This class is subject to change. Programs using this class may require changes with a new version of VirtualLab.
This class contains a number of static member functions performing well-known elementary wave propagation operators. In difference to the ElementaryPropagationOperators class all functions change number of sampling points and the sampling distance automatically the number of sampling points and the sampling distance to avoid numerical errors. Additionally some functions are provided that can estimate the necessary number of sampling points and the sampling distance to avoid numerical errors. More...

Static Public Member Functions
static ComplexAmplitude	FarFieldPropagation (ComplexAmplitude ca, double distance, Complex n, double accuracyFactor, bool automaticOutputFieldSizeShape, double outputFieldSizeFactor, VectorD outputFieldFieldSize, BasicParameter.eApertureShape outputFieldShape, double outputFieldBorderWidth, bool automaticOutputFieldSampling, double outputFieldSamplingFactor, int outputFieldEmbedFrameWidth, SamplingParameters outputFieldSamplingParameters, out bool areNumericalErrors, InterpolationMethod interpolationMethod, FarFieldPropagationMode farFieldPropagationMode, bool isParaxialApproximation, SpreadSheetObjectUsedIn usedIn)
	Performs a far field propagation without paraxial approximation. The far field approximation of the Rayleigh-Sommerfeld propagation is used. Just for paraxial wave the far field is the Fourier Transform of the waist of the wave. In general it is the Fourier Transform plus a coordinate transformation. If a propagation between two far field points is performs it is assumed that the SphericalPhaseRadius information is equal to the distance from the waist. More...

static HarmonicFieldsSet	FarFieldPropagation (HarmonicFieldsSet hfs, double distance, double accuracyFactor, bool automaticOutputFieldSizeShape, double outputFieldSizeFactor, VectorD outputFieldFieldSize, BasicParameter.eApertureShape outputFieldShape, double outputFieldBorderWidth, bool automaticOutputFieldSampling, double outputFieldSamplingFactor, int outputFieldEmbedFrameWidth, SamplingParameters outputFieldSamplingParameters, out bool areNumericalErrors, InterpolationMethod interpolationMethod, FarFieldPropagationMode farFieldPropagationMode, bool isParaxialApproximation, SpreadSheetObjectUsedIn usedIn)
	Performs a far field propagation without paraxial approximation. The far field approximation of the Rayleigh-Sommerfeld propagation is used. Just for paraxial wave the far field is the Fourier Transform of the waist of the wave. In general it is the Fourier Transform plus a coordinate transformation. If a propagation between two far field points is performs it is assumed that the SphericalPhaseRadius information is equal to the distance from the waist. More...

static ComplexAmplitude	Frt (ComplexAmplitude ca, double distance, bool automaticInputFieldSampling, double accuracyFactor, VectorD inputFieldSamplingDistance)
	Propagates given ComplexAmplitude by the specified distance by computing the Fresnel transform. The function can interpolate the complex amplitude by sinc-interpolation to avoid numerical errors. The function uses the WaveParameters of the object to perform an optimal propagation. If no WaveParameters is present function assumes that the harmonic field component is in the waist. Is a spherical phase factor is present the function tries to perform a Fresnel Propagation to the waist by a distance `-SphericalPhaseRadius` and a Fresnel Propagation by a distance `SphericalPhaseRadius + distance` to reduce numerical errors. More...

static ComplexAmplitude	Frt (ComplexAmplitude ca, double distance, Complex n, bool automaticInputFieldSampling, double inputFieldSamplingFactor, VectorD inputFieldSamplingDistance, bool automaticOutputFieldSizeShape, double outputFieldSizeFactor, VectorD outputFieldFieldSize, BasicParameter.eApertureShape outputFieldShape, double outputFieldBorderWidth, bool automaticOutputFieldSampling, double outputFieldSamplingFactor, int outputFieldEmbedFrameWidth, SamplingParameters outputFieldSamplingParameters, out bool areNumericalErrors)
	[AI] Propagates the given ComplexAmplitude by the specified distance by computing the Fresnel propagation. The function modifies the sampling distance of the input field specified in the inputFieldSamplingDistance parameter before the propagation in order to reduce numerical errors. The modification can be done by user or automatically Additionally the user may specify the output field sampling parameters and the field size, shape and broder width of the output field. Is the HasWaveParameters property false the function assumes that the harmonic field component is in the waist. Is a spherical phase factor is present the function tries to perform a Fresnel Propagation to the waist by a distance \(-SphericalPhaseRadius\) and a Fresnel Propagation by a distance \(SphericalPhaseRadius + distance\) to reduce numerical errors. More...

static ComplexAmplitude	Frt (ComplexAmplitude ca, double distance, Complex n, double accuracyFactor, out bool areNumericalErrors)
	Propagates given ComplexAmplitude by the specified distance by computing the Fresnel transform. The function can interpolate the complex amplitude by sinc-interpolation to avoid numerical errors. The function uses the WaveParameters of the object to perform an optimal propagation. If no WaveParameters is present function assumes that the harmonic field component is in the waist. Is a spherical phase factor is present the function tries to perform a Fresnel Propagation to the waist by a distance `-SphericalPhaseRadius` and a Fresnel Propagation by a distance `SphericalPhaseRadius + distance` to reduce numerical errors. The output field size of the propagated field is estimated depending on the WaveParameters. More...

static ComplexAmplitude	Frt (ComplexAmplitude ca, double distance, Complex n, VectorD outputFieldSize, double accuracyFactor, out bool areNumericalErrors)
	Propagates given ComplexAmplitude by the specified distance by computing the Fresnel transform. The function can interpolate the complex amplitude by sinc-interpolation to avoid numerical errors. The function uses the WaveParameters of the object to perform an optimal propagation. If no WaveParameters is present function assumes that the harmonic field component is in the waist. Is a spherical phase factor is present the function tries to perform a Fresnel Propagation to the waist by a distance `-SphericalPhaseRadius` and a Fresnel Propagation by a distance `SphericalPhaseRadius + distance` to reduce numerical errors. The desired output field size of the propagated field must be specified by the user. More...

static VectorD	GetFarFieldPropagationArraySize (ComplexAmplitude ca, double distance, Complex n, FarFieldPropagationMode farFieldPropagationMode, bool isParaxialApproximation)
	Calculates the optimal sampling distance and number of sampling points of the propagated field. The minimum number of sampling points per output plane diameter is 20 x 20. More...

static VectorD	GetFarFieldPropagationSamplingDistance (ComplexAmplitude ca, double distance, Complex n, FarFieldPropagationMode farFieldPropagationMode)
	Calculates the optimal sampling distance of the propagated field. The minimum number of sampling points per output plane diameter is 20 x 20. More...

static VectorD	GetFarFieldPropagationSamplingDistance (ComplexAmplitude ca, double distance, Complex n, FarFieldPropagationMode farFieldPropagationMode, bool isParaxialApproximation)
	Calculates the optimal sampling distance of the propagated field. The minimum number of sampling points per output plane diameter is 20 x 20. More...

static SamplingParameters	GetFarFieldPropagationSamplingParameters (ComplexAmplitude ca, double distance, Complex n, FarFieldPropagationMode farFieldPropagationMode, bool isParaxialApproximation)
	Return the outpuf field sampling parameters of the non paraxial far field propagation. More...

static SamplingParameters	GetFarFieldPropagationSamplingParameters (ComplexAmplitude ca, double distance, Complex n, VectorD diameterOutputField, FarFieldPropagationMode farFieldPropagationMode)
	Calculates the optimal sampling distance and number of sampling points of the propagated field. The minimum number of sampling points per output plane diameter is 20 x 20. More...

static SamplingParameters	GetFarFieldPropagationSamplingParameters (ComplexAmplitude ca, double distance, Complex n, VectorD diameterOutputField, FarFieldPropagationMode farFieldPropagationMode, bool isParaxialApproximation)
	Calculates the optimal sampling distance and number of sampling points of the propagated field. The minimum number of sampling points per output plane diameter is 20 x 20. More...

