Interface for the COMPTEL instrument response function. More...

#include <GCOMResponse.hpp>

Inheritance diagram for GCOMResponse:

Public Member Functions
	GCOMResponse (void)
	Void constructor. More...

	GCOMResponse (const GCOMResponse &rsp)
	Copy constructor. More...

	GCOMResponse (const GCaldb &caldb, const std::string &rspname)
	Response constructor. More...

virtual	~GCOMResponse (void)
	Destructor. More...

virtual GCOMResponse &	operator= (const GCOMResponse &rsp)
	Assignment operator. More...

virtual void	clear (void)
	Clear instance. More...

virtual GCOMResponse *	clone (void) const
	Clone instance. More...

virtual std::string	classname (void) const
	Return class name. More...

virtual bool	use_edisp (void) const
	Signal if energy dispersion will be used. More...

virtual bool	use_tdisp (void) const
	Signal if time dispersion will be used. More...

virtual double	irf (const GEvent &event, const GPhoton &photon, const GObservation &obs) const
	Return value of instrument response function. More...

virtual double	nroi (const GModelSky &model, const GEnergy &obsEng, const GTime &obsTime, const GObservation &obs) const
	Return integral of event probability for a given sky model over ROI. More...

virtual GEbounds	ebounds (const GEnergy &obsEnergy) const
	Return true energy boundaries for a specific observed energy. More...

virtual std::string	print (const GChatter &chatter=NORMAL) const
	Print COMPTEL response information. More...

void	caldb (const GCaldb &caldb)
	Set calibration database. More...

const GCaldb &	caldb (void) const
	Return calibration database. More...

const std::string &	rspname (void) const
	Return response name. More...

void	load (const std::string &rspname)
	Load COMPTEL response. More...

void	read (const GFitsImage &hdu)
	Read COMPTEL response from FITS image. More...

void	write (GFitsImageFloat &image) const
	Write COMPTEL response into FITS image. More...

void	load_cache (const GFilename &filename)
	Load response cache. More...

void	save_cache (const GFilename &filename) const
	Save response cache. More...

Public Member Functions inherited from GResponse
	GResponse (void)
	Void constructor. More...

	GResponse (const GResponse &rsp)
	Copy constructor. More...

virtual	~GResponse (void)
	Destructor. More...

virtual GResponse &	operator= (const GResponse &rsp)
	Assignment operator. More...

virtual double	convolve (const GModelSky &model, const GEvent &event, const GObservation &obs, const bool &grad=true) const
	Convolve sky model with the instrument response. More...

virtual GVector	convolve (const GModelSky &model, const GObservation &obs, GMatrixSparse *gradients=NULL) const
	Convolve sky model with the instrument response. More...

virtual double	irf_spatial (const GEvent &event, const GSource &source, const GObservation &obs) const
	Return instrument response integrated over the spatial model. More...

virtual GVector	irf_spatial (const GModelSky &model, const GObservation &obs, GMatrix *gradients=NULL) const
	Return instrument response vector integrated over the spatial model. More...

virtual void	remove_response_cache (const std::string &name)
	Remove response cache for model. More...

Public Member Functions inherited from GBase
virtual	~GBase (void)
	Destructor. More...

Private Member Functions
void	init_members (void)
	Initialise class members. More...

void	copy_members (const GCOMResponse &rsp)
	Copy class members. More...

void	free_members (void)
	Delete class members. More...

virtual GVector	irf_ptsrc (const GModelSky &model, const GObservation &obs, GMatrix *gradients=NULL) const
	Return instrument response to point source. More...

virtual GVector	irf_radial (const GModelSky &model, const GObservation &obs, GMatrix *gradients=NULL) const
	Return instrument response to radial source. More...

virtual GVector	irf_elliptical (const GModelSky &model, const GObservation &obs, GMatrix *gradients=NULL) const
	Return instrument response to elliptical source. More...

virtual GVector	irf_diffuse (const GModelSky &model, const GObservation &obs, GMatrix *gradients=NULL) const
	Return instrument response to diffuse source. More...

