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Double Gauss Lens
Introduction
A double Gauss lens is a multiple element objective lens commonly used in imaging systems. It is capable of high quality imagery over moderately large field angles, at modest to high speed. In this tutorial, a double Gauss lens model (Figure 1) is constructed using multiple instances of standard parts from the built-in Part Library for the Ray Optics Module. The results of a ray trace will be presented together with a spot diagram and a wavefront aberration diagram.
Figure 1: Overview of the double Gauss lens used in this tutorial. In this view the marginal rays of an on-axis trace are shown, together with the chief ray of 4 additional fields.
Model Definition
The double Gauss lens simulated in this tutorial is an f/1.7, 100.2 mm focal length, 19° field of view lens by Lautebacher & Brendel (Agfa Camera-Werk AG, U.S. Patent 2784643), from Ref. 1, p. 323, although some materials have been replaced with equivalent optical glasses. The prescription of this lens is given in Table 1 and the instructions for creating the lens can be found in the Appendix — Geometry Instructions.
The lens geometry is created by inserting each lens element (including the stop) sequentially, such that each subsequent lens is placed relative to the prior one. This process is simplified by making use of the predefined work planes within the part instances. It is important to appreciate that the ray tracing method used by the Geometrical Optics interface is inherently nonsequential, so the same result could be obtained by placing part instances within the geometry in any order. The double Gauss lens geometry sequence is shown in Figure 2 and the default, Physics-controlled mesh, is seen in Figure 3.
In addition to the lens parameters used to define the lens geometry, a set of parameters are required to define the ray trace. These are detailed in Table 2.
75.050
9.000
33.0
270.700
0.100
33.0
39.270
16.510
27.5
2.000
24.5
25.650
10.990
19.5
13.000
18.6
31.870
7.030
18.5
8.980
21.0
43.510
0.100
21.0
221.140
7.980
23.0
88.790
61.418
23.0
42.5
λvac
550 nm
θx
0°
Nominal x field angle
θy
0°
Nominal y field angle
Nring
18
Number of hexapolar rings. (Nring = 18 will give a total of 1027 rays.)
Pnom
58.941 mm
Pfac1
1.15
Pfac2
0.60
Figure 2: The double Gauss lens geometry sequence.
Figure 3: The default Physics-controlled mesh for the double Gauss lens.
Several of the parameters defined in Table 2 are used to derive additional parameters such as the ray direction vector components, the stop and image plane z-coordinates, as well as the entrance pupil location. Table 3 gives the expressions used to derived these parameters. Note that the pupil shift factor is used in a empirical approximation to ensure that the chief ray passes through the center of the stop at all field angles.
vx
tan θx
vy
tan θy
vz
zstop
Stop z-coordinate, where Tc,n is the central thickness of element n and Tn is the separation between elements n and n+1. Note that the stop is the 4th element in the double Gauss lens.
zimage
Image plane z-coordinate, where Tc,n is the central thickness of element n and Tn is the separation between elements n and n+1. Including the stop, the double Gauss lens has 7 elements.
Pfac
Pfac1 + Pfac2 sinθ
Δxpupil
zpupil + Pfac zstop)tan θx
Pupil shift, x-coordinate
Δypupil
zpupil + Pfac zstop)tan θy
Pupil shift, y-coordinate
Results and Discussion
A ray trace has been made at a single wavelength (550 nm) and field angle (on-axis). In Figure 4 the ray trajectories can be seen colored by optical path length and in Figure 5, a color expression based on the location of the rays at the image plane is used.
Spot diagrams at both the nominal and refocused image plane are shown in Figure 6. The refocused spot diagram in Figure 6 uses an Intersection Point 3D dataset which has been automatically positioned on the plane which minimizes the RMS spot size. At this wavelength and field angle, this plane is located 180 μm ahead of the nominal image surface.
Figure 7 shows the wavefront error. After removing piston and defocus, it is possible to see that spherical aberration dominates the remaining terms.
Figure 4: Ray diagram of the double Gauss lens colored by optical path length.
Figure 5: Ray diagram of the double Gauss lens where the rays are colored by their radial distance from the centroid on the image plane.
