Design a Parametric Off-Axis Mirror Telescope in QUADOA® Optical CAD
This tutorial builds a fully parametric off-axis aspheric mirror telescope in QUADOA® Optical CAD in under 14 minutes. The primary mirror is a parabola with a rectangular, off-axis aperture defined by parameters in the multi-config lookup table. A Qcon aspheric secondary mirror is optimized for spot radius, giving a diffraction-limited image. Finally, both mirrors are turned into volumetric elements for CAD export, and the parametric model is updated simply by changing parameter values.
Key points
- All apertures and decenters are defined by parameters and math expressions in the multi-config lookup table.
- Primary: parabolic form with a rectangular, decentered aperture.
- Mirrors reflect via an ideal mirror coating or a user-defined sequence.
- Secondary: Qcon asphere with variable radius and three polynomial orders, optimized for spot radius.
- The result is diffraction limited on axis.
- Custom elements with dummy back surfaces turn the mirrors into volumetric parts for CAD export.
Terms used in this article
- Off-axis telescope
- A mirror telescope that uses an off-center section of the mirrors, so the secondary does not block the beam.
- Parametric model
- A model in which dimensions are defined by named parameters and formulas, so changing one value updates the whole design.
- Qcon asphere
- A Q-type asphere description based on Forbes polynomials, suited for strongly aspheric surfaces.
- User-defined sequence
- A sequence in which you specify the order of surfaces the rays pass through.
Step 1: Create the primary mirror
- Add a surface and set its identifier to
primary. - Add a parabolic form with a quadratic term of 0.01. If the surface curves in the wrong direction, simply change the sign.
- Add a rectangular aperture.
Step 2: Define the apertures with parameters
Open the multi-config lookup table and place it next to the System Setup view. Then define the parameters and use their names in the aperture fields:
| Parameter | Definition | Used for |
|---|---|---|
| Aperture x | 45 mm | Aperture of the primary in x (used as the Half Size X of the rectangular aperture) |
| Margin | 10 mm | Margin used in other parameters |
| Aperture y | Math expression: aperture x − margin | Aperture of the primary in y |
| Center y | Math expression including the margin | Decenter of the aperture, which makes the telescope off-axis |
A rectangular aperture is defined by Half Size X, Half Size Y and its center (Center X, Center Y) in the local surface coordinate system, so the decenter parameter goes into Center Y. Because the aperture sizes and decenter are linked by formulas, changing one parameter updates the whole geometry. See multi-configuration lookup table for how parameters and math expressions work.
Step 3: Set up the source and sequence
- Add an object surface before the primary and move it 200 mm to the left, with the primary in absolute coordinates.
- In the sequence’s source settings, set the source to a plane wavefront from infinity.
- Take the aperture from the primary mirror and set the aperture sampling to a grid.
- Hide the object surface in the 3D view, since it is only needed as the start of the sequence.
Step 4: Add the secondary mirror and image plane
- Add another surface for the secondary mirror and position it in the reflected beam.
- Make the primary reflect: either add a mirror coating, or convert the sequence to a user sequence and define the surface order. The Auto Sequence reflects at every surface whose coating has a reflectance above 50 %, so an Ideal Mirror coating (100 % reflection) is enough.
- Give the secondary a rectangular aperture with its own parameters (15 mm in x and 10 mm in y), decentered by half its aperture size.
- If the incoming beam is vignetted by the secondary, increase the margin, and increase the aperture sampling for better coverage up to the edge.
- Add an image plane 20 mm behind the primary in absolute coordinates, and an ideal mirror coating on the secondary.
- Name the secondary mirror and the image surface.
Step 5: Optimize the secondary and analyze
- Add a Qcon asphere form to the secondary. Set the radius variable, allow three polynomial orders as variables and use a norm radius of 10 mm, close to the aperture size. Keep the conic at zero, as recommended for Q-type aspheres.
- Create a default merit function that optimizes the spot radius without constraints. Its variables are the curvature and the polynomial terms.
- In the Optimization tab, run the Local Optimizer. The optimized form is found after a short time.
- Reduce the secondary aperture to 8 mm, since it is larger than needed.
In the Analysis tab, the spot diagram shows a diffraction-limited system, and the point spread function looks good. After adding two more fields in the source settings, the PSF of the third field becomes somewhat larger, while the other fields stay close to ideal.
Step 6: Turn the mirrors into volumetric elements for CAD
So far the mirrors are single surfaces. To export them as solid parts to CAD:
- In the Construction tab, add a new custom element, set its positioning to absolute and place it before the primary.
- Drag and drop the primary surface into the element and assign a dummy material to avoid the missing-material error.
- Repeat for the secondary mirror at its position.
- Convert the sequence to a user-defined sequence, so additional dummy surfaces are not traced.
- For each mirror, duplicate the mirror surface, remove its coating and form, and move it along Z (for example 10 mm) to form the back of the substrate.
Each mirror is now a volumetric element that can be exported to CAD. A custom element consists of one material and any number of surfaces; the material is assumed between any two of its surfaces.
Use Export to CAD in the File tab to export the whole model, single elements or assemblies as STEP, IGES or STL. In STEP, spherical surfaces are exported exactly, rotationally symmetric aspheres as rotated spline curves and freeforms as 2D splines. For STEP and IGES, the rays can be exported too, as fans, grids or a solid beam hull.
Step 7: Change the design through its parameters
Because the model is parametric, design changes take seconds:
- Increase the primary aperture to 65 mm: the rays and the PSF update immediately.
- Fix the resulting vignetting by enlarging the secondary aperture to 20 mm × 15 mm.
- Increase the substrate thickness if the mirror is too thin.
Video tutorial: designing a parametric off-axis mirror telescope
This 14-minute video builds the complete parametric off-axis telescope described in this article.
Video length: 13:39 min · Also on YouTube: Design of a parametric off-axis mirror telescope in 13:37 min with QUADOA® Optical CAD
Frequently asked questions
Define named parameters and math expressions in the multi-config lookup table and enter their names instead of numbers, for example for aperture sizes and decenters. Changing a parameter then updates the whole model.
Add a mirror coating, such as an ideal mirror coating, to the surface, or use a user-defined sequence that specifies the order of the surfaces.
Add a rectangular aperture and decenter it, for example with a parameter for the center position.
A Qcon asphere with variable radius and three variable polynomial orders, with a norm radius of 10 mm, optimized for spot radius with the Local Optimizer.
Put each mirror surface into a custom element with a dummy material, use a user-defined sequence, and add a duplicated back surface without coating and form to give each mirror a thickness. Then use Export to CAD for STEP, IGES or STL.
Yes. The spot diagram shows a diffraction-limited system on axis; for an additional outer field the PSF becomes somewhat larger.