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Instrumental Deviations from Beer-Lambert Law

Updated: Aug 9, 2022

This blog entry explores the use of a university textbook during cross-examination of a CFS scientist on "Instrumental Deviations from Beer-Lambert Law".

The purposes of this cross-examination included:

To explore the reasons why measurement instruments in the field may deviate from the linearity alleged by the Beer-Lambert law.

To introduce a university textbook dealing with inter alia:

  1. External Calibration

  2. Creating a Calibration Curve

  3. Limits to Beer's law

  4. No longer linear when the molar absorptivities differ

  5. Instrumental Deviations from Beer-Lambert law

  6. Polychromatic Radiation rather than Monochromatic IR

This is a sample cross-examination of a CFS expert on possible deviations from linearity in the approved instruments used for BAC testing in Ontario - deviations from Beer-Lambert Law. CFS scientists take the position, without empirical evidence, that such deviations will never be gross deviations.

The following image is the front cover of the textbook used. A copy was borrowed from the University of Toronto at Mississauga library.

[Excerpts from cross-examination begin]

MR. BISS: Q. Mr. P, this is a...

A. Skoog and West.

Q. ...a book that I got from the University of

Toronto, Fundamentals Of Analytical Chemistry. And I just

want to ask you, please, to take a look at page 171, where in

the textbook they talk about external standard calibration.

A. Okay.

Q. I just want to ask you, on the first paragraph

there under 8D-2, is that the kind of calibration that we use

when we are calibrating -- or when the factory is calibrating

an Intoxilyzer 8000C?

[Note: Calibration of an individual Intoxilyzer at the factory is not the same thing as a Control test at point of use with a subject. It is the former that makes the individual Intoxilyzer an "instrument". It is the latter that is referred to as "system calibration check" by Parliament in Criminal Code section 320.31(1)(a).]

[Note: The textbook reference to solutions plural.]

[Image from textbook]

[Explanation of "External Calibration" and Creation of a "Calibration Curve" using Known standard solutions]

A. Yes. That first paragraph, yes. That's part

of the calibration of the instrument done by an authorized

person or at the factory.

Q. The second paragraph talks about what the

calibration function is that's created and talks about it as

sometimes being called the calibration curve, sometimes being

called a working curve?

A. All right. So what's your question?

Q. My question is, it says:

"It is often desirable that the calibration curve

be linear in at least the range of the analyte


A. Yes. That's something that we use in our

analytical laboratory all the time. But sometimes, depending

on the response, again, because you're looking at

concentration of drugs from, say, therapeutic to a fatal

level, the curve often is not linear at all.

Q. All right. Going further down that paragraph,

then, that relationship, called the linear relationship:

" then used to predict the concentration of

an unknown analyte solution."

That's what we do with an Intoxilyzer 8000C, but

it's done electronically, rather than manual.

A. Yes.

Q. And then it says down at the next paragraph

after that:

"Computerizing numerical data analysis has largely

replaced graphical calibration methods..."

[As read]

And that's exactly what we have in an Intoxilyzer


A. Well, yes, yeah. We don't do anything by

paper and rulers anymore. Everything is done electronically.

[In other words, this paragraph in the textbook, can be used to help explain the principles and procedure of external calibration and creation of a calibration curve in a new Intoxilyzer 8000C at the factory. On an aging instrument, this is the process used upon re-calibration of an instrument at the factory or Canadian authorized service centre.]

[Note: Defence lawyers should study the proper methodology (the manufacturer's protocol) for re-calibration of an Intoxilyzer at the factory or Canadian authorized service centre.]

[Limits - Potential problems with Beer's law that might affect Intoxilyzer reliability across the measuring interval]

[Problems Resulting from the Method]

Q. Right. So just move on, please, to page 669

under paragraph 24C-3, Limits (indiscernible) as well, page


A. Sorry, you said 6...

Q. Six six nine. Page 669. Just keep going and

you'll find it?

A. Oh, okay, sorry, because the page numbers...

Q. Yeah. I did not reproduce the whole textbook.

THE COURT: Thank you goodness for that.

MR. BISS: It's rather expensive when you're

(indiscernible). Page 669?

A. Yes, Lambert-Beer Law.

Q. Limits to Lambert -- limits to Beer's law. Is

Beer's law the same thing as Lambert-Beer Law?

A. Yes, it depends on which scientist you talk to

about which name should go first and who discovered it first,


Q. All right. So the first sentence says:

"There are few exceptions to the linear

relationship between absorbance and path length at

a fixed concentration."

Then it says:

"We frequently observe deviations from the direct

proportionality between absorbance and


However, even though the path length... In other

words, the length of the sample chamber is constant. Do you

agree with that comment?

