Class ComplexAmplitude

Namespace

VirtualLabAPI.Core.FieldRepresentations

Assembly

VirtualLabAPI.dll

This class represents a complex amplitude of a wave (without time depending part) in a plane or a complex transmission function.
Both X and Y field components are stored. In general all functions are applied to both components.
This class is also used to represent globally polarized fields and transmissions.
It contains one or two ComplexField as mathematical representations for complex fields. See manual for details of physical interpretation.
The ComplexAmplitude class can contain some additional information about the radius (distance from the origin) of a spherical phase factor. Using this information field may contain a spherical phase factor that is undersampled. If the radius of the spherical phase factor is known, the whole complex amplitude at every point can be reconstructed. The radius of the spherical phase factor helps to reduce the number of sampling points. Functions that use the ComplexAmplitude class have to take into account this spherical phase information to avoid numerical errors.
Operators (\(a+b\), \(a-b\), \(a*b\) and \(a/b\)) can be used. Passing \(a\) or \(b\) as Complex is supported. \(a^b\) can be applied for pointwise power function: \(a[x,y] ^ b\) \(b\) must be Complex. Operator \(a|b\) is used for calculation of inner product of two Complex Amplitudes: \(a|b=\sum _{j=0}^{m}\sum _{i=0}^{n}a_{{i,j}}b_{{i,j}^{\star}}\) (\(z^{\star}\) means conjugation of complex number).

[Serializable]
public class ComplexAmplitude : HarmonicFieldBase, IDeserializationCallback, IDisposable, IDocument, IEquatable<IObjectBase>, ICloneable, ISerializable, IProvidesPositioningReferences

Inheritance

object

ObjectBase

SerializableObjectBase

ManualSerialization

FieldRepresentationObject

HarmonicFieldBase

ComplexAmplitude

Implements

IDeserializationCallback

IDisposable

IDocument

IEquatable<IObjectBase>

ICloneable

ISerializable

IProvidesPositioningReferences

Inherited Members

FieldRepresentationObject.EmbeddingMedium

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

Extension Methods

FileHandlingSupport.SaveCompressed(IStorableOnHDD, string, ListOfSavedViewSettings)

Constructors

ComplexAmplitude()

Constructs a globally polarized ComplexAmplitude using the wavelength defined in the GlobalOptions and 3×3 sampling points.

public ComplexAmplitude()

ComplexAmplitude(ComplexAmplitude)

Creates a clone of the given complex amplitude.

public ComplexAmplitude(ComplexAmplitude ca)

Parameters

ca ComplexAmplitude

The complex amplitude to be cloned.

ComplexAmplitude(ComplexField)

Constructs a globally polarized ComplexAmplitude using the wavelength defined in the GlobalOptions and the given ComplexField.

public ComplexAmplitude(ComplexField field)

Parameters

field ComplexField

Complex field used for initialization.

ComplexAmplitude(ComplexField, ComplexField)

Constructs a locally polarized ComplexAmplitude using the wavelength defined in the GlobalOptions and given Ex and Ey component.

public ComplexAmplitude(ComplexField xField, ComplexField yField)

Parameters

xField ComplexField

Ex component complex field.

yField ComplexField

Ey component complex field.

ComplexAmplitude(SamplingParameters, bool, bool)

Constructs a globally polarized ComplexAmplitude using the default wavelength from the GlobalOptions and given SamplingParameters.

public ComplexAmplitude(SamplingParameters samplingParameters, bool IsComplex, bool initializeValues = true)

Parameters

samplingParameters SamplingParameters

Sampling parameter of constructed field.

IsComplex bool

If true real and imaginary part are stored. If false only the real part is stored.

initializeValues bool

If this optional parameter is set to false, the field values are not initialized. Should be used only if the values are initialized immediately afterwards, but then performance is better.

ComplexAmplitude(SamplingParameters, PrecisionMode, bool, bool)

Constructs a globally polarized ComplexAmplitude using the wavelength defined in the GlobalOptions, and given SamplingParameters.

public ComplexAmplitude(SamplingParameters samplingParameters, PrecisionMode precision, bool IsComplex, bool initializeValues = true)

Parameters

samplingParameters SamplingParameters

Sampling parameter of constructed field.

precision PrecisionMode

Obsolete parameter.

IsComplex bool

If true real and imaginary part are stored. Else only the real part is stored.

initializeValues bool

If this optional parameter is set to false, the field values are not initialized. Should be used only if the values are initialized immediately afterwards, but then performance is better.

ComplexAmplitude(SamplingParameters, PrecisionMode, bool, Func<double, double, double>, ParallelizationType)

Constructs a globally polarized ComplexAmplitude using the wavelength defined in the GlobalOptions, and given SamplingParameters. Sampling points are initialized using given real function.

public ComplexAmplitude(SamplingParameters samplingParameters, PrecisionMode precision, bool IsComplex, Func<double, double, double> f, ParallelizationType parallelizationType = ParallelizationType.AutomaticMeasure)

Parameters

samplingParameters SamplingParameters

Sampling parameter of constructed field.

precision PrecisionMode

Obsolete and unused parameter.

