Purpose

Compute absorbance from pre-processed corrected average transmittance images and quantify the colorimetric urea-urease assay response across 8 urea concentrations (0–20 mM). The observation channel has 8 sections of different optical path lengths (30–200 µm), enabling both a calibration curve and a Beer-Lambert validation within a single image.

Method: Green-channel absorbance, A = −log₁₀(T_green), using the green channel (most sensitive to Phenol Red at 559 nm within the TRITC filter passband ~530–590 nm). All 30 frames per concentration are averaged before computing absorbance.

The image below shows a representative raw frame from the 0 mM urea TRITC dataset (cropped, 2× downsampled). The observation channel runs horizontally; the 8 stepped-height sections appear from left-to-right getting successively lighter with channel heights of 200, 150, 120, 90, 70, 50, 40, and 30 μm.

Load T images and compute absorbance

T images are stored as uint16 with T_actual = pixel / 65535. The green channel absorbance is A = −log₁₀(T_green), clipping T to a minimum of 1×10⁻⁶ to avoid undefined values.

Green channel T images

Green channel transmittance for each concentration, displayed on a shared [0, 1] scale. Lower values (darker) indicate greater absorption by Phenol Red at 559 nm. Section ROI boxes are overlaid.

ROI extraction

Mean absorbance in each of the 8 section ROIs at every concentration.

Calibration curves

Linear fit (absorbance vs urea concentration) for each section. Deeper sections show steeper slopes as predicted by Beer-Lambert law (A ∝ depth × concentration).

Beer-Lambert validation

Absorbance vs channel depth (optical path length, 30–200 µm) at each urea concentration. A linear relationship confirms Beer-Lambert behaviour: A = ε·c·l.