A. Yes.

[The path length in the sample chamber in the Intoxilyzer is a constant. The defence concedes that.]

Q. Right.

A. And it's fixed, yes, so we know.

Q. Right. And they talk about some of those

deviations are real deviations. Then it says that others are

as a result of the method that we used to measure absorbance

instrumental deviations. Right?

A. That's what it says, yes.

[Quaere: Does the method, used in an Intoxilyzer, of IR measurement, leave room for variability in aging instruments, because of instrumental deviations, in something which CFS scientists assume is a constant, but is not a constant in fact? What if there is an issue with the IR light source or filters in the Intoxilyzer?]

[Note: The following constant is assumed in Beer's Law.]

[But is this absorption coefficient a constant in an aging instrument?]

Q. Right. Talking about instrumental deviations,

if we could move ahead, please, to page 671.

A. Yes.

Q. Under Instrumental Deviations, Polychromatic

Radiation. It says:

"Beer's law strictly applies only when

measurements are made with monochromatic source

radiation. In practice, polychromatic sources

that have a continuous distribution of wavelengths

are used in conjunction with a grating or a filter

to isolate a nearly symmetric band of wavelengths

surrounding the wavelength to be employed.

[As read]

So my suggestion to you is that Intoxilyzer 8000Cs

use a filter to isolate a nearly symmetric band of

wavelengths surrounding the wavelength to be employed.

A. Sorry, one more time?

Q. Intoxilyzer 8000Cs use a filter...

A. Yes.

Q. optical filter...

A. Yes.

Q. isolate a band of wavelengths

surrounding 9.4 microns.

A. Or 3.4 micrometres, yes.

[The light source in an Intoxilyzer is a light bulb or a pulse that is polychromatic. Optical filters are used to limit the wavelengths of light to about 9.4 micrometres and 3.4 micrometres. The light is still polychromatic, but depending on the quality of the filter, is closer to monochromatic.]

[See figure 24-16. The concentrations, if light is polychromatic, are not linear, because the "molar absoptivities" differ, because the ε value ceases to be a constant:]

Q. All right. On page... it's covered up by the

staple, but 672.

A. Yes.

Q. Halfway down the page it says, "As shown in

figure 24..."

A. Sorry. Sorry. Sorry. As... 672?

Q. Page 672.

A. Okay. Sorry. There. "In addition"?

Q. Yes.

A. It's the third line down.

Q. All right. On page 672, the reference to

figure 24-16. Do you see where in the text it refers to

figure 24-16?

A. At the top, yes.

Q. "As shown in figure 24-16, however, the

relationship between Am and concentration is no

longer linear when the molar absorptivities

differ. In addition, as the difference between...

the two E's ...increases, the deviation from

linearity increases."

Do you understand that?

A. So this is referring to... where are E prime

and E double prime referred to.

Q. (Indiscernible).

A. Equation.

Q. Right back on page 671. Yeah, I recognize

that some of the formulas are somewhat complicated, because

they use logarithmic relationship. But perhaps I can

simplify my question...

A. Okay.

Q. this. In the theory that is being

described in this textbook, they're suggesting that even

though we hope to have a linear relationship as best we can,

because that's how or nearly linear relationship, because

that's how we can use infrared spectroscopy or some other

kind of spectroscopy for purposes of reliable measurement,

the problem is that if the molar absorptivities, in other

words, what is described in the training aid as a constant,

if those numbers differ, then the problem is that the

deviation from linearity increases.

[Note: The expert witness accepts the textbook theory and then acknowledges that the theory contained in the CFS 8000C Training Aid (2013) at p. 39-40 is an oversimplification.]

A. Wow. I think that as it's used here in our

manual is an oversimplification of the actual process that's

taking place, compared to what's written here. Again, I

think you're getting into the area where the engineers would

have figured all of this out at the time of design of the

instrument and the manufacture of the instrument to sort this

out. This is way beyond me with respect to figuring this

out. This is my superficial understanding of the

Lambert-Beer Law with respect to how solutions react or how

compounds react relative to concentration, but this takes it

to a whole new level. And, again, this would have been

established by the engineers and all this kind of

mathematics. They would have people who specialize in this

kind of thing. This is way beyond my area of expertise for

being able to establish this and what kind of curves and how

this is used to establish the concentration of an unknown.

[Note: "this would have been established by the engineers". And so perhaps the police, the Courts, and Parliament should pay attention to whether or not the factory calibration or re-calibration protocol has been followed before pre-determining reliability.]