GVector	irf_extended (const GModelSky &model, const GObservation &obs, const GSkyDir &model_dir, const double &theta_max, GMatrix *gradients=NULL) const

Private Attributes
GCaldb	m_caldb
	Calibration database. More...

std::string	m_rspname
	Response name. More...

std::vector< double >	m_iaq
	IAQ array. More...

int	m_phigeo_bins
	Number of Phigeo bins. More...

int	m_phibar_bins
	Number of Phibar bins. More...

double	m_phigeo_ref_value
	Phigeo reference value (deg) More...

double	m_phigeo_ref_pixel
	Phigeo reference pixel (starting from 1) More...

double	m_phigeo_bin_size
	Phigeo binsize (deg) More...

double	m_phigeo_min
	Phigeo value of first bin (deg) More...

double	m_phibar_ref_value
	Phigeo reference value (deg) More...

double	m_phibar_ref_pixel
	Phigeo reference pixel (starting from 1) More...

double	m_phibar_bin_size
	Phigeo binsize (deg) More...

double	m_phibar_min
	Phigeo value of first bin (deg) More...

Friends
class	GCOMDri

Additional Inherited Members
Protected Member Functions inherited from GResponse
void	init_members (void)
	Initialise class members. More...

void	copy_members (const GResponse &rsp)
	Copy class members. More...

void	free_members (void)
	Delete class members. More...

double	eval_prob (const GModelSky &model, const GEvent &event, const GEnergy &srcEng, const GTime &srcTime, const GObservation &obs, const bool &grad) const
	Convolve sky model with the instrument response. More...

GVector	eval_probs (const GModelSky &model, const GObservation &obs, GMatrixSparse *gradients=NULL) const
	Convolve sky model with the instrument response. More...

int	size_edisp_vector (const GModelSky &model, const GObservation &obs, const bool &grad) const
	Return size of vector for energy dispersion computation. More...

GEbounds	ebounds_model (const GModelSky &model) const
	Return true energy intervals for sky model. More...

virtual double	irf_ptsrc (const GEvent &event, const GSource &source, const GObservation &obs) const
	Return instrument response to point source. More...

virtual double	irf_radial (const GEvent &event, const GSource &source, const GObservation &obs) const
	Return instrument response to radial source. More...

virtual double	irf_elliptical (const GEvent &event, const GSource &source, const GObservation &obs) const
	Return instrument response to elliptical source. More...

virtual double	irf_diffuse (const GEvent &event, const GSource &source, const GObservation &obs) const
	Return instrument response to diffuse source. More...

virtual double	irf_composite (const GEvent &event, const GSource &source, const GObservation &obs) const
	Return instrument response to composite source. More...

virtual GVector	irf_composite (const GModelSky &model, const GObservation &obs, GMatrix *gradients=NULL) const
	Return instrument response to composite source sky model. More...

Protected Attributes inherited from GResponse
bool	m_use_irf_cache
	Control usage of irf cache. More...

bool	m_use_nroi_cache
	Control usage of nroi cache. More...

int	m_irf_radial_iter_theta
	Radial model integration theta iterations. More...

int	m_irf_radial_iter_phi
	Radial model integration phi iterations. More...

int	m_irf_elliptical_iter_theta
	Elliptical model integration theta iterations. More...

int	m_irf_elliptical_iter_phi
	Elliptical model integration phi iterations. More...

double	m_irf_diffuse_resolution
	Angular resolution for diffuse model. More...

GResponseCache	m_irf_cache

GResponseCache	m_nroi_cache

GResponseVectorCache	m_irf_vector_cache

Detailed Description

Interface for the COMPTEL instrument response function.

Definition at line 56 of file GCOMResponse.hpp.

