<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html> <head> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <meta name="Generator" content="Microsoft Word 97"> <meta name="GENERATOR" content="Microsoft FrontPage 4.0"> <title>WaveTrain glossary</title> </head> <body> <p><font face="Arial"><a href="../../copyright.htm" target="_blank">Copyright 1995-2002&nbsp;</a>&nbsp; <a href="http://www.mza.com" target="_top">MZA Associates Corporation</a></font></p> <p><b><font face="Arial" size="6">WaveTrain Glossary</font></b></p> <p><font face="Arial"><b><a href="#Absorbing boundaries">A</a> <a href="#birefringence">B</a> <a href="#Clear 1 Night">C</a> <a href="#DMModel">D</a> E <a href="#FieldSensor">F</a> G <a href="#Hill bump.">H</a> <a href="#incoming">I</a> J <a href="#KolmogorovModel">K</a> L <a href="#Markov approximation"> M</a> N <a href="#outer scale"> O</a> <a href="#PhaseScreen"> P</a> Q <a href="#reference wave"> R</a> <a href="#SpatialFiltering"> S</a> T U V <a href="#wave"> W</a> <a href="#x"> X</a> <a href="#y"> Y</a> <a href="#z"> Z</a></b></font></p> <hr> <p><font face="Arial" size="3"><a NAME="AbsorbingBoundaries"></a><b><a name="Absorbing boundaries">Absorbing boundaries</a></b> <br>Absorbing boundaries are a mechanism sometimes used when simulating optical propagation to avoid <b><a href="#wraparound">wraparound</a></b>. Absorbing boundaries avoid this problem by multiplying the light after each propagation step by a filter ( in the spatial domain, not the spatial frequency domain), which is unity over the central region, then falls smoothly to zero at the edge of the mesh. Absorbing boundaries can themselves produce artifacts, because some light moving toward the edge of the mesh may be reflected back into the inner portion of the mesh, but this is generally less of a problem than wraparound. Absorbing boundaries are often used in combination with <b><a href="#SpatialFiltering">spatial filtering</a></b>, i.e. filtering in the spatial frequency domain. Under some circumstances these techniques can make it possible to use a smaller propagation mesh than would otherwise be needed, reducing simulation execution time.</font> <p><font face="Arial" size="3"><a NAME="AcsAtmSpec"><b>AcsAtmSpec</b> </a> <br>AcsAtmSpec is a C++ class which defines an <i>atmospheric specification</i>, used for a parameter to the WaveTrain components <b><a href="AtmoPath.html">AtmoPath</a></b> and <b><a href="GeneralAtmosphere.html">GeneralAtmosphere</a></b>. This specifies the detailed modeling parameters for a particular optical propagation path through the atmosphere: the path length, the altitude at each end, the number and placement of phase screens, the integrated turbulence strength (C<sub>n</sub><sup>2</sup>) and inner scale for each screen, and so forth. Atmosphere specifications can be created using <b><a href="../../turbtool/index.html">turbtool</a></b>, and for certain common cases (e.g. uniformed turbulence, or scaled Clear1) we have also provided a more convenient function call interface. <a href="../../turbtool/index.html#acsatmspec">Also see this link</a>.</font> <p><font face="Arial" size="3"><a NAME="AoTool"><b>AoTool</b> </a> <br>AoTool is a special purpose graphical interface used for setting up adaptive optics geometries. This includes wavefront sensor subaperture geometries and deformable mirror actuator geometries, influence functions, and slaving relationships. AoTool is implemented using the Matlab<sup>TM</sup> graphical user interface facility, and comes with a number of Matlab m-files for use in analyzing the properties of candidate geometries and setting up wavefront reconstructor matrices.</font> <p class=MsoNormal style="word-spacing: 0; margin: 0">&nbsp;</p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><b><a name="birefringence"><font face="Arial" size="3">birefringence</font></a></b></p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">Birefringence is a property associated with anisotropic optical media, such as certain types of crystals or materials under stress, where the index of refraction differs for different polarization components.</font></p> <p class=MsoNormal style="word-spacing: 0; margin: 0">&nbsp;</p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><b><a name="Clear 1 Night"><font face="Arial" size="3">Clear 1 Night</font></a></b></p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">One of a number of well-known models for the variation of turbulence strength with altitude, derived from experimental data.