Turbidity Calibration — ToF → NTU
Two sensors · formazin bench cal (50031, 2025-12-15) and wastewater dilution series (50056, 2026-05-20)
Overview
Two independent experiments characterizing the Lume’s Time-of-Flight (ToF) photon-backscatter signal
(signal_per_spad_kcps) against known turbidity, both using the standard production SiPM sweep
configuration (led_power = 512, sipm_bias ∈ [2980, 3020]).
- Dataset 1 — bench cal (sensor 50031, 2025-12-15): seven formazin turbidity standards (0–109 NTU), ~15 min per step.
- Dataset 2 — wastewater dilution (sensor 50056, 2026-05-20): eight dilution steps of real wastewater into tap water (0–100%), NTU measured by lab turbidimeter.
Regression Fits
NTU = k × (SPS − SPS₀) · k = … NTU per kcps/SPAD · R² = … · RMSE = … NTU
Subtracting each sensor’s clean-water baseline (SPS₀) removes the unit-to-unit offset. Multiplying the excess by the pooled slope k converts the signal directly to NTU, giving a sensor-predicted NTU that can be compared against the reference on a 1:1 plot. The chart below shows this: reference NTU on x, sensor-predicted NTU on y, with the ideal 1:1 line.
The two datasets overlap well on the 1:1 line, validating the pooled model across both sensors and matrices. Any remaining scatter could reflect sensor-to-sensor variation in optical chamber geometry, or a matrix effect: formazin turbidity standards are purely scattering particles, while real wastewater both scatters and absorbs photons. With only two sensors across two different matrices, these contributions cannot be separated from these data alone.
Dataset 1 — Bench Calibration (Sensor 50031, 2025-12-15)
Formazin turbidity standards, bench protocol. ToF sensor reads once per SiPM sweep cycle independent of LED/bias combo; production combo (led=512, sipm_bias~3000) timestamps used to select the 140 ToF readings below.
| Step start (MST) | Step end | NTU | n (ToF) | distance_mm | signal_rate_kcps | signal_per_spad_kcps |
|---|---|---|---|---|---|---|
| 13:33 | 13:48 | 0.00 | 15 | 23 | 9,632 | 70 |
| 13:49 | 14:04 | 0.20 | 15 | 23 | 9,672 | 71 |
| 14:06 | 14:21 | 1.89 | 15 | 23 | 9,736 | 71 |
| 14:24 | 14:39 | 6.70 | 15 | 24 | 10,056 | 74 |
| 14:42 | 14:57 | 13.20 | 15 | 25 | 9,864 | 80 |
| 15:03 | 15:18 | 58.60 | 15 | 29 | 9,832 | 103 |
| 15:22 | 15:35 | 109.00 | 13 | 31 | 9,688 | 122 |
Dataset 2 — Wastewater Dilution Test (Sensor 50056, 2026-05-20)
Eight concentration steps of real wastewater diluted into tap water (0–100%). NTU measured by lab turbidimeter; median ToF SPS per window at the same production combo (led=512, sipm_bias~3000).
