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Description
The spatial resample feature computes the complex field from an existing coherent rayset and generates a new set of coherent rays that approximately reproduce an incident field over an extended spatial area, with the spatial area being the rectilinear grid corresponding to an Analysis Surface. This feature is most often used when complex rays fail to propagate beyond a certain point in the model due to coherent ray failures or when an increase in ray sampling of an aperture is required.
It is often impractical to calculate the field at sufficiently high resolution to avoid ambiguity in unwrapped phase differences greater than 2p between adjacent pixels. The following assumptions are made as part of the spatial resampling process:
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1.
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The input field's wavefront has tilt and/or is primarily spherical.
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2.
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Once the spherical and tilt contributions are removed from the phase of the input field, the remainder can be unwrapped locally between adjacent pixels.
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The following steps generically describe the process for spatial field resampling:
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1.
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The input field is fitted (either explicitly by the user or by optimization) to a sphere.
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2.
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The spherical and tilt terms from (1) are subtracted from the input phase and what remains is the "perturbed" wavefront.
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3.
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The perturbed wavefront is fit with a new set of coherent rays.
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4.
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The base spherical and tilt terms are added back to the complex field and the rays are adjusted to be normal to the local wavefront.
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Navigation
This feature can be accessed in the following ways:
•Menu > Raytrace > Spatially Resample Field
Controls
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Control
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Inputs / Description
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Defaults
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Analysis Surface
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Existing Analysis Surface to be used for resampling. This Analysis Surface must have the Ray Specification Rays on specified surface "Geometry.XXXX.xxxx" where xxxx is surface on which the rays to be resampled currently reside. Additional Ray Specifications on the selected Analysis Surface are also implemented.
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Currently selected Analysis Surface or first Analysis Surface in folder
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Field Choice
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Use single component...
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The spatial resampling feature can operate on both scalar (non-polarized) and vector (polarized) fields. When this option is unchecked, the spatial resampling will be performed on the scalar field component and vector field components will be ignored. When checked, the user can then activate the vector component(s) they wish to resample and scalar field components will be ignored.
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Unchecked
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Vector field component(s)
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When choosing to resample a vector field (see above) the user can toggle the components of interest that will be resampled.
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X, Y Checked
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Reference Wavefront
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Type
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Specification for reference wavefront to be subtracted from calculated field. The reference wavefront can be specified in terms of 1) tilt and curvature or 2) the center of a sphere. These specifications are given in the coordinate system of the Analysis Surface.
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Tilted spherical specified as tilt and curvature
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Parameters determined by fitting: Number of guesses
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Number of guesses used to determine the reference wavefront. If this parameter is zero then values under User Specified Parameters are used to specify the reference wavefront.
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150
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User Specified Parameters
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Values:
1) X,Y,Z Tilt vector in Analysis Surface coordinate system and reference wavefront curvature
2) center of reference sphere in Analysis Surface coordinate system
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unchecked
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Ray Generation
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Associate with entity
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Entity name with which to associate resampled rays.
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System
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Immersion Material
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Immersion material in which rays begin propagation.
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Air
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Neighbor overlap factor X,Y
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The overlap factor is a multiplier that scales the starting waist size of the individual gaussian beamlets. When the overlap factor is set to 1.0 the individual beamlet waists will match the width of a pixel in the analysis grid. An overlap factor between 1.4 and 1.6 is recommended for most applications. For more information on the effects of the overlap factor, please refer to Coherent Sources Overview.
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1.5
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Relative power cutoff
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Rays are not created at pixel locations when the field magnitude falls below this cutoff value relative to the field power maximum.
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1e-10
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Replace Rays
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Flag indicating whether original rayset is to be deleted after creation of resampled rays. In most cases, the original rayset should be deleted. Newly created rays will be colored opposite the background color of the 3D viewer.
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checked
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Display Pre-resampled Field
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As calculated
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Displays to Chart Viewer the original complex field before subtraction of reference wavefront.
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unchecked
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With reference wavefront subtracted from phase
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Displays to Chart Viewer the residual complex field after subtraction of reference wavefront.
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unchecked
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OK
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Accept settings and close dialog box.
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Cancel
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Cancel and close dialog box.
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Help
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Access this Help page.
