Lens Sag Design Considerations

Lens Sag Design Considerations

Design Importance:

• Sag height, together with lens diameter and refractive index, determines the focal length and optical power of the microlens.
• The higher the sag, the greater the lens’s curvature and optical power—but also the more challenging it becomes to fabricate and characterize.

Process-Dependent Sag Limits:

Fabrication methods have optimal sag ranges based on material properties, process mechanics, and metrology capabilities.

• Greyscale Photolithography:
  • Optimal sag range: 5–40 µm
  • Below ~5 µm, shallow lens profiles become difficult to accurately define due to:
    • Resolution limits of the writing system
    • Insufficient contrast in slope
    • Challenges in metrology equipment to reliably measure sub-micron curvature variations
  • Above ~40 µm:
    • Requires deep photoresists, often with lower aspect ratio fidelity
    • Difficulties arise in controlling resist thickness uniformity and avoiding slumping or profile deformation
• UV Replication:
  • Tolerant of a wide range of sag heights, but still limited by:
    • Mold fidelity and release characteristics
    • Material shrinkage
• Laser Writing, 3D Printing or Direct Etching:
  • Enables higher sags with good accuracy, but slower and less scalable for large-format MLAs

Metrology Limitations:

At low sag values (<5 µm), even the most advanced white light interferometers or confocal profilers may struggle to resolve curvature accurately, particularly in fast f/# lenses or those with subtle slopes. This complicates both development and QC.

Design Alternatives: Micro-Fresnel Lenses

When large lenses (e.g., several mm in diameter) demand high optical power but sag heights exceed feasible fabrication limits, micro-Fresnel lens designs offer a practical alternative.

• Benefits:
  • Achieve high optical power with lower sag
  • Can be fabricated using traditional lithographic or molding techniques
• Trade-offs:
  • Introduce step transitions between Fresnel zones, creating:
    • Dead zones where optical power drops
    • Scattering artifacts
    • Reduced MTF (modulation transfer function)

Typical zone width near the Fresnel edge can be ~2 µm, which may significantly affect image or beam quality in high-performance systems.

Summary of Trade-Offs