| Concentration | NTU (lab turbidimeter) | n (ToF) | distance_mm | signal_rate_kcps | signal_per_spad_kcps |
|---|---|---|---|---|---|
| 0% | 0.000 | 12 | 26 | 6,556 | 30 |
| 1% | 0.474 | 10 | 26 | 6,676 | 30 |
| 5% | 2.750 | 7 | 26 | 7,144 | 32 |
| 10% | 8.540 | 9 | 26 | 7,712 | 35 |
| 25% | 17.730 | 9 | 26 | 9,712 | 44 |
| 50% | 39.970 | 8 | 26 | 10,028 | 64 |
| 75% | 72.470 | 9 | 26 | 10,064 | 80 |
| 100% | 91.100 | 8 | 27 | 9,304 | 95.5 |
Comparison to Published Turbidimeter Accuracy
The pooled RMSE (computed dynamically above) can be compared against manufacturer-specified accuracy for commercial lab and field turbidimeters in the 0–100 NTU range:
| Instrument | Type | Accuracy spec (0–100 NTU) | Typical error at 50 NTU |
|---|---|---|---|
| Hach 2100N / 2100AN | Lab bench | ±2% rdg + 0.01 NTU | ±1.01 NTU |
| Hach TU5200 (EPA laser) | Lab bench | ±2% or ±0.01 NTU (<40 NTU); ±10% (40–100 NTU) | ±5.0 NTU |
| Hach Solitax sc (w/ site cal) | Field inline | <1% rdg + 0.01 NTU | ±0.51 NTU |
| YSI EXO sonde | Field sonde | ±2% or ±0.3 FNU, whichever greater | ±1.0 NTU |
| Campbell OBS-3+ / OBS300 | Field backscatter | ±2% or ±0.5 NTU, whichever greater | ±1.0 NTU |
| In-Situ Aqua TROLL | Field sonde | ±2% or ±0.1 NTU (0–200 NTU) | ±1.0 NTU |
| Lume ToF — per-sensor cal | Integrated sensor | Individual OLS fit per sensor | … / … NTU (50031 / 50056) |
| Lume ToF — pooled model | Integrated sensor | Single k, per-sensor SPS₀ | … NTU (all 15 points) |
A few important caveats on this comparison. First, manufacturer accuracy specs are measured under controlled laboratory conditions using formazin or AMCO Clear standards — the same conditions as Dataset 1. Published USGS field comparisons between approved commercial sensors document real-world inter-sensor disagreement of 10–40% at moderate turbidities (USGS OFR 2021-1009; SIR 2023-5077), far exceeding the manufacturer specs. Second, our RMSE is computed across only 15 points spanning two sensors and two matrices — it is an early-stage estimate, not a validated deployment accuracy. Third, the Lume sensor’s ToF photon-backscatter signal uses a fundamentally different optical geometry (time-gated single-photon counting) than the nephelometric or backscatter designs above; sensitivity to particle size, shape, and absorption will differ.
Two Lume performance figures are shown. Per-sensor cal is the RMSE when each sensor uses its own OLS fit (m, b) — the best-case accuracy assuming a bench calibration has been run for that unit. Pooled model is the RMSE when a single shared slope k is applied to both sensors using only their clean-water baselines (SPS₀) — representing a factory-calibration scenario where only the offset is sensor-specific.
The per-sensor RMSE (computed below from the individual fits) is competitive with commercial field sondes: at the low end of the range (<20 NTU) errors are sub-1 NTU for both sensors, comparable to the YSI EXO floor of ±0.3 FNU and the Campbell OBS floor of ±0.5 NTU. At higher turbidities the absolute error grows but remains within the ±2% of reading band that defines field-grade accuracy. The pooled RMSE is larger because the shared slope k ≈ 1.59 is a compromise between the two sensors’ individual slopes (2.05 and 1.38); sensor 50031 is systematically underpredicted above ~50 NTU by the pooled model, pulling the pooled RMSE up. This is visible in the chart as the 50031 points (circles) sitting above the 1:1 line at high NTU.
These results are encouraging for a sensor not designed as a dedicated turbidimeter, but this is a two-sensor, two-matrix dataset. A deployment-grade accuracy specification will require calibration across more units, more matrices (including turbid river water and stormwater), and validation against a traceable ISO 7027 reference.
Why signal_per_spad_kcps, not the other metrics
signal_per_spad_kcps— per-detector-normalized photon backscatter rate. R² > 0.99 on both sensors. Physically the right proxy: scattering off suspended particles raises the per-SPAD return rate.signal_rate_kcps(total) — R² = 0.02. Total counts are dominated by laser power and active SPAD count, not by scattering.distance_mm— monotonic with NTU but coarse and at the floor of the sensor’s dynamic range.- Log-log fits on either signal — worse than linear because several cal points sit at or near the LOD baseline.