A Gaussian model for the spatial distribution of emission. More...

#include <GaussianShape.h>

Inheritance diagram for casa::GaussianShape:

Public Member Functions
	GaussianShape ()
	The default GaussianShape is at the J2000 North Pole. More...

	GaussianShape (const casacore::MDirection &direction, const casacore::Quantum< casacore::Double > &majorAxis, const casacore::Quantum< casacore::Double > &minorAxis, const casacore::Quantum< casacore::Double > &positionAngle)
	Construct a Gaussian shape centred in the specified direction, specifying the widths & position angle. More...

	GaussianShape (const casacore::MDirection &direction, const casacore::Quantum< casacore::Double > &width, const casacore::Double axialRatio, const casacore::Quantum< casacore::Double > &positionAngle)

	GaussianShape (const GaussianShape &other)
	The copy constructor uses copy semantics. More...

virtual	~GaussianShape ()
	The destructor does nothing special. More...

GaussianShape &	operator= (const GaussianShape &other)
	The assignment operator uses copy semantics. More...

virtual ComponentType::Shape	type () const
	get the type of the shape. More...

virtual void	setWidthInRad (const casacore::Double majorAxis, const casacore::Double minorAxis, const casacore::Double positionAngle)
	set or return the width and orientation of the Gaussian. More...

virtual casacore::Double	majorAxisInRad () const

virtual casacore::Double	minorAxisInRad () const

virtual casacore::Double	positionAngleInRad () const

virtual casacore::Double	axialRatio () const

virtual casacore::Double	sample (const casacore::MDirection &direction, const casacore::MVAngle &pixelLatSize, const casacore::MVAngle &pixelLongSize) const
	Calculate the proportion of the flux that is in a pixel of specified size centered in the specified direction. More...

virtual void	sample (casacore::Vector< casacore::Double > &scale, const casacore::Vector< casacore::MDirection::MVType > &directions, const casacore::MDirection::Ref &refFrame, const casacore::MVAngle &pixelLatSize, const casacore::MVAngle &pixelLongSize) const
	Same as the previous function except that many directions can be sampled at once. More...

virtual casacore::DComplex	visibility (const casacore::Vector< casacore::Double > &uvw, const casacore::Double &frequency) const
	Return the Fourier transform of the component at the specified point in the spatial frequency domain. More...

virtual void	visibility (casacore::Vector< casacore::DComplex > &scale, const casacore::Matrix< casacore::Double > &uvw, const casacore::Double &frequency) const
	Same as the previous function except that many (u,v,w) points can be sampled at once. More...

virtual void	visibility (casacore::Matrix< casacore::DComplex > &scale, const casacore::Matrix< casacore::Double > &uvw, const casacore::Vector< casacore::Double > &frequency) const
	as above but with many frequencies More...

virtual ComponentShape *	clone () const
	Return a pointer to a copy of this object upcast to a ComponentShape object. More...

virtual casacore::Bool	ok () const
	casacore::Function which checks the internal data of this class for correct dimensionality and consistent values. More...

virtual const ComponentShape *	getPtr () const
	return a pointer to this object. More...

virtual casacore::Quantity	getArea () const
	TODO This probably should be made a pure virtual method in TwoSidedShape Return the effective area of the Gaussian (pi/(4ln(2))maj*min. More...

virtual casacore::String	sizeToString () const
	Get the string containing the various size quantities of a component. More...

Public Member Functions inherited from casa::TwoSidedShape
virtual	~TwoSidedShape ()
	a virtual destructor is needed so that the actual destructor in the derived class will be used. More...

void	setWidth (const casacore::Quantum< casacore::Double > &majorAxis, const casacore::Quantum< casacore::Double > &minorAxis, const casacore::Quantum< casacore::Double > &positionAngle)
	set/get the width and orientation of the Shape. More...

void	setWidth (const casacore::Quantum< casacore::Double > &majorAxis, const casacore::Double axialRatio, const casacore::Quantum< casacore::Double > &positionAngle)

casacore::Quantum < casacore::Double >	majorAxis () const

casacore::Quantum < casacore::Double >	minorAxis () const

casacore::Quantum < casacore::Double >	positionAngle () const

casacore::Double	axialRatio () const

void	setErrors (const casacore::Quantum< casacore::Double > &majorAxisError, const casacore::Quantum< casacore::Double > &minorAxisError, const casacore::Quantum< casacore::Double > &positionAngleError)
	set/get the errors on the shape parameters. More...

const casacore::Quantum < casacore::Double > &	majorAxisError () const

const casacore::Quantum < casacore::Double > &	minorAxisError () const

const casacore::Quantum < casacore::Double > &	positionAngleError () const

casacore::Double	axialRatioError () const

virtual casacore::Bool	isSymmetric () const
	determine whether the shape is symmetric or not. More...

