How to Design an Off-Axis Parabolic Mirror

An off-axis parabolic (OAP) mirror offers a key advantage over on-axis reflective optics:
it eliminates central obscuration, allowing unobstructed access to the image plane while maintaining excellent aberration control.

In Zemax OpticStudio, an OAP mirror can be modeled by applying tilt and decenter to a parent parabolic surface.
The workflow described here applies broadly to any decentered or tilted surface, not just off-axis parabolas.

Off-Axis Parabolic Mirror Design Specifications

We will design a commercially available off-axis parabolic mirror with the following parameters:

The design goal is to allow the mirror to be tilted about the X-axis at any position along the optical (Z) axis, while maintaining correct imaging geometry.

Step 1: Define System Settings

Open System Explorer and apply the following settings:

• Aperture

  Type: Entrance Pupil Diameter

  • Value: 100 mm

• Units

  • Lens Units: Millimeters

• Wavelengths

  • Wavelength 1: 0.550 µm

These values establish a simple monochromatic, pupil-defined system suitable for geometric setup.

Step 2: Enter the Basic Geometry

Add one surface after the STOP surface in the Lens Data Editor (LDE).

Define Surfaces 1–3 as follows:

• The Image Surface uses a User-Defined Semi-Diameter of 30 mm
• Surface 1 is co-located with the Image surface and will not be drawn in the layout

This setup simplifies visualization while preserving correct ray behavior.

Step 3: Define the Parabolic Mirror Surface

The surface sag z of a Standard surface in OpticStudio is given by:

Where:

• $c$ = curvature (1 / radius)
• r = radial coordinate
• k = conic constant

Conic Definition

• Conic constant (k): −1 → Parabolic surface

Radius of Curvature

For a parabolic mirror: f = R/2

​Therefore:

• Focal length = 1000 mm
• Radius = −2000 mm

The negative sign indicates the center of curvature lies toward the −Z direction, consistent with reflective optics in OpticStudio.

Step 4: Define the Mirror Substrate

To ensure the back surface of the substrate is flat and perpendicular to the optical axis:

Open Surface Properties and set:

• Thickness: 40 mm
• Back surface: Plano and orthogonal to Z-axis

This represents a realistic mechanical substrate while keeping the optical surface unchanged.

Step 5: Add the Off-Axis Distance

To create the off-axis geometry:

In Surface Properties → Tilt/Decenter (Surface 2):

• Decenter Y: −150 mm

This shifts the usable portion of the parent parabola, forming the off-axis segment.

Step 6: Re-Center the Image Using a Coordinate Break

After decentering, rays propagate away from the original coordinate system.
To correct this:

1. Insert a Coordinate Break surface before the Image surface

2. Apply a Chief Ray solve to:

   • Decenter Y

   • Tilt About X

OpticStudio automatically computes the required tilt and decenter so that:

• The chief ray strikes the Image surface
• The Image surface is centered and normal to the chief ray

This ensures proper imaging geometry without manually calculating angles.

Key Design Takeaways

• Off-axis parabolic mirrors are created by tilting and decentering a parent parabola

• The optical performance remains parabolic; only the usable region changes

• Coordinate Breaks with Chief Ray solves are essential for clean image alignment

• This technique generalizes to:

  • Decentered aspheres

  • Freeform mirrors

  • Off-axis reflective systems