COMPASS

English

한국어

English

한국어

Appearance

Microlens Ray Trace ​

Trace rays through a superellipse microlens to visualize focusing behavior, spot size, and optical crosstalk as a function of lens geometry and chief ray angle.

Microlens Ray Tracing Simulator

Trace rays through a superellipse microlens onto a pixel photodiode. Adjust lens geometry and CRA to observe focusing and crosstalk.

AirSiliconColor filterDTIPD0PD1CollectedLost / CrosstalkPixel 0Pixel 1
Collection efficiency33.3%
Focal length (est.)1.37 um
Lens f-numberf/1.43
Crosstalk rays2

Model scope

Use this browser tool for intuition, relative trends, and design-space exploration. Its local simplified model is not a substitute for RCWA/FDTD sign-off, silicon calibration, or vendor process data.

Learn more

Image Sensor Optics · Microlens & CRA recipe

Physics Notes

Geometric Microlens Ray Tracing

Plain-English Intuition

A microlens sits on top of each pixel like a tiny magnifying glass, focusing incoming light onto the photodiode. This tool draws individual light rays through that lens — bending each one at the surface using basic Snell refraction — and counts how many hit the active area. It is the same idea as ray-tracing a camera lens, just at the micron scale.

This simulator traces rays through a smooth microlens surface using local surface normals and Snell refraction.

Assumptions

  • Rays obey geometric optics and Snell refraction at a smooth superellipse microlens surface.
  • Diffraction, interference, polarization, and wavelength-scale scattering are not solved.
  • The photodiode is represented by a geometric target plane, not by an electrical collection probability field.

Outputs

  • Ray paths, focus position, spot spread, collection efficiency proxy, and CRA sensitivity for a chosen microlens profile.
  • A quick indication of whether lens height, radius, index, or lateral shift moves light toward the intended photodiode.

Validation Example

  • At normal incidence and symmetric geometry, the focused distribution should remain centered on the pixel axis.
  • Increasing CRA without lens shift should move the focus laterally; adding compensating shift should pull it back toward the target.

Core Equations

Superellipse lens profile
$$z(r) = h \left[ 1 - \left( \frac{r}{R} \right)^n \right]^{1/n}$$
  • \(z(r)\): Height at radius $r$
  • \(h\): Lens vertex height (sag)
  • \(R\): Lens aperture radius
  • \(n\): Superellipse exponent

The exponent controls whether the lens is rounded, flat-topped, or steep-edged.

Snell refraction
$$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$$
  • \(n_1, n_2\): Refractive indices across the interface
  • \(\theta_1, \theta_2\): Angles relative to the surface normal

Refraction is evaluated at the local surface normal, not at the global vertical axis.

Spot efficiency proxy
$$\eta_{\text{coll}} \approx \frac{N_{\text{hits}}}{N_{\text{total}}}$$
  • \(\eta_{\text{coll}}\): Geometric collection efficiency
  • \(N_{\text{hits}}\): Number of rays hitting the photodiode

Ray-count efficiency is intuitive but not a wave-optical QE calculation.

Model Interpretation

  • Microlens shift is needed when chief rays arrive at high CRA.
  • Geometric ray tracing breaks down when pixel pitch approaches the wavelength.
  • Use RCWA/FDTD for diffraction, interference, and sub-wavelength metal-grid effects.

Ray-Trace Workflow

  • Define lens sag and local surface normal, apply Snell law at the curved interface, then propagate rays to the photodiode plane.
  • Collection is usually scored by hit fraction or weighted flux inside the photodiode aperture.
  • Sweep CRA and lens shift together; good on-axis focusing does not guarantee edge-pixel collection.

Geometry Sensitivities

  • Increasing sag usually strengthens focusing but can also increase aberration or shift focus above/below the photodiode.
  • A smaller aperture gap improves optical fill factor, but process merger and surface slope become limiting factors.
  • Index contrast between lens and surrounding medium controls bending strength through $n_1\sin\theta_1=n_2\sin\theta_2$.

Known Missing Physics

  • Ray tracing ignores diffraction, interference, polarization, and finite-wavelength scattering.
  • It does not model metal-grid shadowing, DTI waveguiding, or color-filter relief unless those surfaces are explicitly included.
  • For pixels near the wavelength scale, validate ray trends with electromagnetic solvers.

References