#include <HEALPixSkyInstrument.hpp>

Inheritance diagram for HEALPixSkyInstrument:

[legend]

Public Member Functions
Direction	bfkobs (const Position &bfr) const override

Direction	bfky (const Position &bfr) const override

double	crossX () const

double	crossY () const

double	crossZ () const

void	determineSameObserverAsPreceding (const Instrument *precedingInstrument) override

double	observerX () const

double	observerY () const

double	observerZ () const

int	order () const

double	radius () const

double	upX () const

double	upY () const

double	upZ () const

Public Member Functions inherited from Instrument
virtual Direction	bfkobs (const Position &bfr) const =0

virtual Direction	bfky (const Position &bfr) const =0

virtual void	detect (PhotonPacket *pp)=0

virtual void	determineSameObserverAsPreceding (const Instrument *precedingInstrument)=0

void	flush ()

string	instrumentName () const

const WavelengthGrid *	instrumentWavelengthGrid () const

bool	isSameObserverAsPreceding () const

string	itemName () const override

int	numScatteringLevels () const

bool	recordComponents () const

bool	recordPolarization () const

bool	recordStatistics () const

WavelengthGrid *	wavelengthGrid () const

void	write ()

Public Member Functions inherited from SimulationItem
template<class T >
T *	find (bool setup=true) const

template<class T >
T *	interface (int levels=-999999, bool setup=true) const

virtual string	itemName () const

void	setup ()

string	typeAndName () const

Public Member Functions inherited from Item
	Item (const Item &)=delete

virtual	~Item ()

void	addChild (Item *child)

const vector< Item * > &	children () const

virtual void	clearItemListProperty (const PropertyDef *property)

void	destroyChild (Item *child)

virtual bool	getBoolProperty (const PropertyDef *property) const

virtual vector< double >	getDoubleListProperty (const PropertyDef *property) const

virtual double	getDoubleProperty (const PropertyDef *property) const

virtual string	getEnumProperty (const PropertyDef *property) const

virtual int	getIntProperty (const PropertyDef *property) const

virtual vector< Item * >	getItemListProperty (const PropertyDef *property) const

virtual Item *	getItemProperty (const PropertyDef *property) const

virtual string	getStringProperty (const PropertyDef *property) const

int	getUtilityProperty (string name) const

virtual void	insertIntoItemListProperty (const PropertyDef property, int index, Item item)

Item &	operator= (const Item &)=delete

Item *	parent () const

virtual void	removeFromItemListProperty (const PropertyDef *property, int index)

virtual void	setBoolProperty (const PropertyDef *property, bool value)

virtual void	setDoubleListProperty (const PropertyDef *property, vector< double > value)

virtual void	setDoubleProperty (const PropertyDef *property, double value)

virtual void	setEnumProperty (const PropertyDef *property, string value)

virtual void	setIntProperty (const PropertyDef *property, int value)

virtual void	setItemProperty (const PropertyDef property, Item item)

virtual void	setStringProperty (const PropertyDef *property, string value)

void	setUtilityProperty (string name, int value)

virtual string	type () const

Protected Member Functions
	HEALPixSkyInstrument ()

void	detect (PhotonPacket *pp) override

void	setupSelfBefore () override

Protected Member Functions inherited from Instrument
	Instrument ()

	~Instrument ()

FluxRecorder *	instrumentFluxRecorder ()

void	setSameObserverAsPreceding ()

void	setupSelfAfter () override

void	setupSelfBefore () override

Protected Member Functions inherited from SimulationItem
	SimulationItem ()

virtual bool	offersInterface (const std::type_info &interfaceTypeInfo) const

virtual void	setupSelfAfter ()

virtual void	setupSelfBefore ()

Protected Member Functions inherited from Item
	Item ()

Private Types
using	BaseType = Instrument

using	ItemType = HEALPixSkyInstrument

Private Attributes
double	_crossX

double	_crossY

double	_crossZ

const double &	_Cx

const double &	_Cy

const double &	_Cz

int	_Nside

int	_Nx

int	_Ny

double	_observerX

double	_observerY

double	_observerZ

int	_order

const double &	_Ox

const double &	_Oy

const double &	_Oz

double	_radius

HomogeneousTransform	_transform

double	_upX

double	_upY

double	_upZ

const double &	_Ux

const double &	_Uy

const double &	_Uz

Friends
class	ItemRegistry

Detailed Description

The HEALPixSkyInstrument class provides an all-sky instrument that does not perform any projection, but instead records fluxes onto a HEALPix tessellation of the sky sphere that guarantees equal surface areas for all pixels. (See the AllSkyInstrument class for an instrument that does perform a projection).

