This class is subject to change. Programs using this class may require changes with a new version of VirtualLab.
This class contains static member functions for interpolating a complex amplitude to another sampling grid. More...

Static Public Member Functions
static SamplingParameters	CalculateSamplingParametersForCoordinateTransformation (Matrix2x2D trafoMatrix, SamplingParameters oldSamplingParameters)
	Method for calculating sampling parameters for a field which will undergo a 2D coordinate transformation. More...

static ComplexAmplitude	DiscreteOversampling (ComplexAmplitude ca, Vector factor)
	Inserts zero points between sampling points. More...

static ComplexAmplitude	Interpolation (ComplexAmplitude ca, SamplingParameters samplingParameters, VectorD zeroPoint, InterpolationMethod interpolationMethod)
	Interpolates a ComplexAmplitude using the specified interpolation method. It is possible to interpolate a not centered part of the ComplexAmplitude using the zeroPoint parameter. More...

static ComplexAmplitude	ProfileExtractionCoordsPhysical (ComplexAmplitude ca, VectorD startPointPhys, VectorD endPointPhys, int samplingPoints, InterpolationMethod interpolationMethod, bool removeSphericalPhase)
	Extracts a one-dimensional profile from a two-dimensional ComplexAmplitude. There are different interpolation methods supported. More...

static ComplexAmplitude	Rotation2D (ComplexAmplitude ca, Vector newSamplingPoints, double phi, InterpolationMethod interpolationMethod)
	Rotates a ComplexAmplitude in the x-y-plane by angle \(\phi\). The rotation is calculated using the specified interpolation method. More...

static void	SampleAllAnalyticFunctionsAtField (ref ComplexAmplitude ca, InterpolationMethod interpolationMethod)
	Method that samples the lateral offset (via embedding, i.e. zero padding) which is stored at a field as well as its quadratic and linear phase function. More...

static void	SampleLateralOffsetFromAnalyticValuesAtField (ref ComplexAmplitude ca, bool sampleOtherAnalyticFunctionsToo, InterpolationMethod interpMethod=InterpolationMethod.SincFFT)
	Method that samples (via embedding, i.e. zero padding) the lateral offset stored at a given field. More...

static void	SampleLinearPhaseFromAnalyticFunctionAtField (ref ComplexAmplitude ca, InterpolationMethod interpolationMethod)
	Samples the linear phase function stored at a field and multiplies function and field values. More...

static void	SampleLinearPhaseFromDirectionVector (ref ComplexAmplitude ca, InterpolationMethod interpolationMethod)
	Samples the linear phase function stored at a field and multiplies function and field values. More...

static void	SampleQuadraticPhaseFromAnalyticFunctionAtField (ref ComplexAmplitude ca, InterpolationMethod interpolationMethod, bool enableAnalyticalLinearPhaseResultingFromOffset, long maximumNumberPixels=-1)
	Samples a quadratic phase from a given quadratic function and multiplies it with the given ComplexAmplitude More...

static ComplexAmplitude	SampleSphericalPhaseFactor (ComplexAmplitude ca, bool useSamplingWarning=false)
	ComplexAmplitude can contain a separate spherical phase factor. Thus the phase of the sampled complex amplitude can be undersampled. This function resamples the complex amplitude in a way that complies to Nyquist criterion and separate spherical phase is no longer needed. More...

static HarmonicFieldBase	SampleSphericalPhaseFactor (HarmonicFieldBase field, bool useSamplingWarning=false)
	A Harmonic Field can contain a separate spherical phase factor. Thus the phase of the sampled complex amplitude can be undersampled. This function resamples the harmonic field in a way that complies to Nyquist criterion and separate spherical phase factor is no longer needed. More...

static HarmonicFieldsSet	SampleSphericalPhaseFactor (HarmonicFieldsSet hfs, bool useSamplingWarning=false)
	The member fields of a HarmonicFieldsSet can contain a separate spherical phase factor. Thus the phase of the sampled complex amplitude can be undersampled. This function resamples the complex amplitude in a way that complies to Nyquist criterion and separate spherical phase is no longer needed. More...

static ComplexAmplitude	TryToDecreaseSamplingEffort (ComplexAmplitude caIn, bool truncateFieldSize, double minimumOversamplingFactor, double truncationInflationFactor, double powerPortionForEvaluation)
	Method which tries to decrease the sampling effort for a ComplexAmplitude. More...

Detailed Description

This class is subject to change. Programs using this class may require changes with a new version of VirtualLab.
This class contains static member functions for interpolating a complex amplitude to another sampling grid.

Member Function Documentation

◆ CalculateSamplingParametersForCoordinateTransformation()

static SamplingParameters CalculateSamplingParametersForCoordinateTransformation	(	Matrix2x2D	trafoMatrix,
		SamplingParameters	oldSamplingParameters
	)

static

Method for calculating sampling parameters for a field which will undergo a 2D coordinate transformation.

