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Petzval Lens Optimization
Introduction
This example shows how to use an Optimization study to update the optical prescription for a multi-element objective lens when one of the glasses is replaced. Because of slight differences in the refractive index and Abbe number of the replacement glass compared to the original glass, some small adjustments to the geometry sequence are required to ensure that the lens still produces a high-quality image.
For an introduction to ray optics simulation of a Petzval Lens (without the Optimization study), see the tutorial model Ray_Optics_Module/Lenses_Cameras_and_Telescopes/petzval_lens.
Model Definition
The Petzval lens setup used in this example includes two cemented doublets and a field flattener. Each of the two cemented doublets typically consists of a crown glass (low refractive index, less dispersion) on the side the object, and a flint glass (higher index, greater dispersion) on the side facing the image plane.
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.
Dispersion in Optical Glass
The refractive index of an optical glass always depends on the wavelength of the light passing through it. A common way to compare the optical properties of different glasses is by comparing their values of the d-line refractive index nd and Abbe number Vd,
where
•
The d-line is a yellow helium spectral line at about 587.56 nm,
•
The F-line is a blue hydrogen spectral line at about 486.13 nm, and
•
The C-line is a red hydrogen spectral line at about 656.28 nm.
Keeping the d-line refractive index constant, a lower Abbe number means that the refractive index of the glass is more sensitive to changes in the refractive index (greater dispersion), while a higher Abbe number means lower sensitivity (less dispersion).
Historically, optical glasses have been roughly categorized as crown glasses and flint glasses. On average, the crown glasses have lower index and higher Abbe number, while flint glasses have higher index and lower Abbe number. A scatter plot of refractive index versus Abbe number for comparing different glasses is called an Abbe diagram.
A common way to report the Abbe number and d-line refractive index of a glass is through a six-digit glass code. In the glass code, the first three digits are the digits of the refractive index (after the decimal point) and the last three digits are the Abbe number (multiplied by 10). For example, a glass with code 654321 has a d-line refractive index of 1.654 and an Abbe number of 32.1.
Choosing a Replacement Glass
There are many legitimate reasons why an optical designer might want to replace the glass in a lens system:
•
The new glass might be less expensive, more readily available, or be easier to work with.
•
The new glass might have other desirable material properties, such as a lower coefficient of thermal expansion, lower density, or superior scratch resistance.
•
The new glass might be produced in a more environmentally friendly way.
•
The old glass might contain additives such as lead, cadmium, or arsenic that can be hazardous to human health.
Regardless of the reason for the change, the integration of optimization tools into optical ray tracing software can be used to modify an existing optical prescription to use a replacement glass with similar (but not exactly the same) optical properties.
In this example, the geometry sequence is based on the optical prescription shown in Table 1, which in turn was inspired by a prescription from Ref. 1, p. 191. The focal length is 100.0 mm and the focal ratio is approximately f/2.4. The instructions for creating the lens geometry can be found in the Appendix — Geometry Instructions.
Table 1: Petzval lens parameters.
Index
Name
Radius
(mm)
Thickness
(mm)
Material
Clear radius
(mm)
—
Object
 ∞
 ∞
—
—
1
Lens 1
 99.56266
 13.00000
N-BK7
 28.478
2
Lens 2
 -86.84002
 4.00000
S-BAH32
 26.276
—
—
 -1187.63858
 40.00000
—
 22.020
3
Stop
 ∞
 40.00000
—
 16.631
4
Lens 3
 57.47191
 12.00000
N-SK2
 20.543
5
Lens 4
 -54.61865
 3.00000
N-SF5
 20.074
—
—
 -614.68633
 46.82210
—
 16.492
6
Lens 5
 -38.17110
 2.00000
N-SF5
 17.297
—
—
 ∞
 1.9548
—
 18.940
—
Image
 ∞
—
—
 17.904
In 2018 the glass in the second element, S-BAH32 glass from the Ohara corporation, was changed to a “special order” glass (Ref. 2), with a notice that “Special order types may be still available for some time, but we do not guarantee, on your order we can melt these types”. Thereafter, potential replacement glasses for S-BAH32 were considered. The six-digit glass code of the S-BAH32 glass is 670393, meaning it has a d-line refractive index of 1.670 and an Abbe number of 39.3. Two potential replacement glasses were identified:
•
Schott N-BASF64, glass code 704394 (nd = 1.704, Vd = 39.4)
•
Schott N-KZFS5, glass code 654397 (nd = 1.654, Vd = 39.7)
Ultimately the Schott N-KZFS5 glass was chosen. This glass has nearly the same Abbe number as the Ohara S-BAH32 glass but a slightly lower d-line refractive index. Therefore, if the glass is simply replaced without any updates to the geometry sequence, the resolution of the lens system will be significantly diminished. Figure 4 and Figure 5 show the ray and spot diagrams when using the unmodified prescription from Table 1.