Q. All right. Let's look at the next paragraph


A. Which page are we on now?

Q. We're on 67...

A. Three?

Q. ...2.

A. Oh, okay.


Q. "If the band of wavelength selected for

spectrophotometric measurements corresponds to a

region of the absorption spectrum in which the

molar absorptivity of the analyte is essentially

constant, departures from Beer's law will be


[Below please see a figure from the Intoxilyzer 8000C Training Aid 2013 at p. 40. Look for yourself: Are the valleys at 3.4 or 9.4 wide or narrow? How narrow will the filter need to be to only catch 3.4 or 9.4 micrometres? What plus or minus would capture only the 3.4 or 9.4 valley? By capturing only 3.4 or 9.4 the molar absorptivity would be constant. By capturing a wider bandwidth, however, molar absorptivities will not be constant.]

In other words, if we look at the infrared

signature for ethyl alcohol, and we pick the region at 9.4

microns, we've got a question of is... is the shape of that

fingerprint, is the shape of that spectrum relatively

constant at that point or if what we're dealing with are

wavelengths that are including places other than the peak of

the value, the valley or the peak that's being used to

analyze, then the problem is that there will be departure

from Beer's law.

A. That sounds logical. If I may point out that

the absorption spectrum shown on page 40 of 238 of the Centre

of Forensic Sciences' training aid would have been obtained

using a spectrophotometer, which would then, as -- what it

does is it will generate infrared light wavelength by

wavelength. So this would have been obtained by scanning all

the wavelengths of infrared light one at a time in order to

get that. That would be completely different physics from

how the instrument actually calculates or how it sees the

absorption of infrared light.

Q. Right. Because the instrument is just looking

at a broad number of wavelengths, not a specific point of

wavelength. Not a specific wavelength, but a collection of

wavelengths, and doing its calculation based on that?

[Emphasis added.]

A. Correct. Yes.

Q. So the bottom of that paragraph, the last

sentence there it says:

"On the other hand, some absorption bands in the

UV-visible region and many in the IR region are

very narrow, and departures from Beer's law are

common, as illustrated for Band B in figure


So, for example, if you look at the top of page

673, you can see that if what's being analyzed using the

filter is a very, very narrow region at the tip of a peak or

a bottom of a valley in the infrared spectrum, you get a

very, very different kind of effect than if the filter is

analyzing something on the side slope of the valley or the


A. Correct.

[What is the practical effect on Intoxilyzer BAC measurement reliability, of "many [absorption bands] in the IR region [being] very narrow, and departures from Beer's law are common"?]

Q. Right. So I want to suggest to you that

that's the theory behind why linearity is such an essential

concern with respect to any kind of instrument that uses


A. Could you say that one more time?

Q. I want to suggest to you that that is the --

that is part of, at least part of the theory of the

chemical -- of the analytical chemistry theory behind the

reason that we need to be checking linearity on instruments

on a regular basis.

A. Again, I'm going to go back to that safeguards

in place at the time of testing determine whether or not

there's been any significant changes in the instrument that

would require that it be taken out of service and out of use.

[The witness takes the CFS, ATC, and section 320.31(1)(a) policy approach and relies on time of testing control tests as precluding "significant changes in the instrument."]

Q. And the --

A. That's the only way I can answer that


Q. All right.

A. Again, you're getting into -- you've obviously

done a lot of research here and spent a lot of time on this.

But, again, a lot of this is beyond my scope of being able to

answer some of these questions.

[In a full cross-examination the witness would need to be cross-examined on the protocols used to ensure linearity. Such protocols should be followed during annual inspection or upon maintenance. In some instances, full factory re-calibration will be required.]

[Another system in place in the Intoxilyzer 5000C and 8000C to control gross changes in calibration, is the "internal standards" or "ITP" system. These systems electronically check for significant changes in the signals coming out of the filters. However, as instruments age, these systems become wonky. Whenever the instrument's calibration is updated, the ITCs need to be updated as well. See the video below for an example of an instrument that passes single point cal. checks at 100mg/100mls and diagnostics/ITC checks once it is running, but is obviously unreliable.]

[Commentary: CFS/ATC experts need to be cross-examined as to the "safeguards" allegedly in place at time of testing. In the 8000C, one of these safeguards is the internal standards or internal test procedure system (the ITPs). Quaere: How often are the ITPs re-calibrated and what external standards are used? Does an 8000C cease to be reliable if the ITP system needs re-calibration? Do the ITPs run across the measuring interval or are they only applicable at 100 mg/100mls. Lawyers need to be familiar with the inadequacies of such internal standards systems.]

[Here is an excerpt from the 8000C Training Aid ITP page:]

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