Constructor & Destructor Documentation

GCOMResponse::GCOMResponse ( void )

Void constructor.

Creates an empty COMPTEL response.

Definition at line 98 of file GCOMResponse.cpp.

References init_members().

Referenced by clone().

GCOMResponse::GCOMResponse ( const GCOMResponse & rsp )

Copy constructor.

Parameters

[in] rsp COM response.

Definition at line 113 of file GCOMResponse.cpp.

References copy_members(), and init_members().

GCOMResponse::GCOMResponse	(	const GCaldb &	caldb,
		const std::string &	iaqname
	)

Response constructor.

Parameters

[in]	caldb	Calibration database.
[in]	iaqname	IAQ file name.

Create COMPTEL response by loading an IAQ file from a calibration database.

Definition at line 135 of file GCOMResponse.cpp.

References caldb(), init_members(), and load().

GCOMResponse::~GCOMResponse ( void )

virtual

Destructor.

Destroys instance of COMPTEL response object.

Definition at line 157 of file GCOMResponse.cpp.

References free_members().

Member Function Documentation

void GCOMResponse::caldb ( const GCaldb & caldb )

inline

Set calibration database.

Parameters

[in] caldb Calibration database.

Sets the calibration database for the COMPTEL response.

Definition at line 197 of file GCOMResponse.hpp.

References caldb(), and m_caldb.

Referenced by GCOMObservation::response().

const GCaldb & GCOMResponse::caldb ( void ) const

inline

Return calibration database.

Returns: Calibration database.

Definition at line 183 of file GCOMResponse.hpp.

References m_caldb.

Referenced by caldb(), GCOMResponse(), and load().

std::string GCOMResponse::classname ( void ) const

inlinevirtual

Return class name.

Returns: String containing the class name ("GCOMResponse").

Implements GResponse.

Definition at line 147 of file GCOMResponse.hpp.

void GCOMResponse::clear ( void )

virtual

Clear instance.

Clears COMPTEL response object by resetting all members to an initial state. Any information that was present in the object before will be lost.

Implements GResponse.

Definition at line 220 of file GCOMResponse.cpp.

References free_members(), GResponse::free_members(), init_members(), and GResponse::init_members().

Referenced by GCOMObservation::init_members(), load(), and GCOMObservation::response().

GCOMResponse * GCOMResponse::clone ( void ) const

virtual

Clone instance.

Returns: Pointer to deep copy of COMPTEL response.

Implements GResponse.

Definition at line 240 of file GCOMResponse.cpp.

References GCOMResponse().

void GCOMResponse::copy_members ( const GCOMResponse & rsp )

private

Copy class members.

Parameters

[in] rsp COMPTEL response.

Definition at line 819 of file GCOMResponse.cpp.

References m_caldb, m_iaq, m_phibar_bin_size, m_phibar_bins, m_phibar_min, m_phibar_ref_pixel, m_phibar_ref_value, m_phigeo_bin_size, m_phigeo_bins, m_phigeo_min, m_phigeo_ref_pixel, m_phigeo_ref_value, and m_rspname.

Referenced by GCOMResponse(), and operator=().

GEbounds GCOMResponse::ebounds ( const GEnergy & obsEnergy ) const

virtual

Return true energy boundaries for a specific observed energy.

Parameters

[in] obsEnergy Observed Energy.

Returns: True energy boundaries for given observed energy.

Exceptions

GException::feature_not_implemented Method is not implemented.

Implements GResponse.

Definition at line 462 of file GCOMResponse.cpp.

References G_EBOUNDS.

void GCOMResponse::free_members ( void )

private

Delete class members.

Definition at line 844 of file GCOMResponse.cpp.

Referenced by clear(), operator=(), and ~GCOMResponse().

void GCOMResponse::init_members ( void )

private

Initialise class members.

Definition at line 792 of file GCOMResponse.cpp.

