MLA Array Visualizer

Visualize micro lens array (MLA) geometry with configurable array patterns, asymmetric lens radii, and curvature parameters. Switch between contour maps, equal-aspect cross-sections, 3D wireframe surface, and 2D ray tracing views.

Micro Lens Array Visualizer

Visualize superellipse microlens array geometry with contour maps, equal-aspect cross-sections, interactive 3D surface, and 2D ray tracing.

Array:

Radius X: 0.80 um

Radius Y: 0.80 um

Height h: 0.50 um

Shape n: 2.0

Curvature α: 1.00

Spacing X: 1.00 um

Spacing Y: 1.00 um

Sag height0.500 um

Focal length (est.)2.48 um

f-numberf/1.55

Fill factor100.0%

Superellipse: |x/Rx|ⁿ + |y/Ry|ⁿ = 1 | Height: z(r) = h(1 - r²)^1/(2α) | Snell: n₁sinθ₁ = n₂sinθ₂

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.

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Image Sensor Optics

Physics Notes

Microlens Array Surface Geometry

Plain-English Intuition

A real sensor has not one microlens but a whole grid of them — one per pixel, like an array of tiny bumps on a glass sheet. This visualiser stitches a single lens profile into that grid so you can see how pitch, asymmetry, and curvature interact across the array. Gaps between lenses or overlapping skirts both reduce optical fill factor.

The MLA visualizer extends a single lens profile into periodic arrays and shows how pitch, curvature, asymmetry, and ray direction change array behavior.

Assumptions

The array is built by periodically repeating a parametric single-lens height field.
Lens interaction is geometric and surface-based; resist flow, diffraction, and electromagnetic coupling are not solved.
Asymmetric radii and pitch changes represent layout intent, not measured wafer topography.

Outputs

Contour maps, equal-aspect cross sections, 3D wireframe, ray sketches, fill factor, and gap or overlap indicators.
A visual check of whether a lens array is sparse, near zero-space, asymmetric, or likely to create steep edge slopes.

Validation Example

When $R_x=R_y$ and pitch is equal in both axes, the top-view contour should be symmetric.
Reducing pitch at fixed lens radius should reduce gap and eventually show overlap or merger risk.

Core Equations

Anisotropic normalized radius

$$\rho = \left( \left| \frac{x}{R_x} \right|^n + \left| \frac{y}{R_y} \right|^n \right)^{1/n}$$

$\rho$: Normalized radial coordinate
$R_x, R_y$: Lateral radii of the lens

Different Rx and Ry produce astigmatic or rectangular-pixel lens footprints.

Surface sag

$$z(x, y) = h \cdot \max(0, 1 - \rho^\alpha)$$

$z$: Surface height
$\alpha$: Curvature power factor

Height h and curvature alpha set focusing strength and edge steepness.

Array pitch

$$(x, y)_{m,n} = (m P_x, n P_y)$$

$P_x, P_y$: Unit cell spacing in X and Y
$m, n$: Integer array indices

Array spacing controls gap, overlap risk, and fill factor.

Model Interpretation

Array-level gap and asymmetry matter as much as single-lens curvature.
A 3D surface view is geometric evidence, not a wave-optical simulation result.
Use this with the process-shape tool when connecting layout to final reflow geometry.

Array Geometry Checks

Check pitch consistency first: array centers follow $(x,y)_{m,n}=(mP_x,nP_y)$, so anisotropic pitch directly changes gap and fill factor.
Compare footprint exponent and profile exponent separately; one controls plan-view shape and the other controls vertical sag.
Look for edge overlap or residual valley regions because both can signal process or optical fill-factor risk.

Connection To Process

Lithographic island shape, reflow spread, and etch transfer determine the final footprint more than the ideal lens equation alone.
A zero-space design must be checked against merger risk, not just final gap.
AFM/SEM profile samples can calibrate $R_x$, $R_y$, $h$, and exponent values used by this surface model.

Known Missing Physics

The 3D surface is geometric only; it does not compute optical focus, diffraction, or collection efficiency.
It assumes identical repeated lenses and does not include wafer-level process gradients or local defects.
Use ray tracing or FDTD after this view when the shape must be linked to QE or crosstalk.