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Beer-Lambert Law as Stated in Training Aid is Over-Simplified and Inadequate

Updated: Apr 19, 2022

This blog entry contains excerpts from the cross-examination of a CFS scientist during an over 80 trial. It was suggested to the scientist that light in the Intoxilyzer sample chamber is polychromatic, rather than monochromatic. The Beer-Lambert Law as described in the CFS Training Aid assumes that the infrared light in the sample chamber is monochromatic, i.e. that there is one constant co-efficient for ethyl alcohol. Because the infrared infrared light in the sample chamber is in fact polychromatic, the Beer-Lambert Law as stated in the Training Aid, is in error. The coefficient of ethyl alcohol is not a constant, if the IR light is polychromatic.

Linearity across different BAC levels therefore cannot be assumed. Single point calibration, at point of use, as used in Ontario, is therefore inadequate. Calibration checks at a single (100 mg/100 mls) point, as done in Ontario, are inadequate to ensure reliability of the BAC measurement result.

The reliability of evidentiary breath testing in Ontario could be improved by transparent periodic maintenance of approved instruments. It is not safe to assume linearity unless the Courts and the public can count on regular and transparent maintenance of all approved instruments in Ontario. Ontario needs to move in the direction of better metrological supervision of police. Full transparency of maintenance of forensic science tools, is essential to the integrity of the criminal justice system.

Purposes of this Cross-examination:

Crown expert witnesses opine the adequacy of single point control test(s), at time of use, as adequate to verify that calibration of an approved instrument has not changed over time. A purpose of this cross-examination is to suggest that this hypothesis by the Crown witness is not good measurement science.

Another purpose is to obtain admissions that checks of linearity during annual maintenance or other periodic inspection are necessary to confirm linearity, to confirm that the instrument is still calibrated across the whole measuring interval.

More specifically, the purpose of this cross-examination is to obtain an admission that although the Beer-Lambert Law suggests that the relationship between concentration in the sample chamber and the measurement result is linear (after adjusting for the logarithmic relationship of absorption/transmittance), the Beer-Lambert Law is subject to instrumental deviations.

Properly done, such a cross-examination should be supplemented by expert defence evidence from a chemist, physicist, and/or metrologist who can explain instrumental deviations in Beer-Lambert Law, particularly as they apply to IR instruments.

Excerpt from CFS Intoxilyzer 8000C Training Aid December 2013 shown to the witness:

[Begin excerpt from cross-examination]

Q. And, of course, you recognized this as coming

from the Intoxilyzer 8000C Training [Aid], December 2013 version?

A. That's correct. In fact, I wrote this


Q. Oh, good. All right. Then I can maybe

suggest --

A. It may have been not identified since I wrote

it back in 2009, but...

Q. Great. Page 40 of 238, there's a spectrum

that's shown.

A. Yes.

Excerpt from CFS Intoxilyzer 8000C Training Aid December 2013 shown to the witness:

Q. That's the -- that's a visual depiction of the

infrared absorption spectrum for ethanol, ethyl alcohol,

drinking alcohol?

A. Correct.

Q. These are -- this is a graph that shows at

what wavelengths infrared light is most absorbed by ethyl


A. Yes, based on its chemical structure.

Q. And in other cases I've cross-examined you

about all kinds of issues having to do with specificity, and

we've talked about the whole question of how it is that the

Intoxilyzer 8000C identifies ethyl alcohol that it's

sampling, as opposed to something else?

A. Correct.

["Specificity" has to do with whether the instrument is quantifying only ethyl alcohol or if the instrument is confusing acetone, diethyl ether, or some other substance into the calculation.]

Q. And one of the methods that it uses is to

pick -- the manufacture has picked certain wavelengths at

which to analyze the infrared signal?

A. Yes.

[Intoxilyer IR instruments use a polychromatic source of light (light bulb) which is filtered by IR filters to produce a limited range of polychromatic IR light, not monochromatic light. The 8000C uses IR filters to produce and detect IR light that is centred at wavelengths of about 3.4 and 9.4 micrometres.]

Q. 3.4 microns and 9.4 microns in the...

A. Micrometres, yes.

Q. the Intoxilyzer 8000c?

A. Yeah.

Q. And back in [L'Orignal] when I was

cross-examining you, we had a great discussion about

bandwidths, in other words, it's 9.4 plus or minus something

and 3.4 plus or minus something?

[Note the confusion in the discussion below of bandwidth v. the approximate centre point wavelength of the bandwidth range of values.]

A. Well, it's actually probably three decimal

places afterwards.

Q. Yeah. But... I'll get back to that in a

moment but...

A. This is -- these are truncated numbers.

Q. All right.

A. It's actually probably three -- I can't recall

the exact number, but it's, as opposed to 3.4...

Q. All right.

A. ...micrometres.

Q. Page 41 of 238 talks about something called

the Lambert-Beer Law. Now, that's not a law in Canada,

that's a law in science, right?

A. A law in what?

Q. It's not a Canadian law?

A. Oh, no, sorry. Okay, I thought that's what

you said.

Q. It's a concept in science.

A. Yes.

Q. It's a mathematical representation of the

absorption of infrared by molecules?

A. Yes.

Q. Did you write this part?

A. It's going back a few years. I know the first

part, the first two pages I did. I can't recall if I was

also responsible for this.

Q. Okay. So page 41 of 238, the equation that is

there and the explanation of the equation, that's basically

how an Intoxilyzer 8000C works mathematically?

A. Or any scientific instrument that uses...

Q. Infrared spectroscopy.

A. Or ultraviolet, for that matter.

Q. You can do infra -- you can do spectroscopy

with ultraviolet light. You can do spectroscopy with all

sorts of different kinds of light?