This class is based on the official HEALPix algorithm by Górski, K. M. et al. (2005) (https://ui.adsabs.harvard.edu/abs/2005ApJ...622..759G/abstract), as available from https://healpix.sourceforge.io, but only uses the relevant part of the algorithm.

In short, the HEALPix tessellation starts from a base tessellation of the sphere into 12 quadrilaterals. 4 quadrilaterals are formed by subdividing the equator into 4 equal segments, so that each quadrilateral has two equatorial segment endpoints as vertices, complemented with two vertices that are obtained by translating the segment midpoint away from the equator over a zenith angle $θ = \arccos (2 / 3)$ in both directions. The remaining 8 quadrilaterals are formed by connecting the north or south pole of the sphere with 3 vertices of already existing quadrilaterals.

Within this base tessellation, higher order HEALPix tessellations are constructed by subdividing the 12 base quadrilaterals, as if these were simple squares in a flat Euclidian space. To guarantee that all pixels have the same surface area, this subdivision needs to use the same number of sub-pixels along each axis of the base quadrilateral. This number of sub-pixels is referred to as the HEALPix resolution parameter $N_{s i d e}$ . It is common practice within the community to restrict $N_{s i d e} = 2^{k}$ , with $k$ an integer order, although this is not strictly required. We will use this parametrisation, as it allows for a more efficient pixel location algorithm.

After subdivision, the HEALPix tessellation will contain $12 N_{s i d e}^{2}$ pixels. These pixels are ordered so that their centres lie on $4 N_{s i d e} - 1$ rings of equal latitude. On each of these rings, pixel centres are equidistantly spaced in longitude, but the number of pixels in each ring, $i$ , depends on the latitude. For pixels with a ring index $j \in [N_{s i d e}, 3 N_{s i d e}]$ , the number of pixels in the ring is constant and equal to $i = 4 N_{s i d e}$ . Within the polar rings ( $j < N_{s i d e}$ or $j > 3 N_{s i d e}$ ), the number of pixels decreases by 4 for every ring closer to the pole. For the polar rings in the northern hemisphere, the number of pixels is equal to $i = 4 j$ . For the southern hemisphere, it is equal to $i = 4 (N_{s i d e} - j)$ .

HEALPix pixels can be ordered in two ways, depending on the application of interest. For many analysis tools, a hierarchical ordering is advantageous, whereby the index of neighbouring pixels are related. In practice, this so called nested ordering subdivides every base HEALPix pixel into a hierarchical quadtree structure. This is the approach used by e.g. the public Planck data maps. For visualisation purposes, the so called ring ordering is more appropriate, whereby the pixels are indexed per ring from northern to southern hemisphere, and with increasing longitude along each ring.

For our implementation, we use an alternative ordering that closely matches the ring ordering. We compute the indices $j$ and $i$ for each pixel as if we were going to compute the ring pixel index, but then use these indices as the 2D pixel coordinates in a $(4 N_{s i d e} - 1) \times 4 N_{s i d e}$ image. Evidently, this leads to an excess of $4 N_{s i d e}^{2} - 16 N$ pixels in the polar regions, similar to the empty pixels in projected AllSkyInstrument images. The advantage of this approach is that we can easily use the existing 2D image functionality for output, and that we can easily map output pixels to the corresponding HEALPix pixels in ring ordering during analysis.

An HEALPix sky instrument consists of a sphere with a given radius, centered at the location of the instrument. Only photon packets originating outside of this sphere are detected. When a photon packet arrives, the spherical coordinates of its originating position relative to the instrument coordinate system are determined. The two resulting angular coordinates are transformed to pixel coordinates on the HEALPix sphere. The radial coordinate (i.e. the distance from the photon packet's origin to the instrument location) is used for adjusting the photon packet's luminosity contribution to the surface brightness in its target pixel. More details on the flux calibration for this "local" instrument are provided in the header of the FluxRecorder class.

This instrument does not support recording of spatially integrated flux densities.

This item type is displayed only if the Boolean expression "Level2" evaluates to true after replacing the names by true or false depending on their presence.

Constructor & Destructor Documentation

◆ HEALPixSkyInstrument()

HEALPixSkyInstrument::HEALPixSkyInstrument ( )

inlineprotected

Default constructor for concrete Item subclass HEALPixSkyInstrument : "a HEALPix all-sky instrument (for Planck-like observations inside a model)" .

