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Petzval Lens
Introduction
A Petzval lens comprises two positive lens groups that are separated by air. By using a pair of doublets, astigmatism can be controlled over restricted fields of view with modest numerical apertures.
The basic Petzval lens configuration will invariably result in a best focus image surface that is concave. This can be corrected by placing a negative lens element as close as possible to the image plane. In this tutorial, a field-flattened Petzval will be demonstrated.
Figure 1: Overview of the Petzval lens. The lens includes a field-flattening element. In this view the marginal rays of an on-axis trace are shown, together with the chief ray of 5 additional fields.
Model Definition
The field-flattened Petzval lens simulated in this study is based on the prescription from Ref. 1, p. 191. The focal length is 100.0 mm and the focal ratio is approximately f/2.4. An overview of the lens layout can be seen in Figure 1, and the parameters of this lens are shown in Table 1. Note that some of the lens materials have replaced with equivalents from the built-in Optical material library and the back focal length has been adjusted.
The instructions for creating the lens geometry can be found in the Appendix — Geometry Instructions. 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.
Table 1: Petzval lens parameters.
Index
Name
Radius
(mm)
Thickness
(mm)
Material
Clear radius
(mm)
—
Object
 ∞
 ∞
—
—
1
Lens 1
 98.45049
 13.00000
N-BK7
 28.478
2
Lens 2
 -83.29386
 4.00000
N-KZFS5
 26.267
—
—
 -1421.38828
 40.00000
—
 22.020
3
Stop
 ∞
 40.00000
—
 16.631
4
Lens 3
 59.00613
 12.00000
N-SK2
 20.543
5
Lens 4
 -54.36470
 3.00000
N-SF5
 20.074
—
—
 -549.36547
 46.82210
—
 16.492
6
Lens 5
 -39.80076
 2.00000
N-SF5
 17.297
—
—
 ∞
 1.9548
—
 18.940
—
Image
 ∞
—
—
 17.904
 
Table 2: Global parameter definitions.
Parameter
Value
Description
 λvac
 475nm, 550nm, 625nm
Nominal (vacuum) wavelengths
 θx
 0°
Nominal x field angle
 θy
 0°, 6°, 9°
Nominal y field angles
 Nring
 12
Number of hexapolar rings. (Nring = 12 will give a total of 469 rays.)
 Pnom
 41.5 mm
Nominal entrance pupil diameter
 Pfac1
 -1.142
Pupil shift factor 1
 Pfac2
 -0.080
Pupil shift factor 2
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, and the entrance pupil location. Table 3 gives the expressions used to derive these parameters. Note that the pupil shift factor is an empirical approximation to ensure that the chief ray passes through the center of the stop at all field angles.
 