Figure 6: Spot diagram for the double Gauss lens. The spot on the nominal image plane is on the left, and the spot on the best focus plane is seen on the right.
Figure 7: The double Gauss lens optical aberration diagram. The plot on the left uses all Zernike terms. On the right, piston and defocus are removed.
Reference
1. W.J. Smith, Modern lens design, vol. 2. New York, NY, USA: McGraw-Hill, 2005.
Application Library path: Ray_Optics_Module/Lenses_Cameras_and_Telescopes/double_gauss_lens
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Optics>Ray Optics>Geometrical Optics (gop).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select Preset Studies for Selected Physics Interfaces>Ray Tracing.
6
Global Definitions
Parameters 1: Lens Prescription
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, type Parameters 1: Lens Prescription in the Label text field. The lens prescription will be added when the geometry sequence is inserted in the following section.
Parameters 2: General
The double Gauss lens simulation parameters can be loaded from a text file.
1
In the Home toolbar, click  Parameters and choose Add>Parameters.
2
In the Settings window for Parameters, type Parameters 2: General in the Label text field.
3
Locate the Parameters section. Click  Load from File.
4
Component 1 (comp1)
1
In the Model Builder window, click Component 1 (comp1).
2
In the Settings window for Component, locate the Curved Mesh Elements section.
3
From the Geometry shape function list, choose Cubic Lagrange. The ray tracing algorithm used by the Geometrical Optics interface computes the refracted ray direction based on a discretized geometry via the underlying finite element mesh. A cubic geometry shape order usually introduces less discretization error compared to the default, which uses linear and quadratic polynomials.
Double Gauss Lens
Insert the prepared geometry sequence from file. You can read the instructions for creating the geometry in the appendix. Following insertion, the lens definitions will be available in the Parameters node.
1
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2
In the Settings window for Geometry, type Double Gauss Lens in the Label text field.
3
In the Geometry toolbar, click Insert Sequence and choose Insert Sequence.
4
5
In the Geometry toolbar, click  Build All.
6
Click the  Orthographic Projection button in the Graphics toolbar.
7
In the Graphics window toolbar, clicknext to  Go to Default View, then choose Go to ZY View. Orient the view to place the z-axis (optical axis) horizontal and the y-axis vertical. Compare the resulting geometry to Figure 2.
Materials
Load the materials used by each of the lenses.
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Optical>Ohara Glass>Ohara S-LAM 3 Glass.
4
Click Add to Component in the window toolbar.
5
In the tree, select Optical>Ohara Glass>Ohara S-BAH11 Glass.
6
Click Add to Component in the window toolbar.
7
In the tree, select Optical>Schott Glass>Schott N-SF5 Glass.
8
Click Add to Component in the window toolbar.
9
In the Home toolbar, click  Add Material to close the Add Material window.
Materials
Ohara S-LAM 3 Glass (mat1)
1
In the Model Builder window, under Component 1 (comp1)>Materials click Ohara S-LAM 3 Glass (mat1).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Lens Material 1.
Ohara S-BAH11 Glass (mat2)
1
In the Model Builder window, click Ohara S-BAH11 Glass (mat2).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Lens Material 2.
Schott N-SF5 Glass (mat3)
1
In the Model Builder window, click Schott N-SF5 Glass (mat3).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Lens Material 3.
Geometrical Optics (gop)
1
In the Model Builder window, under Component 1 (comp1) click Geometrical Optics (gop).
2
In the Settings window for Geometrical Optics, locate the Ray Release and Propagation section.
3
In the Maximum number of secondary rays text field, type 0. In this simulation stray light is not being traced, so reflected rays will not be produced at the lens surfaces.
4
Select the Use geometry normals for ray-boundary interactions check box. This ensures that geometry normals are used to apply the boundary conditions on all refracting surfaces. This is appropriate for the highest accuracy ray traces in single-physics simulations, where the geometry is not deformed.
5
Locate the Material Properties of Exterior and Unmeshed Domains section. From the Optical dispersion model list, choose Air, Edlen (1953). It is assumed that the double Gauss lens is surrounded by air at room temperature.
6
Locate the Additional Variables section. Select the Compute optical path length check box. The optical path length will be used to create an Optical Aberration plot.