static SamplingParameters	GetFrtInputFieldSamplingParametersFromOutputFieldSize (ComplexAmplitude ca, double distance, Complex n, VectorD outputFieldSize, out bool useBackToWaist)
	Estimates the sampling parameters of the field to propagate so that the output field generated by the FRT will have the diameter as specified by the outputFieldSize parameter. In order to have small numerical errors of the simulation result the outputFieldSize should be so large that the most of the power (typically >99.99%) are included in this area. If a smaller output field size will be selected significant numerical errors may appear. The propagation can be done in a one step or two step process. In case of a one step propagation the propagation is directly done from the plane containing the complex amplitude into the target plane. The two step process tries to propagate back in the source plane of the spherical phase and to perform a second propagation step into the target plane. The two step process can be used if a spherical phase in present and if the required computer memory will be smaller as in case of a one step process. If the returned input field sampling parameters differ from the sampling parameters of the ComplexAmplitude to propagate an interpolation is required. The two step requires probably a further interpolation after the first interpolation step. More...

static void	GetFrtInputFieldSamplingParametersFromOutputFieldSize (SamplingParameters fieldSamplingParameters, bool hasSphericalPhase, double sphericalPhaseRadius, double wavelength, double distance, Complex n, VectorD outputFieldSize, double accuracyFactor, out bool perform2StepPropagation, out SamplingParameters samplingParametersStep1, out SamplingParameters samplingParametersStep2)
	Estimates the sampling parameters of the field to propagate so that the output field generated by the FRT will have the diameter as specified by the outputFieldSize parameter. In order to have small numerical errors of the simulation result the outputFieldSize should be so large that the most of the power (typically >99.99%) are included in this area. If a smaller output field size will be selected significant numerical errors may appear. The propagation can be done in a one step or two step process. In case of a one step propagation the propagation is directly done from the plane containing the complex amplitude into the target plane. The two step process tries to propagate back in the source plane of the spherical phase and to perform a second propagation step into the target plane. The two step process can be used if a spherical phase in present and if the required computer memory will be smaller as in case of a one step process. If the returned input field sampling parameters differ from the sampling parameters of the ComplexAmplitude to propagate an interpolation is required. The two step requires probably a further interpolation after the first interpolation step. More...

static SamplingParameters	GetFrtSamplingParameters (ComplexAmplitude ca, double distance, Complex n)
	Calculates the samplingparameters for the Fresnel Propagation to avoid numerical errors during the propagation. The function can decrease the sampling distance and increase the number of sampling points. More...

static SamplingParameters	GetFrtSamplingParameters (ComplexAmplitude ca, double distance, Complex n, double samplingFactor)
	Calculates the samplingparameters for the Fresnel Propagation to avoid numerical errors during the propagation. The function can decrease the sampling distance and increase the number of sampling points. More...

static SamplingParameters	GetRayleighSommerfeldConvolutionSamplingParameters (ComplexAmplitude ca, double distance, Complex n)
	Calculates the sampling parameters for the Rayleigh-Sommerfeld Convolution propagation to avoid numerical errors during the propagation. The function can decrease the sampling distance and increase the number of sampling points. The function takes into account possible spherical phase factors. More...

static SamplingParameters	GetRayleighSommerfeldConvolutionSamplingParameters (ComplexAmplitude ca, double distance, Complex n, double accuracyFactor)
	Calculates the sampling parameters for the Rayleigh-Sommerfeld Convolution propagation to avoid numerical errors during the propagation. The function can decrease the sampling distance and increase the number of sampling points. The function takes into account possible spherical phase factors. More...

static VectorD	GetRayleighSommerfeldSummationSamplingDistance (ComplexAmplitude ca, double distance, Complex n)
	Calculates the optimal sampling distance of the propagated field. More...

static SamplingParameters	GetSpwInputFieldSamplingParameters (ComplexAmplitude ca, double distance, Complex n, double accuracyFactor)
	Calculates the sampling parameters of the input field to propagate by the spectrum of plane waves propagation to avoid numerical errors during the propagation. The function can increase the number of sampling points and can decrease the sampling distance in case of a present spherical phase factor. The sampling parameters return the width (sampling points mulitplied by sampling distance divided by 2) of the wave after the SPW propagation. Is the width of the returned sampling parameters larger than the width of the ca object embed the field before the propagation. Is the width of the sampling parameters smaler than the width of the ca obect first propagate the field and then extract the necessary sampling points. The function uses the WaveParameters (if present) to approximate the changing of the wave width during the propagation. Is the HasWaveParameters property of the ComplexAmplitude object false then the function assumes the the object is in the waist and sets the WaveParameters. More...

static SamplingParameters	GetSpwInputFieldSamplingParametersFromOutputFieldSize (ComplexAmplitude ca, double distance, Complex n, VectorD outputFieldSize, double accuracyFactor)
	Estimates the sampling parameters of the field to propagate so that the output field generated by the SPW will have the diameter as specified by the outputFieldSize parameter. In order to have small numerical errors of the simulation result the outputFieldSize should be so large that the most of the power (typically >99.99%) are included in this area. If a smaller output field size will be selected significant numerical errors may appear. If the returned input field sampling parameters differ from the sampling parameters Complex Amplitude to propagate an interpolation is required. More...

static SamplingParameters	GetSpwOutputFieldSamplingParameters (ComplexAmplitude ca, double distance, Complex n, double accuracyFactor)
	Calculates the sampling parameters of the output field for the spectrum of plane waves propagation to avoid numerical errors during the propagation. The function can increase the number of sampling points and can decrease the sampling distance in case of a present spherical phase factor. The sampling parameters return the width (sampling points mulitplied by sampling distance divided by 2) of the wave after the SPW propagation. Is the width of the returned sampling parameters larger than the width of the ca object embed the field before the propagation. Is the width of the sampling parameters smaler than the width of the ca obect first propagate the field and then extract the necessary sampling points. The function uses the WaveParameters (if present) to approximate the changing of the wave width during the propagation. Is the HasWaveParameters property of the ComplexAmplitude object false then the function assumes the the object is in the waist and sets the WaveParameters. More...

static ComplexAmplitude	RayleighSommerfeldConvolution (ComplexAmplitude ca, double distance, bool automaticInputFieldSampling, double accuracyFactor, VectorD inputFieldSamplingDistance)
	Propagates the given ComplexAmplitude by the specified distance by a convolution of the complex amplitude and the propagation core (Rayleigh-Sommerfeld integral). The convolution is calculated in the frequency domain. The function can interpolate the complex amplitude by sinc-interpolation to avoid numerical errors. The ComplexAmplitude ca is changed during the propagation. More...

static ComplexAmplitude	RayleighSommerfeldConvolution (ComplexAmplitude ca, double distance, Complex n, bool automaticInputFieldSampling, double accuracyFactor, VectorD inputFieldSamplingDistance, bool automaticOutputFieldSizeShape, double outputFieldSizeFactor, VectorD outputFieldFieldSize, BasicParameter.eApertureShape outputFieldShape, double outputFieldBorderWidth, bool automaticOutputFieldSampling, double outputFieldSamplingFactor, int outputFieldEmbedFrameWidth, SamplingParameters outputFieldSamplingParameters, out bool areNumericalErrors)
	Propagates the given ComplexAmplitude by the specified distance by a convolution of the complex amplitude and the propagation core (Rayleigh-Sommerfeld integral). The convolution is calculated in the frequency domain. The function can interpolate the complex amplitude by sinc-interpolation to avoid numerical errors. The ComplexAmplitude ca is changed during the propagation. More...

static ComplexAmplitude	RayleighSommerfeldSummation (ComplexAmplitude ca, VectorD resultLateralOffset, double distance, bool automaticInputFieldSampling, double accuracyFactor, SamplingParameters inputFieldSamplingParameters, bool automaticOutputFieldSizeShape, double outputFieldSizeFactor, VectorD outputFieldFieldSize, BasicParameter.eApertureShape outputFieldShape, double outputFieldBorderWidth, bool automaticOutputFieldSampling, double outputFieldSamplingFactor, int outputFieldEmbedFrameWidth, SamplingParameters outputFieldSamplingParameters, Complex n, out Boolean areSamplingProblems)
	Propagates the given ComplexAmplitude by the specified distance by a convolution of the complex amplitude and the propagation core (Rayleigh-Sommerfeld integral). The convolution is calculated in the frequency domain. The ComplexAmplitude ca is changed during the propagation. The function ignores present WaveParameters. Because of this additional numerical errors may occure during the propagation. Use areSamplingProblems to check for numerical errors before propagating. More...

static ComplexAmplitude	Spw (ComplexAmplitude ca, double distance, bool automaticInputFieldSampling, double accuracyFactor, SamplingParameters inputFieldSamplingParameters)
	Propagates the given ComplexAmplitude by the specified distance by computing the Angular Spectrum of Plane Waves. The function can increase the number of sampling points to avoid numerical errors. The minimum embedding of the complex amplitude is determined by Globals.SamplingFactor. The function uses the WaveParameters of the object to provide a optimal propagation. Is the HasWaveParameters property false the function assumes that the harmonic field component is in the waist. More...

