ABCDCenterPoint

ABCDCenterPoint is a rule that provides the global three-dimensional surface point location used making the ABCD-matrix calculations.

See also ABCDMatrix and ABCDRotationMatrix.

ABCDConstruction

ABCDConstruction is a option of FindABCDMatrix and several other functions that denotes the type of spatial dimensions represented in the ABCD-matrix construction.

ABCDConstruction->Horizontal specifies the use of the local horizontal (y) and axial (x) coordinates to construct a single 2x2 ABCD matrix format to describe a two-dimensional paraxial system. ABCDConstruction->Vertical denotes the use of the local vertical (z) and axial (x) coordinates to construct a single 2x2 ABCD matrix format to describe a two-dimensional paraxial system. ABCDConstruction->FullForm denotes the use of both horizontal (y) and vertical (z) local coordinates together with local axial (x) coordinates to construct two 2x2 ABCD matrices to describe a fully three-dimensional paraxial system. ABCDConstruction->Automatic retains the default ABCD matrix setting for the system. It is important to note that ABCDConstruction can only be used to reduce the number of spatial dimensions present, but does not increase the number of spatial dimensions above the original system settings.

See also ABCDMatrix, ABCDCenterPoint, and ABCDRotationMatrix.

ABCDRotationMatrix

ABCDRotationMatrix is a rule that gives a 3 x 3 matrix of spatial rotations invoked on the original ABCD-matrix object coordinate system.

ABCDRotationMatrix is used in making the ABCD-matrix calculations. See also ABCDMatrix and ABCDCenterPoint.

AngularMagnification

AngularMagnification is a rule that specifies the angular magnification that occurs between the object and image points in a conjugate imaging system.

See also: TransverseMagnification and SystemABCDMatrix.

ApertureOrder

ApertureOrder is a option that specifies the power of the aperture function.

Astigmatism

Astigmatism is a rule returned by ZernikeFit that gives the astigmatism portion (C yo^2) of the primary Seidel aberration coefficients.

See also: SeidelAberrations.

BackFocalPoint

BackFocalPoint is a rule that indicates the point of focus in three-dimensions at the exit of an imaging system.

BeamAxisStyle

BeamAxisStyle->{graphics primitives} is an option used to give additional rendering properties to the axis line of a Gaussian beam.

See also: BeamStyle.

BeamCurvatureFunction

BeamCurvatureFunction is a rule that designates the radius of phase curvature as a function of axial position for a Gaussian beam.

See also: BeamCurvatureGraphics, BeamSpotSizeFunction, and ComplexBeamParameterFunction.

BeamCurvatureGraphics

BeamCurvatureGraphics is a rule that indicates graphical information to represent the radius of phase curvature as a function of axial position for a Gaussian beam.

See also: BeamSpotSizeGraphics, and ComplexBeamParameterGraphics, and ComplexBeamParameterGraphics.

BeamSpotSizeFunction

BeamSpotSizeFunction is a rule that designates the Gaussian beam radius (at 1/e of its amplitude peak) as a function of axial position for a Gaussian beam.

See also: BeamSpotSizeGraphics, BeamCurvatureFunction, and ComplexBeamParameterFunction.

BeamSpotSizeGraphics

BeamSpotSizeGraphics is a rule that indicates graphical information to represent the Gaussian beam radius (at 1/e of its amplitude peak) as a function of axial position for a Gaussian beam.

See also: BeamCurvatureGraphics, and ComplexBeamParameterGraphics, and ComplexBeamParameterGraphics.

BeamStyle

BeamStyle->{graphics primitives} is an option used to give additional rendering properties to a Gaussian beam.

See also: BeamAxisGraphicsStyle.

ByteCountLimit

ByteCountLimit is a option that specifies the maximum byte-count size permitted for an ongoing calculation. If the byte-count of the calculation should exceed the ByteCountLimit setting, the calculation is immediately terminated.

See also MaxByteCount.

ChopThreshold

ChopThreshold is an option that sets the zero threshold level used by the Chop function.

ChopThreshold is not a direct option of Chop, but rather is passed indirectly to Chop by higher level functions.

Coma

Coma is a rule returned by ZernikeFit that gives the coma portion (F yo) of the primary Seidel aberration coefficients.

See also: SeidelAberrations.

ComplexABCD

ComplexABCD->True/False is a option that specifies the use of complex values in the ABCD-matrix results to represent aperture or wave attenuation/amplification effects.

See also FindABCDMatrix.

ComplexBeamParameterFunction

ComplexBeamParameterFunction is a rule that designates the complex beam parameter q as a function of axial position for a Gaussian beam.

See also: ComplexBeamParameterGraphics, BeamSpotSizeFunction, and BeamCurvatureFunction.

