Results
Running the study causes the following default nodes to appear under Results :
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Results  > Datasets  > Study 1/Solution 1 (sol1) , the default dataset created by most study types,
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Results  > Datasets  > Ray 1 , a dataset for plotting rays,
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Results  > Ray Trajectories (gop)  plot group, and
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Results  > Ray Trajectories (gop)  > Ray Trajectories 1  plot, which displays the ray paths.
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This default plot also has a default Color Expression  attribute (subnode) that colors the rays in proportion to their optical path length.
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The default Filter  attribute node can be used to plot only a specified number or fraction or rays, or filter the rays by a logical expression.
Ray Diagrams
In the following steps, two different ray diagrams are created, one of which uses a custom color expression. Begin by making some modifications to the default Ray Trajectories plot.
Cut Plane 1
1
In the Results toolbar, click Cut Plane . This Cut Plane dataset will be used to render the double Gauss lens cross-section. Use the default settings, which align the cut plane parallel to the yz-plane with an x-coordinate of 0.
Ray Trajectories
1
In the Model Builder window, under Results  click the Ray Trajectories (gop)  plot group.
2
In the Settings window for 3D Plot Group, type Ray Diagram 1 in the Label text field.
3
Locate the Color Legend section. Select the Show units checkbox.
4
From the Position list, choose Bottom.
Filter 1
5
In the Model Builder window, expand the Results  > Ray Diagram 1  > Ray Trajectories 1  node, then click Filter 1 .
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Locate the Ray Selection section. From the Rays to include list, choose Logical expression.
7
In the Logical expression for inclusion text field, type at(0,abs(gop.deltaqx)<0.1[mm]). This logical expression will render rays in the yz-plane. In this expression, at() is a special operator that takes two arguments. It evaluates the second argument at the solution time given by the first argument, so the logical expression abs(gop.deltaqx)<0.1[mm] is being evaluated at the initial ray positions.
The variable gop.deltaqx is the x-component of the displacement of each individual ray relative to the average position of all rays.
In the following steps, the cross-section of the lens is rendered.
Surface 1
1
On the Ray Diagram 1 toolbar, click Surface .
2
Locate the Data section. From the Dataset list, choose Cut Plane 1. This is the sagittal cut plane defined above.
3
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
4
From the Color list, choose Gray.
Line 1
1
On the Ray Diagram 1 toolbar, click Line .
2
Locate the Data section. From the Dataset list, choose Cut Plane 1.
3
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
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From the Color list, choose Black.
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On the Ray Diagram 1 toolbar, click Plot . The figure should look like the figure below:
Ray Diagram 2
For the second ray diagram rays will be colored according to the radial distance from the ray’s location in the image plane to the centroid. This makes it possible to visualize which rays are contributing to the image plane spot aberrations.
1
In the Results toolbar, click 3D Plot Group .
2
In the Settings window for 3D Plot Group, type Ray Diagram 2 in the Label text field.
3
Locate the Data section. From the Dataset list, choose Ray 1.
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Locate the Plot Settings section. From the View list, choose New View.
5
Locate the Color Legend section. Select the Show units checkbox.
Ray Trajectories 1
In the Ray Diagram 2 toolbar, click More Plots and choose Ray Trajectories .
Color Expression 1
1
In the Model Builder window, right-click the Results  > Ray Diagram 2  > Ray Trajectories 1  node and click Color Expression . Alternatively, in the Ray Diagram 2 toolbar, click Color Expression  in the Attributes section.
2
In the settings for Color Expression 1 , locate the Expression section. In the Expression text field, type at(‘last’,gop.rrel). This is the radial coordinate relative to the average ray position in the image plane.
3
From the Unit list, choose µm.
4
Locate the Coloring and Style section. From the Color table list, choose Viridis.
Surface 1
1
On the Ray Diagram 2 toolbar, click Surface .
2
In the settings window for Surface, click the Replace Expression  button in the upper-right corner of the Expression section. From the menu, expand Component 1 (comp1) > Geometrical Optics > Refractive index and choose gop.nrefd - Refractive Index, d-line. This is the refractive index at 587.56 nm.
3
Locate the Coloring and Style section. From the Color table list, choose GrayScale.
Selection 1
1
Right-click Surface 1 and choose Selection .
2
In the Settings window for Selection, locate the Selection section.
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From the Selection list, choose Lens Exteriors.
Transparency 1
1
In the Model Builder window, right-click Surface 1 and choose Transparency . This allows you to see the rays inside the lenses.
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On the Ray Diagram 2 toolbar, click Plot .
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Click the Orthographic Projection button in the Graphics toolbar.
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Click Zoom Extents in the window toolbar. Orient the view so that the color expression in the object plane can be clearly seen. The figure should look like the first figure below. As noted above, in this figure the rays are colored according to their radial distance from the centroid. This makes it possible to visualize which rays contribute most to the overall spot size.
Spot Diagram
In the following steps, a spot diagram is created.
