Water tools

UV dose in a collimated beam test, with its uncertainty

The collimated beam is how UV dose-response is measured. The dose is intensity times time, corrected for the light the water absorbs, the surface reflects and the dish spreads unevenly.

Incident intensity at the surface centremW/cm²

Its uncertainty%

Exposure times

Its uncertaintys

UV transmittance of the sample (1 cm)%

Absorptivity uncertainty1/cm

Sample depthcm

Depth uncertaintycm

Lamp centreline to liquid surfacecm

Distance uncertaintycm

Surface reflectance

Petri factorUsually above 0.9.

Petri factor uncertainty

Dose

124.6mJ/cm²

Uncertainty (root sum of squares)

7.27mJ/cm²

Conservative deliverable dose

117.3mJ/cm²

Absorptivity

0.06501/cm

Water factor

0.929

Divergence factor

0.976

How it works

D = E_{s} t (1 - R) P_{f} \frac{1 - 10^{- k d}}{2.303 k d} \frac{L}{L + d} k = - \log_{10} \frac{U V T}{100}

(1)

U_{D} = \sqrt{\sum_{i} {(u_{i} \frac{\partial D}{\partial V_{i}})}^{2}}

(2)

where

$D$: UV dose, mJ/cm²
$E_{s}$: incident intensity at the surface, mW/cm²
$t$: exposure time, s
$R$: reflectance at the water surface
$P_{f}$: Petri factor
$k$: absorptivity of the sample, 1/cm
$d$: sample depth, cm
$L$: lamp centreline to liquid surface, cm
$U V T$: transmittance through 1 cm, %
$U_{D}$: dose uncertainty, mJ/cm²
$u_{i}$: uncertainty of input i
$V_{i}$: input i

The water factor averages Beer-Lambert absorption over the sample depth; the divergence factor accounts for the beam spreading between the surface and the bottom. The root-sum-of-squares uncertainty is used because the errors are unlikely to peak together; the conservative dose subtracts it. Typical absorbance: groundwater and filtered water 0.01 to 0.07 per cm, raw surface water up to 0.3. Field reactors deliver a dose distribution and are validated by biodosimetry against the collimated beam curve.

UV dose in a collimated beam test, with its uncertainty

How it works

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