static ComplexAmplitude	Spw (ComplexAmplitude ca, double distance, Complex n, bool automaticInputFieldSampling, double accuracyFactor, SamplingParameters inputFieldSamplingParameters, bool automaticOutputFieldSizeShape, double outputFieldSizeFactor, VectorD outputFieldFieldSize, BasicParameter.eApertureShape outputFieldShape, double outputFieldBorderWidth, bool automaticOutputFieldSampling, double outputFieldSamplingFactor, int outputFieldEmbedFrameWidth, SamplingParameters outputFieldSamplingParameters, out bool areNumericalErrors)
	[AI] Propagates the given ComplexAmplitude by the specified distance by computing the Angular Spectrum of Plane Waves. The function modifies the sampling parameters of the input field specified in the inputFieldSamplingParameters parameter before the propagation in order to reduce numerical errors. The modification can be done by user or automatically Additionally the user may specify the output field sampling parameters and the field size, shape and broder width of the output field. Is the HasWaveParameters property false the function assumes that the harmonic field component is in the waist. More...

static ComplexAmplitude	Spw (ComplexAmplitude ca, double distance, Complex n, double accuracyFactor, out bool areNumericalErrors)
	Propagates the given ComplexAmplitude by the specified distance by computing the Angular Spectrum of Plane Waves. The function can increase the number of sampling points to avoid numerical errors. The minimum embedding of the complex amplitude is determined by Globals.SamplingFactor. The function uses the WaveParameters of the object to provide a optimal propagation. Is the HasWaveParameters property false the function assumes that the harmonic field component is in the waist. 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 a number of static member functions performing well-known elementary wave propagation operators. In difference to the ElementaryPropagationOperators class all functions change number of sampling points and the sampling distance automatically the number of sampling points and the sampling distance to avoid numerical errors. Additionally some functions are provided that can estimate the necessary number of sampling points and the sampling distance to avoid numerical errors.

Member Function Documentation

◆ FarFieldPropagation() [1/2]

static ComplexAmplitude FarFieldPropagation	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		double	accuracyFactor,
		bool	automaticOutputFieldSizeShape,
		double	outputFieldSizeFactor,
		VectorD	outputFieldFieldSize,
		BasicParameter.eApertureShape	outputFieldShape,
		double	outputFieldBorderWidth,
		bool	automaticOutputFieldSampling,
		double	outputFieldSamplingFactor,
		int	outputFieldEmbedFrameWidth,
		SamplingParameters	outputFieldSamplingParameters,
		out bool	areNumericalErrors,
		InterpolationMethod	interpolationMethod,
		FarFieldPropagationMode	farFieldPropagationMode,
		bool	isParaxialApproximation,
		SpreadSheetObjectUsedIn	usedIn
	)

static

Performs a far field propagation without paraxial approximation. The far field approximation of the Rayleigh-Sommerfeld propagation is used. Just for paraxial wave the far field is the Fourier Transform of the waist of the wave. In general it is the Fourier Transform plus a coordinate transformation. If a propagation between two far field points is performs it is assumed that the SphericalPhaseRadius information is equal to the distance from the waist.

Parameters

ca	ComplexAmplitude to propagate.
distance	Propagation distance.
n	Complex refractive index of media in which propagation is applied.
accuracyFactor	The accuracy factor. A larger factor leads to more accurate results but to higher computational effort.
automaticOutputFieldSizeShape	If true the output field size, shape and border width are determined by VirtualLab automatically. Otherwise the values can be specified using the outputFieldSize, outputFieldShape and outputFieldBorderWidth parameters.
outputFieldSizeFactor	In case of automaticOutputFieldSizeShape VirtualLab estimates the correct size of the propagated field. The resulting value is multiplied by this factor.
outputFieldFieldSize	The diameter of the output field in meters. The diameter is measured before the beginning of the border decay of amplitude.
outputFieldShape	The shape of the field.
outputFieldBorderWidth	The width of the borders of the field relative to the field diameter. The border width is measured between the begin of the amplitude decay and the zero position of the field.
automaticOutputFieldSampling	Enables automatic determination of the required array size and number of sampling points of the output field to minimize numerical errors. Additionally the user may use the outputFieldSamplingFactor to additionally increase or reduce the number of sampling points. The array size of the output field will be calculated from the estimation of the field size multiplied by the outputFieldSizeFactor plus the outputFieldBorderWidth multiplied by the field size plus the embedFrameWidth multiplied by the sampling distance. If automaticOutputFieldSampling is false the outputFieldSamplingParameters will be used.
outputFieldSamplingFactor	If automaticOutputFieldSampling is true VirtualLab estimates the number of sampling points of the output field and multiplies the value by outputFieldSamplingFactor.
outputFieldEmbedFrameWidth	If automaticOutputFieldSampling is `false` additionally a frame with dark pixels (amplitude equals zero) around the field can be added. This embed frame is required since the continuous field distribution can be reconstructed using a sinc interpolation. This interpolation will introduce small sized loops that are larger than the numerical field size. To take this side loops at least partially into account during the interpolation this embed frame is required. The extension of this frame in sampling points can be specified by this parameter.
outputFieldSamplingParameters	The sampling parameters of the output field. Normally these sampling parameters should be equal to the inputFieldSamplingParameters but the use may change it to any other value.
areNumericalErrors	Returns `true` if the user defined settings of the numerical accuracy parameter may caused numerical errors during the propagation. This is typically the case if numericalAccuracyFactor is smaller than one.
interpolationMethod	A coordinate transform is performed during the propagation. To do this an interpolation is necessary. This parameters specifies the used point wise interpolation method.
farFieldPropagationMode	The far field propagation mode tells the function if a propagation from the waist to the far field or vise versa should be performed.
isParaxialApproximation	If true the far field propagation will be calculated in non-paraxial approximation (Fraunhofer propagation).
usedIn	TODO

Returns: Result of operation.

◆ FarFieldPropagation() [2/2]

static HarmonicFieldsSet FarFieldPropagation	(	HarmonicFieldsSet	hfs,
		double	distance,
		double	accuracyFactor,
		bool	automaticOutputFieldSizeShape,
		double	outputFieldSizeFactor,
		VectorD	outputFieldFieldSize,
		BasicParameter.eApertureShape	outputFieldShape,
		double	outputFieldBorderWidth,
		bool	automaticOutputFieldSampling,
		double	outputFieldSamplingFactor,
		int	outputFieldEmbedFrameWidth,
		SamplingParameters	outputFieldSamplingParameters,
		out bool	areNumericalErrors,
		InterpolationMethod	interpolationMethod,
		FarFieldPropagationMode	farFieldPropagationMode,
		bool	isParaxialApproximation,
		SpreadSheetObjectUsedIn	usedIn
	)

static

Performs a far field propagation without paraxial approximation. The far field approximation of the Rayleigh-Sommerfeld propagation is used. Just for paraxial wave the far field is the Fourier Transform of the waist of the wave. In general it is the Fourier Transform plus a coordinate transformation. If a propagation between two far field points is performs it is assumed that the SphericalPhaseRadius information is equal to the distance from the waist.