IsComplex bool

If true real and imaginary part are stored but the imaginary part is zero because f is a real function. If false only the real part is stored.

f Func<double, double, double>

A method returning a double (the real part) and having two doubles (the physical coordinates) as input parameter.

parallelizationType ParallelizationType

Type of the parallelization. Set it to ParallelizationType.NoParallelization if the method passed by the function delegate is not thread-safe. Otherwise you can choose of the remaining parallelization types (ParallelizationType.AutomaticMeasure is the default).

ComplexAmplitude(SamplingParameters, PrecisionMode, Func<double, double, Complex>, ParallelizationType)

Constructs a globally polarized ComplexAmplitude using the wavelength defined in the GlobalOptions, and given SamplingParameters. Sampling points are initialized using given complex function.
The point (0 m; 0 m) will be placed in the center of the field.

public ComplexAmplitude(SamplingParameters samplingParameters, PrecisionMode precision, Func<double, double, Complex> f, ParallelizationType parallelizationType = ParallelizationType.AutomaticMeasure)

Parameters

samplingParameters SamplingParameters

Sampling parameters of constructed field.

precision PrecisionMode

Obsolete and unused parameter.

f Func<double, double, Complex>

A method returning a Complex (the field value) and having two doubles (the physical coordinates) as input parameter.

parallelizationType ParallelizationType

Type of the parallelization. Set it to ParallelizationType.NoParallelization if the method passed by the function delegate is not thread-safe. Otherwise you can choose of the remaining parallelization types (ParallelizationType.AutomaticMeasure is the default).

ComplexAmplitude(Vector, bool)

Constructs a globally polarized ComplexAmplitude using the wavelength defined in the GlobalOptions and the given number of sampling points.

public ComplexAmplitude(Vector SamplingPoints, bool initializeValues = true)

Parameters

SamplingPoints Vector

Number of sampling points.

initializeValues bool

If this optional parameter is set to false, the field values are not initialized. Should be used only if the values are initialized immediately afterwards, but then performance is better.

ComplexAmplitude(Vector, Complex)

Constructs a globally polarized ComplexAmplitude using the wavelength defined in the GlobalOptions and given number of sampling points. All sampling points are set to the given complex number.

public ComplexAmplitude(Vector SamplingPoints, Complex c)

Parameters

SamplingPoints Vector

Number of sampling points.

c Complex

Complex value all points are initialized to.

ComplexAmplitude(HomogeneousMedium)

Constructs a globally polarized ComplexAmplitude using the wavelength defined in the GlobalOptions and 3×3 sampling points.

public ComplexAmplitude(HomogeneousMedium embeddingMedium)

Parameters

embeddingMedium HomogeneousMedium

The embedding medium of the complex amplitude.

Fields

SamplingDistance

Distance between sampling points in meters.

public VectorD SamplingDistance

Field Value

VectorD

_sphericalFactorIsRemoved

indicates whether a spherical factor has been removed from the sampled data

protected bool _sphericalFactorIsRemoved

Field Value

bool

hasSphericalPhaseRadius

Shows if there are some additionally information about the distance of a spherical phase factor from its origin.

protected bool hasSphericalPhaseRadius

Field Value

bool

hasWaveParameters

If true then the object contains the additional wave parameters like waist width, distance from waist and Rayleigh length for both axis. This parameters are necessary for the propagation. This parameter can be only true if the type is HarmonicFieldComponent.

[NonSerialized]
protected bool hasWaveParameters

Field Value

bool

sphericalPhaseRadius

If there are additional information about the spherical phase (HasSphericalPhaseRadius is true) then this variable contains the radius (this is the distance from the origin) of the spherical phase.

protected double sphericalPhaseRadius

Field Value

double

wavelength

Wavelength in meters.

protected double wavelength

Field Value

double

Properties

CentralDirection

Get and set the central direction of the field. This means a normalized Vector3D which represents an analytically stored global linear phase. If the linear phase information is represented by this CentralDirection vector, it does not have to be sampled on the data which may reduce the sampling effort. The x and y component of the vector are related to k_x and k_y of the field while the sign of its z component is related to the flag PropagatesInPositiveZDirection.

public Vector3D CentralDirection { get; set; }

Property Value

Vector3D

ComplexAmplitudeType

Gets and sets the ComplexAmplitudeType (globally or locally polarized field, transmission, and so on) of this ComplexAmplitude object.

public ComplexAmplitudeType ComplexAmplitudeType { get; set; }

Property Value

ComplexAmplitudeType

CoordinateOffset

Offset of the physical sampling point coordinates.

public VectorD CoordinateOffset { get; set; }

Property Value

VectorD

Field

The complex field containing the scalar field of the globally polarized complex amplitude. In case of a locally polarized ComplexAmplitude, the Ex component is returned on get access. (Set access will raise an exception.)

public ComplexField Field { get; set; }

Property Value

ComplexField

FieldRepresentation

Returns field representation of this ComplexAmplitude.

public override FieldRepresentation FieldRepresentation { get; }

Property Value

FieldRepresentation

The field representation (globally or locally polarized field).