</font></p> <p class=MsoNormal style="word-spacing: 0; margin: 0">&nbsp;</p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><span style='font-family:Arial'><b><a name="coherence length">coherence length</a></b></span></p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><span style='font-family:Arial'>The coherence diameter, sometimes called the  Fried coherence diameter </span></p> <p class=MsoNormal style="word-spacing: 0; margin: 0">&nbsp;</p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><span style='font-family:Arial'><b><a name="collimated">collimated</a></b></span></p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><span style='font-family:Arial'>Collimated light is light which as it propagates remains compact in the dimensions perpendicular to the direction of propagation.<span style="mso-spacerun: yes"> </span>Generally a beam of light will be collimated if and only if it is coherent, the transverse diameter of the beam is very large compared to the wavelength, and the phasefront is very nearly flat.</span></p> <p class=MsoNormal style="word-spacing: 0; margin: 0">&nbsp;</p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><b><a name="Cn2"><font face="Arial" size="3">C<sub>n</sub><sup>2</sup></font></a></b></p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">Cn2 is a measure of the strength of turbulence, defined in terms of random variations in the index of refraction.<span style="mso-spacerun: yes"> </span>For a detailed description, see Goodman, Statistical Optics.</font></p> <p><font face="Arial" size="3"><a NAME="CoordinateSystems"></a><b><a name="Coordinate systems">Coordinate systems</a></b> <br>In WaveTrain different coordinate systems can be used in different parts of a system model, so that in setting up each part of the model you can work in whatever coordinate system is most convenient. Thus for setting up a model of a moving you would generally choose to work in a coordinate system moving with the target, while for modeling a moving optical system you would work in a coordinate system moving with it. Then, at the interfaces between coordinate systems, you use <b><a href="TransverseVelocity.html">TransverseVelocity</a></b> components to perform the appropriate coordinate transformations in x and y. Displacements in z involve optical propagations, which can be modeled using <b><a href="AtmoPath.html">AtmoPath</a></b>, <b><a href="GeneralAtmosphere.html">GeneralAtmosphere</a></b>, or <b><a href="VacuumProp.html">VacuumPropagator</a></b>. Velocity differences in z can generally be neglected.</font> <p style="word-spacing: 0; margin: 0">&nbsp; <p style="word-spacing: 0; margin: 0"><font face="Arial" size="3"><a NAME="DMModel"></a><b>DMModel</b> </font> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">DMModel is a C++ class, part of the WaveTrain class library, which is used to carry all the information necessary to describe a complete adaptive optics geometry (deformable mirror and wavefront sensor), plus the reconstructor matrix used to compute DM actuator commands from wavefront sensor subaperture slopes.</font></p> <p><font face="Arial" size="3"><a NAME="FieldSensor"><b>FieldSensor</b> </a> <br>FieldSensor is the base class for all non-realistic (field sensing) optical sensor models in the WaveTrain component library. It in turn is derived from <b><a href="#WaveSensor">WaveSensor</a></b> which is the base class optical sensor models, both realistic and nonrealistic. WaveSensor takes care of the logic related to opening and closing the shutter, remeasuring the detected light incident illumination changes, readout lag, and so forth; FieldSensor assumes that the quantity measured is the complex field, defined on a rectangular mesh.</font><p><font face="Arial" size="3"><a NAME="Filter"><b>Filter&nbsp;</b></a></font> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">Filter is a C++ class, part of the WaveTrain class library, which is used to specify spatial filters and absorbing boundaries for use in modeling optical propagation.</font></p> <p class=MsoNormal style="word-spacing: 0; margin: 0">&nbsp;</p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><b><a name="Fourier optics propagator"><font face="Arial" size="3">Fourier optics propagator</font></a></b></p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">To propagate a wavefront from one plane to another in WaveTrain, we make use of the fact that in scalar diffraction theory the field at one plane can be computed from the field at another plane using Fourier transforms in combination with quadratic phase factors, as can be seen by inspecting the form of the Fresnel propagation integral.