Setting up the Optimization Study
To improve the image quality when using the replacement glass, an Optimization study was performed. The control parameters for this study were perturbations in the lens radii of curvature. Since the model geometry includes two cemented double lenses and a field flattener with one curved surface, a total of seven control parameters were used. The objective function is the sum of the squares of the root mean square (rms) spot sizes for three different field angles (on-axis, 6°, and 9°). In addition, rays of three different vacuum wavelengths were released (475 nm, 550 nm, and 625 nm).
Although the Optimization study supports both gradient-based and gradient-free optimization methods, only the gradient-free methods are appropriate to use with ray optics simulation, because the degrees of freedom solved for are discrete ray coordinates and directions rather than the values of a continuous field variable. The BOBYQA optimization method was used because it is well-suited to optimization problems with a fairly large number of control parameters but no constraints.
The original model geometry was constructed by repeated insertion of part instances from the COMSOL Part Libraries, mainly the “Spherical Lens 3D” part. Since these parts are parameterized representations of the lens surfaces, it was convenient to add perturbations the radii of curvature of each curved refracting surface.
Results and Discussion
The Petzval lens geometry sequence is shown in Figure 2 and the mesh can be seen in Figure 3.
A ray tracing analysis of the original geometry yields the ray diagram shown in Figure 4 and the spot diagram (in the nominal image plane) shown in Figure 5. The rms spot size is on the order of several hundred micrometers for all three field angles.
After the Optimization study is run, the ray and spot diagrams of the resulting geometry are shown in Figure 6 and Figure 7. Compared to the previous solution, the rms spot sizes have been reduced by a factor of almost 100.
It is important to note that optimization methods generally seek a local minimum in the objective function by varying the control parameters, not a global minimum in the prescribed range of control parameter values. Therefore, different values of the radii of curvature in the optimized geometry may be found, especially if a different set of initial values is given. This may cause the spot diagram to look slightly different from Figure 7, although the spot sizes should be comparable in magnitude. Lens optimization is a rich design space, and the solution presented here is only one of many possible local minima.
Figure 2: The Petzval lens geometry sequence.
Figure 3: The Petzval lens mesh.
Figure 4: Ray diagram of the Petzval lens before optimization. A close-up look shows that the rays are not well focused at the nominal image plane.
Figure 5: Spot diagram of the Petzval lens in the nominal image plane before optimization.
Figure 6: Ray diagram for the optimized Petzval lens. with replacement glass.
Figure 7: Spot diagram array for the optimized Petzval lens with replacement glass.
References
1. M.J. Kidger, Fundamental Optical Design, SPIE Press, 2001.
2. Ohara team, “Review of Glass Portfolio,” published 24 Jan 2018, last accessed 12 Jul 2021, www.ohara-gmbh.com/en/dialog/news/details/news/review-of-glass-portfolio-1.html.
Application Library path: Ray_Optics_Module/Lenses_Cameras_and_Telescopes/petzval_lens_optimization
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_optimization_parameters.txt.
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 1: Lens Prescription 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_optimization_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 Materials 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 the Add to Component button in the window toolbar.
5
In the tree, select Optical > Schott Glass > Schott N-KZFS5 Glass.
6
Click the Add to Component button in the window toolbar.
7
In the tree, select Optical > Schott Glass > Schott N-SK2 Glass.
8
Click the Add to Component button in the window toolbar.
9
In the tree, select Optical > Schott Glass > Schott N-SF5 Glass.
10
Click the Add to Component button in the window toolbar.
11
In the Materials toolbar, click  Add Material to close the Add Material window.
Materials
Schott N-BK7 Glass (mat1)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
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
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
In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose 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 Study toolbar, click  Compute.
Results
Ray Trajectories (gop)
The default plot is a ray diagram with a color expression based on time, which is proportional to optical path length.
1
In the Settings window for 3D Plot Group, locate the Color Legend section.
2
Clear the Show legends checkbox.
3
Click the  Show Grid button in the Graphics toolbar.
4
Click the  Show Axis Orientation button in the Graphics toolbar.
Compare this image to Figure 4. The rays appear to converge some distance away from the nominal image plane.
