Lambert's Law and depth of cure in light-cured filled-resins

Objectives: Existing approaches to determining “depth of cure” are faulty, relying on arbitrary measurements while the point at which maximum degree of conversion is just attained is logically the correct criterion. The Lambert Law may be used to determine the true optical density of unit thickness of material, hence if a reference value of “sufficient” exposure can be identified, a critical depth may be explicitly calculated for any material for a chosen exposure in excess of that reference value, the amount of that excess (i.e. excess subsurface irradiance factor) needs to be chosen. Methods: For thickness varying from about 3.0 to 0.5 mm in 0.5 mm steps, radiometer (Cure-Rite) readings were determined for the transmitted curing light (Optilux 400) for 65 products of many shades, and the linear attenuation coefficient (LAC) determined by Lambert-Law regression. Secondly, the optical density (OD) (Parry DT1405) was determined for thicknesses of ~1 and 2 mm, using filtered QH light, and the true OD for 1 mm calculated (D1), corrected for reflection. The correlation of LAC and D1 was tested. D1 was determined for an additional 75 products. From D1was calculated the critical thickness for cure assuming an excess subsurface irradiance factor of 2. Results: Lambert's Law was found to hold for all products tested. LAC and D1 were significantly correlated (P < 1E-13), intercept not different from zero (P > 0.164), and slope not different from expectation (P > 0.318). Critical thickness varied from ~0.4 to 1.3 mm. There was no correlation with shade letter, but shade number was significant (P = 7.5E-8) Conclusions: Critical depth may provide a good practical guide to filled-resin curing, given a defined exposure.