Parameters

hfs	HarmonicFieldsSet to propagate.
distance	Propagation distance.
accuracyFactor	The accuracy factor. A larger factor leads to more accurate results but to higher computational effort.
automaticOutputFieldSizeShape	If true the output field size, shape and border width are determined by VirtualLab automatically. Otherwise the values can be specified using the outputFieldSize, outputFieldShape and outputFieldBorderWidth parameters.
outputFieldSizeFactor	In case of automaticOutputFieldSizeShape VirtualLab estimates the correct size of the propagated field. The resulting value is multiplied by this factor.
outputFieldFieldSize	The diameter of the output field in meters. The diameter is measured before the beginning of the border decay of amplitude.
outputFieldShape	The shape of the field.
outputFieldBorderWidth	The width of the borders of the field relative to the field diameter. The border width is measured between the begin of the amplitude decay and the zero position of the field.
automaticOutputFieldSampling	Enables automatic determination of the required array size and number of sampling points of the output field to minimize numerical errors. Additionally the user may use the outputFieldSamplingFactor to additionally increase or reduce the number of sampling points. The array size of the output field will be calculated from the estimation of the field size multiplied by the outputFieldSizeFactor plus the outputFieldBorderWidth multiplied by the field size plus the embedFrameWidth multiplied by the sampling distance. If automaticOutputFieldSampling is false the outputFieldSamplingParameters will be used.
outputFieldSamplingFactor	If automaticOutputFieldSampling is true VirtualLab estimates the number of sampling points of the output field and multiplies the value by outputFieldSamplingFactor.
outputFieldEmbedFrameWidth	If automaticOutputFieldSampling is `false` additionally a frame with dark pixels (amplitude equals zero) around the field can be added. This embed frame is required since the continuous field distribution can be reconstructed using a sinc interpolation. This interpolation will introduce small sized loops that are larger than the numerical field size. To take this side loops at least partially into account during the interpolation this embed frame is required. The extension of this frame in sampling points can be specified by this parameter.
outputFieldSamplingParameters	The sampling parameters of the output field. Normally these sampling parameters should be equal to the inputFieldSamplingParameters but the use may change it to any other value.
areNumericalErrors	Returns `true` if the user defined settings of the numerical accuracy parameter may caused numerical errors during the propagation. This is typically the case if numericalAccuracyFactor is smaller than one.
interpolationMethod	A coordinate transform is performed during the propagation. To do this an interpolation is necessary. This parameters specifies the used point wise interpolation method.
farFieldPropagationMode	The far field propagation mode tells the function if a propagation from the waist to the far field or vise versa should be performed.
isParaxialApproximation	If true the far field propagation will be calculated in non-paraxial approximation (Fraunhofer propagation).
usedIn	TODO

Returns: Result of operation.

◆ Frt() [1/4]

static ComplexAmplitude Frt	(	ComplexAmplitude	ca,
		double	distance,
		bool	automaticInputFieldSampling,
		double	accuracyFactor,
		VectorD	inputFieldSamplingDistance
	)

static

Propagates given ComplexAmplitude by the specified distance by computing the Fresnel transform. The function can interpolate the complex amplitude by sinc-interpolation to avoid numerical errors. The function uses the WaveParameters of the object to perform an optimal propagation. If no WaveParameters is present function assumes that the harmonic field component is in the waist. Is a spherical phase factor is present the function tries to perform a Fresnel Propagation to the waist by a distance -SphericalPhaseRadius and a Fresnel Propagation by a distance SphericalPhaseRadius + distance to reduce numerical errors.

Parameters

ca	ComplexAmplitude to be propagated.
distance	Propagation distance in meters.
automaticInputFieldSampling	Enables automatic determination of the required array size and number of sampling points of the input field to minimize numerical errors. Additionally the user may use the accuracyFactor to additionally increase or reduce the number of sampling points and array size. If automaticInputFieldSampling is false the inputFieldSamplingParameters will be used to modify the sampling parameters of the input field before the propagation.
accuracyFactor	The accuracy factor used in case of automatic input field sampling.
inputFieldSamplingDistance	The function modifies the sampling parameters of the input field before the propagation to the values specified here. This parameter allows to modify the input field sampling distance to user defined values. To get an estimation for input field sampling parameters please use the GetSpwSamplingParameters function.

Returns: Result of operation.

◆ Frt() [2/4]

static ComplexAmplitude Frt	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		bool	automaticInputFieldSampling,
		double	inputFieldSamplingFactor,
		VectorD	inputFieldSamplingDistance,
		bool	automaticOutputFieldSizeShape,
		double	outputFieldSizeFactor,
		VectorD	outputFieldFieldSize,
		BasicParameter.eApertureShape	outputFieldShape,
		double	outputFieldBorderWidth,
		bool	automaticOutputFieldSampling,
		double	outputFieldSamplingFactor,
		int	outputFieldEmbedFrameWidth,
		SamplingParameters	outputFieldSamplingParameters,
		out bool	areNumericalErrors
	)

static

[AI] Propagates the given ComplexAmplitude by the specified distance by computing the Fresnel propagation. The function modifies the sampling distance of the input field specified in the inputFieldSamplingDistance parameter before the propagation in order to reduce numerical errors. The modification can be done by user or automatically Additionally the user may specify the output field sampling parameters and the field size, shape and broder width of the output field. Is the HasWaveParameters property false the function assumes that the harmonic field component is in the waist. Is a spherical phase factor is present the function tries to perform a Fresnel Propagation to the waist by a distance \(-SphericalPhaseRadius\) and a Fresnel Propagation by a distance \(SphericalPhaseRadius + distance\) to reduce numerical errors.

Parameters

ca	The field to propagate.
distance	The propagation distance.
n	The refractive index of the homogeneous medium in that the field propagates.
automaticInputFieldSampling	Enables automatic determination of the required number of sampling points and sampling distance of the input field to minimize numerical errors. Additionally the user may use the inputFieldSamplingFactor to additionally increase or reduce the number of sampling points per array size. If automaticInputFieldSampling is false the inputFieldSamplingDistance will be used to modify the sampling parameters of the input field before the propagation.
inputFieldSamplingFactor	In case of automaticInputFieldSampling VirtualLab estimates the required number of sampling points per array size to minimize numerical errors. The resulting estimation of the number of sampling points will be mulitplied by this factor while the array siez is kept constant.
inputFieldSamplingDistance	The function modifies the sampling distance of the input field before the propagation to the value specified here. This parameter allows to modify the input field sampling distance to user defined values. To get an estimation for input field sampling distance please use the GetFrtSamplingParameters function.
automaticOutputFieldSizeShape	If true the output field size, shape and border width are determined by VirtualLab automatically. Otherwise the values can be specified using the outputFieldSize, outputFieldShape and outputFieldBorderWidth parameters.
outputFieldSizeFactor	In case of automaticOutputFieldSizeShape VirtualLab estimates the correct size of the propagated field. The resulting value is multiplied by this factor.
outputFieldFieldSize	The diameter of the output field in meters. The diameter is measured before the beginning of the border decay of amplitude.
outputFieldShape	The shape of the field.
outputFieldBorderWidth	The width of the borders of the field relative to the field diameter. The border width is measured between the begin of the amplitude decay and the zero position of the field.
automaticOutputFieldSampling	Enables automatic determination of the required array size and number of sampling points of the output field to minimize numerical errors. Additionally the user may use the outputFieldSamplingFactor to additionally increase or reduce the number of sampling points. The array size of the output field will be calculated from the estimation of the field size multiplied by the outputFieldSizeFactor plus the outputFieldBorderWidth multiplied by the field size plus the embedFrameWidth multiplid by the sampling distance. If automaticOutputFieldSampling is false the outputFieldSamplingParameters will be used.
outputFieldSamplingFactor	If automaticOutputFieldSampling is true VirtualLab estimates the number of sampling points of the output field and multiplies the value by outputFieldSamplingFactor.
outputFieldEmbedFrameWidth	If automaticOutputFieldSampling is `false` additionally a frame with dark pixels (amplitude equals zero) around the field can be added. This embed frame is required since the continuous field distribution can be reconstructed using a sinc interpolation. This interpolation will introduce small sized loops that are larger than the numerical field size. To take this side loops at least partially into account during the interpolation this embed frame is required. The extension of this frame in sampling points can be specified by this parameter.
outputFieldSamplingParameters	The sampling parameters of the output field. Normally these sampling parameters should be equal to the inputFieldSamplingParameters but the use may change it to any other value.
areNumericalErrors	True if the user defined settings of the input field sampling parameters may caused numerical errors during the propagation. This parameter is just set if automaticInputFieldSampling is false.

Returns: The propagated field.

◆ Frt() [3/4]

static ComplexAmplitude Frt	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		double	accuracyFactor,
		out bool	areNumericalErrors
	)

static

Propagates given ComplexAmplitude by the specified distance by computing the Fresnel transform. The function can interpolate the complex amplitude by sinc-interpolation to avoid numerical errors. The function uses the WaveParameters of the object to perform an optimal propagation. If no WaveParameters is present function assumes that the harmonic field component is in the waist. Is a spherical phase factor is present the function tries to perform a Fresnel Propagation to the waist by a distance -SphericalPhaseRadius and a Fresnel Propagation by a distance SphericalPhaseRadius + distance to reduce numerical errors. The output field size of the propagated field is estimated depending on the WaveParameters.