Medium Properties 1
1
In the Model Builder window, under Component 1 (comp1)>Geometrical Optics (gop) click Medium Properties 1.
2
In the Settings window for Medium Properties, locate the Medium Properties section.
3
From the Refractive index of domains list, choose Get dispersion model from material. Each of the materials added above contain the optical dispersion coefficients which can be used to compute the refractive index as a function of wavelength.
Material Discontinuity 1
1
In the Model Builder window, click Material Discontinuity 1.
2
In the Settings window for Material Discontinuity, locate the Rays to Release section.
3
From the Release reflected rays list, choose Never.
Ray Properties 1
1
In the Model Builder window, click Ray Properties 1.
2
In the Settings window for Ray Properties, locate the Ray Properties section.
3
In the λ0 text field, type lambda. This wavelength is defined in the Parameters node.
Release from Grid 1
Release the rays from a hexapolar grid, using the quantities defined in the Parameters node.
1
In the Physics toolbar, click  Global and choose Release from Grid.
2
In the Settings window for Release from Grid, locate the Initial Coordinates section.
3
From the Grid type list, choose Hexapolar.
4
Specify the qc vector as
The Center location of the hexapolar grid will change according to the field angle.
5
Specify the rc vector as
The Cylinder axis direction is the same as the global optical axis.
6
In the Rc text field, type P_nom/2.
7
In the Nc text field, type N_ring.
8
Locate the Ray Direction Vector section. Specify the L0 vector as
The Ray direction vector is calculated using the field angles defined in the Parameters node.
Obstructions
1
In the Physics toolbar, click  Boundaries and choose Wall.
2
In the Settings window for Wall, type Obstructions in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Obstructions.
4
Locate the Wall Condition section. From the Wall condition list, choose Disappear.
Stop
1
In the Physics toolbar, click  Boundaries and choose Wall.
2
In the Settings window for Wall, type Stop in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Aperture Stop.
4
Locate the Wall Condition section. From the Wall condition list, choose Disappear.
Image
1
In the Physics toolbar, click  Boundaries and choose Wall.
2
In the Settings window for Wall, type Image in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Image Plane. The default Wall condition (Freeze) will be used.
Mesh 1
In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose Build All. The default physics-controlled mesh settings can be used in this simulation. The mesh should look like Figure 3.
Study 1
Step 1: Ray Tracing
1
In the Model Builder window, under Study 1 click Step 1: Ray Tracing.
2
In the Settings window for Ray Tracing, locate the Study Settings section.
3
From the Time-step specification list, choose Specify maximum path length.
4
From the Length unit list, choose mm.
5
In the Lengths text field, type 0 200. The maximum optical path length is sufficient for rays released at large field angles to reach the image plane.
6
In the Home toolbar, click  Compute.
Results
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 trajectory plot. First, define a cut plane which can be used to render the double Gauss lens cross-section.
Cut Plane 1
In the Results toolbar, click  Cut Plane.
Ray Diagram 1
1
In the Model Builder window, under Results click Ray Trajectories (gop).
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 check box.
4
From the Position list, choose Bottom.
5
In the Model Builder window, expand the Ray Diagram 1 node.
Filter 1
1
In the Model Builder window, expand the Results>Ray Diagram 1>Ray Trajectories 1 node, then click Filter 1.
2
In the Settings window for Filter, locate the Ray Selection section.
3
From the Rays to include list, choose Logical expression.
4
In the Logical expression for inclusion text field, type at(0,abs(gop.deltaqx) < 0.1[mm]). Only the sagittal rays are shown in this view.
In the following steps, the cross-section of the lens is rendered.
Surface 1
1
In the Model Builder window, right-click Ray Diagram 1 and choose Surface.
2
In the Settings window for Surface, locate the Data section.
3
From the Dataset list, choose Cut Plane 1.
4
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
5
From the Color list, choose Gray.
Line 1
1
Right-click Ray Diagram 1 and choose Line.
2
In the Settings window for Line, locate the Data section.
3
From the Dataset list, choose Cut Plane 1.
4
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
5
From the Color list, choose Black.
6
In the Ray Diagram 1 toolbar, click  Plot. Compare the resulting image to Figure 4.