<span style="mso-spacerun: yes"> </span>(see Goodman, <u>Introduction to Fourier Optics</u>)<span style="mso-spacerun: yes"> </span>Also, it turns out that by using two Fourier transform rather than just one, one can control the mesh spacing at the propagated plane, which is crucial in wave optics simulation, so wave optics codes generally use a  two-step Fourier optics propagator.</font></p> <p class=MsoNormal style="word-spacing: 0; margin: 0">&nbsp;</p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><b><a name="Hill bump."><font face="Arial" size="3">Hill bump.</font></a></b></p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">The Hill bump is a feature of the power spectrum of fluctuations in the refractive index of air due to turbulence.<span style="mso-spacerun: yes"> </span>Based on work by the Russian mathematician Kolmogorov, the power spectral density curves is expected to consist of three distinct regions: <span style="mso-spacerun: yes"></span>At low frequencies and large scales we expect to see features related to the processes with give rise to the turbulence in the first place; little is known about the actual shape of the spectrum in this regime.<span style="mso-spacerun: yes"> </span>At intermediate frequencies and scales the spectrum goes over to a straight power law, reflecting the self-similarity of the energy cascade as larger turbules contribute energy to smaller turbules; the a slope is  11/3.<span style="mso-spacerun: yes"> </span>At the highest frequencies and smallest scales viscosity becomes a factor, breaking the self-similarity, and the downward slope of the power spectrum increases rapidly. <span style="mso-spacerun: yes"></span>However just before it does so, there is a small region where the power actually goes up appreciably above the  11/3 line; this is the Hill bump.</font></p> <p class=MsoNormal style="word-spacing: 0; margin: 0">&nbsp;</p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><b><a name="Hufnagel-Valley 5/7"><span lang=FR style='mso-ansi-language: FR'><font face="Arial" size="3">Hufnagel-Valley 5/7</font></span></a></b></p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">One of a number of well-known models for the variation of turbulence strength with altitude, derived from experimental data.</font></p> <p><font face="Arial" size="3"><a NAME="incoming"><b>Incoming (describing a WaveTrain input or output ) </b> </a> <br>Many WaveTrain optical components can act upon light incident upon them from either of two opposite directions, and typically these components have two or more WaveTrain inputs and two or more WaveTrain outputs. To help the user keep track of which inputs are related to which outputs, we have adopted a convention of referring to one direction as <i>incoming</i> and the other as <i>outgoing</i>, which by convention refer to light propagating in the direction of decreasing and increasing <b>z</b>, respectively. In general there is nothing to prevent one from connecting a component the opposite way, but for components which act upon the phase of the light one must take the sign reversal into account.</font><p style="word-spacing: 0; margin: 0">&nbsp;<p style="word-spacing: 0; margin: 0"><font face="Arial" size="3"><a NAME="InnerScale"></a><span lang=FR style='mso-ansi-language: FR'><b><a name="inner scale">inner scale</a></b></span></font> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">The inner scale is a feature of the power spectrum of fluctuations in the refractive index of air due to turbulence.<span style="mso-spacerun: yes"> </span>Based on work by the Russian mathematician Kolmogorov, the power spectral density curves is expected to consist of three distinct regions: <span style="mso-spacerun: yes"></span>At low frequencies and large scales we expect to see features related to the processes with give rise to the turbulence in the first place; little is known about the actual shape of the spectrum in this regime.<span style="mso-spacerun: yes"> </span>At intermediate frequencies and scales the spectrum goes over to a straight power law, reflecting the self-similarity of the energy cascade as larger turbules contribute energy to smaller turbules; the a slope is  11/3.<span style="mso-spacerun: yes"> </span>At the highest frequencies and smallest scales viscosity becomes a factor, breaking the self-similarity, and the downward slope of the power spectrum increases rapidly. <span style="mso-spacerun: yes"></span>The scale size marking the transition between these two parts of the spectrum is called the  inner scale .