation in x.
`y_fwhm`	Return the FWHM in the y-direction.
`y_mean`	Return the center of the Gaussian in y.
`y_stddev`	Return the standard deviation in y.

Methods Summary

`combine_with`(psf[, deconvolve])	Combine with another beam.
`convolve_with`(psf)	Convolve with a given PSF.
`copy`()	Return a copy of the Gaussian 2D model.
`deconvolve_with`(psf)	Deconvolve with a given PSF.
`edit_header`(header[, fits_id, beam_name, ...])	Edit a FITS header with the beam parameters.
`encompass`(psf)	Encompass with another beam.
`extent`()	Return the extent in x and y.
`get_beam_map`(grid[, sigmas])	Return a beam map given an output grid.
`get_circular_equivalent_fwhm`()	Return the FWHM of a circular Gaussian with equivalent area.
`get_equivalent`(beam_map, pixel_size)	Return a 2-D Gaussian for a beam map and given pixel size.
`is_circular`()	Return whether the PSF is circular.
`is_encompassing`(psf)	Check if the psf is encompassing the beam.
`parse_header`(header[, size_unit, fits_id])	Set the beam from a FITS header.
`rotate`(angle)	Rotate the beam by a given angle.
`scale`(factor)	Scale the FWHM in both axes by a given amount.
`set_area`(area)	Set the Gaussian parameters based on the overall area of the beam.
`set_equivalent`(beam_map, pixel_size)	Set Gaussian parameters from a given beam map and pixel size.
`set_xy_fwhm`(x_fwhm, y_fwhm)	Set and validate both new x and y FWHM values at once.
`validate`()	Set the (x, y) FWHM and position angle so that x >= y.

Attributes Documentation

AREA_FACTOR = 1.1330900354567985¶

FWHM_TO_SIZE = 1.0644670194312262¶

QUARTER = <Quantity 1.57079633 rad>¶

area¶

Return the area of the PSF.

Returns:

units.Quantity

fwhm¶

Return the average FWHM

Returns:

units.Quantity

major_fwhm¶

Return the major (maximum) FWHM value.

Returns:

units.Quantity or float

minor_fwhm¶

Return the minor (minimum) FWHM value.

Returns:

units.Quantity

peak¶

Return the peak amplitude of the Gaussian.

Returns:

float or units.Quantity

position_angle¶

Return the position angle of the Gaussian.

Returns:

units.Quantity

referenced_attributes¶

Return the names of attributes to be referenced rather than copied.

Returns:

set of str

theta¶

Return the position angle of the Gaussian.

Returns:

units.Quantity

x_fwhm¶

Return the FWHM in the x-direction.

Returns:

units.Quantity

x_mean¶

Return the center of the Gaussian in x.

Returns:

units.Quantity or float

x_stddev¶

Return the standard deviation in x.

Returns:

valueunits.Quantity or float

y_fwhm¶

Return the FWHM in the y-direction.

Returns:

units.Quantity

y_mean¶

Return the center of the Gaussian in y.

Returns:

units.Quantity or float

y_stddev¶

Return the standard deviation in y.

Returns:

valueunits.Quantity or float

Methods Documentation

combine_with(psf, deconvolve=False)[source]¶

Combine with another beam.

Combination consists of either convolution (default) or deconvolution of this beam by another.

Parameters:

psfGaussian2D: The beam to combine.
deconvolvebool, optional: If True, indicates a deconvolution rather than a convolution.

Returns:

None

convolve_with(psf)[source]¶

Convolve with a given PSF.

Parameters:

psfGaussian2D: The Point Spread Function to convolve with.

Returns:

None

copy()[source]¶

Return a copy of the Gaussian 2D model.

Returns:

Gaussian2D

deconvolve_with(psf)[source]¶

Deconvolve with a given PSF.

Parameters:

psfGaussian2D: The Point Spread Function to deconvolve with.

Returns:

None

edit_header(header, fits_id='', beam_name=None, size_unit=None)[source]¶

Edit a FITS header with the beam parameters.

Parameters:

headerastropy.io.fits.header.Header: The FITS header to edit.
fits_idstr, optional: The name prefixing the FITS header BMAJ/BMIN keywords. For example, IBMAJ.
beam_namestr, optional: The name of the beam.
size_unitunits.Unit or units.Quantity or str, optional: If set, convert the major/minor beam values to this unit before setting in the header.