Table 3: Global parameter definitions (Derived).
Parameter
Value
Description
 vx
 tan θx
Ray direction vector, x-component
 vy
 tan θy
Ray direction vector, y-component
 vz
 1
Ray direction vector, z-component
 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 3rd element in the Petzval 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 Petzval lens has 6 elements.
 Pfac
 Pfac1 + Pfac2 sin θ
Pupil shift factor, where
 Δxpupil
 (Δzpupi + Pfac zstop)tan θx
Pupil shift, x-coordinate
 Δypupil
 (Δzpupi + Pfac zstop)tan θy
Pupil shift, y-coordinate
Results and Discussion
In this simulation the lens geometry is constructed by repeated insertions of part instances from the COMSOL Part Libraries. Each lens element is inserted 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 “Spherical Lens 3D” part instance.
It is important to appreciate that the ray tracing method used by the Geometrical Optics interface is inherently non-sequential, so the same result could be obtained by placing part instances within the geometry in any order. In order to limit the rays to those that reach the focal plane, additional aperture stops and obstructions are added to the geometry. These items can also be placed by using the predefined work planes from each of the lens part instances. The Petzval lens geometry sequence is shown in Figure 2 and the mesh can be seen in Figure 3.
Figure 2: The Petzval lens geometry sequence.
Figure 3: The Petzval lens mesh.
A ray trace has been performed at three wavelengths (475 nm, 550 nm, and 625 nm) and three field angles (on-axis, 6°, and 9°). In Figure 4 the ray trajectories can be seen colored by optical path length. The slice plot in the background of this figure indicates the d-line refractive index nd of each material, which highlights the disparity in refractive index between the crown and flint glasses of each cemented doublet. In Figure 5, a color expression based on the location of the rays at the image plane is used. This allows the relative contribution of rays at the pupil to the final image quality to be easily visualized.
Finally, in Figure 6 a spot diagram is shown. In this plot the points are colored according to their initial location in the pupil. This complements the coloring of the ray diagram in Figure 5.
Figure 4: Ray diagram of the Petzval lens colored by radial distance from the centroid.
Figure 5: Ray diagram of the Petzval lens where the rays are colored by their radial distance from the centroid on the image plane.
Figure 6: Spot diagram for the Petzval lens. The color indicates the wavelength.
Reference
1. M.J. Kidger, Fundamental Optical Design, SPIE Press, 2001.
Application Library path: Ray_Optics_Module/Lenses_Cameras_and_Telescopes/petzval_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
Click  Done.
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 Petzval 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
Browse to the model’s Application Libraries folder and double-click the file petzval_lens_parameters.txt.
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.
Petzval 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, locate the Units section.
3
From the Length unit list, choose mm.
4
In the Label text field, type Petzval Lens.
5
In the Geometry toolbar, click Insert Sequence and choose Insert Sequence.
6
Browse to the model’s Application Libraries folder and double-click the file petzval_lens_geom_sequence.mph.
7
In the Geometry toolbar, click  Build All.
8
Click the  Orthographic Projection button in the Graphics toolbar.
9
In the Graphics window toolbar, clicknext to  Go to Default View, then choose Go to ZY View. This will orient the view to place the optical axis (z-axis) horizontal and the y-axis vertical. Compare the resulting geometry to Figure 2.
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>Schott Glass>Schott N-BK7 Glass.
4
Click Add to Component in the window toolbar.
5
In the tree, select Optical>Schott Glass>Schott N-KZFS5 Glass.
6
Click Add to Component in the window toolbar.
7
In the tree, select Optical>Schott Glass>Schott N-SK2 Glass.
8
Click Add to Component in the window toolbar.
9
In the tree, select Optical>Schott Glass>Schott N-SF5 Glass.
10
Click Add to Component in the window toolbar.
11
In the Home toolbar, click  Add Material to close the Add Material window.
Materials
Schott N-BK7 Glass (mat1)
1
In the Model Builder window, under Component 1 (comp1)>Materials click Schott N-BK7 Glass (mat1).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Lens Material 1.
Schott N-KZFS5 Glass (mat2)
1
In the Model Builder window, click Schott N-KZFS5 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-SK2 Glass (mat3)
1
In the Model Builder window, click Schott N-SK2 Glass (mat3).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Lens Material 3.
Schott N-SF5 Glass (mat4)
1
In the Model Builder window, click Schott N-SF5 Glass (mat4).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Lens Material 4.
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
From the Wavelength distribution of released rays list, choose Polychromatic, specify vacuum wavelength. The list of polychromatic wavelengths will be entered below.
4
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.
5
Select the Use geometry normals for ray-boundary interactions check box. In this simulation, the 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.
6
Locate the Material Properties of Exterior and Unmeshed Domains section. From the Optical dispersion model list, choose Air, Edlen (1953). The lenses are assumed to be surrounded by air at room temperature.
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.
Release from Grid 1
Release the rays from a hexapolar grid, using 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
dx1
x
dy1
y
dz
z
The Center location of the hexapolar grid will change according to the field angle.
5
Specify the rc vector as
nix
x
niy
y
niz
z
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
vx1
x
vy1
y
vz
z
The Ray direction vector is calculated using the field angles defined in the Parameters node.
9
Locate the Vacuum Wavelength section. From the Distribution function list, choose List of values.