</font></p> <p><font face="Arial" size="3"><a NAME="integrationMethod"><b>integrationMethod</b> </a></font> <p><font face="Arial" size="3"><a NAME="IntensitySensor"><b>IntensitySensor</b> </a> <br>IntensitySensor is the base class for all realistic (intensity sensing) optical sensor models in the WaveTrain component library. It in turn is derived from <b><a href="#WaveSensor">WaveSensor</a></b> which is the base class optical sensor models, both realistic and nonrealistic. <b><a href="#WaveSensor">WaveSensor</a></b> takes care of the logic related to opening and closing the shutter, remeasuring the detected light incident illumination changes, readout lag, and so forth; IntensitySensor assumes that the quantity measured is intensity, defined on a rectangular mesh, and integrates it for each exposure interval.</font> <p><font face="Arial" size="3"><a NAME="KolmogorovModel"><b>Kolmogorov turbulence model</b> </a></font> <p><font face="Arial" size="3"><a NAME="MarkovApproximation"></a><b><a name="Markov approximation">Markov approximation</a></b> <br>A mathematical approximation underlying the standard wave optics approach for modeling propagation through the turbulent atmosphere. The import in this context is that the turbulence realizations for different phase screens may be generated independently, because the correlation length for phase perturbations is much much smaller than the distances between phase screens.</font><p style="word-spacing: 0; margin: 0">&nbsp;<p style="word-spacing: 0; margin: 0"><font face="Arial" size="3"><a NAME="OuterScale"></a><b><span lang=FR style='mso-ansi-language: FR'><a name="outer scale">outer scale</a></span></b></font> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">The outer scale is a feature of the power spectrum of fluctuations in the refractive index of air due to turbulence.<span style="mso-spacerun: yes"> </span>Based on work by the Russian mathematician Kolmogorov, the power spectral density curves is expected to consist of three distinct regions: <span style="mso-spacerun: yes"></span>At low frequencies and large scales we expect to see features related to the processes with give rise to the turbulence in the first place; little is known about the actual shape of the spectrum in this regime.<span style="mso-spacerun: yes"> </span>At intermediate frequencies and scales the spectrum goes over to a straight power law, reflecting the self-similarity of the energy cascade as larger turbules contribute energy to smaller turbules; the a slope is  11/3.<span style="mso-spacerun: yes"> </span>The scale size marking the transition between these two parts of the spectrum is called the  outer scale .</font></p> <p><font face="Arial" size="3"><a NAME="outgoing"><b>Outgoing (describing a WaveTrain input or output</b> <b> )</b> </a> <br>Many WaveTrain optical components can act upon light incident upon them from either of two opposite directions, and typically these components have two or more WaveTrain inputs and two or more WaveTrain outputs. To help the user keep track of which inputs are related to which outputs, we have adopted a convention of referring to one direction as <i>incoming</i> and the other as <i>outgoing</i>, which by convention refer to light propagating in the direction of decreasing and increasing <b>z</b>, respectively. In general there is nothing to prevent one from connecting a component the opposite way, but for components which act upon the phase of the light one must take the sign reversal into account.</font> <p><font face="Arial" size="3"><a NAME="PhaseScreen"><b>Phase screens</b> </a> <br>Phase screens are surfaces perpendicular to an optical propagation path defining an optical path difference as a function of position in the <b>x</b>-<b>y </b>plane. Phase screens are used in combination with vacuum propagations to model propagation through the turbulent atmosphere. Phase screens are typically generated randomly, but made to conform to a specified power spectrum characteristic of a particular turbulence model, such as the classic <b><a href="#KolmogorovModel">Kolmogorov model</a></b>.</font> <p><font face="Arial" size="3"><a NAME="PointSourceModeling"></a><b><a name="Point source modeling">Point source modeling</a></b> </font> <p class=MsoNormal style="word-spacing: 0; margin: 0">&nbsp;</p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><b><a name="reference wave"><font face="Arial" size="3">reference wave</font></a></b></p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">In wave optics simulation optical wavefronts are represented using a complex mesh, where the complex amplitude corresponds to the field amplitude, and the complex phase angle corresponds to the phase of the wavefront with respect to some  reference wave .