References GCaldb::clear(), m_caldb, m_iaq, m_phibar_bin_size, m_phibar_bins, m_phibar_min, m_phibar_ref_pixel, m_phibar_ref_value, m_phigeo_bin_size, m_phigeo_bins, m_phigeo_min, m_phigeo_ref_pixel, m_phigeo_ref_value, and m_rspname.

Referenced by clear(), GCOMResponse(), and operator=().

double GCOMResponse::irf	(	const GEvent &	event,
		const GPhoton &	photon,
		const GObservation &	obs
	)		const

virtual

Return value of instrument response function.

Parameters

[in]	event	Observed event.
[in]	photon	Incident photon.
[in]	obs	Observation.

Returns: Instrument response function ( \(cm^2 sr^{-1}\))

Exceptions

GException::invalid_argument	Observation is not a COMPTEL observation. Event is not a COMPTEL event bin.
GException::invalid_value	Response not initialised with a valid IAQ

Returns the instrument response function for a given observed photon direction as function of the assumed true photon direction. The result is given by

\[ {\tt IRF} = \frac{{\tt IAQ} \times {\tt DRG} \times {\tt DRX}} {T \times {\tt TOFCOR}} \times {\tt PHASECOR} \]

where

\({\tt IRF}\) is the instrument response function ( \(cm^2 sr^{-1}\)),
\({\tt IAQ}\) is the COMPTEL response matrix ( \(sr^{-1}\)),
\({\tt DRG}\) is the geometry factor (probability),
\({\tt DRX}\) is the exposure ( \(cm^2 s\)),
\(T\) is the ontime ( \(s\)), and
\({\tt TOFCOR}\) is a correction that accounts for the Time of Flight selection window.
\({\tt PHASECOR}\) is a correction that accounts for pulsar phase selection.

The observed photon direction is spanned by the three values \(\Chi\), \(\Psi\), and \(\bar{\varphi})\). \(\Chi\) and \(\Psi\) is the scatter direction of the event, given in sky coordinates. \(\bar{\varphi}\) is the Compton scatter angle, computed from the energy deposits in the two detector planes.

Implements GResponse.

Definition at line 286 of file GCOMResponse.cpp.

References GObservation::deadc(), GCOMInstDir::dir(), GCOMEventBin::dir(), GPhoton::dir(), GSkyDir::dist_deg(), GCOMEventCube::dre(), GCOMObservation::drg(), GCOMObservation::drx(), GObservation::events(), G_IRF, gammalib::is_infinite(), gammalib::is_notanumber(), m_iaq, m_phibar_bin_size, m_phibar_bins, m_phigeo_bin_size, m_phigeo_bins, GCOMDri::map(), GCOMObservation::ontime(), GCOMDri::phase_correction(), GCOMInstDir::phibar(), GPhoton::time(), and GCOMDri::tof_correction().

Referenced by irf_diffuse(), irf_elliptical(), irf_ptsrc(), and irf_radial().

GVector GCOMResponse::irf_diffuse	(	const GModelSky &	model,
		const GObservation &	obs,
		GMatrix *	gradients = `NULL`
	)		const

privatevirtual

Return instrument response to diffuse source.

Parameters

[in]	model	Sky model.
[in]	obs	Observation.
[out]	gradients	Gradients matrix.

Returns: Instrument response to diffuse source for all events in observation ( \(cm^2\)).

Exceptions

GException::invalid_argument	Observation is not a COMPTEL observation.
GException::invalid_value	Response not initialised with a valid IAQ Incompatible IAQ encountered

Returns the instrument response to a diffuse source for all events in the observations. The diffuse source may be energy dependent.

The computation is done by integrating the diffuse model for each pixel in Chi and Psi over a circular region centred on the Chi/Psi pixel with a radius equal to the maximum Phigeo value. The radial integration is done by looping over all Phigeo bins of the response. For each Phigeo value, the azimuthal integration is done by stepping with an angular step size that corresponds to the Phigeo step size (which typically is 1 deg).

gradients is an optional matrix where the number of rows corresponds to the number of events in the observation and the number of columns corresponds to the number of spatial model parameters. Since for point sources no gradients are computed, the method does not alter the content of gradients.