Parameters

ca	ComplexAmplitude to be propagated.
distance	Propagation distance in meters.
n	Complex refractive index of media in which propagation is applied.
accuracyFactor	VirtualLab estimates and modifies the number of sampling points of the input field before the propagation in order to reduce numerical errors. The estimated number of sampling points is multiplied by this factor to to increase or decrease numerical accuracy.
areNumericalErrors	True if numerical errors may appear in the propagated field. This warning appears if samplingFactor is smaller than one.

Returns: Result of operation.

◆ Frt() [4/4]

static ComplexAmplitude Frt	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		VectorD	outputFieldSize,
		double	accuracyFactor,
		out bool	areNumericalErrors
	)

static

Propagates given ComplexAmplitude by the specified distance by computing the Fresnel transform. The function can interpolate the complex amplitude by sinc-interpolation to avoid numerical errors. The function uses the WaveParameters of the object to perform an optimal propagation. If no WaveParameters is present function assumes that the harmonic field component is in the waist. Is a spherical phase factor is present the function tries to perform a Fresnel Propagation to the waist by a distance -SphericalPhaseRadius and a Fresnel Propagation by a distance SphericalPhaseRadius + distance to reduce numerical errors. The desired output field size of the propagated field must be specified by the user.

Parameters

ca	ComplexAmplitude to be propagated.
distance	Propagation distance in meters.
n	Complex refractive index of media in which propagation is applied.
outputFieldSize	The diameter of the output field of the propagation. It should be large enough to contain at least 99% of the power of the output field. the output field diameter is used to control the simulation accuracy of the propagation.
accuracyFactor	VirtualLab estimates and modifies the number of sampling points of the input field before the propagation in order to reduce numerical errors. The estimated number of sampling points is multiplied by this factor to to increase or decrease numerical accuracy.
areNumericalErrors	True if numerical errors may appear in the propagated field. This warning appears if samplingFactor is smaller than one.

Returns: Result of operation.

◆ GetFarFieldPropagationArraySize()

static VectorD GetFarFieldPropagationArraySize	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		FarFieldPropagationMode	farFieldPropagationMode,
		bool	isParaxialApproximation
	)

static

Calculates the optimal sampling distance and number of sampling points of the propagated field. The minimum number of sampling points per output plane diameter is 20 x 20.

Parameters

ca	ComplexAmplitude to propagate.
distance	Propagation distance.
n	Complex refractive index of media in which propagation is applied.
farFieldPropagationMode	The far field propagation mode tells the function if a propagation from the waist to the far field or vise versa should be performed.
isParaxialApproximation	If true the far field propagation will be calculated inparaxial approximation (Fraunhofer propagation).

Returns: The sampling distance and the number of sampling points of the propagated field.

◆ GetFarFieldPropagationSamplingDistance() [1/2]

static VectorD GetFarFieldPropagationSamplingDistance	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		FarFieldPropagationMode	farFieldPropagationMode
	)

static

Calculates the optimal sampling distance of the propagated field. The minimum number of sampling points per output plane diameter is 20 x 20.

Parameters

ca	ComplexAmplitude to propagate.
distance	Propagation distance.
n	Complex refractive index of media in which propagation is applied.
farFieldPropagationMode	The far field propagation mode tells the function if a propagation from the waist to the far field or vise versa should be performed.

Returns: The sampling distance of the propagated field.

◆ GetFarFieldPropagationSamplingDistance() [2/2]

static VectorD GetFarFieldPropagationSamplingDistance	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		FarFieldPropagationMode	farFieldPropagationMode,
		bool	isParaxialApproximation
	)

static

Calculates the optimal sampling distance of the propagated field. The minimum number of sampling points per output plane diameter is 20 x 20.

Parameters

ca	ComplexAmplitude to propagate.
distance	Propagation distance.
n	Complex refractive index of media in which propagation is applied.
farFieldPropagationMode	The far field propagation mode tells the function if a propagation from the waist to the far field or vise versa should be performed.
isParaxialApproximation	If true the far field propagation will be calculated inparaxial approximation (Fraunhofer propagation).

Returns: The sampling distance of the propagated field.

◆ GetFarFieldPropagationSamplingParameters() [1/3]

static SamplingParameters GetFarFieldPropagationSamplingParameters	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		FarFieldPropagationMode	farFieldPropagationMode,
		bool	isParaxialApproximation
	)

static

Return the outpuf field sampling parameters of the non paraxial far field propagation.

Parameters

ca	The complex amplitude to propagate.
distance	Propagation distance.
n	The refractive index of the mediuk containing the wave.
farFieldPropagationMode	The far field propagation mode tells the function if a propagation from the waist to the far field or vise versa should be performed.
isParaxialApproximation	If true the far field propagation will be calculated inparaxial approximation (Fraunhofer propagation).

Returns: The sampling parameters of the output field.

◆ GetFarFieldPropagationSamplingParameters() [2/3]

static SamplingParameters GetFarFieldPropagationSamplingParameters	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		VectorD	diameterOutputField,
		FarFieldPropagationMode	farFieldPropagationMode
	)

static

Calculates the optimal sampling distance and number of sampling points of the propagated field. The minimum number of sampling points per output plane diameter is 20 x 20.

Parameters

ca	ComplexAmplitude to propagate.
distance	Propagation distance.
n	Complex refractive index of media in which propagation is applied.
diameterOutputField	The diameter of the field in the output plane.
farFieldPropagationMode	The far field propagation mode tells the function if a propagation from the waist to the far field or vise versa should be performed.

Returns: The sampling distance and the number of sampling points of the propagated field.

◆ GetFarFieldPropagationSamplingParameters() [3/3]

static SamplingParameters GetFarFieldPropagationSamplingParameters	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		VectorD	diameterOutputField,
		FarFieldPropagationMode	farFieldPropagationMode,
		bool	isParaxialApproximation
	)

static

Calculates the optimal sampling distance and number of sampling points of the propagated field. The minimum number of sampling points per output plane diameter is 20 x 20.

Parameters

ca	ComplexAmplitude to propagate.
distance	Propagation distance.
n	Complex refractive index of media in which propagation is applied.
diameterOutputField	The diameter of the field in the output plane.
farFieldPropagationMode	The far field propagation mode tells the function if a propagation from the waist to the far field or vise versa should be performed.
isParaxialApproximation	If true the far field propagation will be calculated inparaxial approximation (Fraunhofer propagation).

Returns: The sampling distance and the number of sampling points of the propagated field.

◆ GetFrtInputFieldSamplingParametersFromOutputFieldSize() [1/2]

static SamplingParameters GetFrtInputFieldSamplingParametersFromOutputFieldSize	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		VectorD	outputFieldSize,
		out bool	useBackToWaist
	)

static

Estimates the sampling parameters of the field to propagate so that the output field generated by the FRT will have the diameter as specified by the outputFieldSize parameter. In order to have small numerical errors of the simulation result the outputFieldSize should be so large that the most of the power (typically >99.99%) are included in this area. If a smaller output field size will be selected significant numerical errors may appear. The propagation can be done in a one step or two step process. In case of a one step propagation the propagation is directly done from the plane containing the complex amplitude into the target plane. The two step process tries to propagate back in the source plane of the spherical phase and to perform a second propagation step into the target plane. The two step process can be used if a spherical phase in present and if the required computer memory will be smaller as in case of a one step process. If the returned input field sampling parameters differ from the sampling parameters of the ComplexAmplitude to propagate an interpolation is required. The two step requires probably a further interpolation after the first interpolation step.

Parameters

ca	Complex Amplitude to propagate by FRT.
distance	Propagation distance of the FRT.
n	Refractive index of the medium containing the complex amplitude.
outputFieldSize	Desired diameter of the propagated field (output field). Please take into account that this parameter should give an good estimation of the physical field size of the propagated field.
useBackToWaist	If true a two step propagation should be used (see above)

Returns: The sampling parameters of the field to propagated. If these sampling parameters differ from the parameters of the ca an interpolation must be done before the start of the FRT propagation.

