Fast Semi-Diameters vs Clear Semi-Diameter Explained

In optical design, semi-diameters define the physical aperture required at each surface to allow all valid rays to pass without vignetting. In Zemax OpticStudio, these values are usually computed automatically as clear semi-diameters, based on ray tracing across all fields and wavelengths.

Understanding the difference between Fast Semi-Diameters and standard (accurate) clear semi-diameter calculations is essential for balancing accuracy vs optimization speed, especially in complex systems.

Fast Semi-Diameters vs Clear Semi-Diameter in Optical Design

In optical design, semi-diameters define the physical aperture required at each surface to allow all valid rays to pass without vignetting. In Zemax OpticStudio, these values are usually computed automatically as clear semi-diameters, based on ray tracing across all fields and wavelengths.

Understanding the difference between Fast Semi-Diameters and standard (accurate) clear semi-diameter calculations is essential for balancing accuracy vs optimization speed, especially in complex systems.

Automatic Clear Semi-Diameter Calculation

OpticStudio computes automatic clear semi-diameters to estimate the minimum clear aperture required on each surface to transmit all rays for all field points and wavelengths.

Axial Systems

For rotationally symmetric (axial) systems, this calculation is highly efficient and accurate:

• Only two rays are traced per field and wavelength
• These are the top and bottom marginal rays
• Rays are traced in the true tangential plane of the vignetted pupil
• The radial coordinates of these rays determine the required semi-diameter

This approach is fast and reliable for most classical imaging systems.

Limitations in Non-Axial Systems

For non-axial or off-axis systems, this simplified approach may not be accurate enough, particularly when:

• There are tight edge or clear aperture constraints
• The illuminated footprint is irregular
• Vignetting varies strongly with pupil position

In these cases, accurately determining the required clear semi-diameter requires tracing many marginal rays around the pupil perimeter.

Fast Semi-Diameters: Purpose and Behavior

The Fast Semi-Diameters option controls how OpticStudio estimates automatic semi-diameters.

When Fast Semi-Diameters Is ON (Selected)

• OpticStudio traces an increasing number of marginal rays: 2 → 4 → 8 → 16 → …
• Iteration continues until convergence within 0.01% (5 significant figures)
• Designed primarily for axial systems
• Significantly faster during optimization

Note: For non-axial systems, this method may miss critical rays, leading to underestimated apertures. If turning Fast Semi-Diameters ON causes large changes in semi-diameter values compared to OFF, it should remain OFF.

Accurate Semi-Diameter Calculation (Fast Semi-Diameters OFF)

When the option is unchecked:

• OpticStudio traces at least 32 marginal rays around the vignetted pupil
• Additional rays are traced if needed to reach 0.01% convergence
• This method is slower, ,ore robust, safer for non-axial and freeform systems

This approach is recommended when:

• Aperture constraints are critical
• The system includes off-axis mirrors or prisms
• Accurate mechanical clearances are required

Important Accuracy Notes

• Semi-diameter calculations assume the surface size is limited by radial marginal rays
• They do not work reliably for surfaces in a caustic
• For caustic regions:

• • Ray-based footprints or spot diagrams can provide better estimates

  • However, diffraction effects (not modeled by rays) dominate, so extreme precision is usually unnecessary

Performance vs Accuracy Trade-Off

A common workflow is to optimize with Fast Semi-Diameters ON, then final-check with it OFF.