Optical setup: 4× objective + 1.5× zoom, TRITC bandpass filter (~530–590 nm), 0.987 µm/px. Cropped image size: 300 × 1720 px (296 × 1698 µm).
Calibration: 0, 0.5, 1, 2, 5, 10, 15, 20 mM urea. Unknowns: 0.75, 3, 7, 12, 17 mM urea. All solutions prepared from the same stock solutions in the same chip.
Method: Green-channel absorbance A = −log10(T), where T = (meansample − meandark) / (meanflat − meandark), averaged over 30 frames per condition. Eight stepped-height channel sections (S1–S8, 30–200 µm optical path length) each provide an independent calibration and concentration estimate.
Calibration concentrations (top 8) followed by unknown concentrations (bottom 5). White rectangles mark the section ROIs. Darker regions indicate greater Phenol Red absorption at 559 nm.
Linear fit A = slope · c + intercept for each section. Deeper sections have steeper slopes as predicted by Beer–Lambert law.
Table 1. Linear fit equations and R² values.
| Section | Depth (µm) | Equation | R² |
|---|---|---|---|
| S1 | 200 | A = 0.00604·c + 0.1202 | 0.99478 |
| S2 | 150 | A = 0.00482·c + 0.0921 | 0.99458 |
| S3 | 120 | A = 0.00413·c + 0.0775 | 0.99448 |
| S4 | 90 | A = 0.00323·c + 0.0594 | 0.99391 |
| S5 | 70 | A = 0.00268·c + 0.0494 | 0.99413 |
| S6 | 50 | A = 0.00207·c + 0.0376 | 0.99442 |
| S7 | 40 | A = 0.00172·c + 0.0302 | 0.99310 |
| S8 | 30 | A = 0.00135·c + 0.0228 | 0.98927 |
Absorbance vs optical path length at each calibration concentration. Linearity confirms the measurement is quantitative.
Concentrations predicted by inverting each section’s calibration fit: c = (A − intercept) / slope. Mean ± std across S1–S8 is the final estimate.
Table 2. Per-section predictions, mean, std, absolute error, and percent error.
| S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | Mean (mM) | Std (mM) | Error (mM) | Error (%) | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Known (mM) | ||||||||||||
| 0.75 | 0.78 | 0.77 | 0.74 | 0.70 | 0.68 | 0.53 | 0.58 | 0.45 | 0.65 | 0.12 | -0.10 | -13.3 |
| 3.00 | 2.75 | 2.73 | 2.74 | 2.70 | 2.67 | 2.79 | 2.58 | 2.42 | 2.67 | 0.12 | -0.33 | -11.0 |
| 7.00 | 7.15 | 7.18 | 7.26 | 7.30 | 7.33 | 7.35 | 7.57 | 7.91 | 7.38 | 0.25 | 0.38 | 5.4 |
| 12.00 | 13.06 | 13.08 | 13.08 | 13.16 | 13.12 | 13.05 | 13.14 | 13.20 | 13.11 | 0.05 | 1.11 | 9.3 |
| 17.00 | 18.78 | 18.77 | 18.76 | 18.71 | 18.69 | 18.64 | 18.58 | 18.37 | 18.66 | 0.14 | 1.66 | 9.8 |