ComplexAmplitudePointInterpolation Class Reference

This class is subject to change. Programs using this class may require changes with a new version of VirtualLab.
ComplexAmplitudePointInterpolation is a class with static members that are able to interpolate pointwise between different sampling points of a complex amplitude. The point to interpolate is specified in physical coordinates. Additionally for most interpolation methods a non-static optimized version is supported. These functions are optimized for an interpolation on an equidistant grid. Different interpolation methods are supported. For more information see [Lehmann1999]. More...

Public Member Functions
	ComplexAmplitudePointInterpolation ()
	Default constructor for the use of the optimized interpolation functions.
Complex	Cubic4PointInterpolationOpt (ComplexAmplitude ca, VectorD point, bool accessFieldY)
	Performs a cubic 4 point interpolation on a specific point (x,y). The interpolation is done between 4 neighbour points. Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied. The interpolation is optimized for interpolations that work row by row and from the left sampling point to the right sampling point.
Complex	Cubic6PointInterpolationOpt (ComplexAmplitude ca, VectorD point, bool accessFieldY)
	Performs a cubic 6 point interpolation on a specific point (x,y). The interpolation is done between 6 neighbour points. Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied. The interpolation is optimized for interpolations that work row by row and from the left sampling point to the right sampling point.
Complex	Cubic8PointInterpolationOpt (ComplexAmplitude ca, VectorD point, bool accessFieldY)
	Performs a cubic 8 point interpolation on a specific point (x,y). The interpolation is done between 8 neighbour points. Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied. The interpolation is optimized for interpolations that work row by row and from the left sampling point to the right sampling point.
void	ReInitialize ()
	Deletes all temporarely stored interpolation data. Use this function if you plane to interpolate a different ComplexField with the same interpolation method. Not reinitialzing the interpolation object can case numerical errors in such cases.
Complex	SincInterpolationOpt (ComplexAmplitude ca, VectorD point, bool accessFieldY)
	Performs a sinc interpolation on a specific point (x,y). The interpolation is done by adding the sinc-functions of every pixel of the field . Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied. The interpolation is optimized for interpolations that work row by row and from the left sampling point to the right sampling point.
Complex	TruncatedSincInterpolationOpt (ComplexAmplitude ca, VectorD point, bool accessFieldY)
	Performs a truncated sinc interpolation on a specific point (x,y). The interpolation is done between 6 neighbour points . Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied. The interpolation is optimized for interpolations that work row by row and from the left sampling point to the right sampling point.

Static Public Member Functions
static Complex	Cubic4PointInterpolation (ComplexAmplitude ca, VectorD point, bool accessFieldY)
	Performs a cubic 4 point interpolation on a specific point (x,y). The interpolation is done between 4 neighbour points. Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied.
static Complex	Cubic6PointInterpolation (ComplexAmplitude ca, VectorD point, bool accessFieldY)
	Performs a cubic 6 point interpolation on a specific point (x,y). The interpolation is done between 6 neighbour points. Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied.
static Complex	Cubic6PointInterpolation (ComplexAmplitude ca, VectorD point, bool accessFieldY, bool removeSphericalPhase)
	Performs a cubic 6 point interpolation on a specific point (x,y). The interpolation is done between 6 neighbour points. Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is kept or removed at wish.
static Complex	Cubic8PointInterpolation (ComplexAmplitude ca, VectorD point, bool accessFieldY)
	Performs a cubic 8 point interpolation on a specific point (x,y). The interpolation is done between 8 neighbour points. Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied.
static Complex	Interpolation (ComplexAmplitude ca, VectorD point, InterpolationMethod interpolationMethod, bool accessFieldY)
	Performs a interpolation of a ComplexAmplitude on a specific point (x,y) using the specified interpolation method.
static Complex	LinearInterpolation (ComplexAmplitude ca, VectorD point, bool accessFieldY)
	Performs a linear interpolation on a specific point (x,y). The interpolation is done between the amplitude and phase aberations of 4 neighbour points. The function interpolates the phase aberation by interpolating real and imaginary part of the points. The amplitude is interpolated separately. The result of the interpolation is multiplied by the spherical phase factor.
static Complex	NearestNeighbourInterpolation (ComplexAmplitude ca, VectorD point, bool accessFieldY)
	Nearest neighbour interpolation on a specific point (x,y). The interpolation is looking for the nearest neighbour pixel of the amplitude and phase aberrations and returns its value multiplied by the spherical phase factor.
static Complex	SincInterpolation (ComplexAmplitude ca, VectorD point, bool accessFieldY)
	Performs a sinc interpolation on a specific point (x,y). The interpolation is done by adding the sinc-functions of every pixel of the field . Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied.
static Complex	TruncatedSincInterpolation (ComplexAmplitude ca, VectorD point, bool accessFieldY)
	Performs a truncated sinc interpolation on a specific point (x,y). The interpolation is done between 6 neighbour points . Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied.

