Thermal Analysis in QUADOA® Optical CAD
A complete first-order thermal analysis in QUADOA® Optical CAD takes three temperature effects into account: the change of the refractive index, the thermal expansion of the lenses and the thermal expansion of the mechanical mounting. This tutorial shows each step on a Keplerian beam expander designed at 20 °C, which is then optimized for the range from −20 °C to +80 °C. After optimization, the defocus is balanced to about 1.3 λ at both temperature extremes, instead of 1 λ and 1.6 λ before.
Key points
- Set up a multi-configuration with a temperature parameter (here
TEMP) and link it to the environment temperature in System Setup. - Refractive index changes are calculated from the thermal parameters of the material. Without them, no thermal analysis is possible.
- Activate Scale Thermally in the material row to include the thermal expansion of a lens. This works for spheres, aspheres, freeforms and all other surface types.
- Model the expansion of the mechanical mounting with thermal lengths in the multi-config lookup table.
- Use Is Thermal or a local environment if single lenses have a different temperature than the system.
- Optimize with a merit function that evaluates the wavefront error at both temperature extremes.
Terms used in this article
- First-order thermal analysis
- An analysis of how temperature changes the optical performance through refractive index, lens expansion and mount expansion.
- TEMP parameter
- A user-defined parameter in the multi-config lookup table that holds the system temperature of each configuration.
- Environment
- The system-wide conditions in System Setup, such as temperature. Lenses inherit the properties of their environment.
- TCE
- Thermal coefficient of expansion: describes how much a material expands per degree of temperature change.
- Scale Thermally
- Checkbox in the material row of an element that applies the thermal expansion of its material to the lens.
- Thermal length
- A length in the multi-config lookup table that changes with temperature, used to model the expansion of mechanical parts.
Example system: Keplerian beam expander
The example is a beam expander based on a Kepler-type telescope with an expansion factor of 8.
- Two plano-aspheric lenses, both modeled with a QCon asphere form.
- The first lens focuses the light to an intermediate focal point; the second lens collimates the outgoing beam.
- Lens material: F2 from SCHOTT.
- Design temperature: 20 °C.
- Goal: optimize the wavefront error for a system temperature range of −20 °C to +80 °C.
Which thermal effects does the analysis include?
| Effect | Source of the data | How it is enabled in QUADOA® |
|---|---|---|
| Change of refractive index | Thermal parameters of the material in the materials catalog | Applied once the environment temperature is set |
| Thermal expansion of the lenses | TCE of the lens material | Scale Thermally checkbox in the material row |
| Thermal expansion of the mounting | TCE of the mount material (custom value or material such as steel) | Thermal lengths in the multi-config lookup table |
Step 1: Set up the temperature configurations
Each temperature to be analyzed is one configuration of a multi-configuration setup.
- Create a multi-configuration setup with three configurations.
- Define a parameter
TEMPfor the system temperature. - Assign the temperatures: −20 °C (configuration 1), +20 °C (configuration 2) and +80 °C (configuration 3).
- Go to System Setup → Environment and enter
TEMPas the temperature.
The environment defines the temperature in °C and the pressure in bar. They apply to every lens that does not have its own temperature, and to the air between elements.
When you now switch between the configurations, you see a defocus and a change of the wavefront caused by the different temperatures.
Step 2: Refractive index changes with temperature
The defocus in step 1 occurs because the temperature changes the refractive index of the lens material. The materials catalog entry of F2 (SCHOTT) contains thermal parameters that describe how the refractive index varies with temperature, and QUADOA® uses them to calculate the optical changes.
Important: If a material has no thermal parameters, a thermal analysis cannot be performed with this material. Check the materials catalog before you start. In the catalog files, the temperature dependence of the index is described by the coefficients D0, D1, D2, E0, E1 and a reference wavelength, together with the reference temperature of the glass data; manufacturers do not provide them for every glass.
Different temperatures for single lenses
- Is Thermal: Activate the Is Thermal checkbox next to the material in the material row. This enables the material’s own Temperature parameter, so a single element can have a temperature different from the environment.
- Local environment: In System Setup, right-click the main environment and choose Add Local Environment (called sub-environment in the manual). Lenses placed in a local environment inherit its properties, and the medium between their surfaces is taken from it.
Neither option is used in this example; the whole system has one temperature.
Step 3: Thermal expansion of the lenses
When the temperature changes, the lenses also expand or contract physically. This is described by the thermal coefficient of expansion (TCE), which is listed in the materials catalog, for example for F2 (SCHOTT).
- Open the Optical Design Editor.
- In the material row of the first lens, activate Scale Thermally.
- Repeat for the second lens.
The wavefront false color plot changes when you switch Scale Thermally on or off, because the lens geometry now scales with temperature. Thermal scaling works independently of the surface shape: it is not limited to spherical surfaces, but also applies to aspheres, freeform surfaces and all other surface types in QUADOA®.
Tip: To make the effect visible, add a test configuration with an extreme temperature such as 1,000 °C. In the 3D view you can then see the lens expand and shift compared with −20 °C.