Parameters

trafoMatrix	The matrix which describes the transform.
oldSamplingParameters	Old sampling parameters of the field to be transformed.

Returns: The new sampling parameters after the transform.

◆ DiscreteOversampling()

static ComplexAmplitude DiscreteOversampling	(	ComplexAmplitude	ca,
		Vector	factor
	)

static

Inserts zero points between sampling points.

Parameters

ca	ComplexAmplitude operation is applied to.
factor	E.g.: Factor two means, that every second sampling point is zero.

Returns: Result of operation.

◆ Interpolation()

static ComplexAmplitude Interpolation	(	ComplexAmplitude	ca,
		SamplingParameters	samplingParameters,
		VectorD	zeroPoint,
		InterpolationMethod	interpolationMethod
	)

static

Interpolates a ComplexAmplitude using the specified interpolation method. It is possible to interpolate a not centered part of the ComplexAmplitude using the zeroPoint parameter.

Parameters

ca	ComplexAmplitude to interpolate.
samplingParameters	Contains the new number of sampling points and the sampling distance of the ComplexAmplitude after interpolation.
zeroPoint	The zero point parameter specifies the position of the center of the ComplexAmplitude after interpolation.
interpolationMethod	Interpolation Method.

Returns: Result of operation.

◆ ProfileExtractionCoordsPhysical()

static ComplexAmplitude ProfileExtractionCoordsPhysical	(	ComplexAmplitude	ca,
		VectorD	startPointPhys,
		VectorD	endPointPhys,
		int	samplingPoints,
		InterpolationMethod	interpolationMethod,
		bool	removeSphericalPhase
	)

static

Extracts a one-dimensional profile from a two-dimensional ComplexAmplitude. There are different interpolation methods supported.

Parameters

ca	ComplexAmplitude to extract a profile from.
startPointPhys	Start point of the one-dimensional profile in physical coordinates.
endPointPhys	End point of the one-dimensional profile in physical coordinates.
samplingPoints	Number of sampling points of the profile including the start and the end point. So the minimum number is 2.
interpolationMethod	Interpolation method for extraction.
removeSphericalPhase	Additional spherical phase is removed from profile line.

Returns: Result of operation.

◆ Rotation2D()

static ComplexAmplitude Rotation2D	(	ComplexAmplitude	ca,
		Vector	newSamplingPoints,
		double	phi,
		InterpolationMethod	interpolationMethod
	)

static

Rotates a ComplexAmplitude in the x-y-plane by angle \(\phi\). The rotation is calculated using the specified interpolation method.

Parameters

ca	ComplexAmplitude to rotate.
newSamplingPoints	The number of sampling points the rotated field shall have.
phi	Rotation angle in radians.
interpolationMethod	Specifies with which algorithm the point interpolation is done.

Returns: Result of operation.

◆ SampleAllAnalyticFunctionsAtField()

static void SampleAllAnalyticFunctionsAtField	(	ref ComplexAmplitude	ca,
		InterpolationMethod	interpolationMethod
	)

static

Method that samples the lateral offset (via embedding, i.e. zero padding) which is stored at a field as well as its quadratic and linear phase function.

Parameters

ca	Harmonic field whose analytic function parameters shall be sampled.
interpolationMethod	Interpolation method to be used for sampling the quadratic and the linear phase function.

◆ SampleLateralOffsetFromAnalyticValuesAtField()

static void SampleLateralOffsetFromAnalyticValuesAtField	(	ref ComplexAmplitude	ca,
		bool	sampleOtherAnalyticFunctionsToo,
		InterpolationMethod	interpMethod = `InterpolationMethod.SincFFT`
	)

static

Method that samples (via embedding, i.e. zero padding) the lateral offset stored at a given field.

Parameters

ca	Field whose offset shall be sampled.
sampleOtherAnalyticFunctionsToo	If `true`, the sampling of quadratic and linear phase functions will be ensured.
interpMethod	In case the parameter sampleOtherAnalyticFunctionsToo is `true`, the interpolation method for the sampling can be set here.

◆ SampleLinearPhaseFromAnalyticFunctionAtField()

static void SampleLinearPhaseFromAnalyticFunctionAtField	(	ref ComplexAmplitude	ca,
		InterpolationMethod	interpolationMethod
	)

static

Samples the linear phase function stored at a field and multiplies function and field values.

Parameters

ca	ComplexAmplitude to sample the linear phase on. Since this is a ref parameter, it will be modified by the function.
interpolationMethod	Method of interpolation if necessary

◆ SampleLinearPhaseFromDirectionVector()

static void SampleLinearPhaseFromDirectionVector	(	ref ComplexAmplitude	ca,
		InterpolationMethod	interpolationMethod
	)

static

Samples the linear phase function stored at a field and multiplies function and field values.