Member Function Documentation

◆ bfkobs()

Direction HEALPixSkyInstrument::bfkobs ( const Position & bfr ) const

overridevirtual

Returns the direction towards the observer from the given photon packet launching position, expressed in model coordinates.

Implements Instrument.

◆ bfky()

Direction HEALPixSkyInstrument::bfky ( const Position & bfr ) const

overridevirtual

Returns the direction along the positive y-axis in a plane normal to the vector towards the observer from the given photon packet launching position, expressed in model coordinates.

Implements Instrument.

◆ crossX()

HEALPixSkyInstrument::crossX ( ) const

inline

This function returns the value of the discoverable double property crossX : "the position of the crosshair, x component" .

This property represents a physical quantity of type "length" .

The default value for this property is given by the conditional value expression "0" .

◆ crossY()

HEALPixSkyInstrument::crossY ( ) const

inline

This function returns the value of the discoverable double property crossY : "the position of the crosshair, y component" .

This property represents a physical quantity of type "length" .

The default value for this property is given by the conditional value expression "0" .

◆ crossZ()

HEALPixSkyInstrument::crossZ ( ) const

inline

This function returns the value of the discoverable double property crossZ : "the position of the crosshair, z component" .

This property represents a physical quantity of type "length" .

The default value for this property is given by the conditional value expression "0" .

◆ detect()

void HEALPixSkyInstrument::detect ( PhotonPacket * pp )

overrideprotectedvirtual

This function simulates the detection of a photon packet by the instrument.

Implements Instrument.

◆ determineSameObserverAsPreceding()

void HEALPixSkyInstrument::determineSameObserverAsPreceding ( const Instrument * precedingInstrument )

overridevirtual

This function determines whether the specified instrument has the same observer type, position and viewing direction as the receiving instrument, and if so, calls the setSameObserverAsPreceding() function to remember the fact.

Implements Instrument.

◆ observerX()

HEALPixSkyInstrument::observerX ( ) const

inline

This function returns the value of the discoverable double property observerX : "the position of the observer, x component" .

This property represents a physical quantity of type "length" .

◆ observerY()

HEALPixSkyInstrument::observerY ( ) const

inline

This function returns the value of the discoverable double property observerY : "the position of the observer, y component" .

This property represents a physical quantity of type "length" .

◆ observerZ()

HEALPixSkyInstrument::observerZ ( ) const

inline

This function returns the value of the discoverable double property observerZ : "the position of the observer, z component" .

This property represents a physical quantity of type "length" .

◆ order()

HEALPixSkyInstrument::order ( ) const

inline

This function returns the value of the discoverable integer property order : "HEALPix order" .

The minimum value for this property is "0" .

The maximum value for this property is "15" .

The default value for this property is given by the conditional value expression "6" .

◆ radius()

HEALPixSkyInstrument::radius ( ) const

inline

This function returns the value of the discoverable double property radius : "the radius of the observer's all-sky sphere" .

This property represents a physical quantity of type "length" .

The minimum value for this property is "]0" .

◆ setupSelfBefore()

void HEALPixSkyInstrument::setupSelfBefore ( )

overrideprotectedvirtual

This function verifies that all attribute values have been appropriately set and performs setup for the instrument. Its most important task is to determine an appropriate transformation given the instrument position and configuration.

Reimplemented from SimulationItem.

◆ upX()

HEALPixSkyInstrument::upX ( ) const

inline

This function returns the value of the discoverable double property upX : "the upwards direction, x component" .

This property represents a physical quantity of type "length" .

The default value for this property is given by the conditional value expression "0" .

◆ upY()

HEALPixSkyInstrument::upY ( ) const

inline

This function returns the value of the discoverable double property upY : "the upwards direction, y component" .

This property represents a physical quantity of type "length" .

The default value for this property is given by the conditional value expression "0" .

◆ upZ()

HEALPixSkyInstrument::upZ ( ) const

inline

This function returns the value of the discoverable double property upZ : "the upwards direction, z component" .

This property represents a physical quantity of type "length" .

The default value for this property is given by the conditional value expression "1" .

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

HEALPixSkyInstrument.hpp

Public Member Functions

Protected Member Functions

Private Types

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ HEALPixSkyInstrument()

Member Function Documentation

◆ bfkobs()

◆ bfky()

◆ crossX()

◆ crossY()

◆ crossZ()

◆ detect()

◆ determineSameObserverAsPreceding()

◆ observerX()

◆ observerY()

◆ observerZ()

◆ order()

◆ radius()

◆ setupSelfBefore()

◆ upX()

◆ upY()

◆ upZ()