FieldX

The complex field containing the Ex component of the complex amplitude.

public ComplexField FieldX { get; set; }

Property Value

ComplexField

FieldY

The complex field containing the Ey component of the complex amplitude. In case of globally polarized ComplexAmplitude using this property will throw an exception.

public ComplexField FieldY { get; set; }

Property Value

ComplexField

FileExtension

File extension

public override string FileExtension { get; }

Property Value

string

HasSphericalPhaseRadius

Indicates whether there are additionally information about the distance of a spherical phase factor from its origin. The default setting after the initialization of a new complex amplitude is false.

public bool HasSphericalPhaseRadius { get; set; }

Property Value

bool

IsComplexAmplitudeField

Returns true if complex amplitudes represents a complex amplitude.

public bool IsComplexAmplitudeField { get; }

Property Value

bool

IsGloballyPolarizedField

Gets whether this instance represents a globally polarized field.

public bool IsGloballyPolarizedField { get; }

Property Value

bool

IsLocallyPolarized

Returns true if complex amplitude is locally polarized.

public bool IsLocallyPolarized { get; }

Property Value

bool

IsPeriodic

Specifies whether this complex amplitude is a periodic field or transmission.

public bool IsPeriodic { get; set; }

Property Value

bool

IsSpatial

Gets and sets whether the complex amplitudes are in spatial domain.

public override bool IsSpatial { get; set; }

Property Value

bool

IsSpectral

Gets and sets whether the complex amplitudes are in spectral domain.

public bool IsSpectral { get; set; }

Property Value

bool

IsTransmission

Returns true if this complex amplitude represents a transmission.

public bool IsTransmission { get; }

Property Value

bool

this[int, int, bool]

Gets or sets a Complex value on the specified position in the complex amplitude. The coordinate system of x and y is the same like for a ComplexField.

public Complex this[int x, int y, bool accessFieldY] { get; set; }

Parameters

x int

X position in pixels.

y int

Y position in pixels.

accessFieldY bool

If this parameter is true, the Ey component is accessed by the indexer. This is allowed for locally polarized ComplexAmplitudes only. If it is false, then the Ex component is accessed. For globally polarized ComplexAmplitudes this parameter has to be always false.

Property Value

Complex

Complex value at position (x, y).

JonesMatrix

Jones matrix for transmissions.

public Matrix2x2C JonesMatrix { get; set; }

Property Value

Matrix2x2C

JonesVector

Jones vector for globally polarized complex amplitude fields

public VectorC JonesVector { get; set; }

Property Value

VectorC

LinearPhaseFunction

Function that describes the linear phase (in geometrical values). Important: The coefficients have to refer to the geometric distances instead of the phase values. That means the parameters have the meaning of k_x/k and k_y/k resp. (with k = 2π⋅n/λ). Calculating phase values require a multiplication with k = 2π⋅n/λ.

public LinearFunction LinearPhaseFunction { get; set; }

Property Value

LinearFunction

MeasuredQuantityOfCoordinates

Gets the measured quantity of the coordinates (depends on the IsSpatial flag).

public MeasuredQuantity MeasuredQuantityOfCoordinates { get; }

Property Value

MeasuredQuantity

MeasuredQuantityOfFieldData

Gets the measured quantity of the field data (depends on the type of the complex amplitude).

public MeasuredQuantity MeasuredQuantityOfFieldData { get; }

Property Value

MeasuredQuantity

Medium

Property to get the medium the field is located in.

public HomogeneousMedium Medium { get; }

Property Value

HomogeneousMedium

MediumWavelength

Gets the medium wavelength of this ComplexAmplitude.

public double MediumWavelength { get; }

Property Value

double

PropagatesInPositiveZDirection

Is the sign of the z-component of the k-vector positive or not. This flag has meaning for harmonic fields only.

public override bool PropagatesInPositiveZDirection { get; set; }

Property Value

bool

QuadraticPhaseFunction

Public property to set and get the off-axis quadratic wave. Important: The coefficients have to refer to the geometric distances instead of the phase values. So the representation of a spherical wave with phase radius R would be (1/2R)*x^2 + (1/2R)*y^2 + R. Calculating phase values would require a multiplication with k = 2π⋅n/λ.

public QuadraticFunction QuadraticPhaseFunction { get; set; }

Property Value

QuadraticFunction

RefractiveIndex

Gets the complex refractive index of the embedding medium in which the ComplexAmplitude is defined.

public Complex RefractiveIndex { get; }

Property Value

Complex

SamplingDistanceOneD

Gets or sets sampling distance of a one-dimensional ComplexAmplitude.

public double SamplingDistanceOneD { get; set; }

Property Value

double

SamplingParameters

Sets and gets the sampling parameters of this ComplexAmplitude which include sampling distance and number of sampling points. Modification of this property performs equal to changing the parameters using the SamplingDistance and SamplingPoints properties.

public SamplingParameters SamplingParameters { get; set; }

Property Value

SamplingParameters

SamplingPoints

Number of sampling points of current complex amplitude. Setting a new number of sampling points will embed the sampling points in zero samples or extract the central samples.

public Vector SamplingPoints { get; set; }

Property Value

Vector

SamplingPointsOneD

Number of sampling points of one-dimensional field. An exception will be thrown if the field is two-dimensional.

public int SamplingPointsOneD { get; }

Property Value

int

SphericalPhaseRadius

If there is additional information about the spherical phase (HasSphericalPhaseRadius is true) this property returns the radius of the spherical equiphase surfaces, which is equal to the distance from the definition plane of this ComplexAmplitude to the center of the spherical wave front. If HasSphericalPhaseRadius is false, radius = Double.MaxValue is returned. This is similar to an infinite radius. Setting this property in case HasSphericalPhaseRadius is false will switch HasSphericalPhaseRadius to true. This property stores the information about an analytical spherical phase factor only, in order to reconstruct the complex amplitude, even if it is undersampled. Changing the spherical phase radius will have no effect on the sampled data but maybe an error free reconstruction of the complete complex amplitude will be impossible. To change the sampled spherical phase factor and the stored spherical phase radius at once use the functions MultiplySphericalPhaseFactor(double, CancellationToken?) and RemoveSphericalPhaseFactor(CancellationToken?) instead.

public double SphericalPhaseRadius { get; set; }

Property Value

double

Exceptions

ArgumentException

Thrown if the spherical phase radius is set to zero.