<span style="mso-spacerun: yes"> </span><span style="mso-spacerun: yes"></span>Depending on the particular modeling problem, one might choose to use a planar or spherical reference wave, converging or diverging, depending on the nature of the light sources and sensors to be modeled and the size of the regions of interest at either end of the propagation path.<span style="mso-spacerun: yes"> </span>You can use different reference waves for different light sources, as described in (ADD LINK TO USER S GUIDE).</font></p> <p class=MsoNormal style="word-spacing: 0; margin: 0">&nbsp;</p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3"><b><a name="SpeedOfLight">s</a></b><a name="SpeedOfLight"><b>peedOfLight&nbsp;</b></a></font></p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">speedOfLight is a constant, equal to the speed of light in vacuum (c = 2.997925x10<sup>8</sup> m/s), defined in the file  PhysicalConstants.h , which is used by the WaveTrain library, so the symbol speedOfLight is always available for use in setting expressions.<span style="mso-spacerun: yes"> </span>It is most often useful for synchronizing event timing between one end of the optical propagation path and the other, as described in (ADD LINK TO USER S GUIDE).<span style="mso-spacerun: yes"> </span>It can also be useful in computing the lead ahead angles (e.g. v/c) for applications involving active illumination imaging and/or beam projection.&nbsp;</font></p> <p><font face="Arial" size="3"><a NAME="SpatialFiltering"><b>Spatial filtering</b> </a> </font> <p><font face="Arial" size="3"><a NAME="SpeckleModel"></a><b>SpeckleModel</b></font> <p><font face="Arial" size="3"><a NAME="SpeckleRealization"></a><b><a name="Speckle realizations">Speckle realizations</a></b> <br>Speckle realizations are used to model the light from an incoherent source. First, the total intensity incident on the reflector is computed, then multiplied by the specified reflectance map to obtain the reflected intensity. For each speckle realization, we create a field with that intensity pattern and a random phase pattern. Two different approaches for generating the random phase pattern are presently supported. In the first approach the phase is uniformly distributed on [-p:p] and delta-correlated. This results in putting significant energy into the highest spatial frequencies (highest angles) represented on the propgation mesh; depending on the mesh spacing, mesh size, propagation distance, and wavelength this can lead to wraparound when we propagate, where energy leaves one side of the mesh, then reappears on the other. To avoid this, we can use <b><a href="#SpatialFiltering">spatial filtering</a></b> and/or <b><a href="#AbsorbingBoundaries">absorbing boundaries</a></b>, or we can turn to the second speckle approach. In the second approach we generate a delta-correlated phase pattern as before, and combine it with the reflected intensity to create a field, also as before. However we then perform a vacuum propagation back to the target plane, then multiply the resulting field by a (spatial domain) filter which is set to unity over a region somewhat larger than the receiving aperture, then rolls off smoothly to zero. Finally, we do a second vacuum propagation, back to the source plane, and that gives us the speckle field. The net result is similar to spatial filtering, except that the effective spatial filter varies gradually as one moves across the source mesh, at each point preserving just that part of the radiation which after propagation will wind up near the receiver aperture. For large incoherent sources this can sometimes reduce the size of the propagation mesh required significantly, reducing simulation execution time.</font> <p class=MsoNormal style="word-spacing: 0; margin: 0">&nbsp;</p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><b><font face="Arial" size="3"><a name="Strehl ratio">Strehl ratio</a></font></b></p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">The Strehl ratio is one of the most commonly used performance metrics for both imaging and beam projection systems.<span style="mso-spacerun: yes"> </span>It is defined as the ratio of the on-axis intensity obtained for a given system under given conditions to the on-axis intensity which would have been obtained with a diffraction limited system with the same aperture and total power at the same range.