◆ GetFrtInputFieldSamplingParametersFromOutputFieldSize() [2/2]

static void GetFrtInputFieldSamplingParametersFromOutputFieldSize	(	SamplingParameters	fieldSamplingParameters,
		bool	hasSphericalPhase,
		double	sphericalPhaseRadius,
		double	wavelength,
		double	distance,
		Complex	n,
		VectorD	outputFieldSize,
		double	accuracyFactor,
		out bool	perform2StepPropagation,
		out SamplingParameters	samplingParametersStep1,
		out SamplingParameters	samplingParametersStep2
	)

static

Estimates the sampling parameters of the field to propagate so that the output field generated by the FRT will have the diameter as specified by the outputFieldSize parameter. In order to have small numerical errors of the simulation result the outputFieldSize should be so large that the most of the power (typically >99.99%) are included in this area. If a smaller output field size will be selected significant numerical errors may appear. The propagation can be done in a one step or two step process. In case of a one step propagation the propagation is directly done from the plane containing the complex amplitude into the target plane. The two step process tries to propagate back in the source plane of the spherical phase and to perform a second propagation step into the target plane. The two step process can be used if a spherical phase in present and if the required computer memory will be smaller as in case of a one step process. If the returned input field sampling parameters differ from the sampling parameters of the ComplexAmplitude to propagate an interpolation is required. The two step requires probably a further interpolation after the first interpolation step.

Parameters

fieldSamplingParameters	The sampling parameters of the complex amplitude to propagate.
hasSphericalPhase	Indicates if the complex amplitude to propagate contains a spherical phase radius.
sphericalPhaseRadius	The spherical phase radius of the complex amplitude to propagate.
wavelength	The wavelength of the complex amplitude to propagate.
distance	The propagation distance. This means the distance from the plane containing the complex amplitude to propagate to the target plane.
n	The complex refractive index of the homogeneous medium containing the complex amplitude to propagate.
outputFieldSize	The desired diameter of the output field. The output field size should by huge enough so that it will contain more than 99% of the power of the field. Otherwise numerical errors may appear.
accuracyFactor	The accuracy factor is just used for the two step propagation (see above). For the back propagation into the source plane of the spherical phase the field size in this plane must be estimated. The estimated field size will be multiplied by this accuracy factor.
perform2StepPropagation	If true a two step propagation should be used (see above).
samplingParametersStep1	The required sampling parameters of the complex amplitude of the first propagations step. The complex amplitude to propagate must be interpolated to this sampling parameters before starting the first propagation step.
samplingParametersStep2	The required sampling parameters of the complex amplitude of the second propagations step. The resulting complex amplitude after the first propagation step must be interpolated to this sampling parameters before starting the second step. If perform2StepPropagation is false no second propagation step is required and null will be returned.

◆ GetFrtSamplingParameters() [1/2]

static SamplingParameters GetFrtSamplingParameters	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n
	)

static

Calculates the samplingparameters for the Fresnel Propagation to avoid numerical errors during the propagation. The function can decrease the sampling distance and increase the number of sampling points.

Parameters

ca	Complex amplitude to propagate.
distance	Propagation distance.
n	Refractive index of the homogeneous medium.

Returns: Sampling parameters.

◆ GetFrtSamplingParameters() [2/2]

static SamplingParameters GetFrtSamplingParameters	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		double	samplingFactor
	)

static

Calculates the samplingparameters for the Fresnel Propagation to avoid numerical errors during the propagation. The function can decrease the sampling distance and increase the number of sampling points.

Parameters

ca	Complex amplitude to propagate.
distance	Propagation distance.
n	Refractive index of the homogeneous medium.
samplingFactor	VirtualLab estimates and modifies the number of sampling points and sampling distance of the input field before the propagation in order to reduce numerical errors. The estimated number of sampling points is multiplied by this factor to to increase or decrease numerical accuracy.

Returns: Sampling parameters.

◆ GetRayleighSommerfeldConvolutionSamplingParameters() [1/2]

static SamplingParameters GetRayleighSommerfeldConvolutionSamplingParameters	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n
	)

static

Calculates the sampling parameters for the Rayleigh-Sommerfeld Convolution propagation to avoid numerical errors during the propagation. The function can decrease the sampling distance and increase the number of sampling points. The function takes into account possible spherical phase factors.

Parameters

ca	Complex amplitude to propagate.
distance	Propagation distance.
n	Refractive index of the homogeneous medium.

Returns: Sampling parameters.

◆ GetRayleighSommerfeldConvolutionSamplingParameters() [2/2]

static SamplingParameters GetRayleighSommerfeldConvolutionSamplingParameters	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		double	accuracyFactor
	)

static

Calculates the sampling parameters for the Rayleigh-Sommerfeld Convolution propagation to avoid numerical errors during the propagation. The function can decrease the sampling distance and increase the number of sampling points. The function takes into account possible spherical phase factors.

Parameters

ca	Complex amplitude to propagate.
distance	Propagation distance.
n	Refractive index of the homogeneous medium.
accuracyFactor	VirtualLab estimates the numerical parameters of the input field to propagate in order to reduce numerical errors. The estimated number of sampling points is multiplied by this factor to to increase or decrease numerical accuracy.

Returns: Sampling parameters.

◆ GetRayleighSommerfeldSummationSamplingDistance()

static VectorD GetRayleighSommerfeldSummationSamplingDistance	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n
	)

static

Calculates the optimal sampling distance of the propagated field.

Parameters

ca	ComplexAmplitude to propagate.
distance	Propagation distance.
n	Complex refractive index of media in which propagation is applied.

Returns: Result of operation.

◆ GetSpwInputFieldSamplingParameters()

static SamplingParameters GetSpwInputFieldSamplingParameters	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		double	accuracyFactor
	)

static

Calculates the sampling parameters of the input field to propagate by the spectrum of plane waves propagation to avoid numerical errors during the propagation. The function can increase the number of sampling points and can decrease the sampling distance in case of a present spherical phase factor. The sampling parameters return the width (sampling points mulitplied by sampling distance divided by 2) of the wave after the SPW propagation. Is the width of the returned sampling parameters larger than the width of the ca object embed the field before the propagation. Is the width of the sampling parameters smaler than the width of the ca obect first propagate the field and then extract the necessary sampling points. The function uses the WaveParameters (if present) to approximate the changing of the wave width during the propagation. Is the HasWaveParameters property of the ComplexAmplitude object false then the function assumes the the object is in the waist and sets the WaveParameters.

Parameters

ca	Complex amplitude component to propagate. Has to be a harmonic field component.
distance	Propagation distance.
n	Refractive index of the homogeneous medium.
accuracyFactor	The accuracy factor.

Returns: Sampling parameters.

◆ GetSpwInputFieldSamplingParametersFromOutputFieldSize()

static SamplingParameters GetSpwInputFieldSamplingParametersFromOutputFieldSize	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		VectorD	outputFieldSize,
		double	accuracyFactor
	)

static

Estimates the sampling parameters of the field to propagate so that the output field generated by the SPW will have the diameter as specified by the outputFieldSize parameter. In order to have small numerical errors of the simulation result the outputFieldSize should be so large that the most of the power (typically >99.99%) are included in this area. If a smaller output field size will be selected significant numerical errors may appear. If the returned input field sampling parameters differ from the sampling parameters Complex Amplitude to propagate an interpolation is required.

Parameters

ca	Complex Amplitude to propagate by SPW.
distance	Propagation distance of the SPW.
n	Refractive index of the medium containing the complex amplitude.
outputFieldSize	Desired diameter of the propagated field (output field). Please take into account that this parameter should give an good estimation of the physical field size of the propagated field.
accuracyFactor	Increasing this factor to values larger than one will lead to more accurate simulation results during SPW propagation on the cost of memory and computational time. This parameter has just an effect if a spherical phase radius is set.

Returns: The sampling parameters of the field to propagated. If these sampling parameters differ from the parameters of the ca an interpolation must be done before the start of the FRT propagation.

◆ GetSpwOutputFieldSamplingParameters()

static SamplingParameters GetSpwOutputFieldSamplingParameters	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		double	accuracyFactor
	)

static

Calculates the sampling parameters of the output field for the spectrum of plane waves propagation to avoid numerical errors during the propagation. The function can increase the number of sampling points and can decrease the sampling distance in case of a present spherical phase factor. The sampling parameters return the width (sampling points mulitplied by sampling distance divided by 2) of the wave after the SPW propagation. Is the width of the returned sampling parameters larger than the width of the ca object embed the field before the propagation. Is the width of the sampling parameters smaler than the width of the ca obect first propagate the field and then extract the necessary sampling points. The function uses the WaveParameters (if present) to approximate the changing of the wave width during the propagation. Is the HasWaveParameters property of the ComplexAmplitude object false then the function assumes the the object is in the waist and sets the WaveParameters.

Parameters

ca	Complex amplitude component to propagate. Has to be a harmonic field component.
distance	Propagation distance.
n	Refractive index of the homogeneous medium.
accuracyFactor	The accuracy factor.

