Petzval Lens STOP Analysis Isothermal Sweep

Many optical systems are required to be operated in extreme environments, where temperature changes are significant. This will invariably induce deformations in the optical geometry. In order to simulate the effects of structural and thermal deformation on the optical performance of a lens a structural-thermal-optical performance (STOP) analysis should be performed. In this tutorial an integrated STOP analysis is demonstrated.

The Petzval Lens STOP Analysis tutorial is used as the basis for this model. In that example, a Petzval lens is modeled together with a simple barrel geometry (see Figure 1) and subjected to uniform temperature of −25°C. In this tutorial, a over a range of temperatures is performed. The assumption remains that the lens assembly is isothermal. At each temperature the effect on the image quality and focus position is computed.

A simulation of this kind could be used as the basis for confirming or optimizing an athermal lens assembly design. The STOP analysis could be also be extended to include surface-to-surface radiation or a non-linear material model for the elastomeric mounts. See Petzval Lens STOP Analysis with Surface-to-Surface Radiation and Petzval Lens STOP Analysis with Hyperelasticity for example simulations made at a single nominal temperature.

Figure 1: An overview of the Petzval Lens STOP analysis geometry. The lenses are shown in blue, the lens supports are colored red, and the detector assembly is dark gray. A simple barrel assembly connects these elements.

Model Definition

Details of the lens simulated in this tutorial can be found in the Petzval Lens tutorial (see Ref. 1, p. 191). For this model a simple barrel geometry and detector assembly has been added. The instructions for creating the geometry used in this model can be found in the appendix of Petzval Lens STOP Analysis. The material properties and all other details of the simulation remain unchanged.

Results and Discussion

A is performed across a range of temperatures; T0 = −25°C, 0°C, +25°C, and +50°C. The ray trace is performed using three wavelengths (475 nm, 550 nm, and 625 nm) over three field angles (0°, 3.5°, and 7.0°). After ensuring that the dataset is using a solution from the parametric sweep, it is possible to step through the on each of the Temperature and Displacements plots to see the results.

Figure 2 to Figure 5 show the temperature (which is uniform) together with the von Mises stress along the cross-sections. The stresses are greatest at the extrema of the temperature ranges, where the results of the large difference in the coefficients of thermal expansion (CTE) of the elements in the second lens group becomes apparent.

Figure 6 to Figure 9 shows the same stress plots together with the absolute lens displacement.

In Figure 10 the image quality on the nominal image plane is shown as a function of temperature. The nominal image plane is the detector surface after deformation. Figure 11 shows the image quality on the “best focus” image surface. In the current tutorial this is defined as the plane where the on-axis spot size is minimized. The focus offsets are summarized in Table 1. The first column in this table gives the offset between the deformed detector surface and it’s location at T0 = 20°C. The second column is the offset between the “best focus” image plane and the deformed detector surface.

Table 1: Summary of Image Plane Offsets.
Temperature	Nominal Δz = z(T) − z(T = 20°C)	Best focus Δz = zbest focus − z(T)
-25.0°C	-56.9 μm	72.5 μm
0.0°C	-25.3 μm	31.4 μm
25.0°C	6.3 μm	-9.4 μm
50.0°C	37.9 μm	-50.3 μm

Figure 2: A ray trace shown together with a 3/4 section view of the Petzval lens assembly. The von Mises Stress field is on the cross-sections. In this figure the temperature is T = -25°C.

Figure 3: A ray trace shown together with a 3/4 section view of the Petzval lens assembly. The von Mises Stress field is on the cross-sections. In this figure the temperature is T = 0°C.

Figure 4: A ray trace shown together with a 3/4 section view of the Petzval lens assembly. The von Mises Stress field is on the cross-sections. In this figure the temperature is T = 25°C.

Figure 5: A ray trace shown together with a 3/4 section view of the Petzval lens assembly. The von Mises Stress field is on the cross-sections. In this figure the temperature is T = 50°C.

Figure 6: In this ray trace, the displacement field is shown together with the von Mises stress for a temperature T = -25°C.

Figure 7: In this ray trace, the displacement field is shown together with the von Mises stress for a temperature T = 0°C.

Figure 8: In this ray trace, the displacement field is shown together with the von Mises stress for a temperature T = 25°C.

Figure 9: In this ray trace, the displacement field is shown together with the von Mises stress for a temperature T = 50°C.

Figure 10: The image quality on the nominal image plane as a function of temperature. This plane is coincident with the detector surface after deformation. Δz = z(T) - z(T=20°C).

Figure 11: Image quality on the best focus plane as a function of temperature. This is the plane on which the on-axis RMS spot size is minimized. Δz = z(best focus) - z(T).

References

1. M.J. Kidger, Fundamental Optical Design. Bellingham WA, USA: SPIE Press, 2001.

2. https://www.us.schott.com/english/index.html.

3. http://www.oharacorp.com/catalog.html.

4. M.A. Salama, W.M. Rowe, and R.K. Yasui, “Thermoelatic Analysis of Solar Cell Arrays and their Material Properties”, Technical Memorandum 33-626, NASA, 1973.