TypeOfDocument

Gets the type of the document. For a ComplexAmplitude, this depends on the ComplexAmplitudeType: either JonesMatrixTransmission or HarmonicFieldsSet.

public override DocumentType TypeOfDocument { get; }

Property Value

DocumentType

Wavelength

Sets or gets the vacuum wavelength of this ComplexAmplitude.

public double Wavelength { get; set; }

Property Value

double

Methods

AddEqual(ComplexAmplitude)

Adds a given ComplexAmplitude to this one taking into account the spherical phase radius. The result is stored in this ComplexAmplitude. Both operands must have same number of sampling points. Other parameters like sampling distance or wavelength will not be changed.

public void AddEqual(ComplexAmplitude ca)

Parameters

ca ComplexAmplitude

ComplexAmplitude to be added to current one.

AddEqual(Complex)

Adds a complex number to this ComplexAmplitude.

public void AddEqual(Complex c)

Parameters

c Complex

Complex number to be added.

AddWithResampling(ComplexAmplitude, ComplexAmplitude, InterpolationMethod, InterpolationMethod)

Checks both ComplexAmplitude operands for identical sampling parameters, does the interpolation if one or both operands have to be resampled, then the second ComplexAmplitude is added to the first ComplexAmplitude.

public static ComplexAmplitude AddWithResampling(ComplexAmplitude cac1, ComplexAmplitude cac2, InterpolationMethod method1, InterpolationMethod method2)

Parameters

cac1 ComplexAmplitude

First ComplexAmplitude operand.

cac2 ComplexAmplitude

Second ComplexAmplitude operand.

method1 InterpolationMethod

How to interpolate 1. operand, if it is a transmission

method2 InterpolationMethod

How to interpolate 2. operand, if it is a transmission

Returns

ComplexAmplitude

The resulting harmonic field.

ApplyAnalyticallyLinearPhaseToDataPoints_withoutResampling(CancellationToken)

public support method to apply the analytically linear phase value onto the data points

public void ApplyAnalyticallyLinearPhaseToDataPoints_withoutResampling(CancellationToken cancellationToken)

Parameters

cancellationToken CancellationToken

The token for cooperative task cancellation.

ApplyAnalyticallyQuadraticPhaseToDataPoints_withoutResampling(CancellationToken, bool)

public support method to apply the analytically quadratic phase value onto the data points

public void ApplyAnalyticallyQuadraticPhaseToDataPoints_withoutResampling(CancellationToken cancellationToken, bool enableAnalyticalLinearPhaseResultingFromOffset = false)

Parameters

cancellationToken CancellationToken

The token for cooperative task cancellation.

enableAnalyticalLinearPhaseResultingFromOffset bool

If true, the underlying CA may contain an additional analytical linear phase, which results from the quadratic phase if there is a lateral offset.

ApplyAperture(eApertureShape, double)

Applies an aperture function to the Complex Amplitude.

public void ApplyAperture(BasicParameter.eApertureShape shape, double absoluteEdgeWidth)

Parameters

shape BasicParameter.eApertureShape

The shape of the aperture to be applied.

absoluteEdgeWidth double

The absolute edge width to be applied.

ChangeFieldRepresentation(bool)

Changes field representation of this ComplexAmplitude, i.e. whether the field is complex.

public void ChangeFieldRepresentation(bool isComplex)

Parameters

isComplex bool

Whether this ComplexAmplitude should be changed to complex-valued data (true) or to real-valued data false.

ClipAmplitude(double)

Sets all amplitude values of this ComplexAmplitude greater than the clippingLevel to the clippingLevel.

public void ClipAmplitude(double clippingLevel)

Parameters

clippingLevel double

Maximal value of amplitude.

Clone()

Clones this ComplexAmplitude.

public override object Clone()

Returns

object

A deep copy of this complex amplitude.

Conjugate()

Conjugates this ComplexAmplitude.

public void Conjugate()

ConvertToLocallyPolarizedField()

Converts this instance to a locally polarized field (if this is not already the case).

public void ConvertToLocallyPolarizedField()

ConvoluteWithResampling(ComplexAmplitude, ComplexAmplitude, InterpolationMethod, InterpolationMethod)

Checks both ComplexAmplitude operands for identical sampling parameters, does the interpolation if one or both operands have to be resampled, then the convolution of both ComplexAmplitude operands is performed.

public static ComplexAmplitude ConvoluteWithResampling(ComplexAmplitude cac1, ComplexAmplitude cac2, InterpolationMethod method1, InterpolationMethod method2)

Parameters

cac1 ComplexAmplitude

First ComplexAmplitude operand.

cac2 ComplexAmplitude

Second ComplexAmplitude operand.

method1 InterpolationMethod

How to interpolate 1. operand, if it is a transmission.

method2 InterpolationMethod

How to interpolate 2. operand, if it is a transmission.