Reimplemented from GResponse.

Definition at line 1394 of file GCOMResponse.cpp.

References GSkyMap::contains(), GCOMObservation::deadc(), gammalib::deg2rad, GCOMInstDir::dir(), GCOMEventBin::dir(), GCOMEventCube::dre(), GCOMObservation::drg(), GCOMObservation::drx(), GCOMEventBin::energy(), GModelSpatial::eval(), GObservation::events(), G_IRF_DIFFUSE, GObservation::id(), irf(), m_iaq, m_phibar_bins, m_phigeo_bin_size, m_phigeo_bins, m_phigeo_min, GCOMDri::map(), GObservation::name(), GCOMEventCube::naxis(), GCOMObservation::ontime(), GCOMDri::phase_correction(), GSkyMap::pixels(), GSkyDir::rotate(), sin(), GCOMEventCube::size(), GModelSky::spatial(), gammalib::str(), GCOMEventBin::time(), GCOMDri::tof_correction(), and gammalib::twopi.

GVector GCOMResponse::irf_elliptical	(	const GModelSky &	model,
		const GObservation &	obs,
		GMatrix *	gradients = `NULL`
	)		const

privatevirtual

Return instrument response to elliptical source.

Parameters

[in]	model	Sky model.
[in]	obs	Observation.
[out]	gradients	Gradients matrix.

Returns: Instrument response to elliptical source for all events in observation ( \(cm^2\)).

Exceptions

GException::invalid_argument	Observation is not a COMPTEL observation. Event is not a COMPTEL event bin.
GException::invalid_value	Response not initialised with a valid IAQ Incompatible IAQ encountered

Returns the instrument response to an elliptical source for all events in the observations. See GCOMResponse::irf_extended for more information.

Reimplemented from GResponse.

Definition at line 1213 of file GCOMResponse.cpp.

References GCOMObservation::deadc(), GSkyDir::dec_deg(), gammalib::deg2rad, GCOMInstDir::dir(), GCOMEventBin::dir(), GModelSpatialElliptical::dir(), GSkyDir::dist(), GCOMEventCube::dre(), GCOMObservation::drg(), GCOMObservation::drx(), GMatrix::eulery(), GMatrix::eulerz(), GObservation::events(), GIntegrals::fixed_iter(), G_IRF_ELLIPTICAL, GObservation::id(), irf(), gammalib::iter_rho(), m_iaq, m_phibar_bins, m_phigeo_bin_size, m_phigeo_bins, m_phigeo_min, GCOMDri::map(), GObservation::name(), GCOMEventCube::naxis(), GCOMObservation::ontime(), GCOMDri::phase_correction(), GSkyMap::pixels(), GSkyDir::ra_deg(), GIntegrals::romberg(), GCOMEventCube::size(), GModelSky::spatial(), gammalib::str(), GModelSpatialElliptical::theta_max(), and GCOMDri::tof_correction().

GVector GCOMResponse::irf_extended	(	const GModelSky &	model,
		const GObservation &	obs,
		const GSkyDir &	model_dir,
		const double &	theta_max,
		GMatrix *	gradients = `NULL`
	)		const

private

GVector GCOMResponse::irf_ptsrc	(	const GModelSky &	model,
		const GObservation &	obs,
		GMatrix *	gradients = `NULL`
	)		const

privatevirtual

Return instrument response to point source.

Parameters

[in]	model	Sky model.
[in]	obs	Observation.
[out]	gradients	Gradients matrix.

Returns: Instrument response to point source for all events in observation ( \(cm^2\)).