Detailed Description

This class is subject to change. Programs using this class may require changes with a new version of VirtualLab.
ComplexAmplitudePointInterpolation is a class with static members that are able to interpolate pointwise between different sampling points of a complex amplitude. The point to interpolate is specified in physical coordinates. Additionally for most interpolation methods a non-static optimized version is supported. These functions are optimized for an interpolation on an equidistant grid. Different interpolation methods are supported. For more information see [Lehmann1999].

Member Function Documentation

Cubic4PointInterpolation()

static Complex Cubic4PointInterpolation ( ComplexAmplitude  ca, VectorD  point, bool  accessFieldY  )

static

Performs a cubic 4 point interpolation on a specific point (x,y). The interpolation is done between 4 neighbour points. Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied.

Parameters

ca	ComplexAmplitude for interpolation.
point	Position to interpolate in meters.
accessFieldY	If true the y field component will be interpolted otherwise the x field component.

Returns

Result of operation.

Cubic4PointInterpolationOpt()

Complex Cubic4PointInterpolationOpt	(	ComplexAmplitude	ca,
		VectorD	point,
		bool	accessFieldY
	)

Performs a cubic 4 point interpolation on a specific point (x,y). The interpolation is done between 4 neighbour points. Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied. The interpolation is optimized for interpolations that work row by row and from the left sampling point to the right sampling point.

Parameters

ca	ComplexAmplitude for interpolation.
point	Position to interpolate in meters.
accessFieldY	If true the y field component will be interpolted otherwise the x field component.

Returns

Result of operation.

Cubic6PointInterpolation() [1/2]

static Complex Cubic6PointInterpolation ( ComplexAmplitude  ca, VectorD  point, bool  accessFieldY  )

static

Performs a cubic 6 point interpolation on a specific point (x,y). The interpolation is done between 6 neighbour points. Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied.

Parameters

ca	Complex amplitude for interpolation.
point	Position to interpolate in meters.
accessFieldY	If true the y field component will be interpolated, otherwise the x field component.

Returns

Result of operation.

Cubic6PointInterpolation() [2/2]

static Complex Cubic6PointInterpolation ( ComplexAmplitude  ca, VectorD  point, bool  accessFieldY, bool  removeSphericalPhase  )

static

Performs a cubic 6 point interpolation on a specific point (x,y). The interpolation is done between 6 neighbour points. Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is kept or removed at wish.

Parameters

ca	Complex amplitude for interpolation.
point	Position to interpolate in meters.
accessFieldY	If true the y field component will be interpolated, otherwise the x field component.
removeSphericalPhase	remove spherical phase factor after interpolation, if any

Returns

Result of operation.

Cubic6PointInterpolationOpt()

Complex Cubic6PointInterpolationOpt	(	ComplexAmplitude	ca,
		VectorD	point,
		bool	accessFieldY
	)

Performs a cubic 6 point interpolation on a specific point (x,y). The interpolation is done between 6 neighbour points. Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied. The interpolation is optimized for interpolations that work row by row and from the left sampling point to the right sampling point.

Parameters

ca	ComplexAmplitude for interpolation.
point	Position to interpolate in meters.
accessFieldY	If true the y field component will be interpolted otherwise the x field component.

Returns

Result of operation.

Cubic8PointInterpolation()

static Complex Cubic8PointInterpolation ( ComplexAmplitude  ca, VectorD  point, bool  accessFieldY  )

static

Performs a cubic 8 point interpolation on a specific point (x,y). The interpolation is done between 8 neighbour points. Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied.

Parameters

ca	ComplexAmplitude for interpolation.
point	Position to interpolate in meters.
accessFieldY	If true the y field component will be interpolted otherwise the x field component.

Returns

Result of operation.