Returns

ComplexAmplitude

The resulting harmonic field.

Convolution(ComplexAmplitude, ComplexAmplitude)

Returns convolution of \(a\) and \(b\): Convolute(a, b) := ℱ⁻¹(ℱ(a) ⋅ ℱ(b)).

public static ComplexAmplitude Convolution(ComplexAmplitude cac1, ComplexAmplitude cac2)

Parameters

cac1 ComplexAmplitude

Operator \(a\).

cac2 ComplexAmplitude

Operator \(b\).

Returns

ComplexAmplitude

Result of operation.

DefaultField(ComplexAmplitudeType)

Gets a default field which can be used e.g. as initial value for both the Stored Lateral Field and Stored Complete Field light source.

public static ComplexAmplitude DefaultField(ComplexAmplitudeType fieldType = ComplexAmplitudeType.GloballyPolSpatialComplexAmplitudeField)

Parameters

fieldType ComplexAmplitudeType

Optional type of the field (transmission, spatial harmonic field and so on). If not specified, a globally polarized spatial field is generated. In case of a transmission a periodic transmission is returned.

Returns

ComplexAmplitude

A field with 5 × 5 sampling points and the given type.

DivEqual(ComplexAmplitude)

Divides this ComplexAmplitude by the given one taking into account the spherical phase radius. The result is stored in this ComplexAmplitude. Both operands must have same number of sampling points. Other parameters like sampling distance or wavelength will not be changed.

public void DivEqual(ComplexAmplitude ca)

Parameters

ca ComplexAmplitude

The ComplexAmplitude this one is divided by.

DivEqual(Complex)

Divides this ComplexAmplitude by given complex number.

public void DivEqual(Complex c)

Parameters

c Complex

Complex number this ComplexAmplitude is to be divided by.

DivideWithResampling(ComplexAmplitude, ComplexAmplitude, InterpolationMethod, InterpolationMethod)

Checks both ComplexAmplitude operands for identical sampling parameters, does the interpolation if one or both operands have to be resampled, then the first ComplexAmplitude is divided by the second ComplexAmplitude.

public static ComplexAmplitude DivideWithResampling(ComplexAmplitude cac1, ComplexAmplitude cac2, InterpolationMethod method1, InterpolationMethod method2)

Parameters

cac1 ComplexAmplitude

First ComplexAmplitude operand (dividend).

cac2 ComplexAmplitude

Second ComplexAmplitude operand (divisor).

method1 InterpolationMethod

How to interpolate 1. operand, if it is a transmission.

method2 InterpolationMethod

How to interpolate 2. operand, if it is a transmission.

Returns

ComplexAmplitude

The resulting harmonic field.

EmbedCorner(Vector)

This ComplexAmplitude is embedded into sampling points having the value zero so that the resulting size is twice the original size. In contrast to the EmbedExtract(Vector) method, this method places the original field in the bottom left quadrant of the changed field, not in the center.

public void EmbedCorner(Vector newSize)

Parameters

newSize Vector

New size in pixels.

EmbedExtract()

This ComplexAmplitude is embedded centrically into sampling points having the value zero so that the resulting size is twice the original size.

public void EmbedExtract()

EmbedExtract(Rectangle)

Embeds current complex amplitude into the given rectangle.

public ComplexAmplitude EmbedExtract(Rectangle rectangle)

Parameters

rectangle Rectangle

Region to extract. Pixels outside of this ComplexAmplitude are set to zero.

Returns

ComplexAmplitude

Modified ComplexAmplitude.

EmbedExtract(Vector)

Changes this ComplexAmplitude to the given size.

public void EmbedExtract(Vector newSize)

Parameters

newSize Vector

New size in pixels. If the new size is larger than the original number of sampling points, the field is embedded centrically into sampling points having the value zero. If the size is smaller than the the original number of sampling points, the central region of the field is extracted.

Equals(object, EqualityIntent)

Determines whether the specified object is equal to this instance.

public override bool Equals(object otherObject, EqualityIntent equalityIntent)

Parameters

otherObject object

The object to compare with this instance.

equalityIntent EqualityIntent

Defines what kind of equality you want to check when comparing two objects, for example all values or just physical equality.

Returns

bool

true if the specified object is equal to this instance; otherwise, false.

Extract(Vector, Vector)

Extracts the defined piece from this ComplexAmplitude.

public ComplexAmplitude Extract(Vector size, Vector position)

Parameters

size Vector

The size of the region to extract in pixels.

position Vector

The zero-position of the region to extract in pixel coordinates.

Returns

ComplexAmplitude

Extracted region as a new ComplexAmplitude.

ExtractColumn(int, bool)

Extracts a column from this ComplexAmplitude.

public ComplexAmplitude ExtractColumn(int colIndex, bool considerSphericalPhase)

Parameters

colIndex int

index of the column to extract in pixel coordinates.

considerSphericalPhase bool

true: The analytical spherical phase factor is sampled in the resulting field. false: The analytical spherical phase factor is not present in the resulting field.

Returns

ComplexAmplitude

Extracted column as a new ComplexAmplitude.