5. T.M. Mower, “Thermomechanical behavior of aerospace-grade RTV (silicone adhesive).” International Journal of Adhesions and Adhesives 87 (2018): 64-72.

6. P.R. Yoder, Jr., Opto-Mechanical Systems Design, Bellingham WA, USA: SPIE Press, 2006.

Ray_Optics_Module/Structural_Thermal_Optical_Performance_Analysis/petzval_lens_stop_analysis_isothermal_sweep

Modeling Instructions

Root

Open the Petzval Lens STOP Analysis model.

Application Libraries

From the menu, choose .

In the window, select in the tree.

Click

Study 1

Update the study settings so that the existing results can be reused.

In the window, click .

In the window for , locate the section.

Clear the check box.

Parametric Sweep

In the toolbar, click

In the window for , locate the section.

Click

In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
T0 (Nominal camera temperature)	-25 0 25 50	degC

In the toolbar, click

Results

In the window, click .

In the window for , locate the section.

Select the check box.

Ray 1

In the window, expand the node, then click .

In the window for , locate the section.

From the list, choose . This is the solution dataset for the parametric sweep.

To see the effect on the stress and displacement fields, cycle through the parameter sweep steps in each of the existing Temperature and Displacement plots.

Temperature

In the window, under click .

In the window for , locate the section.

From the list, choose .

In the toolbar, click

. Compare to Figure 2.

From the list, choose .

In the toolbar, click

. Compare to Figure 3.

From the list, choose .

In the toolbar, click

. Compare to Figure 4.

From the list, choose .

In the toolbar, click

. Compare to Figure 5.

Displacement

In the window, click .

In the window for , locate the section.

From the list, choose .

In the toolbar, click

. Compare to Figure 6.

From the list, choose .

In the toolbar, click

. Compare to Figure 7.

From the list, choose .

In the toolbar, click

. Compare to Figure 8.

From the list, choose .

In the toolbar, click

. Compare to Figure 9.

Intersection Point 3D 1

In the following steps the datasets are duplicated so that they can be referred to a single temperature. These will be used to create spot diagrams as a function of temperature.

In the window, under click .

In the window for , locate the section.

From the list, choose .

In the list, select .

Locate the section. From the list, choose .

Intersection Point 3D 3

Right-click and choose .

In the window for , locate the section.

In the list, select .

Intersection Point 3D 4

Right-click and choose .

In the window for , locate the section.

In the list, select .

Intersection Point 3D 5

Right-click and choose .

In the window for , locate the section.

In the list, select .

Spot Diagram 1

In the window, expand the node, then click .

In the window for , click to expand the section.

Clear the check box.

From the list, choose .

Spot Diagram 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Click to expand the section. In the text field, type 0.1.

Click to expand the section. From the list, choose .

Spot Diagram 3

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type 0.2.

Spot Diagram 4

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type 0.3.

Annotation 1

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type $T = eval(T0-0[degC])^\circ$C \\ $\Delta z = eval((aveop1(z)-z_image)/1[um])\,\unicode{\mu}$m. The position of the undeformed image plane is z_image.

From the list, choose .

Locate the section. In the text field, type -0.01.

Click to expand the section. In the text field, type 3.

Locate the section. Select the check box.

Locate the section. Clear the check box.

From the list, choose .

Annotation 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type 0.1.

Annotation 3

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type 0.2.

Annotation 4

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type 0.3.

In the toolbar, click

Click the

button in the toolbar. The figure should match to Figure 10.

Intersection Point 3D 2

In the window, under click .

In the window for , locate the section.

From the list, choose .

In the list, select .

Intersection Point 3D 6

Right-click and choose .

In the window for , locate the section.

In the list, select .

Intersection Point 3D 7

Right-click and choose .

In the window for , locate the section.

In the list, select .

Intersection Point 3D 8

Right-click and choose .

In the window for , locate the section.

In the list, select .

Spot Diagram 1

In the window, under click .

In the window for , locate the section.

In the text field, type 2.

Click to collapse the section. Locate the section. Clear the check box.

From the list, choose .

Click to collapse the section. Locate the section. Select the check box.

In the toolbar, click

Click to expand the section. Click .

Locate the section. Clear the check box.

Spot Diagram 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. Select the check box.

In the toolbar, click

Locate the section. Click .

Locate the section. Clear the check box.

Locate the section. In the text field, type 0.1.

Locate the section. From the list, choose .

Spot Diagram 3

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. Select the check box.

In the toolbar, click

Locate the section. Click .

Locate the section. Clear the check box.

Locate the section. In the text field, type 0.2.

Spot Diagram 4

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. Select the check box.

In the toolbar, click

Locate the section. Click .

Locate the section. Clear the check box.

Locate the section. In the text field, type 0.3.

Annotation 1

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type $T = eval(T0-0[degC])^\circ$C \\ $\Delta z = eval((162.79248823021723[mm]-aveop1(z))/1[um])\,\unicode{\mu}$m. The numerical value is the z-component of the dataset for this plot.

From the list, choose .