The Photometer measures RB, the Broadband absorption ratio. RB has a linear relationship to RN, the Narrow band absorption ratio. RN has an approximately linear relationship to PH

The narrow band absorption ratio  RN relationship to pH is shown below.

pH = equConstant + log10 (( RN – e1)/(1-RN*e23) )

Figure 1. RN to PH

rntoph

The photometer takes advantage of a direct relationship of RB and RN.  Rn can be estimated from RB once a calibration procedure produces enough data to compute the  equation of the line shown in  Figure 2.  Bo Yang et.al.  found this empirical relationship which was used as their “one time” calibration of their broadband photometer.

RN = (1.1892) RB – 0.3079

Figure 2. Rn as a function of Rb

rnrb

Below, the relevant equations from the Bo Yang paper translated into C++ :

double pH, equConstant,R, e1,e2,e3, e23;
double T, S; // temp and salinity

// set default values for S and T
// for salinity S values from 20 to 40
// for temperatures T from 278.15 K to 308.15 K
S = 30;
T = 303;

// eq 5
e1 = -0.007762 + (4.5174 / pow(10.0,5.0)) * T;
(10.0,4.0) *(S-35);
e23 = -0.020813 + (2.60262 / pow (10.0,4.0))*T + (1.0436 / pow (10.0,4.0)) * (S-35) ;
// eq 7 equilibrium constant equConstant
double a,b,c,d;

a = -246.64209 + 0.315971 * S + (2.8855/pow (10.0,4.0)) * S * S ;
b= 7229.23864 – 7.098137* S – 0.057034 * S * S;
c = 44.493382-0.052711 * S;
d = 0.0781344;

equConstant = a + b / T + c * log(T) – d*T; // log is the natural log ln

// eq 2
pH = equConstant + log10 (( RN – e1)/(1-RN*e23) );

 

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