How Does Refractive Index Extraction via Fresnel Transmission Equations Quantify Porosity

Refractive index extraction via Fresnel transmission equations quantifies tablet porosity by determining the complex refractive index of compacted pharmaceutical cores from transmitted terahertz phase delays and applying Effective Medium Approximations to calculate internal micro-pore air volume fractions without mercury intrusion.

The internal porosity of a compressed pharmaceutical tablet dictates its liquid disintegration rate, bioavailability, and dissolution profile: highly porous tablets disintegrate rapidly in the gastrointestinal tract, whereas over-compacted tablets dissolve too slowly to achieve therapeutic efficacy. Historically, measuring porosity required helium pycnometry or mercury intrusion porosimetry—techniques that are destructive, slow, and hazardous. Terahertz spectroscopy provides a rapid, non-destructive optical alternative. In transmission geometry, a terahertz pulse passes directly through the tablet core; comparing the transmitted time-domain waveform with an unobstructed air reference pulse yields both the amplitude attenuation and the phase delay. Inverting Fresnel transmission equations extracts the effective real refractive index (n_eff) of the composite tablet. Because the tablet is a heterogeneous mixture of solid pharmaceutical excipients (solid index n_solid roughly 1.65) and microscopic interstitial air pores (air index n=1.0), the effective refractive index directly reflects porosity. Applying Effective Medium Approximations (such as the Bruggeman or Landau-Lifshitz-Looyenga models) calculates absolute tablet porosity with accuracy exceeding one percent within milliseconds.

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