Linearized optical sensor calibration for measuring calcium

Patent metadata

Field	Value
Publication number	US-12287283-B2
Application number	US-202117363657-A
Country	US
Kind code	B2
Filing date	Jun 30, 2021
Priority date	Jun 30, 2020
Publication date	Apr 29, 2025
Grant date	Apr 29, 2025

Abstract

An optical sensor may be used to measure the concentration of calcium in a water sample, such as a water sample obtained from industrial process water system like a cooling tower system, a boiler water system, or a waste water system. To measure the concentration of calcium, an indicator or reagent may be added to the water sample to form a complex that absorbs light. The absorbance profile of the complex may be non-linear over a range of calcium concentrations. However, the absorbance profile can be linearized to provide calibration coefficients that are subsequently used to determine the concentration of calcium in samples having unknown calcium concentrations. The linearization of the absorbance profile can allow the optical sensor to be calibrated using two solutions. This can reduce the complexity and cost of calibrating the optical sensor, which may otherwise require at least three calibration solutions to capture the non-linear profile of the absorbance curve.

First claim

The invention claimed is:

1. A method of calibrating an optical sensor for measuring calcium, the method comprising:
measuring, with an optical sensor, an optical response of a first calibration solution at a first wavelength to provide a first measured optical response for the first calibration solution and at a second wavelength to provide a second measured optical response for the first calibration solution, the first calibration solution comprising a first known concentration of calcium;
measuring, with the optical sensor, the optical response of a second calibration solution at the first wavelength to provide a first measured optical response for the second calibration solution and at a second wavelength to provide a second measured optical response, the second calibration solution having a second known concentration of calcium;
determining a first optical response ratio for the first calibration solution based on the first measured optical response for the first calibration solution and the second measured optical response for the first calibration solution;
determining a second optical response ratio for the second calibration solution based on the first measured optical response for the second calibration solution and the second measured optical response for the second calibration solution;
determining coefficients for a linear calibration curve relating an optical response measurement made by the optical sensor to a calcium concentration in a solution based on the first known concentration of calcium and first optical response ratio and the second known calcium concentration and the second optical response ratio, wherein the linear calibration curve is a first order equation having a form y=m*x+b, where m is a slope coefficient and x is the first optical response ratio divided by the second optical response ratio and (i) y is a square root of the calcium concentration and b is an intercept coefficient or (ii) y is a natural log of the calcium concentration and b is a natural log of the intercept coefficient, and
storing the coefficients for the linear calibration curve in a memory associated with the optical sensor.

2. The method of claim 1 , wherein y is the square root of the calcium concentration in the solution and b is the intercept coefficient.

3. The method of claim 1 , wherein y is the natural log of the calcium concentration in the solution and b is the natural log of the intercept coefficient.

4. The method of claim 1 , wherein
determining the first optical response ratio comprises dividing the first measured optical response for the first calibration solution by the second measured optical response for the first calibration solution; and
determining the second optical response ratio for the second calibration solution comprises dividing the first measured optical response for the second calibration solution by the second measured optical response for the second calibration solution.

5. The method of claim 1 , wherein the first wavelength is within a range from 625 nm to 725 nm, and the second wavelength is within a range from 475 nm to 575 nm.

6. The method of claim 1 , wherein the first wavelength is 668 nm and the second wavelength is 521 nm.

7. The method of claim 1 , wherein at least one of the first wavelength and the second wavelength is a wavelength at an absorbance peak.

8. The method of claim 1 , wherein the first known concentration of calcium and the second known concentration of calcium are each greater than 0.

9. The method of claim 1 , wherein:
the first known concentration of calcium is 0 ppm calcium; and
the second known concentration of calcium is within a range from 10 ppm calcium to 2000 ppm calcium.

10. The method of claim 1 , wherein the first calibration solution and the second calibration solution each comprise an indicator.

11. The method of claim 10 , wherein the indicator is Chlorophosphonazo-III.

12. The method of claim 1 , further comprising:
automatically generating the first calibration solution by mixing a reagent comprising at least an indicator with a first calcium stock solution; and
automatically generating the second calibration solution by mixing the reagent comprising at least an indicator with a second calcium stock solution.

13. The method of claim 1 , wherein:
a relationship between the optical response measurement made by the optical sensor and the calcium concentration in the solution is non-linear across a range of calcium concentrations;
determining coefficients for the linear calibration curve comprises at least one of:
(1) determining coefficients for a first order equation fitted to a line defined by a square root of the first known concentration of calcium and the first optical response ratio and a square root of the second known concentration of calcium and the second optical response ratio; and
(2) determining coefficients for a first order equation fitted to a line defined by a natural log of the first known concentration of calcium and the first optical response ratio and a natural log of the second known concentration of calcium and the second optical response ratio.

14. The method of claim 1 , further comprising:
extracting a sample of water containing an unknown concentration of calcium from an industrial water system;
mixing an indicator with the sample to form the solution,
measuring, with the optical sensor, the optical response of solution at the first wavelength and the second wavelength,
determining the calcium concentration in the solution based on the optical response of the solution measured at the first wavelength and the second wavelength and the stored coefficients for the linear calibration curve.

15. The method of claim 14 , further comprising controlling addition of a calcium control agent into the industrial water system based on the determined calcium concentration.

16. The method of claim 1 , wherein the optical response is absorbance.

17. A method of calibrating an optical sensor for measuring calcium, the method comprising:
measuring, with an optical sensor, an optical response of a first calibration solution at a first wavelength that is 668 nm to provide a first measured optical response for the first calibration solution and at a second wavelength that is 521 nm to provide a second measured optical response for the first calibration solution, the first calibration solution comprising a first known concentration of calcium;
measuring, with the optical sensor, the optical response of a second calibration solution at the first wavelength to provide a first measured optical response for the second calibration solution and at a second wavelength to provide a second measured optical response, the second calibration solution having a second known concentration of calcium;
determining a first optical response ratio for the first calibration solution based on the first measured optical response for the first calibration solution and the second measured optical response for the first calibration solution;
determining a second optical response ratio for the second calibration solution based on the first measured optical response for the second calibration solution and the second measured optical response for the second calibration solution;
determining coefficients for a linear calibration curve relating an optical response measurement made by the optical sensor to a calcium concentration in a solution based on the first known concentration of calcium and first optical response ratio and the second known calcium concentration and the second optical response ratio; a

Assignees

• Ecolab Usa Inc

Inventors

• Li Hui
• Chen Bingzhi
• Davis Brandon

Classifications

• G01N2201/12746

  Calibration values determination · CPC title

• G01N33/1826

  Organic contamination in water · CPC title

• G01N21/78

  producing a change of colour · CPC title

• G01N33/1853

  Hardness of water · CPC title

• G01N21/31 Primary

  Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry {(G01N21/72 takes precedence)} · CPC title