Parameters

ca	ComplexAmplitude to sample the linear phase on. Since this is a ref parameter, it will be modified by the function.
interpolationMethod	Method of interpolation if necessary

◆ SampleQuadraticPhaseFromAnalyticFunctionAtField()

static void SampleQuadraticPhaseFromAnalyticFunctionAtField	(	ref ComplexAmplitude	ca,
		InterpolationMethod	interpolationMethod,
		bool	enableAnalyticalLinearPhaseResultingFromOffset,
		long	maximumNumberPixels = `-1`
	)

static

Samples a quadratic phase from a given quadratic function and multiplies it with the given ComplexAmplitude

Parameters

ca	ComplexAmplitude to sample the quadratic phase on. Since this is a ref parameter, it will be modified by the function.
interpolationMethod	Method of interpolation if necessary
enableAnalyticalLinearPhaseResultingFromOffset	If true, the result may contain an additional analytical linear phase, which results from the quadratic phase if there is a lateral offset.
maximumNumberPixels	maximum number of pixels to use

◆ SampleSphericalPhaseFactor() [1/3]

static ComplexAmplitude SampleSphericalPhaseFactor	(	ComplexAmplitude	ca,
		bool	useSamplingWarning = `false`
	)

static

ComplexAmplitude can contain a separate spherical phase factor. Thus the phase of the sampled complex amplitude can be undersampled. This function resamples the complex amplitude in a way that complies to Nyquist criterion and separate spherical phase is no longer needed.

Parameters

ca	ComplexAmplitude to sample the spherical phase for.
useSamplingWarning	Obsolete parameter which has no effect.

Returns: Result of operation.

◆ SampleSphericalPhaseFactor() [2/3]

static HarmonicFieldBase SampleSphericalPhaseFactor	(	HarmonicFieldBase	field,
		bool	useSamplingWarning = `false`
	)

static

A Harmonic Field can contain a separate spherical phase factor. Thus the phase of the sampled complex amplitude can be undersampled. This function resamples the harmonic field in a way that complies to Nyquist criterion and separate spherical phase factor is no longer needed.

Parameters

field	ComplexAmplitude to sample the spherical phase for.
useSamplingWarning	TRUE: If the number of sampling points exceeds the warnings levels set in the Global Options dialog, a message box is shown asking the user whether to proceed. If the user decides to not generate such a large field, `null` is returned.

Returns: Result of operation.

◆ SampleSphericalPhaseFactor() [3/3]

static HarmonicFieldsSet SampleSphericalPhaseFactor	(	HarmonicFieldsSet	hfs,
		bool	useSamplingWarning = `false`
	)

static

The member fields of a HarmonicFieldsSet can contain a separate spherical phase factor. Thus the phase of the sampled complex amplitude can be undersampled. This function resamples the complex amplitude in a way that complies to Nyquist criterion and separate spherical phase is no longer needed.

Parameters

hfs	The HarmonicFieldsSet whose member fields shall be resampled according to the spherical phase factor.
useSamplingWarning	TRUE: If the number of sampling points exceeds the warnings levels set in the Global Options dialog, a message box is shown asking the user whether to proceed. If the user decides to not generate such a large field, `null` is returned.

Returns: Result of operation. Null if the sampling warning was shown and the user decided to not create such a large field.

◆ TryToDecreaseSamplingEffort()

static ComplexAmplitude TryToDecreaseSamplingEffort	(	ComplexAmplitude	caIn,
		bool	truncateFieldSize,
		double	minimumOversamplingFactor,
		double	truncationInflationFactor,
		double	powerPortionForEvaluation
	)

static

Method which tries to decrease the sampling effort for a ComplexAmplitude.

Parameters

caIn	ComplexAmplitude whose sampling shall be optimized.
truncateFieldSize	If `true`, a truncation of the field is tried.
minimumOversamplingFactor	Minimum oversampling factor, independent of the factor given in Globals. The larger value of both will be used.
truncationInflationFactor	If the truncation flag is `true`, this factor will be applied to the minimum detected field size.
powerPortionForEvaluation	the power portion that shall be used for evaluation in case of truncation. If truncateFieldSize is `false`, this parameter will be ignored.

Returns: A ComplexAmplitude which uses less sampling than the input if possible.

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ CalculateSamplingParametersForCoordinateTransformation()

◆ DiscreteOversampling()

◆ Interpolation()

◆ ProfileExtractionCoordsPhysical()

◆ Rotation2D()

◆ SampleAllAnalyticFunctionsAtField()

◆ SampleLateralOffsetFromAnalyticValuesAtField()

◆ SampleLinearPhaseFromAnalyticFunctionAtField()

◆ SampleLinearPhaseFromDirectionVector()

◆ SampleQuadraticPhaseFromAnalyticFunctionAtField()

◆ SampleSphericalPhaseFactor() [1/3]

◆ SampleSphericalPhaseFactor() [2/3]

◆ SampleSphericalPhaseFactor() [3/3]

◆ TryToDecreaseSamplingEffort()