ExtractComplexValue(VectorD, VectorialComponent)

Public method to get a complex value for a defined physical position for a specified vectorial component.

public Complex ExtractComplexValue(VectorD position, VectorialComponent comp)

Parameters

position VectorD

The position where the value has to be extracted.

comp VectorialComponent

The vectorial component which shall be used.

Returns

Complex

The complex value on the defined position.

ExtractDiagonal(double)

Extracts data from a diagonal line right through the center of this ComplexAmplitude.

public ComplexAmplitude ExtractDiagonal(double alpha)

Parameters

alpha double

The orientation angle of the diagonal line in radians. A angle of zero means that a line in x-direction is extracted. An angle of \(\frac{\pi}{2}\) means that a line in y-direction is extracted.

Returns

ComplexAmplitude

Extracted data as new one-dimensional ComplexAmplitude.

ExtractRow(int, bool)

Extracts a row from this ComplexAmplitude.

public ComplexAmplitude ExtractRow(int rowIndex, bool considerSphericalPhase)

Parameters

rowIndex int

index of the row to extract in pixel coordinates.

considerSphericalPhase bool

true: The analytical spherical phase factor is sampled in the resulting field. false: The analytical spherical phase factor is not present in the resulting field.

Returns

ComplexAmplitude

Extracted row as a new one-dimensional ComplexAmplitude.

Fill(Complex)

Sets all pixels of this ComplexAmplitude to the given complex value.

public void Fill(Complex c)

Parameters

c Complex

Complex value to fill the field with.

Fill(Complex, Rectangle, bool)

Sets all pixels of this ComplexAmplitude to the given complex value.

public void Fill(Complex c, Rectangle marker, bool inside)

Parameters

c Complex

Complex value to fill the field with.

marker Rectangle

Marker that decides where to fill.

inside bool

Fill inside or outside of the marker.

GetAnalyticLinearPhaseValueAtPosition(double, double)

Function to get the complex value of the analytic linear phase at a specific position.

public Complex GetAnalyticLinearPhaseValueAtPosition(double x, double y)

Parameters

x double

x-position.

y double

y-position.

Returns

Complex

The complex value for the analytically stored linear phase at the specified position.

GetAnalyticLinearPhaseValueAtPosition(VectorD)

Function to get the complex value of the analytic linear phase at a specific position.

public Complex GetAnalyticLinearPhaseValueAtPosition(VectorD position)

Parameters

position VectorD

The position where the linear phase should be evaluated.

Returns

Complex

The complex value for the analytically stored linear phase at the specified position.

GetFields()

Gets all member fields in the harmonic field.

public override IEnumerable<ComplexAmplitude> GetFields()

Returns

IEnumerable<ComplexAmplitude>

Collection of the member fields.

GetLocalFieldVector(int, int)

Gets the field vector (Ex; Ey) at a certain position (x; y) in pixels. Only works for Harmonic Fields, not Transmissions.

public VectorC GetLocalFieldVector(int x, int y)

Parameters

x int

The x-position in pixels.

y int

The y-position in pixels.

Returns

VectorC

The local field vector (Ex; Ey).

HorizontalMirror_physicalCoordinates()

Performs a horizontal mirroring of this ComplexAmplitude. The physical coordinate origin is maintained.

public void HorizontalMirror_physicalCoordinates()

HorizontalMirror_pixelCoordinates()

Performs a horizontal mirroring of this ComplexAmplitude. \([SamplingPoints.X - x - 1, y] = [x, y]\)

public void HorizontalMirror_pixelCoordinates()

Insert(ComplexAmplitude, Vector)

Inserts the given ComplexAmplitude into this ComplexAmplitude at the given position. Points exceeding boundaries will be ignored.

public void Insert(ComplexAmplitude ca, Vector position)

Parameters

ca ComplexAmplitude

Complex amplitude to be inserted.

position Vector

Position at which the field is to be inserted.

JonesMatrixMultiplication(Matrix2x2C)

Multiplies a ComplexAmplitude with a Matrix2x2C.

public ComplexAmplitude JonesMatrixMultiplication(Matrix2x2C m)

Parameters

m Matrix2x2C

The complex transformation matrix.

Returns

ComplexAmplitude

ComplexAmplitude multiplied with the given matrix.

LiftPositive()

Lifts complex amplitude to positive. See also LiftPositive().

public void LiftPositive()

Load(string)

Loads the specified file name. Works independently from whether the document has been saved without view settings (as prior to VirtualLab 6.0) or with view settings.

public static ComplexAmplitude Load(string fileName)

Parameters

fileName string

Name of the file.

Returns

ComplexAmplitude

The specified document.

ModifyComplexPart(ComplexPart, bool)

Extracts, shifts or swaps complex part of this ComplexAmplitude.

public void ModifyComplexPart(ComplexPart complexPart, bool makeRealValuedIfSuitable = false)

Parameters

complexPart ComplexPart

ComplexPart enum defining the desired action.

makeRealValuedIfSuitable bool

If this optional parameter is set to true the field is made real-valued if the imaginary part is zeroized. This is e.g. the case for “extract amplitude” and “shift phase to real”.

MultEqual(ComplexAmplitude)

Multiplies the given ComplexAmplitude with this one taking into account the spherical phase radius. The result is stored in this ComplexAmplitude. Both operands must have same number of sampling points. Other parameters like sampling distance or wavelength will not be changed.

public void MultEqual(ComplexAmplitude ca)

Parameters

ca ComplexAmplitude

ComplexAmplitude to be multiplied with current one.