Returns:

None

encompass(psf)[source]¶

Encompass with another beam.

Parameters:

psfGaussian2D or units.Quantity: Another Gaussian PSF or the FWHM of another Gaussian PSF.

Returns:

None

extent()[source]¶

Return the extent in x and y.

The extent is the maximum (x, y) deviation away from the center of the psf in the native coordinate frame, accounting for rotation by the position angle.

Returns:

extentCoordinate2D: The extent in x and y.

get_beam_map(grid, sigmas=3.0)[source]¶

Return a beam map given an output grid.

Parameters:

gridGrid2D: The output grid on which the beam map should be projected.
sigmasfloat, optional: The number of Gaussian sigmas to be encapsulated within the map (determines the size of the map).

Returns:

beam_mapnumpy.ndarray (float): A 2-D beam map image.

get_circular_equivalent_fwhm()[source]¶

Return the FWHM of a circular Gaussian with equivalent area.

Returns:

units.Quantity

static get_equivalent(beam_map, pixel_size)[source]¶

Return a 2-D Gaussian for a beam map and given pixel size.

The equivalent psf if circular with a FWHM equal to that determined from the beam map.

Parameters:

beam_mapnumpy.ndarray (float): A map of the beam of shape (ky, kx).
pixel_sizeCoordinate2D or numpy.ndarray or float or units.Quantity: The pixel size.

Returns:

Gaussian2D

is_circular()[source]¶

Return whether the PSF is circular.

Returns:

bool

is_encompassing(psf)[source]¶

Check if the psf is encompassing the beam.

Parameters:

psfGaussian2D

Returns:

bool

parse_header(header, size_unit=None, fits_id='')[source]¶

Set the beam from a FITS header.

Reads a FITS header to determine:

- The major FWHM (BMAJ)
- The minor FWHM (BMIN)
- The position angle (BPA)

By default, an attempt will be made to determine the size unit for the FWHMs from the header comments, although a fixed unit may be supplied by the size_unit parameter. The same process will occur for the position angle, but no overriding unit may be supplied. In case no unit is determined, all parameters will default to ‘degree’.

Parameters:

headerastropy.io.fits.header.Header
size_unitunits.Unit or units.Quantity or str: The size unit to apply to the header values. If None, an attempt will be made to determine the size unit from the header comments for the appropriate keywords, and if not found, will default to ‘degree’. Any other supplied value will take priority.
fits_idstr, optional: The name prefixing the FITS header BMAJ/BMIN keywords. For example, IBMAJ.

Returns:

None

rotate(angle)[source]¶

Rotate the beam by a given angle.

Parameters:

angleunits.Quantity

Returns:

None

scale(factor)[source]¶

Scale the FWHM in both axes by a given amount.

Parameters:

factorfloat

Returns:

None

set_area(area)[source]¶

Set the Gaussian parameters based on the overall area of the beam.

Parameters:

areafloat or units.Quantity

Returns:

None

set_equivalent(beam_map, pixel_size)[source]¶

Set Gaussian parameters from a given beam map and pixel size.

The area and thus FWHM are determined from the input parameters. Therefore, only a circular Gaussian will be set with zero position angle.

Parameters:

beam_mapnumpy.ndarray (float): A map of the beam of shape (ky, kx).
pixel_sizeCoordinate2D or numpy.ndarray or float or units.Quantity: The pixel size.

Returns:

None

set_xy_fwhm(x_fwhm, y_fwhm)[source]¶

Set and validate both new x and y FWHM values at once.

The correct position angle must be set for the process to occur correctly. This is so both FWHMs get set correctly, as doing it sequentially may result in one of the values getting overwritten by the other.

Parameters:

x_fwhmunits.Quantity
y_fwhmunits.Quantity

Returns:

None

validate()[source]¶

Set the (x, y) FWHM and position angle so that x >= y.

For consistency, the major and minor axes of the Gaussian FWHM are set so they are equal to the (x, y) axes. This will result in a 90 degree offset to the position angle if y > x on input.

Returns:

None

Navigation

Gaussian2D¶