10
In the Values text field, type 475[nm] 550[nm] 625[nm].
Release from Grid 2
1
Right-click Release from Grid 1 and choose Duplicate.
2
In the Settings window for Release from Grid, locate the Initial Coordinates section.
3
Specify the qc vector as
dx2
x
dy2
y
4
Locate the Ray Direction Vector section. Specify the L0 vector as
vx2
x
vy2
y
Release from Grid 3
1
Right-click Release from Grid 2 and choose Duplicate.
2
In the Settings window for Release from Grid, locate the Initial Coordinates section.
3
Specify the qc vector as
dx3
x
dy3
y
4
Locate the Ray Direction Vector section. Specify the L0 vector as
vx3
x
vy3
y
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.
Mesh 1
1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2
In the Settings window for Mesh, locate the Physics-Controlled Mesh section.
3
From the Element size list, choose Fine. Slightly refine the mesh for this study to ensure that rays passing close the edge of apertures are traced.
4
Click  Build All. The mesh should looks 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
Ray Diagram 1
Create a plot showing the ray trajectories, as well as a spot diagram showing the intersection of the rays with the image plane.
1
In the Settings window for 3D Plot Group, type Ray Diagram 1 in the Label text field.
2
Locate the Color Legend section. Select the Show units check box.
3
From the Position list, choose Bottom.
4
In the Model Builder window, expand the Ray Diagram 1 node.
Color Expression 1
1
In the Model Builder window, expand the Results>Ray Diagram 1>Ray Trajectories 1 node, then click Color Expression 1.
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.
Filter 1
1
In the Model Builder window, 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))<1[mm].
Cut Plane 1
In the Results toolbar, click  Cut Plane.
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
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.
5
Locate the Coloring and Style section. From the Color table list, choose GrayScale.
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
From the Time (s) list, choose 0.
5
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
6
From the Color list, choose Black.
7
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.
Add a Surface plot to render the lens elements as solids.
Surface 1
1
In the Model Builder window, right-click Ray Diagram 2 and choose Surface.
2
In the Settings window for Surface, locate the Data section.
3
From the Dataset list, choose Study 1/Solution 1 (sol1).
4
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
5
From the Color list, choose Gray.
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. Orient the view to match Figure 5 to show the all the rays.
Spot Diagram
In the following steps, a spot diagram is created, and a custom color expression is added.
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.
Spot Diagram 1
In the Spot Diagram toolbar, click  More Plots and choose Spot Diagram.
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 gop.lambda0.
4
From the Unit list, choose nm.
5
Click to expand the Range section. Select the Manual color range check box.
6
In the Minimum text field, type 450.
7
In the Maximum text field, type 650.
8
In the Spot Diagram toolbar, click  Plot.
9
Click the  Zoom Extents button in the Graphics toolbar. Compare the resulting image to Figure 6.
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
Click  Done.
Global Definitions
The detailed parameters of the lens can be imported from a text file. The prescription for the Petzval lens with a field flattener can be found in Ref. 1, pg 192.
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
Browse to the model’s Application Libraries folder and double-click the file petzval_lens_geom_sequence_parameters.txt.
Petzval Lens Parameters
The parameters that define the Petzval lens geometric sequence are found in petzval_lens_geom_sequence_parameters.txt. These will be described in the tables below.
1
First, define the global optical axis. This is used to orient the first lens only. The orientation of each subsequent lens will be relative to the preceding one.
Parameter
Description
nix
Global optical axis, x-component
niy
Global optical axis, y-component
niz
Global optical axis, z-component
2
Next, define the parameters for each of the lens elements. Each lens requires 8 parameters in addition to the ray incident directions (which are set using the global values).
Parameter
Description
R1_[n]
Radius of curvature, surface 1, lens [n]
R2_[n]
Radius of curvature, surface 2, lens [n]
Tc_[n]
Center thickness, lens [n]
d0_[n]
Outer diameter, lens [n]
d1_[n]
Diameter, surface 1, lens [n]
d2_[n]
Diameter, surface 2, lens [n]
d1_clear_[n]
Clear aperture diameter, surface 1, lens [n]
d2_clear_[n]
Clear aperture diameter, surface 2, lens [n]
3
Finally, define the remaining lens parameters.
Parameter
Description
T_[n]
Distance between lenses [n] and [n+1].
d0_S
Stop maximum (outer) diameter
d1_S
Stop minimum (clear) diameter
d0_D
Diameter of image plane
Petzval 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 Petzval 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 Petzval 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 5 Petzval Lens elements.
Petzval Lens Geometry Sequence
Lens 1
1
In the Model Builder window, under Component 1 (comp1)>Petzval 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 petzval_lens_geom_sequence_lens1.txt. The files petzval_lens_geom_sequence_lens[m,m=1..5].txt contains references to each of the individual lens parameters. This avoids having to enter the values manually. Note that the z-axis is the optical axis throughout this geometry; that is, nix=niy=0, niz=1.
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. This will orient 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, Lens Material 4, Lens Exteriors, 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)>Petzval Lens Geometry Sequence click Lens 1 (pi1).
2
In the Settings window for Part Instance, click to expand the Domain Selections section.
3
In the table, enter the following settings:
Name
Keep
Physics
Contribute to
All
 