MultEqual(Complex)

Multiplies a complex number to this ComplexAmplitude.

public void MultEqual(Complex c)

Parameters

c Complex

Complex number to be multiplied.

MultiplySphericalPhaseFactor(double, CancellationToken?)

Samples a spherical phase factor with specified distance from source plane and sets the SphericalPhaseRadius property. Function uses the present sampling distance of the this ComplexAmplitude to sample the spherical phase factor.

public void MultiplySphericalPhaseFactor(double newRadius, CancellationToken? cancellationToken = null)

Parameters

newRadius double

Distance of the spherical phase factor from origin plane.

cancellationToken CancellationToken?

Optional token for cooperative task cancellation.

MultiplyWithResampling(ComplexAmplitude, ComplexAmplitude, InterpolationMethod, InterpolationMethod)

Checks both ComplexAmplitude operands for identical sampling parameters, does the interpolation if one or both operands have to be resampled, then the second ComplexAmplitude is multiplied with the first ComplexAmplitude.

public static ComplexAmplitude MultiplyWithResampling(ComplexAmplitude cac1, ComplexAmplitude cac2, InterpolationMethod method1, InterpolationMethod method2)

Parameters

cac1 ComplexAmplitude

First ComplexAmplitude operand.

cac2 ComplexAmplitude

Second ComplexAmplitude operand.

method1 InterpolationMethod

How to interpolate 1. operand, if it is a transmission.

method2 InterpolationMethod

How to interpolate 2. operand, if it is a transmission.

Returns

ComplexAmplitude

The resulting harmonic field.

Normalize()

Normalizes this ComplexAmplitude so that the maximal amplitude is one.

public void Normalize()

Normalize(Rectangle)

Normalizes this ComplexAmplitude so that the maximal amplitude in given rectangle is one.

public void Normalize(Rectangle rectangle)

Parameters

rectangle Rectangle

Region to which normalization refers.

PowerEqual(Complex)

Raises every element of this ComplexAmplitude to the power of the given complex number.

public void PowerEqual(Complex c)

Parameters

c Complex

Complex exponent this complex amplitude is raised to.

RemoveSphericalPhaseFactor(CancellationToken?)

Removes a sampled spherical phase factor whose distance from the source plane is specified in the SphericalPhaseRadius property. The sampled complex field is divided by the corresponding spherical phase function.

public override void RemoveSphericalPhaseFactor(CancellationToken? cancellationToken = null)

Parameters

cancellationToken CancellationToken?

Optional token for cooperative task cancellation.

Replicate_Periodic(Vector)

Replicates this ComplexAmplitude periodically, original field is centered around (0; 0).

public void Replicate_Periodic(Vector newSize)

Parameters

newSize Vector

New size in pixels.

Save(string)

Saves this ComplexAmplitude into a file.

public override void Save(string fileName)

Parameters

fileName string

Complete path of the file.

SetBothComponentsAtOnce(ComplexField, ComplexField)

Because both Ex and Ey component must have same size, a function is needed to change both components at once.

public void SetBothComponentsAtOnce(ComplexField fieldX, ComplexField fieldY)

Parameters

fieldX ComplexField

Complex field containing Ex component.

fieldY ComplexField

Complex field containing Ey component.

Shift(Vector)

Shifts this ComplexAmplitude by a specified number of sampling points. Size is not modified, so sampling points can get lost.

public void Shift(Vector shift)

Parameters

shift Vector

Field shift in pixels.

SplitLocallyPolarizedField(out ComplexAmplitude, out ComplexAmplitude)

Splits current complex amplitude into Ex and Ey component.

public void SplitLocallyPolarizedField(out ComplexAmplitude caX, out ComplexAmplitude caY)

Parameters

caX ComplexAmplitude

Returns new ComplexAmplitude containing Ex component of this ComplexAmplitude.

caY ComplexAmplitude

Returns new ComplexAmplitude containing Ey component of this ComplexAmplitude.

SubEqual(ComplexAmplitude)

Subtracts the given ComplexAmplitude from current one taking into account the spherical phase radius. The result is stored in this ComplexAmplitude. Both operands must have same number of sampling points. Other parameters like sampling distance or wavelength will not be changed.

public void SubEqual(ComplexAmplitude ca)

Parameters

ca ComplexAmplitude

ComplexAmplitude to be subtracted from current one.

SubtractWithResampling(ComplexAmplitude, ComplexAmplitude, InterpolationMethod, InterpolationMethod)

Checks both ComplexAmplitude operands for identical sampling parameters, does the interpolation if one or both operands have to be resampled, then the second ComplexAmplitude is subtracted from the first ComplexAmplitude.

public static ComplexAmplitude SubtractWithResampling(ComplexAmplitude cac1, ComplexAmplitude cac2, InterpolationMethod method1, InterpolationMethod method2)

Parameters

cac1 ComplexAmplitude

First ComplexAmplitude operand (minuend).

cac2 ComplexAmplitude

Second ComplexAmplitude operand (subtrahend).

method1 InterpolationMethod

How to interpolate 1. operand, if it is a transmission.

method2 InterpolationMethod

How to interpolate 2. operand, if it is a transmission.

Returns

ComplexAmplitude

The resulting harmonic field.

ToString()

The overridden ToString function for ComplexAmplitudes

public override string ToString()

Returns

string

either "Transmission", "Signal Region", "Complex Amplitude"

Transpose()

Transposes this ComplexAmplitude. This means \([x, y] = [y, x]\).

public void Transpose()

VerticalMirror_physicalCoordinates()

Performs a vertical mirroring of this ComplexAmplitude. The physical coordinate origin is maintained.

public void VerticalMirror_physicalCoordinates()

VerticalMirror_pixelCoordinates()

Performs a vertical mirroring of this ComplexAmplitude. \([x, SamplingPoints.Y - y - 1] = [x, y]\)

public void VerticalMirror_pixelCoordinates()

Operators

operator +(ComplexAmplitude, ComplexAmplitude)

Adds two ComplexAmplitude objects. The sampling distance and the wavelength are ignored during the operation. The resulting object has the same sampling distance and wavelength as the first operand.

[Obsolete("Keep in mind that the AddEqual method is more performant than the += operator.")]
public static ComplexAmplitude operator +(ComplexAmplitude cac1, ComplexAmplitude cac2)

Parameters

cac1 ComplexAmplitude

First ComplexAmplitude operand.

cac2 ComplexAmplitude

Second ComplexAmplitude operand.

Returns

ComplexAmplitude

The result of the operator.

operator +(ComplexAmplitude, Complex)

Adds a Complex value to a ComplexAmplitude.

public static ComplexAmplitude operator +(ComplexAmplitude ca, Complex c)

Parameters

ca ComplexAmplitude

The ComplexAmplitude.

c Complex

The complex value.

Returns

ComplexAmplitude

A new ComplexAmplitude where the given Complex value has been added to every pixel.

operator +(Complex, ComplexAmplitude)

Adds a Complex value to a ComplexAmplitude.

public static ComplexAmplitude operator +(Complex c, ComplexAmplitude ca)

Parameters

c Complex

The complex value.

ca ComplexAmplitude

The ComplexAmplitude.

Returns

ComplexAmplitude

A new ComplexAmplitude where the given Complex value has been added to every pixel.

operator /(ComplexAmplitude, ComplexAmplitude)

Divides two ComplexAmplitude objects.

public static ComplexAmplitude operator /(ComplexAmplitude cac1, ComplexAmplitude cac2)

Parameters

cac1 ComplexAmplitude

First ComplexAmplitude operand (dividend).

cac2 ComplexAmplitude

Second ComplexAmplitude operand (divisor).

Returns

ComplexAmplitude

Quotient of the two ComplexAmplitude objects.

operator /(ComplexAmplitude, Complex)

Divides a ComplexAmplitude by a Complex value.

public static ComplexAmplitude operator /(ComplexAmplitude ca, Complex c)

Parameters

ca ComplexAmplitude

The ComplexAmplitude.

c Complex

The complex value.

Returns

ComplexAmplitude

The quotient of the ComplexAmplitude and the complex value.

operator ^(ComplexAmplitude, Complex)

Raises a ComplexAmplitude to a complex value

public static ComplexAmplitude operator ^(ComplexAmplitude ca, Complex c)

Parameters

ca ComplexAmplitude

the first ComplexAmplitude

c Complex

the complex value

Returns

ComplexAmplitude

the power .

operator *(ComplexAmplitude, ComplexAmplitude)

Multiplies two ComplexAmplitude objects.

[Obsolete("Keep in mind that the MultEqual method is more performant than the *= operator.")]
public static ComplexAmplitude operator *(ComplexAmplitude cac1, ComplexAmplitude cac2)

Parameters

cac1 ComplexAmplitude

First ComplexAmplitude operand.

cac2 ComplexAmplitude

Second ComplexAmplitude operand.

Returns

ComplexAmplitude

Product of the two ComplexAmplitude objects.

operator *(ComplexAmplitude, Complex)

Multiplies a ComplexAmplitude with a complex value.

public static ComplexAmplitude operator *(ComplexAmplitude ca, Complex c)

Parameters

ca ComplexAmplitude

The ComplexAmplitude.

c Complex

The complex value.

Returns

ComplexAmplitude

The product of the ComplexAmplitude and the complex value.

operator *(Complex, ComplexAmplitude)

Multiplies a complex value with a ComplexAmplitude.

public static ComplexAmplitude operator *(Complex c, ComplexAmplitude ca)

Parameters

c Complex

The complex value.

ca ComplexAmplitude

The ComplexAmplitude.

Returns

ComplexAmplitude

The product of the ComplexAmplitude and the complex value.

operator -(ComplexAmplitude, ComplexAmplitude)

Subtracts two ComplexAmplitude objects.

public static ComplexAmplitude operator -(ComplexAmplitude cac1, ComplexAmplitude cac2)

Parameters

cac1 ComplexAmplitude

First ComplexAmplitude operand (minuend).

cac2 ComplexAmplitude

Second ComplexAmplitude operand (subtrahend).

Returns

ComplexAmplitude

The result of the operator.

operator -(ComplexAmplitude, Complex)

Subtracts a ComplexAmplitude and a Complex value.

public static ComplexAmplitude operator -(ComplexAmplitude ca, Complex c)

Parameters

ca ComplexAmplitude

The ComplexAmplitude.

c Complex

The complex value.

Returns

ComplexAmplitude

The difference of the ComplexAmplitude and the complex value.