Resin Cure Depth Formula
The Beer-Lambert cure depth formula for SLA and MSLA resin printing: Cd = Dp x ln(E/Ec).
Explains exposure, overcure, and layer thickness trade-offs.
The Formula
This is the Jacobs working curve equation, derived from the Beer-Lambert law of light absorption. Cd is the cure depth in mm, Dp is the depth of penetration of the resin (a material constant), E is the exposure energy at the surface in mJ/cm², and Ec is the critical exposure energy at which curing begins (the resin's gelation threshold).
Variables
| Symbol | Meaning |
|---|---|
| Cd | Cure depth (mm) |
| Dp | Depth of penetration constant for the resin (mm) |
| E | Exposure energy at the surface (mJ/cm²) |
| Ec | Critical exposure energy to begin gelation (mJ/cm²) |
Example
Standard grey resin: Dp = 0.175 mm, Ec = 8 mJ/cm². Printer delivers 30 mJ/cm² at normal exposure.
Cd = 0.175 × ln(30 / 8) = 0.175 × ln(3.75)
Cd = 0.175 × 1.322
Cd = 0.231 mm cure depth
For a 0.05mm layer height, this means the current layer is curing 0.181mm into the previous layer. That overlap is what bonds layers together. If Cd equals exactly the layer height, you get no overlap and layers peel apart.
Key Notes
- Dp and Ec are resin-specific constants. Some manufacturers publish them; most do not. They can be measured by printing a series of exposures and measuring cure depth with calipers, then fitting the log-linear curve.
- The logarithmic relationship means doubling your exposure time does not double cure depth. Adding 0.3 ln(2) x Dp per doubling is the typical gain. This is why exposure time tuning has diminishing returns.
- Overcure expands features. If Cd is much larger than the layer height, UV light bleeds horizontally through transparent regions and cures areas that should remain hollow. This is the cause of elephant foot on the first layers and closed holes on small features.
- Pigmented resins have smaller Dp than clear resins because the pigment particles scatter and absorb UV. This reduces Z-overcure but also requires longer exposure times to achieve the same layer bond strength.
- Exposure energy E = irradiance (mW/cm²) x exposure_time (s) x 1000. A printer with 3 mW/cm² at the FEP for 2 seconds delivers 6 mJ/cm². If Ec = 8 mJ/cm², the layer will not cure at all at these settings.