Returns: Sampling parameters.

◆ RayleighSommerfeldConvolution() [1/2]

static ComplexAmplitude RayleighSommerfeldConvolution	(	ComplexAmplitude	ca,
		double	distance,
		bool	automaticInputFieldSampling,
		double	accuracyFactor,
		VectorD	inputFieldSamplingDistance
	)

static

Propagates the given ComplexAmplitude by the specified distance by a convolution of the complex amplitude and the propagation core (Rayleigh-Sommerfeld integral). The convolution is calculated in the frequency domain. The function can interpolate the complex amplitude by sinc-interpolation to avoid numerical errors. The ComplexAmplitude ca is changed during the propagation.

Parameters

ca	ComplexAmplitude to be propagated.
distance	Propagation distance in meters.
automaticInputFieldSampling	Enables automatic determination of the required array size and number of sampling points of the input field to minimize numerical errors. Additionally the user may use the accuracyFactor to additionally increase or reduce the number of sampling points and array size. If automaticInputFieldSampling is false the inputFieldSamplingParameters will be used to modify the sampling parameters of the input field before the propagation.
accuracyFactor	The accuracy factor used in case of automatic input field sampling.
inputFieldSamplingDistance	The function modifies the sampling parameters of the input field before the propagation to the values specified here. This parameter allows to modify the input field sampling distance to user defined values. To get an estimation for input field sampling parameters please use the GetSpwSamplingParameters function.

Returns: Result of operation.

◆ RayleighSommerfeldConvolution() [2/2]

static ComplexAmplitude RayleighSommerfeldConvolution	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		bool	automaticInputFieldSampling,
		double	accuracyFactor,
		VectorD	inputFieldSamplingDistance,
		bool	automaticOutputFieldSizeShape,
		double	outputFieldSizeFactor,
		VectorD	outputFieldFieldSize,
		BasicParameter.eApertureShape	outputFieldShape,
		double	outputFieldBorderWidth,
		bool	automaticOutputFieldSampling,
		double	outputFieldSamplingFactor,
		int	outputFieldEmbedFrameWidth,
		SamplingParameters	outputFieldSamplingParameters,
		out bool	areNumericalErrors
	)

static

Propagates the given ComplexAmplitude by the specified distance by a convolution of the complex amplitude and the propagation core (Rayleigh-Sommerfeld integral). The convolution is calculated in the frequency domain. The function can interpolate the complex amplitude by sinc-interpolation to avoid numerical errors. The ComplexAmplitude ca is changed during the propagation.

Parameters

ca	ComplexAmplitude to be propagated.
distance	Propagation distance in meters.
n	Complex refractive index of media in which propagation is applied.
automaticInputFieldSampling	if set to `true` [automatic input field sampling].
accuracyFactor	The accuracy factor. A larger factor leads to more accurate results but to higher computational effort.
inputFieldSamplingDistance	The input field sampling distance.
automaticOutputFieldSizeShape	If true the output field size, shape and border width are determined by VirtualLab automatically. Otherwise the values can be specified using the outputFieldSize, outputFieldShape and outputFieldBorderWidth parameters.
outputFieldSizeFactor	In case of automaticOutputFieldSizeShape VirtualLab estimates the correct size of the propagated field. The resulting value is multiplied by this factor.
outputFieldFieldSize	The diameter of the output field in meters. The diameter is measured before the beginning of the border decay of amplitude.
outputFieldShape	The shape of the field.
outputFieldBorderWidth	The width of the borders of the field relative to the field diameter. The border width is measured between the begin of the amplitude decay and the zero position of the field.
automaticOutputFieldSampling	Enables automatic determination of the required array size and number of sampling points of the output field to minimize numerical errors. Additionally the user may use the outputFieldSamplingFactor to additionally increase or reduce the number of sampling points. The array size of the output field will be calculated from the estimation of the field size multiplied by the outputFieldSizeFactor plus the outputFieldBorderWidth multiplied by the field size plus the embedFrameWidth multiplid by the sampling distance. If automaticOutputFieldSampling is false the outputFieldSamplingParameters will be used.
outputFieldSamplingFactor	If automaticOutputFieldSampling is true VirtualLab estimates the number of sampling points of the output field and multiplies the value by outputFieldSamplingFactor.
outputFieldEmbedFrameWidth	If automaticOutputFieldSampling is `false` additionally a frame with dark pixels (amplitude equals zero) around the field can be added. This embed frame is required since the continuous field distribution can be reconstructed using a sinc interpolation. This interpolation will introduce small sized loops that are larger than the numerical field size. To take this side loops at least partially into account during the interpolation this embed frame is required. The extension of this frame in sampling points can be specified by this parameter.
outputFieldSamplingParameters	The sampling parameters of the output field. Normally these sampling parameters should be equal to the inputFieldSamplingParameters but the use may change it to any other value.
areNumericalErrors	Returns `true` if the user defined settings of the numerical accuracy parameter may caused numerical errors during the propagation. This is typically the case if numericalAccuracyFactor is smaller than one.

Returns: Result of operation.

◆ RayleighSommerfeldSummation()

static ComplexAmplitude RayleighSommerfeldSummation	(	ComplexAmplitude	ca,
		VectorD	resultLateralOffset,
		double	distance,
		bool	automaticInputFieldSampling,
		double	accuracyFactor,
		SamplingParameters	inputFieldSamplingParameters,
		bool	automaticOutputFieldSizeShape,
		double	outputFieldSizeFactor,
		VectorD	outputFieldFieldSize,
		BasicParameter.eApertureShape	outputFieldShape,
		double	outputFieldBorderWidth,
		bool	automaticOutputFieldSampling,
		double	outputFieldSamplingFactor,
		int	outputFieldEmbedFrameWidth,
		SamplingParameters	outputFieldSamplingParameters,
		Complex	n,
		out Boolean	areSamplingProblems
	)

static

Propagates the given ComplexAmplitude by the specified distance by a convolution of the complex amplitude and the propagation core (Rayleigh-Sommerfeld integral). The convolution is calculated in the frequency domain. The ComplexAmplitude ca is changed during the propagation. The function ignores present WaveParameters. Because of this additional numerical errors may occure during the propagation. Use areSamplingProblems to check for numerical errors before propagating.

Parameters

ca	ComplexAmplitude to propagate.
resultLateralOffset	Lateral offset of propagated field.
distance	Propagation distance.
automaticInputFieldSampling	if set to `true` [automatic input field sampling].
accuracyFactor	The accuracy factor.
inputFieldSamplingParameters	The input field sampling parameters.
automaticOutputFieldSizeShape	If true the output field size, shape and border width are determined by VirtualLab automatically. Otherwise the values can be specified using the outputFieldSize, outputFieldShape and outputFieldBorderWidth parameters.
outputFieldSizeFactor	In case of automaticOutputFieldSizeShape VirtualLab estimates the correct size of the propagated field. The resulting value is multiplied by this factor.
outputFieldFieldSize	The diameter of the output field in meters. The diameter is measured before the beginning of the border decay of amplitude.
outputFieldShape	The shape of the field.
outputFieldBorderWidth	The width of the borders of the field relative to the field diameter. The border width is measured between the beginn of the amplitude decay and the zero position of the field.
automaticOutputFieldSampling	Enables automatic determination of the required array size and number of sampling points of the output field to minimize numerical errors. Additionally the user may use the outputFieldSamplingFactor to additionally increase or reduce the number of sampling points. The array size of the output field will be calculated from the estimation of the field size multiplied by the outputFieldSizeFactor plus the outputFieldBorderWidth multiplied by the field size plus the embedFrameWidth multiplid by the sampling distance. If automaticOutputFieldSampling is false the outputFieldSamplingParameters will be used.
outputFieldSamplingFactor	If automaticOutputFieldSampling is true VirtualLab estimates the number of sampling points of the output field and mulitplies the value by outputFieldSamplingFactor.
outputFieldEmbedFrameWidth	If automaticOutputFieldSampling is `false` additionally a frame with dark pixels (amplitude equals zero) around the field can be added. This embed frame is required since the continuous field distribution can be reconstructed using a sinc interpolation. This interpolation will introduce small sized loops that are larger than the numerical field size. To take this side loops at least partially into account during the interpolation this embed frame is required. The extension of this frame in sampling points can be specified by this parameter.
outputFieldSamplingParameters	The sampling parameters of the output field. Normally these sampling parameters should be equal to the inputFieldSamplingParameters but the use may change it to any other value.
n	Complex refractive index of media in which propagation is applied.
areSamplingProblems	Out parameter indicating if sampling problems can occur in the propagated field.