2D Plot Group 3
1
In the Results toolbar, click 2D Plot Group .
2
In the Settings window for 2D Plot Group, type Spot Diagram in the Label text field.
3
Locate the Color Legend section. Select the Show units checkbox.
4
From the Position list, choose Bottom.
Spot Diagram 1
1
On the Spot Diagram toolbar, click More Plots and choose Spot Diagram .
2
In the Settings window, click to expand the Annotations section.
3
Select the Show spot coordinates checkbox. Then from the Coordinate system list, choose Global. Using the Global coordinate systems allows the z coordinate to be displayed.
4
In the Display precision text field, type 6.
Color Expression 1
1
Right-click Spot Diagram 1 and choose Color Expression .
2
Locate the Expression section. In the Expression text field, type at(0,gop.rrel). This is the radial coordinate relative to the centroid at the location of the ray release. This allows the origin of each ray to be visualized.
3
Locate the Coloring and Style section. From the Color table list, choose Viridis.
The first spot diagram shows the intersection of the rays with the nominal image plane. This surface has been positioned so as to give the best image quality over a large range of field angles when using polychromatic light. A second spot diagram can be generated automatically on the plane which minimizes the RMS image quality for a selected field angle and wavelength.
Spot Diagram 2
1
In the Model Builder window, right-click Spot Diagram 1  and choose Duplicate .
2
In the Settings window for Spot Diagram 2 , click to expand the Focal Plane Orientation section. This section is used to control how the best focus plane is determined.
3
From the Normal to focal plane list, choose User defined. In this model, the image plane is assumed to be tangential to the optical axis which is also the z-axis. This happens to also be the default, so no changes are needed.
4
Click Create Focal Plane Dataset. This creates an Intersection Point 3D dataset on a plane. In this model, which has a single on-axis field and monochromatic light, the location of the best focus plane happens to be in front of the nominal image surface. The focal plane is located 180 microns in front of the nominal image surface.
Note: If the best focus plane lies behind the image plane, then the Freeze condition on the Wall defining the Image surface should be disabled. Currently the Intersection Point dataset can only compute real intersections of rays with the plane, not intersections of extrapolated ray positions.
5
Click to expand the Position section. In the x text field, type 0.25.
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Click to expand the Inherit Style section. From the Plot list, choose Spot Diagram 1. This will cause the color expressions in both Spot Diagram plots to use the same color scale, making direct comparison possible. It also ensures that only a single color legend will be shown.
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In the Spot Diagram toolbar, click Plot .
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Click the Zoom Extents button in the Graphics toolbar. Compare the resulting image to the figure below:
The double Gauss lens spot diagram. On the left is the spot on the nominal image surface. The spot on the right is located at the “best focus” image plane that has been computed automatically.
Optical Aberration Diagram
In the following steps, an optical aberration diagram is created.
2D Plot Group 4
1
In the Results toolbar, click 2D Plot Group .
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In the Settings window for 2D Plot Group, type Optical Aberration Diagram in the Label text field.
3
Locate the Color Legend section. Select the Show maximum and minimum values checkbox.
4
From the Position list, choose Bottom.
Optical Aberration 1
1
In the Optical Aberration Diagram toolbar, click More Plots and choose Optical Aberration .
2
In the Settings window for Optical Aberration, locate the Focal Plane Orientation section.
3
From the Normal to focal plane list, choose User defined. As with the Spot Diagram, the image plane is assumed to be tangential to the optical axis which is also the z-axis.
4
Click Create Reference Hemisphere Dataset. This creates an Intersection Point 3D dataset on a reference hemisphere.
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Locate the Coloring and Style section. From the Color table list, choose Dipole. From the Scale list, choose Linear symmetric.
The advantage of using the Dipole color table with a symmetric color scale is that positive wavefront error will be shown in shades of red whereas negative wavefront error will be shown in blue. Bands of white indicate regions where the wavefront error is zero.
Optical Aberration 2
1
Right-click Optical Aberration 1  and choose Duplicate .
2
In the Settings window for Optical Aberration 2 , locate the Zernike Polynomials section.
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From the Terms to include list, choose Select individual terms.
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Click Select All.
5
Clear the Z(0,0), piston and Z(2,0), defocus checkboxes. The piston and defocus terms are removed from the wavefront error.
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Locate the Position section. In the x text field, type 2.5. The position coordinates are dimensionless; with the Optical Aberration  plot, combinations of Zernike polynomials are always plotted on a unit circle.
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Click to expand the Inherit Style section. From the Plot list, choose Optical Aberration 1.
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In the Optical Aberration Diagram toolbar, click Plot .
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Click the Zoom Extents button in the Graphics toolbar. Compare the resulting image to the figure below. The remaining wavefront error (about 0.6 waves) is dominated by spherical aberration.
The double Gauss lens optical aberration diagram. The plot on the left uses all Zernike terms. In the plot on the right, the piston and defocus terms have been removed. Spherical aberration dominates the remaining terms.