Exceptions

GException::invalid_argument	Observation is not a COMPTEL observation. Event is not a COMPTEL event bin.
GException::invalid_value	Response not initialised with a valid IAQ Incompatible IAQ encountered

Returns the instrument response to a point source for all events in the observations.

gradients is an optional matrix where the number of rows corresponds to the number of events in the observation and the number of columns corresponds to the number of spatial model parameters. Since for point sources no gradients are computed, the method does not alter the content of gradients.

Reimplemented from GResponse.

Definition at line 876 of file GCOMResponse.cpp.

References GCOMObservation::deadc(), GCOMInstDir::dir(), GCOMEventBin::dir(), GSkyDir::dist_deg(), GCOMEventCube::dre(), GCOMObservation::drg(), GCOMObservation::drx(), GObservation::events(), G_IRF_PTSRC, GObservation::id(), irf(), m_iaq, m_phibar_bins, m_phigeo_bin_size, m_phigeo_bins, GCOMDri::map(), GObservation::name(), GCOMEventCube::naxis(), GCOMObservation::ontime(), GCOMDri::phase_correction(), GSkyMap::pixels(), GCOMEventCube::size(), GModelSky::spatial(), gammalib::str(), and GCOMDri::tof_correction().

GVector GCOMResponse::irf_radial	(	const GModelSky &	model,
		const GObservation &	obs,
		GMatrix *	gradients = `NULL`
	)		const

privatevirtual

Return instrument response to radial source.

Parameters

[in]	model	Sky model.
[in]	obs	Observation.
[out]	gradients	Gradients matrix.

Returns: Instrument response to radial source for all events in observation ( \(cm^2\)).

Exceptions

GException::invalid_argument	Observation is not a COMPTEL observation. Event is not a COMPTEL event bin.
GException::invalid_value	Response not initialised with a valid IAQ Incompatible IAQ encountered

Returns the instrument response to a radial source for all events in the observations. See GCOMResponse::irf_extended for more information.

Reimplemented from GResponse.

Definition at line 1042 of file GCOMResponse.cpp.

References GCOMObservation::deadc(), GSkyDir::dec_deg(), gammalib::deg2rad, GCOMInstDir::dir(), GCOMEventBin::dir(), GModelSpatialRadial::dir(), GSkyDir::dist(), GCOMEventCube::dre(), GCOMObservation::drg(), GCOMObservation::drx(), GMatrix::eulery(), GMatrix::eulerz(), GObservation::events(), GIntegrals::fixed_iter(), G_IRF_RADIAL, GObservation::id(), irf(), gammalib::iter_rho(), m_iaq, m_phibar_bins, m_phigeo_bin_size, m_phigeo_bins, m_phigeo_min, GCOMDri::map(), GObservation::name(), GCOMEventCube::naxis(), GCOMObservation::ontime(), GCOMDri::phase_correction(), GSkyMap::pixels(), GSkyDir::ra_deg(), GIntegrals::romberg(), GCOMEventCube::size(), GModelSky::spatial(), gammalib::str(), GModelSpatialRadial::theta_max(), and GCOMDri::tof_correction().

void GCOMResponse::load ( const std::string & rspname )

Load COMPTEL response.

Parameters

[in] rspname COMPTEL response name.

Loads the COMPTEL response with specified name rspname.

The method first attempts to interpret rspname as a file name and to load the corresponding response.

If rspname is not a FITS file the method searches for an appropriate response in the calibration database. If no appropriate response is found, the method takes the CALDB root path and response name to build the full path to the response file, and tries to load the response from these paths.

If also this fails an exception is thrown.

Definition at line 494 of file GCOMResponse.cpp.

References caldb(), clear(), GFits::close(), GFilename::exists(), GCaldb::filename(), gammalib::filepath(), GFits::image(), GFilename::is_empty(), GFilename::is_fits(), m_caldb, m_rspname, read(), GCaldb::rootdir(), and rspname().