Spot Diagram
In the following steps, a spot diagram is created, and a custom color expression is added.
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.
Spot Diagram 1
In the Spot Diagram toolbar, click  More Plots and choose Spot Diagram.
Color Expression 1
1
In the Spot Diagram toolbar, click  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 checkbox.
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 5.
Global Definitions
Parameters 3: Optimization
1
In the Home toolbar, click  Parameters and choose Add > Parameters.
2
In the Settings window for Parameters, type Parameters 3: Optimization 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_optimization_opt_parameters.txt.
Parameters 1: Lens Prescription
1
In the Model Builder window, click Parameters 1: Lens Prescription.
2
In the Settings window for Parameters, locate the Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
R1_1
99.56266[mm]+dR1_1
0.099563 m
L1, surface 1 radius of curvature
R2_1
-86.84002[mm]+dR2_1
-0.08684 m
L1, surface 2 radius of curvature
R2_2
-1187.63858[mm]+dR2_2
-1.1876 m
L2, surface 2 radius of curvature
R1_4
57.47191[mm]+dR1_4
0.057472 m
L3, surface 1 radius of curvature
R2_4
-54.61865[mm]+dR2_4
-0.054619 m
L3, surface 2 radius of curvature
R2_5
-614.68633[mm]+dR2_5
-0.61469 m
L4, surface 2 radius of curvature
R1_6
-38.17110[mm]+dR1_6
-0.038171 m
L5, surface 1 radius of curvature
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select Preset Studies for Selected Physics Interfaces > Ray Tracing.
4
Click the Add Study button in the window toolbar.
5
In the Home toolbar, click  Add Study to close the Add Study window.
Study 2
Step 1: Ray Tracing
1
In the Settings window for Ray Tracing, locate the Study Settings section.
2
From the Time-step specification list, choose Specify maximum path length.
3
In the Lengths text field, type 0 200.
4
From the Length unit list, choose mm.
Parameter Optimization
1
In the Study toolbar, click  Optimization and choose Parameter Optimization.
2
In the Settings window for Parameter Optimization, locate the Optimization Solver section.
3
From the Method list, choose BOBYQA.
4
In the Optimality tolerance text field, type 0.02.
5
Locate the Objective Function section. In the table, enter the following settings:
Expression
Description
Evaluate for
comp1.gop.relg1.rrms^2
 
Ray Tracing
comp1.gop.relg2.rrms^2
 
Ray Tracing
comp1.gop.relg3.rrms^2
 
Ray Tracing
6
Locate the Control Parameters section. Click  Load from File.
7
Browse to the model’s Application Libraries folder and double-click the file petzval_lens_optimization_study_settings.txt.
Solution 2 (sol2)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 2 (sol2) node, then click Time-Dependent Solver 1.
3
In the Settings window for Time-Dependent Solver, click to expand the Time Stepping section.
4
From the Steps taken by solver list, choose Manual.
5
In the Time step text field, type 200[mm]/c_const.
6
In the Study toolbar, click  Compute.
Results
Ray Trajectories (gop) 1
1
In the Settings window for 3D Plot Group, locate the Color Legend section.
2
Clear the Show legends checkbox.
3
In the Ray Trajectories (gop) 1 toolbar, click  Plot.
Compare this image to Figure 6. The rays appear to converge some distance away from the nominal image plane.
Spot Diagram 1
1
In the Model Builder window, right-click Spot Diagram and choose Duplicate.
2
In the Settings window for 2D Plot Group, locate the Data section.
3
From the Dataset list, choose Ray 2.
4
In the Spot Diagram 1 toolbar, click  Plot.
Compare this image to Figure 7.
5
Click the  Zoom Extents button in the Graphics toolbar.
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_optimization_geom_sequence_parameters.txt.
Petzval Lens Parameters
The parameters that define the Petzval lens geometric sequence are found in petzval_lens_optimization_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 Geometry toolbar, click  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, 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_optimization_geom_sequence_lens1.txt. The files petzval_lens_optimization_geom_sequence_lensm.txt, where m=1,...,5, contain 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 (that is, the z-axis) horizontally and the y-axis vertically.
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  Part Instance 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_optimization_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 zwi 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  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 zwi 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 similarly defined. Next, add the third lens element.
1
In the Geometry toolbar, click  Part Instance 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_optimization_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 zwi 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  Part Instance 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_optimization_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 zwi 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  Part Instance 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_optimization_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 zwi 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  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 zwi 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  Part Instance 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  Part Instance 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  Part Instance 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.