√
Lens Material 1
4
Click to expand the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Exterior
 
√
Lens Exteriors
Surface 1
 
√
Clear Apertures
Surface 2
 
√
Clear Apertures
Surface 1 obstruction
 
√
Obstructions
Surface 2 obstruction
 
√
Obstructions
Edges
 
√
Obstructions
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
Browse to the model’s Application Libraries folder and double-click the file petzval_lens_geom_sequence_lens2.txt.
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 vertex on the exit surface of the prior 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 exit surface of lens 1 and the entrance surface of lens 2.
8
Locate the Domain Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
All
 
√
Lens Material 2
9
Locate the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Exterior
 
√
Lens Exteriors
Surface 1
 
√
Clear Apertures
Surface 2
 
√
Clear Apertures
Surface 1 obstruction
 
√
Obstructions
Surface 2 obstruction
 
√
Obstructions
Edges
 
√
Obstructions
Part Libraries
Next, insert the 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.
Petzval Lens Geometry Sequence
Stop
1
In the Model Builder window, under Component 1 (comp1)>Petzval Lens Geometry Sequence click Circular Planar Annulus 1 (pi3).
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:
Name
Expression
Value
Description
d0
d0_S
58 mm
Diameter, outer
d1
d1_S
33.262 mm
Diameter, inner
nix
0
0
Local optical axis, x-component
niy
0
0
Local optical axis, y-component
niz
1
1
Local optical axis, z-component
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 2 (pi2).
5
From the Work plane list, choose Surface 2 vertex intersection (wp2).
6
Find the Displacement subsection. In the zw text field, type T_2+Tc_3.
7
Locate the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
All
 
√
Aperture Stop
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
Browse to the model’s Application Libraries folder and double-click the file petzval_lens_geom_sequence_lens3.txt.
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 (pi3).
6
From the Work plane list, choose Surface (wp1).
7
Find the Displacement subsection. In the zw text field, type T_3.
8
Locate the Domain Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
All
 
√
Lens Material 3
9
Locate the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Exterior
 
√
Lens Exteriors
Surface 1
 
√
Clear Apertures
Surface 2
 
√
Clear Apertures
Surface 1 obstruction
 
√
Obstructions
Surface 2 obstruction
 
√
Obstructions
Edges
 
√
Obstructions
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
Browse to the model’s Application Libraries folder and double-click the file petzval_lens_geom_sequence_lens4.txt.
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 3 (pi4).
6
From the Work plane list, choose Surface 2 vertex intersection (wp2).
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:
Name
Keep
Physics
Contribute to
All
 
√
Lens Material 4
9
Locate the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Exterior
 
√
Lens Exteriors
Surface 1
 
√
Clear Apertures
Surface 2
 
√
Clear Apertures
Surface 1 obstruction
 
√
Obstructions
Surface 2 obstruction
 
√
Obstructions
Edges
 
√
Obstructions
Lens 5
Now, add the fifth and last lens element. This element gives the Petzval a flat image plane.
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
Browse to the model’s Application Libraries folder and double-click the file petzval_lens_geom_sequence_lens5.txt.
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:
Name
Keep
Physics
Contribute to
All
 