Ray Diagram 2
For the second ray diagram the 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 Home toolbar, click  Add Plot Group and choose 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.
4
Locate the Plot Settings section. From the View list, choose New view.
5
Locate the Color Legend section. Select the Show units check box.
Ray Trajectories 1
In the Ray Diagram 2 toolbar, click  More Plots and choose Ray Trajectories.
Color Expression 1
1
Right-click Ray Trajectories 1 and choose Color Expression.
2
In the Settings window for Color Expression, locate the Expression section.
3
In the Expression text field, type at('last',gop.rrel). This is the radial coordinate relative to the centroid of each release feature at the image plane.
4
From the Unit list, choose µm.
5
Locate the Coloring and Style section. From the Color table list, choose Viridis.
Surface 1
1
In the Model Builder window, right-click Ray Diagram 2 and choose Surface.
2
In the Settings window for Surface, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Geometrical Optics>Refractive index>gop.nrefd - Refractive index, d-line.
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.
3
From the Selection list, choose Lens Exteriors.
Transparency 1
1
In the Model Builder window, right-click Surface 1 and choose Transparency.
2
In the Ray Diagram 2 toolbar, click  Plot.
3
Click the  Orthographic Projection button in the Graphics toolbar.
4
Click the  Zoom Extents button in the Graphics toolbar. Orient the view to match Figure 5 so that the color expression in the object plane can be clearly seen.
Spot Diagram
In the following steps, a spot diagram is created.
Spot Diagram
1
In the Home toolbar, click  Add Plot Group and choose 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 check box.
4
From the Position list, choose Bottom.
Spot Diagram 1
1
In the Spot Diagram toolbar, click  More Plots and choose Spot Diagram.
2
In the Settings window for Spot Diagram, click to expand the Annotations section.
3
Select the Show spot coordinates check box.
4
From the Coordinate system list, choose Global. Using the Global coordinate system allows the z coordinate to be displayed.
5
In the Display precision text field, type 6.
Color Expression 1
1
Right-click Spot Diagram 1 and choose Color Expression.
2
In the Settings window for Color Expression, locate the Expression section.
3
In the Expression text field, type at(0,gop.rrel). This is the radial coordinate relative to the center at the location of the ray release.
4
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 spot size for a selected field angle and wavelength.
Spot Diagram 2
1
In the Model Builder window, under Results>Spot Diagram right-click Spot Diagram 1 and choose Duplicate.
2
In the Settings window for Spot Diagram, click to expand the Focal Plane Orientation section.
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.
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. If the best focus plane lies behind the image plane, then the Freeze condition on the Wall defining the image surface should be disabled. Note that the focal plane is located about 180 microns in front of the nominal image surface.
5
Click to expand the Position section. In the x text field, type 0.25.
6
Click to expand the Inherit Style section. From the Plot list, choose Spot Diagram 1.
7
In the Spot Diagram toolbar, click  Plot.
8
Click the  Zoom Extents button in the Graphics toolbar. Compare the resulting image to Figure 6.
Optical Aberration Diagram
In the following steps, an optical aberration diagram is created.
Optical Aberration Diagram
1
In the Home toolbar, click  Add Plot Group and choose 2D Plot Group.
2
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 check box.
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.
5
Locate the Coloring and Style section. From the Color table list, choose Dipole.
6
From the Scale list, choose Linear symmetric.
Optical Aberration 2
1
Right-click Optical Aberration 1 and choose Duplicate. Duplicate this Aberration plot so that some Zernike terms can be removed.
2
In the Settings window for Optical Aberration, locate the Zernike Polynomials section.
3
From the Terms to include list, choose Select individual terms.
4
Click Select All.
5
Clear the Z(0,0), piston check box.
6
Clear the Z(2,0), defocus check box. The piston and defocus terms are removed.
7
Locate the Position section. In the x text field, type 2.5.
8
Click to expand the Inherit Style section. From the Plot list, choose Optical Aberration 1.
9
In the Optical Aberration Diagram toolbar, click  Plot.
10
Click the  Zoom Extents button in the Graphics toolbar. Compare the resulting image to Figure 7. The remaining wavefront error (about 0.6 waves) is dominated by spherical aberration.