Returns: Result of operation.

◆ Spw() [1/3]

static ComplexAmplitude Spw	(	ComplexAmplitude	ca,
		double	distance,
		bool	automaticInputFieldSampling,
		double	accuracyFactor,
		SamplingParameters	inputFieldSamplingParameters
	)

static

Propagates the given ComplexAmplitude by the specified distance by computing the Angular Spectrum of Plane Waves. The function can increase the number of sampling points to avoid numerical errors. The minimum embedding of the complex amplitude is determined by Globals.SamplingFactor. The function uses the WaveParameters of the object to provide a optimal propagation. Is the HasWaveParameters property false the function assumes that the harmonic field component is in the waist.

Parameters

ca	ComplexAmplitude to be propagated.
distance	Propagation distance in meters.
automaticInputFieldSampling	Enables automatic determination of the required array size and number of sampling points of the input field to minimize numerical errors. Additionally the user may use the accuracyFactor to additionally increase or reduce the number of sampling points and array size. If automaticInputFieldSampling is false the inputFieldSamplingParameters will be used to modify the sampling parameters of the input field before the propagation.
accuracyFactor	The accuracy factor used in case of automatic input field sampling.
inputFieldSamplingParameters	The function modifies the sampling parameters of the input field before the propagation to the values specified here. This parameter allows to modify the input field sampling parameters to user defined values. To get an estimation for input field sampling parameters please use the GetSpwSamplingParameters function.

Returns: Result of operation.

◆ Spw() [2/3]

static ComplexAmplitude Spw	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		bool	automaticInputFieldSampling,
		double	accuracyFactor,
		SamplingParameters	inputFieldSamplingParameters,
		bool	automaticOutputFieldSizeShape,
		double	outputFieldSizeFactor,
		VectorD	outputFieldFieldSize,
		BasicParameter.eApertureShape	outputFieldShape,
		double	outputFieldBorderWidth,
		bool	automaticOutputFieldSampling,
		double	outputFieldSamplingFactor,
		int	outputFieldEmbedFrameWidth,
		SamplingParameters	outputFieldSamplingParameters,
		out bool	areNumericalErrors
	)

static

[AI] Propagates the given ComplexAmplitude by the specified distance by computing the Angular Spectrum of Plane Waves. The function modifies the sampling parameters of the input field specified in the inputFieldSamplingParameters parameter before the propagation in order to reduce numerical errors. The modification can be done by user or automatically Additionally the user may specify the output field sampling parameters and the field size, shape and broder width of the output field. Is the HasWaveParameters property false the function assumes that the harmonic field component is in the waist.

Parameters

ca	The field to propagate.
distance	The propagation distance.
n	The refractive index of the homogeneous medium in that the field propagates.
automaticInputFieldSampling	Enables automatic determination of the required array size and number of sampling points of the input field to minimize numerical errors. Additionally the user may use the inputFieldSamplingFactor and inputFieldArraySizeFactor to additionally increase or reduce the number of sampling points and array size. If automaticInputFieldSampling is false the inputFieldSamplingParameters will be used to modify the sampling parameters of the input field before the propagation.
accuracyFactor	The accuracy factor.
inputFieldSamplingParameters	The function modifies the sampling parameters of the input field before the propagation to the values specified here. This parameter allows to modify the input field sampling parameters to user defined values. To get an estimation for input field sampling parameters please use the GetSpwSamplingParameters function.
automaticOutputFieldSizeShape	If true the output field size, shape and border width are determined by VirtualLab automatically. Otherwise the values can be specified using the outputFieldSize, outputFieldShape and outputFieldBorderWidth parameters.
outputFieldSizeFactor	In case of automaticOutputFieldSizeShape VirtualLab estimates the correct size of the propagated field. The resulting value is multiplied by this factor.
outputFieldFieldSize	The diameter of the output field in meters. The diameter is measured before the beginning of the border decay of amplitude.
outputFieldShape	The shape of the field.
outputFieldBorderWidth	The width of the borders of the field relative to the field diameter. The border width is measured between the begin of the amplitude decay and the zero position of the field.
automaticOutputFieldSampling	Enables automatic determination of the required array size and number of sampling points of the output field to minimize numerical errors. Additionally the user may use the outputFieldSamplingFactor to additionally increase or reduce the number of sampling points. The array size of the output field will be calculated from the estimation of the field size multiplied by the outputFieldSizeFactor plus the outputFieldBorderWidth multiplied by the field size plus the embedFrameWidth multiplid by the sampling distance. If automaticOutputFieldSampling is false the outputFieldSamplingParameters will be used.
outputFieldSamplingFactor	If automaticOutputFieldSampling is true VirtualLab estimates the number of sampling points of the output field and multiplies the value by outputFieldSamplingFactor.
outputFieldEmbedFrameWidth	If automaticOutputFieldSampling is `false` additionally a frame with dark pixels (amplitude equals zero) around the field can be added. This embed frame is required since the continuous field distribution can be reconstructed using a sinc interpolation. This interpolation will introduce small sized loops that are larger than the numerical field size. To take this side loops at least partially into account during the interpolation this embed frame is required. The extension of this frame in sampling points can be specified by this parameter.
outputFieldSamplingParameters	The sampling parameters of the output field. Normally these sampling parameters should be equal to the inputFieldSamplingParameters but the use may change it to any other value.
areNumericalErrors	True if the user defined settings of the input field sampling parameters may caused numerical errors during the propagation. This parameter is just set if automaticInputFieldSampling is false.

Returns: The propagated field.

◆ Spw() [3/3]

static ComplexAmplitude Spw	(	ComplexAmplitude	ca,
		double	distance,
		Complex	n,
		double	accuracyFactor,
		out bool	areNumericalErrors
	)

static

Propagates the given ComplexAmplitude by the specified distance by computing the Angular Spectrum of Plane Waves. The function can increase the number of sampling points to avoid numerical errors. The minimum embedding of the complex amplitude is determined by Globals.SamplingFactor. The function uses the WaveParameters of the object to provide a optimal propagation. Is the HasWaveParameters property false the function assumes that the harmonic field component is in the waist.

Parameters

ca	ComplexAmplitude to be propagated.
distance	Propagation distance in meters.
n	Complex refractive index of media in which propagation is applied.
accuracyFactor	VirtualLab estimates and modifies array size and number of sampling points of the input field before the propagation in order to reduce numerical errors. The estimated number of sampling points and the estimated array size is multiplied by this factor to increase or decrease numerical accuracy.
areNumericalErrors	True if numerical errors may appear in the propagated field. This warning appears if arraySizeFactor or SamplingFactor is smaller than one.

Returns: Result of operation.

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ FarFieldPropagation() [1/2]

◆ FarFieldPropagation() [2/2]

◆ Frt() [1/4]

◆ Frt() [2/4]

◆ Frt() [3/4]

◆ Frt() [4/4]

◆ GetFarFieldPropagationArraySize()

◆ GetFarFieldPropagationSamplingDistance() [1/2]

◆ GetFarFieldPropagationSamplingDistance() [2/2]

◆ GetFarFieldPropagationSamplingParameters() [1/3]

◆ GetFarFieldPropagationSamplingParameters() [2/3]

◆ GetFarFieldPropagationSamplingParameters() [3/3]

◆ GetFrtInputFieldSamplingParametersFromOutputFieldSize() [1/2]

◆ GetFrtInputFieldSamplingParametersFromOutputFieldSize() [2/2]

◆ GetFrtSamplingParameters() [1/2]

◆ GetFrtSamplingParameters() [2/2]

◆ GetRayleighSommerfeldConvolutionSamplingParameters() [1/2]

◆ GetRayleighSommerfeldConvolutionSamplingParameters() [2/2]

◆ GetRayleighSommerfeldSummationSamplingDistance()

◆ GetSpwInputFieldSamplingParameters()

◆ GetSpwInputFieldSamplingParametersFromOutputFieldSize()

◆ GetSpwOutputFieldSamplingParameters()

◆ RayleighSommerfeldConvolution() [1/2]

◆ RayleighSommerfeldConvolution() [2/2]

◆ RayleighSommerfeldSummation()

◆ Spw() [1/3]

◆ Spw() [2/3]

◆ Spw() [3/3]