virtual casacore::uInt	nParameters () const
	set/get the shape parameters associated with this shape. More...

virtual void	setParameters (const casacore::Vector< casacore::Double > &newParms)

virtual casacore::Vector < casacore::Double >	parameters () const

virtual void	setErrors (const casacore::Vector< casacore::Double > &newParms)

virtual casacore::Vector < casacore::Double >	errors () const

virtual casacore::Vector < casacore::Double >	optParameters () const

virtual void	setOptParameters (const casacore::Vector< casacore::Double > &newOptParms)

virtual casacore::Bool	fromRecord (casacore::String &errorMessage, const casacore::RecordInterface &record)
	This functions convert between a casacore::Record and a shape derived from this class. More...

virtual casacore::Bool	toRecord (casacore::String &errorMessage, casacore::RecordInterface &record) const
	Convert the class to an Record representation. More...

virtual casacore::Bool	convertUnit (casacore::String &errorMessage, const casacore::RecordInterface &record)
	Convert the parameters of the component to the specified units. More...

virtual casacore::Vector < casacore::Double >	toPixel (const casacore::DirectionCoordinate &dirCoord) const
	Convert component shape to absolute pixels (longitude, latitude, major axis, minor axis, position angle [positive +x -> +y ; rad]) More...

virtual casacore::Bool	fromPixel (const casacore::Vector< casacore::Double > &parameters, const casacore::DirectionCoordinate &dirCoord)
	Fill the shape from the vector (longitude, latitude, major axis, minor axis, position angle [positive +x -> +y ; rad]). More...

Public Member Functions inherited from casa::ComponentShape
virtual	~ComponentShape ()

virtual const casacore::String &	ident () const
	Specify the identification of the record (e.g. More...

void	setRefDirection (const casacore::MDirection &newRefDir)

const casacore::MDirection &	refDirection () const

void	setRefDirectionError (const casacore::Quantum< casacore::Double > &newRefDirErrLat, const casacore::Quantum< casacore::Double > &newRefDirErrLong)

const casacore::Quantum < casacore::Double > &	refDirectionErrorLat () const

const casacore::Quantum < casacore::Double > &	refDirectionErrorLong () const

void	copyDirectionInfo (const ComponentShape &that)

Public Member Functions inherited from casacore::RecordTransformable
virtual	~RecordTransformable ()
	The destructor must be virtual so that the destructor of derived classes is actually used. More...

virtual Bool	fromString (String &error, const String &inString)
	Initialise the class from a String representation. More...

Private Member Functions
void	updateFT ()

Private Attributes
casacore::Gaussian2D < casacore::Double >	itsShape

casacore::Gaussian2D < casacore::Double >	itsFT

Additional Inherited Members
Static Public Member Functions inherited from casa::TwoSidedShape
static casacore::String	sizeToString (casacore::Quantity major, casacore::Quantity minor, casacore::Quantity posangle, casacore::Bool includeUncertainties=true, casacore::Quantity majorErr=0, casacore::Quantity minorErr=0, casacore::Quantity posanErr=0)
	casacore::Format the string containing the various size quantities of a component. More...

Static Public Member Functions inherited from casa::ComponentShape
static ComponentType::Shape	getType (casacore::String &errorMessage, const casacore::RecordInterface &record)

Protected Member Functions inherited from casa::TwoSidedShape
	TwoSidedShape ()
	The constructors and assignment operator are protected as only derived classes should use them. More...

	TwoSidedShape (const casacore::MDirection &direction, const casacore::Unit &majorAxisUnit, const casacore::Unit &minorAxisUnit, const casacore::Unit &paUnit)

	TwoSidedShape (const TwoSidedShape &other)

TwoSidedShape &	operator= (const TwoSidedShape &other)

Protected Member Functions inherited from casa::ComponentShape
	ComponentShape ()

	ComponentShape (const casacore::MDirection &direction)

	ComponentShape (const ComponentShape &other)

ComponentShape &	operator= (const ComponentShape &other)

Static Protected Member Functions inherited from casa::ComponentShape
static casacore::Bool	differentRefs (const casacore::MeasRef< casacore::MDirection > &ref1, const casacore::MeasRef< casacore::MDirection > &ref2)

static casacore::Bool	badError (const casacore::Quantum< casacore::Double > &quantum)

static casacore::Bool	fromAngQRecord (casacore::Quantum< casacore::Double > &returnValue, casacore::String &errorMessage, const casacore::String &fieldString, const casacore::RecordInterface &record)

Detailed Description

A Gaussian model for the spatial distribution of emission.

Intended use:

Public interface

Review Status

Date Reviewed:: yyyy/mm/dd
Test programs:: tGaussianShape
Demo programs:: dTwoSidedShape

Prerequisite

TwoSidedShape

Synopsis

A GaussianShape models the spatial distribution of radiation from the sky as a two-dimensional Gaussian function with user specified major axis width, minor axis width and position angle.