Step 4: Thermal expansion of the mechanical mounting
The mounting expands as well, which changes the distances between the lenses. In the example, each lens sits in a seat mount and is held by a retaining ring on the other side. When the mount expands, the distance between the mounting surfaces changes accordingly.
The expansion of the mount is modeled with thermal lengths in the multi-config lookup table. Two thermal lengths are used so that the intermediate focus stays unchanged.
Steps
- In the multi-config lookup table, click Add Thermal Expansion Length twice and name the lengths
Length 1andLength 2. - In the temperature parameter field, enter
TEMP, so the mount uses the system temperature. - Enter the nominal length at the reference temperature of 20 °C: the current Z positions of the two elements (here 10 mm and 74.62 mm).
- Assign a material to the mount with TEC Type: enter a custom expansion coefficient in dL/dT, choose a material type from the drop-down, or use a material from the model. In this example both lengths use steel.
- Replace the Z positions of the two elements with
Length 1andLength 2.
How the thermal length is calculated
A thermal expansion length has the parameters Temp Param (the temperature parameter, here TEMP), Nom Length Lnom, Extra Length Lext, TEC Type, dL/dT (the expansion coefficient TEC) and Nom. Temp Tnom. At temperature T the length is:
L = Lnom + (Lnom + Lext) · TEC · (T − Tnom)
The Extra Length accounts for mechanical parts whose expanding length differs from the optical distance, for example a spacer that is longer than the air gap it defines.
Result
| Temperature | Length 1 | Length 2 |
|---|---|---|
| −20 °C | Slightly below 10 mm | Slightly below 74.62 mm |
| +20 °C (nominal) | 10 mm | 74.62 mm |
| +80 °C | 10.007 mm | 74.67 mm |
At the nominal temperature the system matches the original geometry. Lower temperatures shorten the distances, higher temperatures lengthen them.
Step 5: Optimize for the full temperature range
Before optimization, the system shows a defocus of about 1 λ at −20 °C and 1.6 λ at +80 °C. The goal is a compromise with balanced performance at both temperature extremes.
Create the merit function
- In System Setup → Optimization, right-click and choose Add Merit Function. Name it
Thermal. - Open the merit function and add a ray trace with the trace goal Wavefront RMS error.
- Duplicate the ray trace. Assign configuration 1 (−20 °C) to the first and configuration 3 (+80 °C) to the second.
The trace goals now show different wavefront errors for the two temperatures, caused by thermal expansion and refractive index changes.
Define the variable and optimize
- Select the new merit function (in the example, merit function 3,
Thermal). - Make the Z position of the second lens variable. Because this position refers to
Length 2, activate the variable checkbox ofLength 2in the multi-config lookup table. - Go to Optimization → Local Optimization, select the merit function
Thermaland click Optimize.
Result
| Temperature | Defocus before | Defocus after |
|---|---|---|
| −20 °C | about 1 λ | about 1.3 λ |
| +80 °C | about 1.6 λ | about 1.3 λ |
Tip for glass substitution: If you also let the Extended Optimizer exchange glasses in a thermal design, set its Glass Selector to Random. The Smart selector chooses glasses only by dispersion and ignores properties such as thermal expansion, which matter in models with several thermal configurations.
The maximum defocus over the full range drops from 1.6 λ to about 1.3 λ, with all key thermal effects included: the expansion of the aspheric lenses, the change of the refractive index and the expansion of the mounting. This completes the first-order thermal analysis.
Video tutorial: thermal analysis of a beam expander
This 14-minute video walks through the complete thermal analysis and optimization of the beam expander described in this article.
Video length: 14:09 min · Also on YouTube: Thermal Analysis in QUADOA® Optical CAD
Frequently asked questions
It includes three effects: the change of the refractive index with temperature, the thermal expansion of the lenses (activated with Scale Thermally) and the thermal expansion of the mechanical mounting (modeled with thermal lengths in the multi-config lookup table).
Create a multi-configuration setup with a temperature parameter, for example TEMP, and assign one temperature per configuration. Then enter this parameter as the temperature in System Setup under Environment.
The material needs thermal parameters that describe how its refractive index changes with temperature. If the materials catalog entry has no thermal parameters, a thermal analysis cannot be performed with that material.
Yes. Activate Is Thermal next to the material in the material row to assign a separate temperature to one element, or add a local environment in System Setup so that lenses inherit its properties.
Yes. Thermal scaling with Scale Thermally works independently of the surface shape. It applies to spherical surfaces, aspheres, freeform surfaces and all other surface types in QUADOA®.
Add thermal expansion lengths in the multi-config lookup table, link them to the temperature parameter, enter the nominal length at the reference temperature, assign a mount material such as steel, and replace the element positions with these thermal lengths. The length is calculated as L = Lnom + (Lnom + Lext) · TEC · (T − Tnom).
Create a merit function with a ray trace for each temperature extreme, for example the wavefront RMS error at −20 °C and +80 °C, set a suitable variable such as a lens position, and run a local optimization with this merit function.