Instrumentation & calibration curve related

[electronica75]

I am new to instruments. My project is to modify an existing colorimeter which presently measure several chemical compositions in water. Colorimeters as you know is a simple version of a atomic absorption spectro-photometer (as far as I understand) which uses only the visible light spectrum to detect optical density of a liquid and converts the absorbance into chemical concentration. I have to add new programs to detect new chemicals to the instrument.

We had some data with the new chemical (to be added in the newer version). I used LABFIT to find the best fit curve equation. Instead of absorbance we are measuring the RATIO (Blank/Specimen, photo sensor voltage ratios). My questions are as follows:

1) The best fit curve I find doesn’t start at Ratio=1.0, concentration=0.0, so what I did, I added an offset correction to the equation. Is is OK? or I have to find an equation which
gives concentration=0.0 at RATIO=1.0 accurately?

2) Can I divide the curve in multiple sections and use different equations for those sections? It seems that it fits the experimental data more accurately with less error. But I would like to know can I do it? Or only one equation is to be used only changing the constant parameters of the equation in different section?

3) How do you usually find the best fit curve and which type of curve (the degree of the equation) is suitable for these sort of cases? I mean which software are good for accurate curve fitting.

4) Is there any software available which can make multi-sectioned curves and automatically calculates parameters in different sections to best fit the curve (this question is related to Question no 2, I mean to ask that using same equation finding the constants of the equation in user defined section number and region)? I need this to understand Hardware Calibration and find hardware calibration parameters.

5) This calibration curve is for that specific instrument which was used to find the test data. but when new batch of products is produced the changes of LEDs and other physical properties needs hardware calibration. I studied the software (firmware) of the colorimeter and found that they use some equation to change the slope and offset of test point. What is the theory behind this? I mean this hardware calibration. I also need to understand "one-point" and "two point" calibration. Where I can find details of those.

Please suggest me any links for this or related topics if you know.

 

[ShawnD]

1) The best fit curve I find doesn’t start at Ratio=1.0, concentration=0.0, so what I did, I added an offset correction to the equation. Is is OK? or I have to find an equation which
gives concentration=0.0 at RATIO=1.0 accurately?

I'm not quite sure what you're asking on this one. Generally you should set darkness as 0 transmittance (2 absorbance) and the blank at 100% transmittance (0 absorbance). You can change the scale so it's based on your highest and lowest readings, but you need to be absolutely certain that your primary standards are good, or you'll introduce huge errors. Basically it gains precision at the cost of accuracy; I don't think it's worth doing in most cases.

2) Can I divide the curve in multiple sections and use different equations for those sections? It seems that it fits the experimental data more accurately with less error. But I would like to know can I do it? Or only one equation is to be used only changing the constant parameters of the equation in different section?

I suppose you could do this, but generally this means your solutions are in the wrong concentration range. When you're using an analytical instrument, there's something called the "linear dynamic range" where the concentration and detector signal have a good linear realtionship. The relationship starts to become nonlinear if your concentration is too high, and this is particularly true for things that give a very strong reading such as permanganate ions in a spectrometer.

3) How do you usually find the best fit curve and which type of curve (the degree of the equation) is suitable for these sort of cases? I mean which software are good for accurate curve fitting.

If you're in the right concentration range, it should be linear. Past the linear range, I would expect it to be logarithmic. Microsoft Excel is good software to use.

4) Is there any software available which can make multi-sectioned curves and automatically calculates parameters in different sections to best fit the curve (this question is related to Question no 2, I mean to ask that using same equation finding the constants of the equation in user defined section number and region)? I need this to understand Hardware Calibration and find hardware calibration parameters.

I'm not sure such software exists. Most people I know just plot a graph in excel then hold a sheet of paper against the screen to see if certain parts are linear or not. Sometimes you can see concavity by doing that as well.

5) This calibration curve is for that specific instrument which was used to find the test data. but when new batch of products is produced the changes of LEDs and other physical properties needs hardware calibration. I studied the software (firmware) of the colorimeter and found that they use some equation to change the slope and offset of test point. What is the theory behind this? I mean this hardware calibration. I also need to understand "one-point" and "two point" calibration. Where I can find details of those.

Not sure about the firmware thing, but I can explain the 1 and 2 point calibration. 1 point calibration is when you take 1 reading and use a ratio with no intercept to find an unknown value. If 10ppm of something gives a reading of 10, that would mean a reading of 11 is 11ppm. 1 point calibration is generally ok if you're staying in a very tight range, or you're looking at samples that are in a pass/fail type of test, which is very common in QC testing. If my limit is 10ppm lead and my low budget 1-point calibration says the sample is 13ppm, it could be 13 or 15 or 17ppm and it fails in all cases, so accuracy is not too important.
2-point calibration gets a slope as well as an intercept. It's more usable for a greater range of samples. Taking a point at 0ppm then a point at 10ppm might allow for testing between 0-10ppm, but a single point reading at 10ppm might only be good for 8-12ppm, for example.

