From geometric voxels to evolving material fields
Model fidelity is not one ladder. An optical model can be detailed while its chemistry is a threshold; a kinetic model can be rich while its scan path is reduced to a local dose.
| Layer | Compact model | Richer model | Current lab |
|---|---|---|---|
| Geometry | Fixed ellipsoid | Sliced path through arbitrary occupancy | Deterministic benchmark occupancy |
| Optics | Gaussian focus | Vectorial diffraction with aberrations | Vectorial Debye field |
| Excitation | Binary dose | Pulse-resolved nonlinear initiation | Voxel-averaged I² source |
| Chemistry | Conversion threshold | Multi-species kinetic network | Reaction–diffusion fields |
| Development | Delete below threshold | Moving-boundary transport | Bath-accessible dissolution |
| Mechanics | Ignored | Shrinkage, stress and collapse | Outside scope |
| Calibration | Relative coefficients | Fitted parameters with uncertainty | Exploratory chemistry |
How is light distributed around the focus?
A Gaussian approximation can capture a compact, ellipsoidal focus and is often enough for rapid process-window reasoning. Scalar diffraction adds pupil and propagation structure. At high numerical aperture, vectorial models represent polarization and longitudinal field components that a scalar picture cannot.
Further layers can include measured pupil illumination, objective transmission, interface mismatch, spherical aberration, scattering, or spatially varying refractive index. The right level depends on whether the question concerns a broad trend, voxel shape, or quantitative dose.
Is exposure a scalar dose or a timed event sequence?
The most compact models integrate a local intensity proxy into one dose and compare it with a threshold. A richer model separates average power, repetition rate, pulse duration, scan speed, and path timing. Pulse-resolved models can follow excitation within and between individual pulses, at a much greater computational cost.
Dose equivalence is therefore conditional. The same nominal energy per length does not guarantee the same nonlinear source or chemical history when pulse statistics and dark intervals differ.
What happens after excitation?
Threshold models jump from exposure to cured material. Kinetic models introduce initiator depletion, radical generation, propagation, oxygen quenching, and termination. Reaction–diffusion models also allow species to move between neighboring regions, coupling the exposed voxel to its surroundings.
Exposure does not end when the laser stops
A binary development model retains every location above a conversion threshold. More detailed models make dissolution rate depend on local conversion or network density. Transport-aware approaches represent how developer reaches internal surfaces; moving-boundary models evolve the interface as material is removed.
This layer is essential when two exposure histories produce similar conversion but different access paths, gradients, or weak connections.
Survival can become a structural problem
A chemically insoluble feature may still shrink, detach, bend, or collapse. Mechanics models can couple conversion to modulus and shrinkage, include adhesion at the substrate, and represent capillary forces during drying. These effects matter especially for high-aspect-ratio or weakly supported structures.
More equations do not automatically create more truth
Parameters must be identifiable from measurements relevant to the model. A detailed reaction network with guessed coefficients can be less predictive than a compact empirical model fitted within a controlled process window. Calibration should state the measured observables, uncertainty, parameter correlations, and the range over which extrapolation is attempted.
A causal sketch between threshold and calibration
The browser laboratory combines a vectorial focus, a two-photon source, a timed three-dimensional scan path, reaction–diffusion fields, conversion, gelation, and bath-accessible development. It is more mechanistic than a fixed-voxel or dose-threshold visualizer, but its chemistry coefficients remain exploratory and dimensionless.
Its purpose is to expose dependencies and counterfactuals: what changed, through which mechanism, and where the result diverged from the target. Quantitative prediction remains a separate calibration task.
Foundations represented in the model map
- 01Electromagnetic diffraction in optical systems, IIRichards & Wolf · Proceedings of the Royal Society A · 1959↗
- 02Model for polymerization and self-deactivation in two-photon nanolithographyJohnson, Chen & Xu · Optics Express · 2022↗
- 03Impact of Oxygen on Photopolymerization Kinetics and Polymer StructureO’Brien & Bowman · Macromolecules · 2006↗
- 04Improved development procedure to enhance the stability of microstructuresPurtov et al. · Microelectronic Engineering · 2018↗