Internal Presentation

Phase Grating Calibration for Direct Write Lithography

Recovering process parameters from far-field diffraction measurements.

Zihan Zang, Do Young Kim, Yifeng Zeng
UCLA • March 2026
01
Background

Direct Write Lithography & Diffractive Optics

DWL: Maskless Grayscale Fabrication

  • Focused 405 nm laser scans substrate pixel-by-pixel
  • AOM controls intensity — 65,536 grayscale levels
  • Continuous surface relief in a single pass
  • No physical mask needed — rapid prototyping

Applications

  • Diffractive lenses, beam shapers, holograms
  • Blazed gratings, microlens arrays
  • Any 2.5D surface topography on photoresist

DOE: Height = Phase

Incident plane wave h₁ h₂ h₃ h₄ Photoresist (n ≈ 1.5) Transmitted wave (phase-shifted) φ = 2π(n−1)h / λ
02
Process Model

Dose → Depth → Phase: Two Unknowns

Grayscale lithography maps designed dose to physical phase through a two-component transfer function. Both components must be calibrated by measurement.

D(x,y) Designed dose h(D) Nonlinear F MTF Spatial filter F⁻¹ φ(x,y) Actual phase

h(D) — Dose to Phase Depth

Dose D Resist Expose + Develop Remaining depth φ phase Nonlinear chemistry: threshold, saturation, S-curve

MTF — Spatial Resolution Filter

Lens PSF Spot ~800 nm + Developer Lateral diffusion = MTF Low-pass Combined spatial blur ≈ Gaussian filter
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Process Parameters

h(D) and MTF: What We Need to Measure

h(D): Nonlinear Transfer Curve

Dose D φ = h(D) h_max ideal linear
  • Threshold → ramp → saturation
  • Varies with resist chemistry & process
  • Must be measured, not assumed

MTF: Resolution Rolloff

Spatial frequency f MTF(f) 1 f₁ f₂ f₃
  • Gaussian model: MTF(f) = exp(-f²/2σ²)
  • Same as imaging OTF you know well
  • Sampled at discrete grating frequencies
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Motivation

Why Not Directly Measure the Surface?

  • White-light interferometry — fails on transparent substrates (glass, fused silica)
  • AFM — extremely slow, tip convolution distorts sidewalls, no optical phase
  • SEM — no quantitative height; destructive
  • Confocal — z-resolution ~500 nm, insufficient for sub-λ DOE features
We need optical phase across the full spatial frequency range — diffraction gives both in one shot.
AFM Probe Limitation Substrate Tip Can't reach! Slow: <100×100 μm No optical phase info Transparent substrates Spatial frequency coverage
05
Key Idea

Phase Gratings as Calibration Probes

Fabricate periodic phase structures → measure far-field diffraction → extract process parameters. Two grating types, two unknowns.

Sinusoidal Grating → MTF

Single spatial frequency. Pre-compensated dose decouples h(D). Diffraction follows Bessel functions — direct MTF readout at each grating period.

Binary Grating → h(D)

Large period, swept amplitude. Ratio η₁/η₀ encodes phase step. Self-referencing, no prior calibration. MTF-decoupled at low frequencies.

Sinusoidal → MTF(f) at each frequency  |  Binary → h(D) at each dose level
06
Grating I

Sinusoidal Phase Grating

t(x) = exp[i·m·sin(2πfgx)] — Jacobi-Anger expansion:

ηn = |Jn(m)|²
  • Symmetric: η-n = ηn
  • Energy conserved: Σ Jn² = 1
  • Weak phase (m«1): only ±1 orders matter

With pre-compensated dose: ηn = Jn²(m·MTF). Pure MTF probe.

1.20 rad
07
Grating II

Binary (Square Wave) Phase Grating

50% duty, phase step Δφ. Odd orders only:

ηn = (4/π²n²) sin²(Δφ/2)

Self-Referencing MTF Check

  • Ideal: η3/η1 = 1/9, η5/η1 = 1/25
  • Departure ⇒ MTF contamination detected
  • No knowledge of Δφ or h(D) needed
2.00 rad
08
Calibration I

MTF Calibration: Pre-Compensated Sinusoidal

Why Small Modulation?

  • At small m, h(D) ≈ linear (1st-order Taylor)
  • Nonlinearity becomes negligible
  • Only MTF attenuation remains
MTF(fg) = meff / m

Extraction Strategies

  • Multi-order LS — fit all ηn jointly (best)
  • η1/η0 ratio — self-normalizing, no power cal
  • η0 inversion — simplest, invert J0²
10³
m = 10%   N: photons (shot-noise limited)
09
Calibration II

h(D) Calibration: Binary Grating Interferometer

Method

  • Large-period binary grating
  • Fix Dlow, sweep Dhigh
  • η1/η0 ratio encodes Δφ
Δφ = 2 arctan(π/2 · √(η₁/η₀))

Estimation Strategies

  • η1/η0 ratio — self-normalizing, monotonic on [0,π)
  • Multi-order fit — use all odd orders jointly
  • Parametric fit — fit Hill or polynomial to swept data
0.60 10³ N: photons (shot-noise limited)
10
Open Source

OpticsFlux — opticsflux.com

Open-source web platform for DWL calibration: interactive simulation, automated measurement, and real-time analysis. Everything in the browser.

Software Tools

  • Pattern generator — calibration gratings, Fresnel lenses, arbitrary DOE
  • Simulators — diffraction, MTF, binary interferometer, Fisher information
  • Analysis pipeline — data import, model fitting, strategy comparison
  • Export — DWL-ready BMP/NPY, publication figures

Hardware Integration

  • Thorlabs motorized translation stage
  • Thorlabs optical power meter
  • 520 nm laser pointer (low-cost probe)
  • WebUSB direct browser connection — no drivers
  • Fully automated scan + extraction pipeline

Python + FastAPI backend · Vanilla JS + Plotly.js frontend

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Summary

Contributions & Status

Motivation

  • Grayscale DWL needs process calibration for accurate DOE fabrication
  • Traditional metrology fails on transparent substrates and sub-λ features
  • Need optical phase, not just surface height

Contributions

  • Two-component model (h(D) + MTF) with independent calibration strategies
  • Sinusoidal gratings for direct MTF measurement via pre-compensation
  • Binary interferometer for model-free, self-referencing h(D) extraction
  • Open-source platform (OpticsFlux) with full simulation + hardware integration

Status

Simulation — Complete
Web platform — v2 deployed
Hardware — Integration tested
Experiments — In progress
Thank you • Questions?
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