 

[mgb_phys]

1) The best fit curve I find doesn’t start at Ratio=1.0, concentration=0.0, so what I did, I added an offset correction to the equation. Is is OK? or I have to find an equation which
gives concentration=0.0 at RATIO=1.0 accurately?

Not sure - it would depend on the nature of the detector, is there some backgound signal even at no level.

2) Can I divide the curve in multiple sections and use different equations for those sections? It seems that it fits the experimental data more accurately with less error. But I would like to know can I do it? Or only one equation is to be used only changing the constant parameters of the equation in different section?

That's ideally what you do - split the calibration into as many sections as possible.
One typical technique is to create a lookup table by measuring the actual output at as many fixed inpouts as possible then interpolating between these values, either with a straight line or a known curve.

3) How do you usually find the best fit curve and which type of curve (the degree of the equation) is suitable for these sort of cases? I mean which software are good for accurate curve fitting.

Start with something simple like excel

4) Is there any software available which can make multi-sectioned curves and automatically calculates parameters in different sections to best fit the curve (this question is related to Question no 2, I mean to ask that using same equation finding the constants of the equation in user defined section number and region)? I need this to understand Hardware Calibration and find hardware calibration parameters.

Just split the data into regions and fit a curve to each of the regions. It might be easier to decide a single curve function but fit different constant for each section.

5) This calibration curve is for that specific instrument which was used to find the test data. but when new batch of products is produced the changes of LEDs and other physical properties needs hardware calibration. I studied the software (firmware) of the colorimeter and found that they use some equation to change the slope and offset of test point. What is the theory behind this? I mean this hardware calibration. I also need to understand "one-point" and "two point" calibration. Where I can find details of those.

One point calibration is simplest, you adjust the output to be correct for only a single point in the middle of the range by just changing the offset.
Two point make the output correct at two points by setting the offset and gain.
For more points it is more usual to make a lookup/callibration table where you measure the output at a number of fixed intervals and treat these as many little two poitn calibrations.

This should be discussed in any experimental science / statistics book.

 

[electronica75]

Thanks Guys for your support!It was really helpful!

 

[electronica75]

Could you suggest me any algorithm for a two or a non-iterative mulptipoint calibration? Please if possible give me the links for details.

Thanks in advance!

 

[electronica75]

Suppose my calibration curve function y=f(x); i.e. concentration= f(Ratio) in the original meter.

In a new meter I found deviation from y=f(x). but I need to use the y=f(x) equation because it cannot be generated for each meter. right?

So what I do is take one (two for two point calibration, right?) standard solution and get the reading and find the deviation D from original reading found from y=f(x);

Now what is this deviation D? for one point calibration this is offset? and we define y=f(x) + D for the whole range? if I do like this it would shift the zero point? Could you explain?

And for a two point calibration I find the Slope (it is the gain, right?) M and the offset C. So the new equation for the new meter would be

y=Mf(x)+C ?? Could you explain?

 

[chemisttree]

Suppose my calibration curve function y=f(x); i.e. concentration= f(Ratio) in the original meter.

In a new meter I found deviation from y=f(x). but I need to use the y=f(x) equation because it cannot be generated for each meter. right?

Why not?

So what I do is take one (two for two point calibration, right?) standard solution and get the reading and find the deviation D from original reading found from y=f(x);

Now what is this deviation D? for one point calibration this is offset? and we define y=f(x) + D for the whole range? if I do like this it would shift the zero point? Could you explain?

The deviation D represents the difference in response between the two meters. Since you are only performing a one point calibration, you only know the deviation around a single meter reading. It would be very speculative to apply it to the entire range of the meter but it might work in your case.

And for a two point calibration I find the Slope (it is the gain, right?) M and the offset C. So the new equation for the new meter would be

y=Mf(x)+C ?? Could you explain?

If you are performing a two point calibration and you assume that you are in a linear response region, the new equation for the new meter would be as you have listed it. You should be aware that D should not be used for this case (you use C). C should be very small or very close to the value you determined for the other meter. Ideally, you should force your equation to pass through zero (set C=0) and examine the values of r^2 for the best fit lines. In that case you will have two meters with slightly different slopes (response factors) but with identical offsets.