Convert Surface Form Wizard in QUADOA® Optical CAD
The Convert Surface Form Wizard in QUADOA® Optical CAD changes the mathematical description of a surface without changing its shape. It fits the new form to the old one and shows the fitting error. In this tutorial, a standard asphere is converted into a Q-type (Qbfs) asphere with a fitting error of about 0.00 nm.
Key points
- Open the wizard with a right-click on the surface → Convert Form, or under Construction → Actions.
- The old form is shown at the top; the new form is added at the bottom.
- Set the variables of the new form, for example radius and polynomial terms, with Set All Variable.
- For rotationally symmetric forms, check Assume Rotational Symmetry.
- The wizard shows the fitting error before you accept the conversion.
Terms used in this article
- Q-type asphere (Qbfs)
- An asphere description based on Forbes polynomials around a best-fit sphere.
- Norm radius
- The radius used to normalize the polynomial terms, usually the aperture radius.
- Fitting error
- The deviation between the original surface and the fitted new form.
Why convert a surface form?
The same shape can be described by different formulas. Some descriptions are better suited for optimization or manufacturing; Q-type aspheres, for example, use orthogonal polynomials. The wizard changes only the description, not the shape.
How to open the Convert Surface Form Wizard
- Right-click the surface you want to convert and choose Convert Form, or
- Select the surface and open the Construction tab, Actions → Form → Convert Form Wizard, or
- Use Convert or Import Form in the menu bar of the Optical Design Editor.
The old form, here the standard asphere, is shown at the top of the wizard. The new form is defined at the bottom.
How to define the new form
- At the bottom, right-click and choose Add Form, then select the new form, for example Asphere Q-Type Qbfs. Keep its conic at zero: the conic term is not part of the original Q-type definition and impairs the numerical behavior, especially during optimization.
- Set the radius to variable.
- Set the norm radius, for example to the aperture radius of the original asphere (25 mm in the video).
- Choose the number of polynomials, for example 10, and set them all to variable with a right-click → Set All Variable.
- For a rotationally symmetric form, check Assume Rotational Symmetry.
How to convert and check the result
- Click Convert. The wizard fits the new form to the old one.
- Check the fitting error on the right. In the video it is about 0.00 nm.
- Click OK. The Qbfs form replaces the original asphere.
QBfs or QCon?
Both are aspheres based on the polynomials introduced by G. Forbes. QBfs describes the departure from a best-fit sphere, QCon the departure from a conic base. QCon is used, for example, for the secondary mirror in the off-axis telescope. For both, QUADOA® includes a conic parameter only for compatibility with other software, and recommends leaving it at zero.
The same fitting approach is used to describe measured or simulated surface deformations; see adding measurement and FEM data.
Video tutorial: the Convert Surface Form Wizard
This 3-minute video converts a standard asphere into a Q-type Qbfs asphere with the Convert Surface Form Wizard.
Video length: 3:03 min · Also on YouTube: Convert Surface Form Wizard in QUADOA® Optical CAD
Frequently asked questions
Right-click the surface, choose Convert Form, add the Q-type Qbfs form at the bottom of the wizard, set norm radius and number of polynomials, set them variable, click Convert, check the fitting error and click OK.
No. The wizard fits the new description to the existing shape; only the mathematical description changes. The fitting error shows how closely they match.
Typically the aperture radius of the surface, as in the video, where the norm radius equals the 25 mm aperture radius.
It restricts the new form to rotationally symmetric terms, which is appropriate when the original surface is rotationally symmetric.
No. The conic is included only for compatibility with other software. It is not part of the original Q-type definition and impairs the numerical properties, especially during optimization, so it should stay at zero.