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Application Notes
Reference wavefront tilt vector and sphere center
The tilt vector and sphere center for the reference wavefront are specified in the coordinate system of the selected Analysis Surface and are relative to the center of the Analysis Surface. The curvature is defined as positive for a reference sphere surface that bends in the direction of the tilt vector.
Analysis surface autoscaling
Analysis surfaces with autoscaling are fully supported, but one needs to keep in mind that tilts and curvature are relative to the plane's center, which will vary depending on the results of the autoscaling. Because of this, it is best to not use autoscaling unless reference wavefront fitting is selected.
Beamlet overlap
The Beam overlap factor for each resampled coherent ray is 1.5 and is not directly adjustable by the user.
Sizing the resampling analysis surface
Upon resampling, a coherent ray is created at the center of each pixel of the selected Analysis Surface. Consideration must therefore be given to Analysis Surface pixel spacing with respect to the fundamental limitations of complex raytracing. As a general rule, the pixel spacing should be much greater than a wavelength to avoid coherent ray errors related to Invariant violations or secondary ray failures. For more information on this topic, see Introduction to Coherent Sources.
Output window information
When this feature is implemented, standard complex field output is printed to the Output Window. If the fitting routine is used, this output is followed by a summary containing the number of rays created, number of rays deleted and fit results for the reference wavefront.
Afocal telescope example
This accompanying FRED file for this example, exampleSpatiallyResampleAfocalTelescope.frd, is found in the <install dir>\Resources\Samples\Tutorials & Examples installation directory and illustrates FRED’s Field Resampling feature applied in the case of a Galilean afocal which truncates the input from a Nd:YAG laser with 1/e2 half-width of 1 mm.
As shown below, the beam enters the 1st lens (PCV) producing a divergent ray bundle which causes significant reduction in spatial sampling at the 2nd lens (PCX). If the source is incoherent, then simply increasing ray density entering PCV addresses the problem adequately. However, if the source is coherent, an arbitrary increase in ray grid density at PCV leads to complications which will be discussed in this example.
The Field Resampling feature offers a solution to this predicament by resampling the incident wavefront just before entering PCX and, in effect, resizing the beamlets such that they sample its aperture . To that end, two planes are created a small distance to the left of PCX. The first of these planes “.resample.Surf 1” is transmissive and sized such that it intercepts all the rays exiting PCV. This is of utmost importance since the field will be resampled at this plane and therefore must include the coherent contribution of each and every ray. Attached to “.resample.Surf 1” are two Analysis Surfaces, “full beam before L2” and “Resample AS”. The first of these, “full beam before L2” is used simply to examine the irradiance pattern in the resample plane. The second Analysis Surface, “Resample AS” will be used for the function of resampling the beam. Note that “Resample AS” is sized slightly larger (26mm half-height) than the 25mm clear aperture of PCX since it is only over this area resampled beamlets need be created. Also note that "Resample AS" is shifted by a small distance off of the surface “.resample.Surf 1”. The second surface “.resample.Surf 2” is an absorbing surface located between “.resample.Surf 1” and PCX with a rectangular Outer Trim Volume of half-height 30mm and a circular Inner Trim Volume equal to the clear aperture of PCX. The surface “.resample.Surf 2” acts to block resampled beamlets outside the aperture of PCX as would any opto-mechanical mount.
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The following steps can be executed manually from the GUI to perform the resampling:
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1.
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From the Advanced Raytrace dialog, trace the source rays to the resampling plane using the resampling plane "Geometry.resample.Surf full" as the stopping surface.
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2.
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Open the Spatially Resample Field Dialog box and select Analysis Surface "Resample AS". Accept the default settings for Reference Wavefront allowing FRED to guess the wavefront curvature and tilt vector as well as Ray Generation starting the rays on the System Entity immersed in Air. It is recommended that the "as calculated" and residual fields be displayed to confirm the calculation.
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3.
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With rays now existing after the Resampling feature has executed, trace these new rays through the remainder of the system by employing Trace Existing and Render or Trace Existing Rays.
.png) .bmp)
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4.
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Finally, calculate the irradiance pattern of the rayset transmitted through the PCX lens using the Analysis Surface "Obs Plane". The pattern shown below is indicative of a highly truncated yet collimated Gaussian beam.
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Related Topics
Spatially Resample Scalar Field - Script
Coherent Sources Overview
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