Referenced by GCOMResponse(), and GCOMObservation::response().

void GCOMResponse::load_cache ( const GFilename & filename )

Load response cache.

Parameters

[in] filename Response cache filename.

Loads response cache from FITS file.

Definition at line 697 of file GCOMResponse.cpp.

References GResponseVectorCache::load(), and GResponse::m_irf_vector_cache.

Referenced by GCOMObservation::read().

double GCOMResponse::nroi	(	const GModelSky &	model,
		const GEnergy &	obsEng,
		const GTime &	obsTime,
		const GObservation &	obs
	)		const

virtual

Return integral of event probability for a given sky model over ROI.

Parameters

[in]	model	Sky model.
[in]	obsEng	Observed photon energy.
[in]	obsTime	Observed photon arrival time.
[in]	obs	Observation.

Returns: 0.0

Exceptions

GException::feature_not_implemented Method is not implemented.

Implements GResponse.

Definition at line 438 of file GCOMResponse.cpp.

References G_NROI.

GCOMResponse & GCOMResponse::operator= ( const GCOMResponse & rsp )

virtual

Assignment operator.

Parameters

[in] rsp COMPTEL response.

Returns: COMPTEL response.

Assigns COMPTEL response object to another COMPTEL response object. The assignment performs a deep copy of all information, hence the original object from which the assignment has been performed can be destroyed after this operation without any loss of information.

Definition at line 184 of file GCOMResponse.cpp.

References copy_members(), free_members(), init_members(), and GResponse::operator=().

std::string GCOMResponse::print ( const GChatter & chatter = NORMAL ) const

virtual

Print COMPTEL response information.

Parameters

[in] chatter Chattiness.

Returns: String containing COMPTEL response information.

Implements GResponse.

Definition at line 730 of file GCOMResponse.cpp.

References EXPLICIT, m_caldb, m_phibar_bin_size, m_phibar_bins, m_phibar_min, m_phibar_ref_pixel, m_phibar_ref_value, m_phigeo_bin_size, m_phigeo_bins, m_phigeo_min, m_phigeo_ref_pixel, m_phigeo_ref_value, m_rspname, gammalib::parformat(), GCaldb::print(), SILENT, gammalib::str(), and VERBOSE.

void GCOMResponse::read ( const GFitsImage & image )

Read COMPTEL response from FITS image.

Parameters

[in] image FITS image.

Read the COMPTEL response from IAQ FITS file and convert the IAQ values into a probability per steradian.

The IAQ values are divided by the solid angle of a Phigeo bin which is given by

\begin{eqnarray*} \Omega & = & 2 \pi \left[ \left( 1 - \cos \left( \varphi_{\rm geo} + \frac{1}{2} \Delta \varphi_{\rm geo} \right) \right) - \left( 1 - \cos \left( \varphi_{\rm geo} - \frac{1}{2} \Delta \varphi_{\rm geo} \right) \right) \right] \\ &=& 2 \pi \left[ \cos \left( \varphi_{\rm geo} - \frac{1}{2} \Delta \varphi_{\rm geo} \right) - \cos \left( \varphi_{\rm geo} + \frac{1}{2} \Delta \varphi_{\rm geo} \right) \right] \\ &=& 4 \pi \sin \left( \varphi_{\rm geo} \right) \sin \left( \frac{1}{2} \Delta \varphi_{\rm geo} \right) \end{eqnarray*}

Definition at line 576 of file GCOMResponse.cpp.

References gammalib::deg2rad, gammalib::fourpi, m_iaq, m_phibar_bin_size, m_phibar_bins, m_phibar_min, m_phibar_ref_pixel, m_phibar_ref_value, m_phigeo_bin_size, m_phigeo_bins, m_phigeo_min, m_phigeo_ref_pixel, m_phigeo_ref_value, GFitsImage::naxes(), GFitsImage::naxis(), GFitsImage::pixel(), GFitsHDU::real(), and sin().