Appendix — Geometry Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
Global Definitions
The detailed parameters of the lens can be imported from a text file. This lens is from Ref. 1, pg 323.
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Double Gauss Lens Parameters
The parameters that define the Double Gauss Lens geometry sequence are found in double_gauss_lens_geom_sequence_parameters.txt. These will be described in the tables below.
1
2
3
Double Gauss Lens Geometry Sequence
Start constructing the lens geometry.
1
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2
In the Settings window for Geometry, type Double Gauss Lens Geometry Sequence in the Label text field.
3
Locate the Units section. From the Length unit list, choose mm.
Insert the first of the Double Gauss Lens elements.
Part Libraries
1
In the Home toolbar, click  Windows and choose Part Libraries.
2
In the Part Libraries window, select Ray Optics Module>3D>Spherical Lenses>spherical_lens_3d in the tree.
3
Click  Add to Geometry.
4
In the Select Part Variant dialog box, select Specify clear aperture diameter in the Select part variant list.
5
Click OK. This part is used for each of the 6 Double Gauss Lens elements.
Double Gauss Lens Geometry Sequence
Lens 1
1
In the Model Builder window, under Component 1 (comp1)>Double Gauss Lens Geometry Sequence click Spherical Lens 3D 1 (pi1).
2
In the Settings window for Part Instance, type Lens 1 in the Label text field.
3
Locate the Input Parameters section. Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file double_gauss_lens_geom_sequence_lens1.txt. The files double_gauss_lens_geom_sequence_lens[m,m=1..6].txt contains references to each of the individual lens parameters. This avoids having to enter the values manually.
5
Click  Build Selected.
6
Click the  Orthographic Projection button in the Graphics toolbar.
7
In the Graphics window toolbar, clicknext to  Go to Default View, then choose Go to ZY View. Switch the view to orthographic, and orientate the view to place the optical axis (z-axis) horizontal and the y-axis vertical.
Create cumulative selections defining the materials, clear apertures, obstructions and image plane that can be used within the final ray trace.
Cumulative Selections
In the Geometry toolbar, click  Selections and choose Cumulative Selections.
Lens Material 1
1
Right-click Cumulative Selections and choose Cumulative Selection.
2
In the Settings window for Selection, type Lens Material 1 in the Label text field.
Lens Material 2
1
In the Model Builder window, right-click Cumulative Selections and choose Cumulative Selection.
2
In the Settings window for Selection, type Lens Material 2 in the Label text field. In the same manner, add selections for Lens Material 3, Clear Apertures, Obstructions, Aperture Stop, and Image Plane.
Lens 1 (pi1)
Now, apply these selections.
1
In the Model Builder window, under Component 1 (comp1)>Double Gauss Lens Geometry Sequence click Lens 1 (pi1).
2
In the Settings window for Part Instance, click to expand the Domain Selections section.
3
4
Click to expand the Boundary Selections section. In the table, enter the following settings:
Lens 2
Continue constructing the lens. Add the second lens element.
1
In the Geometry toolbar, click  Parts and choose Spherical Lens 3D.
2
In the Settings window for Part Instance, type Lens 2 in the Label text field.
3
Locate the Input Parameters section. Click  Load from File.
4
Each lens element can be positioned in the geometry by referencing it to an existing work plane. For this example, use a work plane that is defined by the intersection of a plane tangential to the optical axis with the vertex on the exit surface of the preceding lens element.
5
Locate the Position and Orientation of Output section. Find the Coordinate system to match subsection. From the Take work plane from list, choose Lens 1 (pi1).
6
From the Work plane list, choose Surface 2 vertex intersection (wp2).
7
Find the Displacement subsection. In the zw text field, type T_1. This is the distance along the optical axis between the vertex on the exit surface of lens 1 and the vertex on the entrance surface of lens 2.
8
Locate the Domain Selections section. In the table, enter the following settings:
9
Locate the Boundary Selections section. In the table, enter the following settings:
Lens 3
The remaining lenses are similarily defined. Next, add the third lens element.
1
In the Geometry toolbar, click  Parts and choose Spherical Lens 3D.
2
In the Settings window for Part Instance, type Lens 3 in the Label text field.