ComplexBeamParameterGraphics

ComplexBeamParameterGraphics is a rule that indicates graphical information to represent the the complex beam parameter q as a function of axial position for a Gaussian beam.

See also: BeamSpotSizeGraphics, and ComplexBeamParameterGraphics, and BeamCurvatureGraphics.

DecomposeABCD

DecomposeABCD->True/False is a option that specifies whether the output should be broken down into several ABCD-matrices that describe each elemental matrix operation within the optical system.

See also FindABCDMatrix.

DiffractionSpotSize

DiffractionSpotSize is a rule returned by PointSpreadFunction that gives the maximum image diameter of the point spread function that includes diffraction effects.

Distortion

Distortion is a rule returned by ZernikeFit that gives the distortion portion (E yo^3) of the primary Seidel aberration coefficients.

See also: SeidelAberrations.

EliminateCrossTerms

EliminateCrossTerms is a option of SymbolicTrace that specifies whether an expression should have specified symbolic variable cross-terms removed.

EliminateCrossTerms is used internally by SymbolicTrace to reduce the intermediate size of expressions that will ultimately become linear functions. In particular, FindABCDMatrix always calls SymbolicTrace with the EliminateCrossTerms->True option setting. Note that EliminateCrossTerms should only be used with linearized expressions (ie: SeriesOrder->1).

EntrancePupilDistance

EntrancePupilDistance is a rule that indicates the geometric distance, along the chief ray axis, from entrance pupil and the first lens surface.

ExitPupilDistance

ExitPupilDistance is a rule that indicates the geometric distance, along the chief ray axis, from exit pupil and the last lens surface.

ExpandAlways

ExpandAlways is a option that specifies whether the Taylor-series expansion of a symbolic calculation shall be restricted to a maximum byte-count size for the expression.

For ExpandAlways->False, if the byte-count of the calculation should exceed the 50*MaxByteCount setting, any Taylor-series expansions of the expression is suspended.

See also MaxByteCount.

FieldCurvature

FieldCurvature is a rule returned by ZernikeFit that gives the curvature of field portion (D yo^2) of the primary Seidel aberration coefficients.

See also: SeidelAberrations.

FieldStopPosition

FieldStopPosition is an option of FindLensParameters that specifies whether the field stop position should be calculated by FindLensParameters.

FieldStopPosition->Automatic uses the paraxial imaging theory together with the optical surface aperture dimensions to determine the limiting aperture for the particular imaging system. FieldStopPosition->number uses the field stop that corresponds with the optical surface position given by the specified number.

FinalFormat

FinalFormat is a option that specifies whether the output should be manipulated into its simplest form.

FinalFormat->False skips such time consuming formatting procedures.

FindABCDMatrix

FindABCDMatrix[opticalsystem, assumptions, options] is a function that finds the symbolic or numerical ABCD-matrix representation of the optical system.

FindABCDMatrix internally calls SymbolicTrace.

See also SymbolicTrace

FindGratingFunction

FindGratingFunction[system, options] is a function that determines the grating function between an object wavefront and reference wavefront hitting the last optical surface in the specified optical system.

As input, FindGratingFunction takes either an optical system containing two wavefronts or two light sources with one or more optical components. FindGratingFunction first calls FindWaveFronts to obtain the WaveVectorFunction for each light source hitting the last surface. FindGratingFunction assumes that first wavefront corresponds with the object wave and the second wavefront corresponds with the reference wave. FindGratingFunction then calculates the grating function by subtracting the object wave vector from the reference wave vector. FindGratingFunction works equally well for both point sources and planar sources. In addition, the light source need only contain a small number of rays (since the actual number of rays is internally specified).

If one-dimensional light sources are used (ie. WedgeOfRays or LineOfRays), then a one-dimensional grating function is calculated. If two-dimensional light sources are used (ie. PointOfRays or GridOfRays), then a two-dimensional grating function is determined.

See also: Hologram, Grating, FindWaveFronts, and OpticalPathDifference.

FindImagePoint

FindImagePoint is an option of FindLensParameters that indicates whether the three-dimensional image point measurement is taken automatically at the last optical surface or systematically determined with FindFocus.

FindImagePoint->True uses FindFocus to search for an optimal image focus in three-dimensions according to the FocalFraction option. FindImagePoint->False uses the last optical surface as the image point.

FindInterference

FindInterference[system, options] is a function that determines the interference function between multiple wavefronts hitting the last optical surface in an optical system.

As input, FindInterference takes either an optical system containing multiple light sources or the output from one or more FindWaveFronts calculations. FindInterference calculates the interference function by adding together the complex fields from the individual wavefronts hitting the optical surface and multiplying by the complex conjugate to get the intensity distribution on the surface. FindInterference works equally well for both point sources and planar sources. In addition, the light source need only contain a small number of rays (since the actual number of rays is internally specified).