√
Lens Material 4
9
Locate the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Exterior
 
√
Lens Exteriors
Surface 1
 
√
Clear Apertures
Surface 2
 
√
Clear Apertures
Surface 1 obstruction
 
√
Obstructions
Surface 2 obstruction
 
√
Obstructions
Edges
 
√
Obstructions
Part Libraries
Define the square image plane.
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>rectangular_planar_annulus in the tree.
3
Click  Add to Geometry.
Petzval Lens Geometry Sequence
Image
1
In the Model Builder window, under Component 1 (comp1)>Petzval Lens Geometry Sequence click Rectangular Planar Annulus 1 (pi7).
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:
Name
Expression
Value
Description
w0
d0_D
35.808 mm
Width, outer
h0
d0_D
35.808 mm
Height, outer
w1
0
0 m
Width, inner
h1
0
0 m
Height, inner
nix
0
0
Local optical axis, x-component
niy
0
0
Local optical axis, y-component
niz
1
1
Local optical axis, z-component
nwx
1
1
Rectangle width direction, x component
nwy
0
0
Rectangle width direction, y component
nwz
0
0
Rectangle width direction, z component
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 5 (pi6).
5
From the Work plane list, choose Surface 2 vertex intersection (wp2).
6
Find the Displacement subsection. In the zw text field, type T_6.
7
Locate the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
All
 
√
Image Plane
8
Click  Build All Objects.
9
Click the  Zoom Extents button in the Graphics toolbar.
Create a selection that includes all lenses. This can be used to define physics features.
All Lenses
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type All Lenses in the Label text field.
3
On the object pi1, select Domain 1 only.
4
On the object pi2, select Domain 1 only.
5
On the object pi4, select Domain 1 only.
6
On the object pi5, select Domain 1 only.
7
On the object pi6, select Domain 1 only.
Petzval Lens Apertures
The following commands are used to insert each of the lens apertures. The annulus clear aperture diameters are determined by the outer diameter of the current lens element. Each lens aperture is positioned at either the entrance or exit lens surface edges.
Group 1 Aperture
1
In the Geometry toolbar, click  Parts and choose Circular Planar Annulus.
2
In the Settings window for Part Instance, type Group 1 Aperture in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
Name
Expression
Value
Description
d0
1.25*d0_1
72.5 mm
Diameter, outer
d1
d0_1
58 mm
Diameter, inner
nix
0
0
Local optical axis, x-component
niy
0
0
Local optical axis, y-component
niz
1
1
Local optical axis, z-component
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 1 (pi1).
5
From the Work plane list, choose Surface 1 edge (wp3).
6
Locate the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
All
 
√
Obstructions
Group 2 Aperture
1
In the Geometry toolbar, click  Parts and choose Circular Planar Annulus.
2
In the Settings window for Part Instance, type Group 2 Aperture in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
Name
Expression
Value
Description
d0
1.25*d0_4
56.25 mm
Diameter, outer
d1
d0_4
45 mm
Diameter, inner
nix
0
0
Local optical axis, x-component
niy
0
0
Local optical axis, y-component
niz
1
1
Local optical axis, z-component
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 (pi4).
5
From the Work plane list, choose Surface 1 edge (wp3).
6
Locate the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
All
 
√
Obstructions
Group 3 Aperture
1
In the Geometry toolbar, click  Parts and choose Circular Planar Annulus.
2
In the Settings window for Part Instance, type Group 3 Aperture in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
Name
Expression
Value
Description
d0
1.25*d0_6
53.125 mm
Diameter, outer
d1
d0_6
42.5 mm
Diameter, inner
nix
0
0
Local optical axis, x-component
niy
0
0
Local optical axis, y-component
niz
1
1
Local optical axis, z-component
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 5 (pi6).
5
From the Work plane list, choose Surface 1 edge (wp3).
6
Locate the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
All
 
√
Obstructions
7
In the Geometry toolbar, click  Build All. Compare the resulting image to Figure 2.