3
Locate the Input Parameters section. Click  Load from File.
4
5
Locate the Position and Orientation of Output section. Find the Coordinate system to match subsection. From the Take work plane from list, choose Lens 2 (pi2).
6
From the Work plane list, choose Surface 2 vertex intersection (wp2).
7
Find the Displacement subsection. In the zw text field, type T_2.
8
Locate the Domain Selections section. In the table, enter the following settings:
9
Locate the Boundary Selections section. In the table, enter the following settings:
Part Libraries
Next, insert the aperture stop.
1
In the Geometry toolbar, click  Parts and choose Part Libraries.
2
In the Part Libraries window, select Ray Optics Module>3D>Apertures and Obstructions>circular_planar_annulus in the tree.
3
Click  Add to Geometry. This part is also used to define the image plane and additional obstructions.
Double Gauss Lens Geometry Sequence
Stop
1
In the Model Builder window, under Component 1 (comp1)>Double Gauss Lens Geometry Sequence click Circular Planar Annulus 1 (pi4).
2
In the Settings window for Part Instance, type Stop in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
4
Locate the Position and Orientation of Output section. Find the Coordinate system to match subsection. From the Take work plane from list, choose Lens 3 (pi3).
5
From the Work plane list, choose Surface 2 vertex intersection (wp2).
6
Find the Displacement subsection. In the zw text field, type T_3+Tc_4.
7
Locate the Boundary Selections section. In the table, enter the following settings:
Lens 4
Next, add the fourth lens element.
1
In the Geometry toolbar, click  Parts and choose Spherical Lens 3D.
2
In the Settings window for Part Instance, type Lens 4 in the Label text field.
3
Locate the Input Parameters section. Click  Load from File.
4
5
Locate the Position and Orientation of Output section. Find the Coordinate system to match subsection. From the Take work plane from list, choose Stop (pi4).
6
From the Work plane list, choose Surface (wp1).
7
Find the Displacement subsection. In the zw text field, type T_4.
8
Locate the Domain Selections section. In the table, enter the following settings:
9
Locate the Boundary Selections section. In the table, enter the following settings:
Lens 5
Next, add the fifth lens element.
1
In the Geometry toolbar, click  Parts and choose Spherical Lens 3D.
2
In the Settings window for Part Instance, type Lens 5 in the Label text field.
3
Locate the Input Parameters section. Click  Load from File.
4
5
Locate the Position and Orientation of Output section. Find the Coordinate system to match subsection. From the Take work plane from list, choose Lens 4 (pi5).
6
From the Work plane list, choose Surface 2 vertex intersection (wp2).
7
Find the Displacement subsection. In the zw text field, type T_5.
8
Locate the Domain Selections section. In the table, enter the following settings:
9
Locate the Boundary Selections section. In the table, enter the following settings:
Lens 6
Add the final (sixth) lens element.
1
In the Geometry toolbar, click  Parts and choose Spherical Lens 3D.
2
In the Settings window for Part Instance, type Lens 6 in the Label text field.
3
Locate the Input Parameters section. Click  Load from File.
4
5
Locate the Position and Orientation of Output section. Find the Coordinate system to match subsection. From the Take work plane from list, choose Lens 5 (pi6).
6
From the Work plane list, choose Surface 2 vertex intersection (wp2).
7
Find the Displacement subsection. In the zw text field, type T_6.
8
Locate the Domain Selections section. In the table, enter the following settings:
9
Locate the Boundary Selections section. In the table, enter the following settings:
Image
Now, add a surface to define the image plane.
1
In the Geometry toolbar, click  Parts and choose Circular Planar Annulus.
2
In the Settings window for Part Instance, type Image in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
4
Locate the Position and Orientation of Output section. Find the Coordinate system to match subsection. From the Take work plane from list, choose Lens 6 (pi7).
5
From the Work plane list, choose Surface 2 vertex intersection (wp2).
6
Find the Displacement subsection. In the zw text field, type T_7.
7
Locate the Boundary Selections section. In the table, enter the following settings:
8
Click  Build All Objects.
9
Click the  Zoom Extents button in the Graphics toolbar. Compare the resulting image to Figure 2.