If one-dimensional light sources are used (ie. WedgeOfRays or LineOfRays), then a one-dimensional interference function is calculated. If two-dimensional light sources are used (ie. PointOfRays or GridOfRays), then a two-dimensional interference function is determined. FindInterference is also a label used with the RenderedParameters option. See also: FindWaveFronts, InterferenceFunction, OpticalPathDifference, WaveFrontIntensity, and OpticalLengthFunction.

FindLensParameters

FindLensParameters[opticalsystem, options] is a function that determines the paraxial lens characteristics of an imaging system.

FindLensParameters returns complete information about focal length, principle planes, field stop, and pupils. In addition to the necessary lens elements, the opticalsystem parameter should include a light source. FindLensParameters is also capable of analyzing asigmatic imaging systems with the ABCDContruction->FullForm option setting.

See also: FieldStopSurface, FocalLength, BackFocalLength, BackFocalPoint, FrontFocalLength, FrontFocalPoint, EntrancePupilDistance, EntrancePupilPosition, EntrancePupilBoundary, EntrancePupilOffset, EntrancePupilRotationMatrix, ExitPupilDistance, ExitPupilPosition, ExitPupilBoundary, ExitPupilOffset, ExitPupilRotationMatrix, PrinciplePointSeparation, PrinciplePoints, and ABCDMatrix.

FindPupils

FindPupils is an option of FindLensParameters that specifies whether entrance and exit pupil boundaries and positions should be calculated by FindLensParameters.

FindPupils->True calculates the front and back entrace pupil shape and position according to the FieldStopPosition option. FindPupils->False does not calculate the entrance pupil information at all. See also: FieldStopPosition.

FindWaveFronts

FindWaveFronts[system, options] is a function designed to find the optical path length function and wave intensity function on a last surface in the optical system.

FindWaveFronts calculates the wavefront function and the intensity mapping function at the final surface. This information is used together by FindInterference to calculate the complex field as well as the interference at the surface. As input, FindWaveFronts uses an optical system containing one or more light sources. FindWaveFronts works equally well for both point sources and planar sources. In addition, the light source need only contain a small number of rays (since the actual number of rays is internally specified).

If a one-dimensional light source is used (ie. WedgeOfRays or LineOfRays), then one-dimensional wavefront and intensity functions are calculated. If a two-dimensional light source is used (ie. PointOfRays or GridOfRays), then two-dimensional wavefront and intensity functions are determined. FindWaveFronts is also a label used with the RenderedParameters option. See also: FindInterference, OpticalPathDifference, WaveFrontIntensity, and OpticalLengthFunction.

FocalFraction

FocalFraction is an option of FindLensParameters that specifies the focal point position relative to the paraxial and marginal focal points.

If FocalFraction -> 0 is given, the paraxial focal point position is used (determined by tracing paraxial rays through the system.) If FocalFraction -> 1 is given, the marginal focal point position is used (determined by the tracing outer marginal rays through the system.) If FocalFraction -> Automatic is given, the focal plane with the smallest overall spot size is chosen by tracing a filled source of rays ( also known as the circle of least confusion.) FocalFraction is normally used with FindImagePoint->True, however a user specified FocalFraction setting will over-ride the default FindImagePoint->False setting.

FrontFocalPoint

FrontFocalPoint is a rule that indicates the point of reverse focus in three-dimensions in the entrance of an imaging system.

GaussianPlot

GaussianPlot[opticalsystem, assumptions, options] is a function that propagates and plots one or more Gaussian beams through the optical system.

Note that one or more GaussianBeam sources must be present in the system before ShowGaussian can produce any results. GaussianPlot has two different plotting modes that are governed by the Plot3D option. For Plot3D->True, a full three-dimensional representation of the beam curvature together with the beam spot size (at 1/e of amplitude) are shown. For Plot3D->False, a paraxial depiction of the beam parameters indicated with the RenderedParameters option is presented in the form of two-dimensional plots. RenderedParameters takes a list containing one or more of the following values: BeamSpotSize, BeamCurvature, and ComplexBeamParameter. When Plot3D->True is invoked, then RenderedParameters->ComplexBeamParameter is not available. GaussianPlot internally calls GaussianTrace. GuassianPlot is also called internally by ShowSystem for the rendering of Gaussian beam information by Wavica.

See also: GaussianTrace, RenderedParameters, BeamCurvatureFunction, BeamCurvatureGraphics, BeamSpotSizeFunction, BeamSpotSizeGraphics, ComplexBeamParameterFunction, ComplexBeamParameterGraphics, and ShowGaussian.

GaussianTrace

GaussianTrace[opticalsystem, assumptions, options] is a function that propagates one or more Gaussian beams through the optical system.

