Fill Factor

Fill Factor

Posted at h in Application Notes by

Fill Factor and Transition Zones

Each microlens in an array needs to blend smoothly into its neighbor. The transition zone is the boundary where the curvature from one lens shape morphs into the next. In this zone, the lens profile no longer follows the intended ideal shape—and thus does not perform optimally over its intended Clear Aperture (CA).

  • Rule of Thumb:
    The typical width of this transition zone is ~1 µm, though this can vary:

    • Shallow lenses: ~0.5 µm transition is achievable
    • Steep or high-sag lenses: >1 µm transitions are common due to slope discontinuities
  • Impact on Fill Factor:
    As pitch decreases (i.e., lenses are packed more closely together), the transition zone becomes a larger fraction of each lens’s aperture. This reduces the effective optical area, leading to:

    • Lower light throughput
    • Increased optical crosstalk
    • Non-uniformity in beam homogenization or sensor illumination

 

Example:

  • For a 20 µm pitch with a 1 µm transition, 5% of each lens’s diameter is in the transition zone.
  • For a 50 µm pitch, this drops to just 2%.

Practical Layouts and Pitch Constraints

Array Type Packing Geometry Typical Fill Factor
Square grid Straight alignment >99%
Hex grid Diagonal packing >99%

Tighter packing decreases fill factor geometrically—but the optical fill factor also depends on how much of each lens can actually perform as designed, which is where pitch-to-transition zone ratio becomes critical.

Trade-offs Summary

Pitch Optical Fill Factor Transition Impact Trade-offs
Tight (<20 µm) Lower theoretical fill factor Transition zones consume more % area Excellent density, but possible performance loss at edges
Moderate (30–50 µm) Balanced Transition zones less dominant Good performance-to-density ratio
Wide (>100 µm) Higher fill factor Minimal edge blending impact Easier metrology and fabrication, lower resolution

Design Guidance

  • In high-precision applications (e.g. sensor coupling), transition zones must be minimized to preserve MTF and uniformity.
  • Always analyze the sag + pitch combination, as steep slopes (from high sag) in tight pitches exaggerate the edge blending loss.
  • For beam shaping or illumination applications, where uniformity is more important than high resolution, slightly looser pitches may be beneficial.

 

Print page