Cubic8PointInterpolationOpt()

Complex Cubic8PointInterpolationOpt	(	ComplexAmplitude	ca,
		VectorD	point,
		bool	accessFieldY
	)

Performs a cubic 8 point interpolation on a specific point (x,y). The interpolation is done between 8 neighbour points. Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied. The interpolation is optimized for interpolations that work row by row and from the left sampling point to the right sampling point.

Parameters

ca	ComplexAmplitude for interpolation.
point	Position to interpolate in meters.
accessFieldY	If true the y field component will be interpolted otherwise the x field component.

Returns

Result of operation.

Interpolation()

static Complex Interpolation ( ComplexAmplitude  ca, VectorD  point, InterpolationMethod  interpolationMethod, bool  accessFieldY  )

static

Performs a interpolation of a ComplexAmplitude on a specific point (x,y) using the specified interpolation method.

Parameters

ca	ComplexAmplitude for interpolation.
point	Position to interpolate in meters.
interpolationMethod	Interpolation method.
accessFieldY	If true the y field component will be interpolted otherwise the x field component.

Returns

Result of operation.

LinearInterpolation()

static Complex LinearInterpolation ( ComplexAmplitude  ca, VectorD  point, bool  accessFieldY  )

static

Performs a linear interpolation on a specific point (x,y). The interpolation is done between the amplitude and phase aberations of 4 neighbour points. The function interpolates the phase aberation by interpolating real and imaginary part of the points. The amplitude is interpolated separately. The result of the interpolation is multiplied by the spherical phase factor.

Parameters

ca	ComplexAmplitude for interpolation.
point	Position to interpolate in meters.
accessFieldY	If true the y field component will be interpolted otherwise the x field component.

Returns

Result of operation.

NearestNeighbourInterpolation()

static Complex NearestNeighbourInterpolation ( ComplexAmplitude  ca, VectorD  point, bool  accessFieldY  )

static

Nearest neighbour interpolation on a specific point (x,y). The interpolation is looking for the nearest neighbour pixel of the amplitude and phase aberrations and returns its value multiplied by the spherical phase factor.

Parameters

ca	ComplexAmplitude for interpolation.
point	Position to interpolation in meter.
accessFieldY	If true the y field component will be interpolted otherwise the x field component.

Returns

Result of operation.

SincInterpolation()

static Complex SincInterpolation ( ComplexAmplitude  ca, VectorD  point, bool  accessFieldY  )

static

Performs a sinc interpolation on a specific point (x,y). The interpolation is done by adding the sinc-functions of every pixel of the field . Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied.

Parameters

ca	ComplexAmplitude for interpolation.
point	Position to interpolate in meters.
accessFieldY	If true the y field component will be interpolted otherwise the x field component.

Returns

Result of operation.

SincInterpolationOpt()

Complex SincInterpolationOpt	(	ComplexAmplitude	ca,
		VectorD	point,
		bool	accessFieldY
	)

Performs a sinc interpolation on a specific point (x,y). The interpolation is done by adding the sinc-functions of every pixel of the field . Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied. The interpolation is optimized for interpolations that work row by row and from the left sampling point to the right sampling point.

Parameters

ca	ComplexAmplitude for interpolation.
point	Position to interpolate in meters.
accessFieldY	If true the y field component will be interpolted otherwise the x field component.

Returns

Result of operation.

TruncatedSincInterpolation()

static Complex TruncatedSincInterpolation ( ComplexAmplitude  ca, VectorD  point, bool  accessFieldY  )

static

Performs a truncated sinc interpolation on a specific point (x,y). The interpolation is done between 6 neighbour points . Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied.

Parameters

ca	ComplexAmplitude for interpolation.
point	Position to interpolate in meters.
accessFieldY	If true the y field component will be interpolted otherwise the x field component.

Returns

Result of operation.

TruncatedSincInterpolationOpt()

Complex TruncatedSincInterpolationOpt	(	ComplexAmplitude	ca,
		VectorD	point,
		bool	accessFieldY
	)

Performs a truncated sinc interpolation on a specific point (x,y). The interpolation is done between 6 neighbour points . Only the amplitude and phase aberrations are interpolated. After interpolation the spherical phase factor is multiplied. The interpolation is optimized for interpolations that work row by row and from the left sampling point to the right sampling point.

Parameters

ca	ComplexAmplitude for interpolation.
point	Position to interpolate in meters.
accessFieldY	If true the y field component will be interpolted otherwise the x field component.

Returns

Result of operation.