GaussianTrace returns the Gaussian beam parameter information for each of the surfaces specified in ReportedSurfaces. GaussianTrace internally calls FindABCDMatrix.

See also GaussianPlot.

GeometricLength

GeometricLength is a rule that gives the total geometric path length of the ray from the beginning of its creation up to a particular surface.

See also OpticalLength.

GeometricPointSpreadFunction

GeometricPointSpreadFunction[system, options] calculates the intensity function at the focal plane of an imaging system.

GeometricPointSpreadFunction internally calls FindIntensity and can work directly with multiple wavelength (white light) incoherent sources, since it works only with the intensity information (not amplitude and phase). The optical system must contain a light source followed by the imaging optics with the approximate focal surface as its last element. For FindImagePoint->True, the last system element need not be the exact focal surface, since the exact focal surface position is automatically determined. When the default FindImagePoint->False is given, the last system element is assumed to be the exact focal surface. In addition, the light source need only contain a small number of rays (since the actual number of rays is internally specified). The user can also give as input a specific focal point or exit pupil position with the FocalPoint and ExitPupilPosition options, although GeometricPointSpreadFunction does not make use of the exit pupil information.

Note: GeometricPointSpreadFunction works equally well for both point sources and planar sources, as long as the described imaging system contains a focus. If a one-dimensional light source is used (ie. WedgeOfRays or LineOfRays), then a one-dimensional geometric point spread function is calculated. If a two-dimensional light source is used (ie. PointOfRays or GridOfRays), then the geometric point spread calculations are carried out in two-dimensions.

GeometricPointSpreadFunction does not utilize PupilFunction. GeometricPointSpreadFunction is also an option of OpticalTransferFunction and PointSpreadFunction that indicates whether the diffraction point spread function or the geometric point spread function is to be used. GeometricPointSpreadFunction->False invokes the direct use of PointSpreadFunction, while GeometricPointSpreadFunction->True invokes the use of GeometricPointSpreadFunction.

FindIntensity uses the KernelScale and SmoothKernelSize options to specify a Gaussian smoothing kernel that gets convolved with the intensity data. This smoothing kernel can be set to the diffraction-limited spot-size of the systen in order to incorporate the diffraction-limited behavior with the geometric ray-trace data.

See also: KernelScale, SmoothKernelSize, SmoothKernelRange, FindLensParameters, GeometricFocalData, GPSF, FindIntensity, and OpticalTransferFunction.

GeometricPSF

GeometricPSF[system, options] is an alias to GeometricPointSpreadFunction[system, options].

GlobalSurfaceCoordinates

GlobalSurfaceCoordinates is a option that indicates whether or not the symbolic solutions generated from each surface gets transformed into global coordinates or remains in local coordinates.

GPSF

GPSF[system, options] is an alias to GeometricPointSpreadFunction[system, options].

ImagePlaneTilt

ImagePlaneTilt is a rule that specifies three-dimensional tilt vector of the chief ray at the image plane.

ImagePoint

ImagePoint is a rule that specifies the point of focus in three-dimensions of the image point.

ImagingOptics

ImagingOptics is a rule returned by FindLensParameters that gives all the optical components listed within the input optical system, excluding all light sources.

IntensityTransform

IntensityTransform is an option of PointSpreadFunction and OpticalTransferFunction that indicates whether the imaging system behaves linearly with amplitude (coherent system) or intensity (incoherent system).

For IntensityTransform->True, then PointSpreadFunction returns the real-valued intensity distribution of the point spread function and OpticalTransferFunction returns the intensity-based modulation and phase transfer functions. For IntensityTransform->False, then PointSpreadFunction returns the magnitude and phase field distribution of the amplitude point spread function and OpticalTransferFunction returns the complex-amplitude-based modulation and phase transfer functions.

IntensityTransform also affects the PaddingFactor->Automatic setting. PaddingFactor->Automatic uses a factor of zero for the amplitude transform (IntensityTransform->False) and a factor of one for the intensity transform (IntensityTransform->True).

InterferenceFunction

InterferenceFunction is a rule returned by FindInterference that gives a continuous intensity interference function at a designated surface.

InterferenceFunction is also a label used with the RenderedParameters option.

LensABCDMatrix

LensABCDMatrix is a rule that specifies the ABCD matrix representation of the bare lens optics that does not include the object-to-lens and lens-to-image distances taken from the light source and final surface positions.

See also: SystemABCDMatrix.

LoadWavicaFiles

LoadWavicaFiles[foldername, filename] is a utility to load Wavica files after having saved them. Interface files are loaded in the public Wavica context, the rest is loaded in the Wavica private context. Both parameters can be a list to load multiple files.