This class like the other component shapes becomes more useful when used through the SkyComponent class, which incorperates the flux and spectral variation of the emission, or through the ComponentList class, which handles groups of SkyComponent objects.

The reference direction is defined in celestial co-ordinates, using a MDirection object. It indicates where the centre of the Gaussian is on the sky. The direction can be specified both in the constructor or with the setRefDirection function.

The width of the Gaussian is defined as the angle subtended by the full width at half maximum of the Gaussian. The major axis has the larger width and is aligned North-South when the position angle is zero. A positive position angle moves the Northern side of the component to the East. The axial ratio is the ratio of the minor to major axis widths. The major axis MUST not be smaller than the minor axis otherwise an exception (casacore::AipsError) is thrown.

These parameters of the Gaussian (width, position angle, direction etc.) can be specified at construction time, using the *inRad functions or through functions in the base classes (TwoSidedShape & ComponentShape). The base classes also implement functions for inter-converting this object into a record representation.

The flux, or integrated intensity, is always normalised to one. This class does not model the actual flux or its variation with frequency. It solely models the way the emission varies with position on the sky.

The scale member function is used to sample the component at any point on the sky. The scale factor calculated by this function is the proportion of the flux that is within a specified pixel size centered on the specified direction. Ultimatly this function will integrate the emission from the Gaussian over the entire pixel but currently it just assumes the flux can be calculated by the height of the Gaussian at the centre of the pixel scaled by the pixel area. This is NOT accurate for Gaussians whose width is small compared with the pixel size.

This class contains functions that return the Fourier transform of the component at a specified spatial frequency. There are described more fully in the description of the visibility functions below.

Example

Suppose I had an image of a region of the sky and we wanted to subtract a extended source from it. This could be done as follows:

Construct a SkyComponent with a Gaussian of width that is similar to the extended source.
Project the component onto an image
Convolve the image by the point spread function
subtract the convolved model from the dirty image.

Shown below is the code to perform the first step in this process, ie construct the SkyComponent. This example is also available in the dTwoSidedShape.cc file. Note that it is more accurate to do subtraction of components in the (u,v) domain.

{ // Construct a Gaussian shape
casacore::MDirection blob_dir;
{ // get the right direction into blob_dir
casacore::Quantity blob_ra; casacore::MVAngle::read(blob_ra, "19:39:");
casacore::Quantity blob_dec; casacore::MVAngle::read(blob_dec, "-63.43.");
blob_dir = casacore::MDirection(blob_ra, blob_dec, casacore::MDirection::J2000);
}
{
const Flux<casacore::Double> flux(6.28, 0.1, 0.15, 0.01);
const GaussianShape shape(blob_dir,
casacore::Quantity(30, "arcmin"), 
casacore::Quantity(2000, "mas"), 
casacore::Quantity(C::pi_2, "rad"));
const ConstantSpectrum spectrum;
SkyComponent component(flux, shape, spectrum);
printShape(shape);
}
}

The printShape function is the example shown for the TwoSidedShape class.

To Do

Use Measures & Quanta in the interface to the visibility functions.
Use a better way of integrating over the pixel area in the sample function.

Definition at line 158 of file GaussianShape.h.

Constructor & Destructor Documentation

casa::GaussianShape::GaussianShape ( )

The default GaussianShape is at the J2000 North Pole.

with a full width at half maximum (FWHM) on both axes of 1 arc-min.

casa::GaussianShape::GaussianShape	(	const casacore::MDirection &	direction,
		const casacore::Quantum< casacore::Double > &	majorAxis,
		const casacore::Quantum< casacore::Double > &	minorAxis,
		const casacore::Quantum< casacore::Double > &	positionAngle
	)

Construct a Gaussian shape centred in the specified direction, specifying the widths & position angle.

casa::GaussianShape::GaussianShape	(	const casacore::MDirection &	direction,
		const casacore::Quantum< casacore::Double > &	width,
		const casacore::Double	axialRatio,
		const casacore::Quantum< casacore::Double > &	positionAngle
	)

casa::GaussianShape::GaussianShape ( const GaussianShape & other )

The copy constructor uses copy semantics.

virtual casa::GaussianShape::~GaussianShape ( )

virtual

The destructor does nothing special.

Member Function Documentation

virtual casacore::Double casa::GaussianShape::axialRatio ( ) const

virtual

virtual ComponentShape* casa::GaussianShape::clone ( ) const

virtual

Return a pointer to a copy of this object upcast to a ComponentShape object.

The class that uses this function is responsible for deleting the pointer. This is used to implement a virtual copy constructor.

