Raytrace - Coherent Field Synthesis

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Coherent Field Synthesis

Page Contents

Description

Navigation

Controls

Application Notes

•How field synthesis works

•Clipping the field with a curve

•Importing fields from file

Related Topics

References

Description

This feature creates a new coherent rayset using Gabor synthesis from a user-calculated complex field. The new rayset is synthesized from a collection of Gaussian beamlets whose amplitude, phase and directional distribution are determined by the complex field characteristics as well as the area and spatial resolution over which the original field was calculated. The Gaussian Beamlet Parameters in the Coherent Field Synthesis dialog allow the appropriate method of synthesis to be selected from possibilities spanning two limiting cases; the pure positional synthesis, which creates gaussian beamlets on a rectilinear grid and the pure directional synthesis, which creates all beamlets at the center of the analysis surface area each having different directions, amplitudes and phases. The synthesized rayset will propagate along the +Z axis of the associated analysis grid.

Navigation

This feature can be accessed in the following ways:

•		Menu > Raytrace > Coherent Field Synthesis
•		Right mouse click in the chart viewer after calculating a complex scalar or vector field and select Coherent Field Operations > Synthesize Field from the list menu

Controls

Control	Inputs / Description	Defaults
Location/Orientation
Location/Orientation	Set coordinate system and Location/Orientation of the new rayset.	Global/None
Gaussian Beamlet Parameters
Semi-Ape at exp(-p)	X and Y Halfwidths of individual Gaussian beamlets given as an integer. Min val = 2 Max val = N (number of pixels in X or Y)	2,2
Max Ray Shift	Integer number of extra beams supplied for smoothing. Min val = 0 Max value = Int(N/Semi-Ape integer)/2 + 1	0,0
Max Ray Angle	Integer value corresponding to the Maximum ray angle (in degrees) measured from plane normal direction. Min val = 0 Max val = N/2	0,0
Wavelength (mm)	Source wavelength	Default system wl
Immersion material	Rays are immersed in this material.	Air
Power Cutoff Threshold	Specify Absolute Ray Power and Fraction of Max Ray Power. Discard rays with powers below these thresholds.	0,0
Polarization	Sets the polarization of the synthesized source. If the field is a vector field, then this option is disabled.	Unpolarized
Scalar Field Sample Grid
Grid cells	Displays the real and imaginary values at each field point. Field edit options can be accessed by right mouse clicking in the cell area: •Set Size •Read from File •Write to File •Modify Field Values	0,0

Create Rays	Create coherent rays from input data.
Append/Replace Rays	Append to current rayset or Replace current rayset.	Append
Dismiss	Dismiss dialog box.
Help	Access this Help page.

Application Notes

How field synthesis works

The general approach behind Coherent Field Synthesis is the creation of a coherent rayset that, when coherently summed, yields a desired coherent scalar field. The rayset consists of a collection of coherent Gaussian beamlets each having the same size. The spatial distribution of this collection is a rectilinear array which may span the spatial size of the scalar field or emanate from a central location. The angular distribution is a rectilinear array in direction cosine space which may span a predetermined angular size. That is, at each spatial location there is a number of rays all pointing in different directions.

The coherent field to be synthesized can be entered directly in the dialog box data area or read from a text file. FRED can create a text file representation of a coherent field after calculating the Coherent Scalar Wave Field by accessing the 'Save Complex Field to File' option from the popup menu in the Chart Viewer. The Analysis Surface used in calculating the Coherent Scalar Wave Field specifies the sampling of the scalar field to be synthesized. The relationship between angular and spatial frequency is given by 1/N = Df * Dx where N is the number of samples in a given dimension, Df is the angular frequency and Dx is the pixel dimension.

The Coherent Field Synthesis dialog is used to specify the Gaussian beamlet size "L" (defined as the exp(-p) amplitude point, and is related to the angular frequency by Df = 1/L), the wavelength l, and the refractive index "n" of immersion material. Once this information is specified, the spatial and angular array spacings are automatically determined. The spatial array spacing is equal to the beamlet size, L. The angular spacing in direction cosine space is determined from the equation sin(q_i) = i* l/(n*L) = i* l Df/n. The user has direct control in the dialog box over the spatial and angular extent of rays that are created.

In practice it is often difficult to specify the proper field sampling, beamlet size, spatial limit, and angular limits in order to create a rayset that accurately synthesizes the given field. The user must often try many different combinations of parameters before arriving at a satisfactory result. However, there are some general rules that can be used to guide this process.

•	Never assume that the computed rayset gives an accurate synthesis of the field without verification. In this regard, it is recommended that a coherent field analysis be done and compared this with the original field.
•	The more densely sampled the original scalar field the better. Sparse sampling can lead to inaccuracy regardless of how the user-specified parameters are set.
•	In general, the more rays created, the more accurate the result will be.
•	With regard to the ray size "L", bigger is better. The algorithm computes faster for bigger rays and is also numerically more accurate. In fact, small rays can be inaccurate by a very large amount.
•	Wider angular ranges are better than smaller ranges. When possible, however, limit the angular range of the rayset to the acceptance cone of the receiving optical system.
•	You can extend spatial range to one position bigger than extent of the field using the L parameter. Occasionally, you may need a slightly bigger range to accurately model field edge effects.
•	The total number of spatial ray positions is the main factor in determining how long the calculation will take. The more ray positions, the longer the time required for the calculation. The effect of more ray directions is less important.
•	Smoother fields can be synthesized with fewer rays than fields with sharp discontinuities.
•	The angular divergence of individual beamlets is inversely proportional to the beamlet size. Smaller beamlets spread more rapidly than big beamlets as they propagate.
•	A beam overlap factor has been added to address the limiting case of a directional synthesis where all beams emit from a single point each having different directions, amplitudes and phases. The recommended value is 1/1.5 or 0.67.

Clipping the Field with a Curve

It is also possible to apply clipping to a complex field from the chart viewer by right mouse clicking in the chart view and selecting Coherent Field Operations > Apply Clipping to Field. When this option is selected, a drop down menu will present a list of valid clipping curves. NOTE: Aperture Curve Collections are the only valid clipping curve types. As always, an Aperture Curve Collection may contain more than one curve and specifies whether to keep what is inside (Clear Aperture) or outside (Hole,Obscuration) of the curve. The same philosophy applies here as with the use of curves for trimming surfaces. All curves must be closed either by their definition or as Composite Curves.

As an example, the scalar field calculated below is to be clipped by a triangular curve keeping only the field inside the triangle.The following steps are taken.

1.	Create a triangular segmented curve.
2.	Place the segmented curve into an aperture curve collection and specify its use as Clear Aperture.
3.	Calculate the coherent field, right mouse click in the 3D chart view and select Coherent Field Operations > Apply Clipping to Field (see also ClipFieldInFile script command).
4.	Choose the aperture curve collection from step 2 as the clipping curve.

The following images show the segmented curve definition, aperture collection curve and the resulting clipped field (original field was a simple plane wave).

Importing vector fields

*.fgd and *.dat files can be imported into the coherent scalar field synthesis dialog by right mouse clicking in the scalar field sample grid and selecting "Read From File". If a vector field file is chosen for import, FRED will prompt the user to choose either the X or Y field component for synthesis.