LocalCoordinateExpansions

LocalCoordinateExpansions is a option that specifies that type and order of local coordinate variables used in Taylor series expansions.

See also: SeriesOrder and SeriesExpand.

MakeFloatingPoint

MakeFloatingPoint -> parameters is a option of SymbolicTrace that turns any integer and fractional number quantities found in the specified parameters into floating point numbers.

For MakeFloatingPoint->True/All, all possible parameters are converted. MakeFloatingPoint->False leaves all integers and fractional values intact. Two parameters commonly used with MakeFloatingPoint are RefractiveIndex and SymbolicWaveLength. MakeFloatingPoint uses NP to construct floating point representations. See also: NumericalResults and NP.

MaxByteCount

MaxByteCount is a option that specifies the maximum byte-count size used by the Simplify and FullSimplify functions. If the byte-count of the calculation should exceed the MaxByteCount setting, ongoing efforts to simplify the calculation results are dismissed.

See also ByteCountLimit.

NestSurfaceSolutions

NestSurfaceSolutions is a option that indicates whether or not the symbolic solutions generated from each surface is nested and combined into a single result.

NormalizeSurfaceNormal

NormalizeSurfaceNormal is a option that indicates whether or not the surface normal information gets renormalized during symbolic calculations.

NumberOfFilledRays

NumberOfFilledRays is an option of FindLensParameters that gives the number of rays used in tracing the focal point for the circle of least confusion.

NumericalResults

NumericalResults is a option that specifies whether the resulting calculations are based on symbolic or numerical information.

For NumericalResults->True, numerical information is used instead of symbolic information during the calculation. With NumericalResults->False, any symbolic variables present are used in the calculation. See also: MakeFloatingPoint.

ObjectSource

ObjectSource is a rule returned by FindLensParameters that gives the first light source listed within the input optical system.

OpticalLengthFunction

OpticalLengthFunction is a rule returned by FindWaveFronts and FindInterference that gives a continuous optical path length function at a designated surface.

OpticalLengthFunction is also a label used with the RenderedParameters option.

OpticalPathDifference

OpticalPathDifference is a rule returned by PupilFunction and FindWaveFront that gives a continuous wavefront function at a designated surface.

OpticalPathDifference is also a label used with the RenderedParameters option.

OpticalPathRange

OpticalPathRange is a rule returned by FindWaveFronts that gives the minimum and maximum optical path length values of a wavefront.

OpticalTransferFunction

OpticalTransferFunction[system, options] calculates the modulation and phase transfer functions of the optical system for a given object source input.

OpticalTransferFunction works together with either GeometricPointSpreadFunction, FindIntensity, and PointSpreadFunction. OpticalTransferFunction first calls either GeometricPointSpreadFunction or PointSpreadFunction to find the point spread function of the imaging system. Finally, OpticalTransferFunction calculates a modulation and phase transfer function by using the Fourier transform of the point spread function. As input, OpticalTransferFunction takes either an optical system or the returned output from either GeometricPointSpreadFunction, FindIntensity, or PointSpreadFunction. The optical system must contain a light source followed by the imaging optics with the approximate focal surface as its last element. For FindImagePoint->True, the last system element need not be the exact focal surface, since the exact focal surface position is automatically determined. When the default FindImagePoint->False is given, the last system element is assumed to be the exact focal surface. In addition, the light source need only contain a small number of rays (since the actual number of rays is internally specified). When FindPupils->False is used, the optical surface preceding the image surface is taken as the field stop. The user can also give as input a specific focal point or exit pupil position with the FocalPoint and ExitPupilPosition options.

Note: OpticalTransferFunction works equally well for both point sources and planar sources, as long as the described imaging system contains a focus. If a one-dimensional light source is used (ie. WedgeOfRays or LineOfRays), then a one-dimensional modulation transfer function is calculated. If a two-dimensional light source is used (ie. PointOfRays or GridOfRays), then the optical transfer function calculations are carried out in two-dimensions. Warning: in general, most one-dimensional and two-dimensional results are not fully equivalent to each other.

OpticalTransferFunction is also a label used with the RenderedParameters option. See also: IntensityTransform, FindLensParameters, PupilFunction, PointSpreadFunction, ModulationTransferFunction, PhaseTransferFunction, OTF, MTF, FindIntensity, and GeometricPointSpreadFunction.

OTF

OTF[system, options] is an alias to OpticalTransferFunction[system, options].

ParaxialReductionRatio

ParaxialReductionRatio is an option of FindLensParameters that gives the size reduction factor used internally to construct a paraxial light source from the user-specified, non-paraxial source.

ParentFunction

ParentFunction is a option that supplies the name of the original function used to make a calculation.

PerfectModulationTransferFunction

PerfectModulationTransferFunction is a rule returned by OpticalTransferFunction gives the diffraction-limited modulation transfer function of an imaging system for a specific image point.

PerfectPhaseTransferFunction

PerfectPhaseTransferFunction is a rule returned by OpticalTransferFunction gives the diffraction-limited phase transfer function of an imaging system for a specific image point.

PerfectPointSpreadFunction

PerfectPointSpreadFunction is a rule returned by PointSpreadFunction that gives the equivalent diffraction-limited point spread function result.

PerfectPointSpreadPhaseFunction

PerfectPointSpreadPhaseFunction is a rule returned by PointSpreadFunction gives the equivalent diffraction-limited point spread phase function result of a coherent imaging system for a specific image point.

PointSpreadPhaseFunction is also a label used with the RenderedParameters option.

PF

PF[system, options] is an alias to PupilFunction[system, options].

PhaseOnly

PhaseOnly -> True/False is a option of FindInterference that specifies the amplitude information to be unity.

PointSpreadFunction

PointSpreadFunction[system, options] calculates the point spread function of the optical system at a particular wavelength.

PointSpreadFunction first calls PupilFunction to calculate the exit pupil function. Finally, PointSpreadFunction calculates a point spread function by using the Fourier transform of the calculated complex field. As input, PointSpreadFunction takes either an optical system or the returned output from PupilFunction. The optical system must contain a light source followed by the imaging optics with the approximate focal surface as its last element. For FindImagePoint->True, the last system element need not be the exact focal surface, since the exact focal surface position is automatically determined. When the default FindImagePoint->False is given, the last system element is assumed to be the exact focal surface. In addition, the light source need only contain a small number of rays (since the actual number of rays is internally specified). When FindPupils->False is used, the optical surface preceding the image surface is taken as the field stop. The user can also give as input a specific focal point or exit pupil position with the FocalPoint and ExitPupilPosition options.

Note: PointSpreadFunction works equally well for both point sources and planar sources, as long as the described imaging system contains a focus. If a one-dimensional light source is used (ie. WedgeOfRays or LineOfRays), then a one-dimensional point spread function is calculated. If a two-dimensional light source is used (ie. PointOfRays or GridOfRays), then the point spread calculations are carried out in two-dimensions. Warning: in general, one-dimensional and two-dimensional results are not fully equivalent to each other.

PointSpreadFunction is also a label used with the RenderedParameters option. PointSpreadFunction is also the name of a returned rule from PointSpreadFunction that gives the point spread function result for a specific image point. See also: IntensityTransform, FindLensParameters, PupilFunction, PSF, and OpticalTransferFunction.

PointSpreadPhaseFunction

PointSpreadPhaseFunction is a rule returned by PointSpreadFunction gives the point spread phase function result of a coherent imaging system for a specific image point.

PointSpreadPhaseFunction is also a label used with the RenderedParameters option.

PrinciplePoints

PrinciplePoints is a rule that indicates the three-dimensions of the front and back principle plane centers of an imaging system.

PSF

PSF[system, options] is an alias to PointSpreadFunction[system, options].

PupilFunction

PupilFunction[system, options] is a function designed to find and extract the optical path difference and intensity profile on a spherical surface at the exit pupil of an imaging system.

PupilFunction first calls FindLensParameters to characterize the system. Then, PupilFunction calculates a wavefront function and the intensity mapping function at the exit pupil. This information can be used together to calculate the complex field at the exit pupil. As input, PupilFunction takes either an optical system or the returned output from FindLensParameters. The optical system must contain a light source followed by the imaging optics with the approximate focal surface as its last element. For FindImagePoint->True, the last system element need not be the exact focal surface, since the exact focal surface position is automatically determined. When the default FindImagePoint->False is given, the last system element is assumed to be the exact focal surface. In addition, the light source need only contain a small number of rays (since the actual number of rays is internally specified). PupilFunction uses information from FindLensParameters about the field stop position. When FindPupils->False is used, the optical surface preceding the image surface is taken as the field stop. The user can also give as input a specific focal point or exit pupil position with the FocalPoint and ExitPupilPosition options.

Note: PupilFunction works equally well for both point sources and planar sources, as long as the described imaging system contains a focus. If a one-dimensional light source is used (ie. WedgeOfRays or LineOfRays), then a one-dimensional pupil function is calculated. If a two-dimensional light source is used (ie. PointOfRays or GridOfRays), then the two-dimensional pupil function is determined.

PupilFunction works together with both PointSpreadFunction and OpticalTransferFunction. PupilFunction is also a label used with the RenderedParameters option. See also: FindLensParameters, PupilIntensityFunction, PointSpreadFunction, PF, and OpticalTransferFunction.

ResidualFitError

ResidualFitError is a rule returned by ZernikeFit that gives the leftover rms error (in wavelength units) between the Zernike polynomial equation and the original wavefront data points.

See also: ZernikeFit, ZernikePolynomial, SeidelAberrations, and ZernikeOrder.

SeidelAberrations

SeidelAberrations is a rule returned by ZernikeFit that gives the primary-Seidel aberration terms for the given wavefront.

These Seidel aberration terms are called SphericalAberration (B), Astigmatism (C), FieldCurvature (D), Distortion (E), and Coma (F), and are given by the equation: phasedifference = -1/4 B rho^4 - C yo^2 rho^2 Cos[theta]^2 - 1/2 D yo^2 rho^2 + E yo^3 rho Cos[theta] + F yo rho^3 Cos[theta]. See also: ZernikeFit, ZernikePolynomial, ResidualFitError, and ZernikeOrder.

SeriesExpand

SeriesExpand->parameters is a option that specifies which symbolic parameters are Taylor-series expanded.

SeriesExpand->Automatic is the default and most common setting. SeriesExpand->{SymbolicRayTilt, SymbolicRayEnd} would be an example of a user-specified setting.

See also: SeriesOrder and LocalCoordinateExpansions.

SeriesOrder

SeriesOrder is a option that specifies Taylor series expansion order used for symbolic calculations.

See also: SeriesExpand and LocalCoordinateExpansions.

ShowGaussian

ShowGaussian is an option of ShowSystem that renders a depiction of the Gaussian beam curvature and spot size (at 1/e of the amplitude) together in the optical system.

Note that one or more GaussianBeam sources must be present in the optical system input before ShowGaussian can produce any results.

See also: BeamSpotSizeGraphics, BeamCurvatureGraphics, and GaussianPlot.

ShowPerfectCase

ShowPerfectCase is an option of PointSpreadFunction and OpticalTransferFunction that indicates whether the ideal behavior of the equivalent diffraction-limited imaging system should be plotted as a reference line (or curve).

SignalPlotCutoff

SignalPlotCutoff is an option of PointSpreadFunction that gives the threshold factor to select the plot domain of the displayed point spread function data.

The SignalPlotCutoff threshold is defined as the ratio of the minimum signal to the peak signal. Note that SignalPlotCutoff does not change the actual point spread function data output, which is left uneffected. SignalPlotCutoff is also used to calculate the DiffractionSpotSize value. For SignalPlotCutoff->False, the plot domain is the entire data set and DiffractionSpotSize measures the half-maximum signal level.

SkipSimplify

SkipSimplify->{identification numbers} is an option that specifies a set of Simplify operations to be skipped during the symbolic calculation process.

SkipSimplify is used primarily by SymbolicTrace and related functions. During the symbolic calculation a unique identification number is assigned to each Simplify call event and used with SkipSimplify. These numbers are printed to the screen with the option setting RunningCommentary->Simplify or RunningCommentary->All.

See also SymbolicTrace, FindABCDMatrix, $SimplifyID, and GaussianTrace

SphericalAberration

SphericalAberration is a rule returned by ZernikeFit that gives the spherical portion (B) of the primary Seidel aberration coefficients.

See also: SeidelAberrations.

StrehlRatio

StrehlRatio is a rule returned by PointSpreadFunction that gives the ratio of the peak intensity of a perfect system to the peak intensity of the actual system.

SymbolicABCDCenterPoint

SymbolicABCDCenterPoint is a rule that provides the symbolic global three-dimensional surface point location used making the symbolic ABCD-matrix calculations.

See also SymbolicABCDMatrix and SymbolicABCDRotationMatrix.

SymbolicABCDMatrix

SymbolicABCDMatrix is a rule that indicates symbolic ABCD-matrix data.

See also: ABCDMatrix, ABCDCenterPoint, and ABCDRotationMatrix.

SymbolicABCDRotationMatrix

SymbolicABCDRotationMatrix is a rule that gives a symbolic 3 x 3 matrix of spatial rotations invoked on the original ABCD-matrix object coordinate system.

SymbolicABCDRotationMatrix is used in making the SymbolicABCD-matrix calculations. See also SymbolicABCDMatrix and SymbolicABCDCenterPoint.

SymbolicAperture

SymbolicAperture is a rule used with symbolic calculations that specifies an analytic expression for the transmittance of intensity at a particular surface.

See also SymbolicIntensity.

SymbolicTrace

SymbolicTrace[opticalsystem, assumptions, options] is a function that finds the symbolic solution of one or more light sources passing through optical system.

SymbolicTrace can also take the symbolic Taylor-series expansion of one or more specified parameters, as given in assumptions, in order to reduce the overall complexity of the resulting solution.

SystemABCDMatrix

SystemABCDMatrix is a rule that specifies the ABCD matrix representation of the complete optical system as originally specified.

See also: LensABCDMatrix.

TaylorSeries

TaylorSeries[f, {x, x0, n}] generates a power series expansion for f about the point x = x0 to order (x - x0)^n. TaylorSeries[f, {x, x0, nx}, {y, y0, ny}] successively finds series expansions with respect to y, then x. TaylorSeries performs the same mathematical operations as the built-in Series function of Mathematica, but overcomes some apparent difficulties with Mathematica's built-in Series function.

In particular, in some cases, the built-in Series function appears to freeze Mathematica under varying conditions. However in cases with very large calculations, the new TaylorSeries function may perform much more slowly than the built-in Series function. Therefore, in order to handle these varying conditions, TaylorSeries is also an option name of the TaylorSeries function that indicates which internal algorythm is used by TaylorSeries. TaylorSeries->(TaylorSeries or True) always uses the TaylorSeries algorythm. TaylorSeries->Automatic switches to the built-in Series function for order terms larger than 2. TaylorSeries->(Series or False) uses the internal Series function at all times.

See also: Series.

TransverseMagnification

TransverseMagnification is a rule that specifies the transverse magnification that occurs between the object and image points in a conjugate imaging system.

See also: AngularMagnification and SystemABCDMatrix.

WaveFrontIntensity

WaveFrontIntensity is a returned rule that gives a continuous intensity function at a designated surface.

WaveFrontIntensity is also a label used with the RenderedParameters option.

Wavica

Wavica is an extension of Wavica for wave propagation-related activities. This version 1.0 has the build-date Dec 14, 2004.

See also: Needs, $SystemSymbolsInWavica.

WavicaPrivate

WavicaPrivate[switch] put the Wavica private context on the $ContextPath (switch equals True) or remove it (switch equals False). See also: SwitchContextPath.

WavicaSymbols

WavicaSymbols[string] returns a list of names defined in Wavica that are related to the given parameter string. It is fixed at the ending of the loading process and derived from ListedSymbolNames.

ZernikeFit

ZernikeFit[{{coordinatepoint, opticalpathlength},...}, options] is a utility function that attempts to find a Zernike polynomial equation fit to the wavefront data as given by a list of two-dimensional coordinates and optical path length values (in wavelength units).

ZernikeFit->True is also a option that indicates the use of a Zernike polynomial equation fit to a wavefront. ZernikeFit->False usually indicates the use of an Interpolation function instead.

See also: ZernikePolynomial, ZernikeOrder, SeidelAberrations, and ResidualFitError.

ZernikeOrder

ZernikeOrder is a option to ZernikeFit that indicates the maximum series order to be fitted in the Zernike polynomial series.

See also: ZernikeFit, ZernikePolynomial, SeidelAberrations, and ResidualFitError.

ZernikePolynomial

ZernikePolynomial is a rule returned by ZernikeFit that gives the Zernike polynomial equation fit to a optical path data (in wavelength units).

See also: ZernikeFit, ZernikeOrder, SeidelAberrations, and ResidualFitError.

$SimplifyByteConstraint

$SimplifyByteConstraint is an global variable used internally by SymbolicTrace to limit the ByteCount size of expressions. Initially, $SimplifyByteConstraint is set to be equal to the MaxByteCount option setting. In the event that a Simplify evaluation of an expression exceeds its TimeConstraint, the value of $SimplifyByteConstraint is reset to the offending expression's ByteCount multiplied by a factor of 0.75.

$SimplifyID

$SimplifyID is an global variable used internally by SymbolicTrace to track specific Simplify call events. The value of $SimplifyID is automatically incremented with every new internal call to a Simplify or FullSimplify function and is used in the SkipSimplify option to skip particular simplify operations.

$SystemSymbolsInWavica

$SystemSymbolsInWavica is a list of symbols in the System context, used specially or modified in Wavica.

$WavicaContext

$WavicaContext is the public context of Wavica.

$WavicaData

$WavicaData is the data directory of Wavica.

$WavicaHome

$WavicaHome is the home directory of Wavica.

$WavicaMainFile

$WavicaMainFile is the filename of the central file of Wavica.

$WavicaMessageFile

If Wavica use a message file, $WavicaMessageFile is taken.

$WavicaPalette

$WavicaPalette is the filename of the loading palette of Wavica.

$WavicaPaletteName

$WavicaPaletteName is the filename with path of the loading palette of Wavica.

$WavicaPalettes

$WavicaPalettes is the palettes directory of Wavica.

$WavicaPrivateContext

$WavicaPrivateContext is the private context of Wavica.

$WavicaUserContext

$WavicaUserContext is the public context of Wavica for files provided by a user.

$WavicaUserPrivateContext

$WavicaUserPrivateContext is the private context of Wavica for files provided by a user.

Created by Mathematica (July 11, 2005)