Implements casa::TwoSidedShape.

virtual casacore::Quantity casa::GaussianShape::getArea ( ) const

virtual

TODO This probably should be made a pure virtual method in TwoSidedShape Return the effective area of the Gaussian (pi/(4*ln(2))*maj*min.

Units of the returned casacore::Quantity are steradians.

virtual const ComponentShape* casa::GaussianShape::getPtr ( ) const

virtual

return a pointer to this object.

Implements casa::ComponentShape.

virtual casacore::Double casa::GaussianShape::majorAxisInRad ( ) const

virtual

Implements casa::TwoSidedShape.

virtual casacore::Double casa::GaussianShape::minorAxisInRad ( ) const

virtual

Implements casa::TwoSidedShape.

virtual casacore::Bool casa::GaussianShape::ok ( ) const

virtual

casacore::Function which checks the internal data of this class for correct dimensionality and consistent values.

Returns true if everything is fine otherwise returns false.

Reimplemented from casa::TwoSidedShape.

GaussianShape& casa::GaussianShape::operator= ( const GaussianShape & other )

The assignment operator uses copy semantics.

virtual casacore::Double casa::GaussianShape::positionAngleInRad ( ) const

virtual

Implements casa::TwoSidedShape.

virtual casacore::Double casa::GaussianShape::sample	(	const casacore::MDirection &	direction,
		const casacore::MVAngle &	pixelLatSize,
		const casacore::MVAngle &	pixelLongSize
	)		const

virtual

Calculate the proportion of the flux that is in a pixel of specified size centered in the specified direction.

The returned value will always be between zero and one (inclusive).

Implements casa::TwoSidedShape.

virtual void casa::GaussianShape::sample	(	casacore::Vector< casacore::Double > &	scale,
		const casacore::Vector< casacore::MDirection::MVType > &	directions,
		const casacore::MDirection::Ref &	refFrame,
		const casacore::MVAngle &	pixelLatSize,
		const casacore::MVAngle &	pixelLongSize
	)		const

virtual

Same as the previous function except that many directions can be sampled at once.

The reference frame and pixel size must be the same for all the specified directions.

Implements casa::TwoSidedShape.

virtual void casa::GaussianShape::setWidthInRad	(	const casacore::Double	majorAxis,
		const casacore::Double	minorAxis,
		const casacore::Double	positionAngle
	)

virtual

set or return the width and orientation of the Gaussian.

All numerical values are in radians. There are also functions in the base class for doing this with other angular units.

Implements casa::TwoSidedShape.

virtual casacore::String casa::GaussianShape::sizeToString ( ) const

virtual

Get the string containing the various size quantities of a component.

Implements casa::TwoSidedShape.

virtual ComponentType::Shape casa::GaussianShape::type ( ) const

virtual

get the type of the shape.

This function always returns ComponentType::GAUSSIAN.

Implements casa::TwoSidedShape.

void casa::GaussianShape::updateFT ( )

private

virtual casacore::DComplex casa::GaussianShape::visibility	(	const casacore::Vector< casacore::Double > &	uvw,
		const casacore::Double &	frequency
	)		const

virtual

Return the Fourier transform of the component at the specified point in the spatial frequency domain.

The point is specified by a 3 element vector (u,v,w) that has units of meters and the frequency of the observation, in Hertz. These two quantities can be used to derive the required spatial frequency (s = uvw*freq/c). The w component is not used in these functions.

The reference position for the transform is the direction of the component. As this component is symmetric about this point the transform is always a real value.

Implements casa::TwoSidedShape.

virtual void casa::GaussianShape::visibility	(	casacore::Vector< casacore::DComplex > &	scale,
		const casacore::Matrix< casacore::Double > &	uvw,
		const casacore::Double &	frequency
	)		const

virtual

Same as the previous function except that many (u,v,w) points can be sampled at once.

The uvw casacore::Matrix must have a first dimension of three, and a second dimension that is the same as the length of the scale Vector. Otherwise and exception is thrown (when compiled in debug mode).

Implements casa::TwoSidedShape.

virtual void casa::GaussianShape::visibility	(	casacore::Matrix< casacore::DComplex > &	scale,
		const casacore::Matrix< casacore::Double > &	uvw,
		const casacore::Vector< casacore::Double > &	frequency
	)		const

virtual

as above but with many frequencies

Implements casa::TwoSidedShape.

Member Data Documentation

casacore::Gaussian2D<casacore::Double> casa::GaussianShape::itsFT

private

Definition at line 269 of file GaussianShape.h.

casacore::Gaussian2D<casacore::Double> casa::GaussianShape::itsShape

private

Definition at line 267 of file GaussianShape.h.

The documentation for this class was generated from the following file:

casa/code/components/ComponentModels/GaussianShape.h

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Intended use:

Review Status

Prerequisite

Synopsis

Example

To Do

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation