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would make the object fully transparent to Red objects but opaque for Green and Blue objects. Transparency only affects the display of rendered objects in the Model Window.

Importance Sampling Standard Expert

Importance sampling is a Monte Carlo technique in which rays are generated and propagated in specific directions in the optical system, which are “important” in determining the results you need. This improves sampling by increasing the number of rays reaching the surface or surfaces of interest to you. For a conceptual explanation of Importance Sampling, including a section titled “When Do I Need Importance Sampling?”, see “Importance Sampling” on page 7.2 in the Technical Reference chapter.

Importance Sampling can be applied to improve ray sampling for the following applications:

•Surface Scatter

•Bulk Scatter (see “Bulk Scattering” on page 4.6)

•Diffraction (see “Diffraction” on page 4.33)

•Surface Sources (see “Surface Sources” on page 5.22)

The solid angles for importance sampling are defined by circular, annular, or rectangular patches called importance sampling targets. These targets are not part of the solid model and are used only for importance sampling.

These Importance Targets are defined in one of two ways, manually or automatically. The Automatic Setup Of Importance Sampling can be used for optical systems for which a sequential prescription of surfaces can be defined. Models containing multiple potential stray light paths require manual setup of the targets. It is also possible to use the Automatic Setup to define Importance targets, and then add additional targets manually.

There are two classes of importance sampling targets, one for surfaces and one for objects. Surface importance sampling targets are applied to surfaces and affect rays generated from surfaces, i.e. surface scatter, aperture diffraction and surface sources. Object Importance sampling targets are used for generating bulk scattered rays.

Once Importance Sampling targets have been defined, they can also be edited, deleted and displayed. See “Display Importance” on page 2.47.

Defining Importance Sampling Targets (Manually)

You can manually specify importance sampling targets by selecting Define|Apply Properties and choosing the Importance Sampling tab of the Apply Properties dialog box (see Figure 4.18). The Importance Sampling targets dialog box allows you to directly specify the location, orientation, and dimensions of importance sampling targets. You can choose either Rectangular or Annular importance targets.

Note: Importance Targets may be displayed in the Model Window. See “Display Importance” on page 2.47.

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FIGURE 4.18 - The Apply Properties dialog box - Importance Sampling tab

The steps required to manually define Importance Targets are as follows:

1.Press Add to define a new importance sampling target.

2.Specify the number of importance rays. This is the number of rays generated upon scatter, diffraction, and so forth that are directed to or away from the Importance Target.

3.Specify the direction of the importance rays (either toward or away from the target).

4.Select the shape of the importance sampling target and enter the parameters for the location, orientation, and dimensions of the target.

5.Press Apply to store the information and update the surface with the Importance Sampling Property.

These five steps are discussed in more detail in the sections below.

Importance sampling can be further enhanced by specifying more than one importance sampling target for a given scattering surface. As many importance sampling targets as you wish can be specified for each scattering surface.

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TABLE 4.3. Fields in the Importance Sampling Dialog Box

Target	Target to add or modify.
Ray/cell	Specify the number of rays you want to go toward (or away from) the target.
Direction	Specify ‘Toward’ or ‘Away’ depending on whether you want the rays to go
	toward the selected importance sampling target or away from it.
Shape	Specify ‘Annular’ or ‘Rectangular’ as the shape of the importance sampling tar-
	get. The remaining dialog box options vary depending on which of these two
	you have selected.
Target Center	Specify the coordinates x, y, and z to establish the position of the importance
	sample surface.
Normal Vector	Specify the direction x, y, and z to establish the target normal.
Up Vector	Specify the direction x, y, and z to establish the up direction or height.
Target Size	Specify Outer and Inner radius for Annual target or the X and Y widths for rect-
	angular targets you have selected. An annular region with a zero inner radius
	will be an circle.
Cells	Specify the number of segments to use for the target. One segment is the
	default. For more information about “Cells”, see page 4.25.
Add Button	Press this button to add an importance sampling target as currently defined by
	the rest of the dialog box. To associate importance sampling with a particular
	surface, you must first select that surface in your model before you press the
	Add Button.
Apply Button	Press this button when you have completed defining or editing properties for
	the selected importance sampling target so that the changes take effect.

Delete Button Press this button to delete the displayed Importance Target

Adding Targets

To add an importance sampling target:

1.Select Define|Apply Properties.

2.With the Apply Properties dialog box open, select the Importance Sampling tab.

3.Select a surface (for surface scatter, diffraction, or surface source) or object (for bulk scatter) to which to apply an importance sampling target. Note that in the dialog box, a small drop-down box displays the number of importance sampling targets currently defined on the surface that you select.

4.Press the Add button to add an empty target.

5.Enter the values for the target direction, shape, size and orientation.

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6.Enter the number of rays to target to each cell.

7.Press Apply to save the data and apply the target.

You can also reach the manual setup of importance sampling by clicking the model window with the right mouse button, then by selecting Properties from the pop-up menu obtained.

Number of Importance Rays

Importance sampling will collect the flux from a random ray, caused by scattering for example, and aim it towards the defined target. The flux can be divided into multiple rays to improve the sampling of the ray trace by directing many rays toward each importance sampling target

If the importance sampling target subtends too large a solid angle OR the BSDF of the surface varies significantly (more than an order of magnitude) over the subtended angle OR if more sampling is desired, divide the target into cells.

Shape, Dimensions, and Location of Importance Targets

When setting up importance sampling targets manually, it is important that the solid angle subtended by the importance sampling target is less than one steradian. It might be necessary to select multiple samples to keep the solid angle of each segment small. This is especially important if the BSDF varies strongly with angle (for example, for a polished surface such as a mirror or lens). Reducing the size of the target or using multiple cells can overcome this issue.

Cells

When it is important to have more uniform sampling than is provided by pure random sampling, use this option to divide each dimension of the target into segments, creating smaller cells in which random ray aiming points are selected.

Stratified Importance Sampling

If the importance sampling target subtends too large a solid angle, or the BSDF of the surface varies significantly (more than an order of magnitude) over the subtended angle or if more uniform sampling is desired, you should divide the importance sampling target into cells to create a stratified target. A circular or annular target is partitioned into segmented rings of equal area as shown in Figure 4.19. This is done by dividing the annulus equally in angle and calculating radii to give equal area to each cell.

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FIGURE 4.19 - Stratified annular (circular in this case) importance sampling target with four radial segments and four azimuthal segments. The 16 resulting cells all have equal area.

The radii of the rings are determined by the formula

ri + 1 =	A	– ri	2	(4.2)
	-----
	πn

where n is the number of rings, the ring edges are numbered 0,...i,...n, A is the

area of the annular target (A = π(R2outer – R2inner) ), and ri is the radius of ring edge i. r0 is equal to Rinner, the inner radius of the annular target. For a circular target,

Rinner = 0.

A rectangular target is partitioned into segmented rectangles of equal area as shown in Figure 4.20.

FIGURE 4.20 - Rectangular target with 2x3 (XxY) segments.

Rectangular segments are all the same shape as well as being equal in area.

To specify the segmentation of an importance sampling target, select the number of cells in each direction (radius and angle for an annular target, x and y for a rectangular target).

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