. 2011 Aug 15;2(9):2599–2613. doi: 10.1364/BOE.2.002599

Table 1. Fitted calibration relations for 7 batches of calibration samples.

Samples	Concentration of alumina (mg/ml)	Concentration of carbon black (mg/ml)	Fitted concentration dependencies for backscattered amplitude.	Fitted concentration dependencies for total attenuation
01 to 16	1.0 to 60.0	0	$0.63 \sqrt{C_{A l}}$	$0.20 C_{A l}$
17 to 24	0 to 41.9	0.3	$\sqrt{{0.63}^{2} C_{A l} + {0.41}^{2} C_{C B}}$	$0.20 C_{A l} + 4.30 C_{C B}$
25 to 32	0 to 42.5	0.6	$\sqrt{{0.69}^{2} C_{A l} + {0.46}^{2} C_{C B}}$	$0.22 C_{A l} + 2.92 C_{C B}$
33 to 40	0	0.2 to 1.6	$0.90 \sqrt{C_{C B}}$	$5.12 C_{C B}$
41 to 48	10.3	0 to 0.8	$\sqrt{{0.48}^{2} C_{A l} + {1.21}^{2} C_{C B}}$	$0.17 C_{A l} + 5.61 C_{C B}$
49 to 56	20.3	0 to 0.8	$\sqrt{{0.58}^{2} C_{A l} + {1.84}^{2} C_{C B}}$	$0.17 C_{A l} + 4.50 C_{C B}$
57 to 64	30.2	0 to 0.8	$\sqrt{{0.63}^{2} C_{A l} + {2.58}^{2} C_{C B}}$	$0.16 C_{A l} + 5.90 C_{C B}$