<span style="mso-spacerun: yes"> </span>A rated quantity, sometimes called  peak Strehl is often used for systems operating under conditions where the maximum of the intensity is not necessarily expected to occur on-axis.<span style="mso-spacerun: yes"> </span>Peak Strehl is defined as the ratio of maximum of the long-term average intensity to the on-axis intensity for the corresponding diffraction limited system.</font></p> <p><font face="Arial" size="3"><a NAME="wave"><b>Wave</b> </a> </font> <p class=MsoNormal style="word-spacing: 0; margin: 0">&nbsp;</p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><b><span style='text-decoration: none; text-underline: none'><font face="Arial" size="3"><a name="wave optics">wave optics</a></font></span></b></p> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">Wave optics, or wave optics simulation, is a well-established paradigm for the numerical modeling of optical effects, including diffraction effects. <span style="mso-spacerun: yes"></span>Wave optics is based upon scalar diffraction theory, as described in Goodman, <u>Fourier Optics</u>.</font></p> <p><font face="Arial" size="3"><a NAME="WavefrontReconstruction"></a><b><a name="Wavefront reconstruction">Wavefront reconstruction</a></b> </font><p style="word-spacing: 0; margin: 0">&nbsp;<p style="word-spacing: 0; margin: 0"><font face="Arial" size="3"><a NAME="WaveReceiverDescription"></a><b><a name="WaveReceiverDescription&nbsp;">WaveReceiverDescription&nbsp;</a></b></font> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">WaveReceiverDescription is a C++ class, part of the WaveTrain library, used to carry all them information about an optical receiver, e.g. a sensor, necessary for the correct modeling the propagation of light from an arbitrary light source to that receiver.<span style="mso-spacerun: yes"> </span>This includes, for example, the minimum and maximum wavelength the receiver is sensitive to, and the physical location of the receiver.&nbsp;</font></p> <p><font face="Arial" size="3"><a NAME="WaveSensor"></a><b>WaveSensor</b> </font> <p><font face="Arial" size="3"><a NAME="WaveTrain class library"></a><b>WaveTrain class library</b> </font><p style="word-spacing: 0; margin: 0">&nbsp;<p style="word-spacing: 0; margin: 0"><font face="Arial" size="3"><a NAME="WaveTrain"></a><b><a name="WaveTrain&nbsp;">WaveTrain&nbsp;</a></b></font> <p class=MsoNormal style="word-spacing: 0; margin: 0"><font face="Arial" size="3">WaveTrain is a C++ class, part of the WaveTrain library, used to model optical interfaces, such as the interfaces between different optical components.<span style="mso-spacerun: yes"> </span>Most subsystems in the WaveTrain component library have one or more inputs and/or outrputs of type WaveTrain.<span style="mso-spacerun: yes"> </span>Light sources, e.g. lasers, generally have a single WaveTrain input, while optical sensors, e.g. cameras generally have a single WaveTrain input.<span style="mso-spacerun: yes"> </span>Two-way optical components, e.g. lens and mirrors, typically have two WaveTrain inputs and two WaveTrain outputs, one of each for each propagation direction.</font></p> <p><font face="Arial" size="3"><a NAME="wraparound"></a><b>Wraparound</b> <br>Wraparound is a common problem encountered when simulating optical propagation, a consequence of the finite extent of the propagation mesh: any light which in the course of propagation goes past the edge of the mesh on one side immediately reappears on the other. This is a simulation artifact, not representative of the behavior of the physical system being modeled, so it is a source of error.</font> <p><font face="Arial" size="3"><a NAME="x"></a><b><a name="X (coordinate axis)">X (coordinate axis)</a></b> </font> <p><font face="Arial" size="3"><a NAME="y"></a><b><a name="Y (coordinate axis)">Y (coordinate axis)</a></b> </font> <p><font face="Arial" size="3"><a NAME="z"></a><b><a name="Z (coordinate axis)">Z (coordinate axis)</a></b> <br>The z axis of all coordinate systems used in WaveTrain is defined to lie along the nominal propagation direction. By convention z=0 corresponds to the aperture of the main optical system, while the object being imaged or illuminated lies at some z>0. For purposes of labeling the WaveTrain input and outputs of two-way optical systems, the direction of increasing and decreasing z is referred to as <b><a href="#outgoing">outgoing</a></b> and <b><a href="#incoming">incoming</a></b> respectively.</font> </body> </html>