A. Even visible light, yes.

Q. All right. The Lambert-Beer Law is a

mathematical representation, and the reason why we use

Lambert-Beer Law is because if we know the absorption of

infrared light at a particular wavelength for a particular

type of thing, like ethyl alcohol, we can find a relationship

between concentration of ethanol in the breath sample in

relationship to the absorption that takes place of that

infrared light by the ethyl alcohol molecules.

A. Yes.

Q. Have I got that right?

A. Yep.

Q. And that equation, Lambert-Beer Law, as you've

said, is used for all sorts of different kinds of analysis in

analytical chemistry. But I want to suggest to you that it

assumes that there is something, and it is the fourth equal

sign down, the one that looks like the... I don't know what

it's called. Is that a Greek number... Greek... it looks

like an E?

A. Yes.

[Note the following line in the Excerpt from the Training Aid above]

Q. Equals absorption coefficient of ethanol.

A. Yes.

Q. Now, that assumes that there is an absorption

coefficient of ethanol, right?

A. Yes, that's been determined.

Q. It's been determined for a particular


A. Yes.

Q. There's a different absorption coefficient for

alcohol for every different wavelength?

A. Yes, there would be.

Q. So assuming that we are using monochromatic

infrared light, one colour of infrared light, one


A. One wavelength, okay.

Q. ...of infrared light, then the Lambert-Beer

Law works, right?

A. Yes.

Q. But if you are dealing with polychromatic, in

other words, multiple wavelength light passing through the

sample chamber and being read by the detector in the

instrument, then that changes the way that the Lambert-Beer

Law works, because the absorption coefficient of alcohol

varies with the particular wavelength of the light that's

passing through, right?

A. Yes, and the detector only monitors for

those -- even though it's sending a signal that looks at a

wide range of infrared light, the detectors are set up to

only filter those two particular wavelengths.

[The witness says the detectors are set up to only filter those two particular wavelengths. But how do they do that and how good are they to "only filter"? How wide are the filters? Is it 9.4 plus or minus .5 or .005? That's the issue.]

Q. All right. So we know that the emitter, the

thing that sends the infrared light out, the...

A. The light source.

Q. The light source is polychromatic?

A. Yes.

Q. But it's all infrared?

A. Yes.

Q. Right. The detector contains a filter that

filters the light that comes through to the detector, and

does its best to control so that it's only looking at light

at approximately 3.4 microns and 9.4 microns.

A. Correct.

Q. So that --

A. You can think of it, you can think of it, Your

Honour, as like a pair of sunglasses with two different

coloured lenses on it. That's what's being monitored here.

There's two particular lenses that are allowing only those

particular wavelengths of infrared light to come through.

Q. But a pair of sunglasses only permits through

a group of wavelengths. It doesn't limit the wavelengths to

one wavelength, right?

A. Yes.

[The issue is one wavelength v. group of wavelengths. And how wide is that group?]

Q. And I want to suggest to you that the

difficulty with the way that this page is drafted of the

Intoxilyzer 8000C Training Aid, is that it suggests,

essentially, that the light that is being read by the

detector on an Intoxilyzer 8000C is monochromatic, only at

one wavelength, rather than at many wavelengths,


A. On page 40.

Q. On page 40, my suggestion to you is that

essentially the instrument is looking at the light that's

coming through its filter -- let's just talk about the one

near 9.4 microns for a moment, because that's the one where

the quantification of ethyl alcohol takes place, right?

A. Yes.

Q. The other one, [the other 3.4 filter], the other one is used for

issues related to specificity of making sure that things like

acetone aren't interfering with the result?

A. Well, the instrument records both values.

Q. Yes.

A. And determines both values. And it looks at

the relationship between the two, but the result that is

printed on the test record card or that's displayed on the

instrument itself is from the 9.4 micro metre wavelength.

[The 9.4 micrometre filter is used on the 8000C to quantitate the alcohol.]

Q. All right. My suggestion, the problem with

this equation, the way that it's expressed in the Intoxilyzer

8000C training aid is that it depends on how wide the window

is, how wide the filter is. So just to give you a graphical

explanation, I've got a ruler that's got a little window in

it. And my suggestion is that if the filter -- His Honour

can just see what I'm holding up here. It's just a ruler

with a little window in it. The question is, how wide is the

window? Is the window wide enough that it only permits light

through at 9 point and then that 3 decimal places that you

talked about, or is the window wide enough that it allows

light through between, say, 9.1 microns and 9.7 microns, or

9.0 microns and 9.8 microns?

A. Well, that again goes back to our case in

[L'Orignal] where we know that there's a bandwidth, so it

allows 9.395 micrometres, plus or minus whatever that value

was of which I can't recall at this time.

[Excerpt from CFS 8000C Training Aid follows with plastic ruler in front of it to show the concept of bandwidth within the plastic window.]

Q. I want to suggest to you that there was

correspondence subsequent to that case [the one in L'Orignal], and correspondence

during the [R. v.] Ocampo case that you and I were both involved


A. Yes.

Q. ...where I wrote to you and I suggested that

the Centre of Forensic Sciences needed to make inquiry of the

manufacturer to find out what the actual bandwidth of the

filters was, not just the centre of the bandwidth, but the

actual bandwidth of the filters.

A. But you already had a document from CMI that

said what the actual filter wavelength was and what the

variability of the bandwidth was.

Q. With respect, I'm going to suggest to you that

that letter [see excerpt below] showed us the multiple decimal places of the

centre of the filter, but not the bandwidth. Because you

will recall that subsequently both you and Dr. Langille both

had to deal with that issue in the following period of time,

and, and as best I know, the answer I was given back from the

Centre of Forensic Sciences was the Centre of Forensic

Sciences did not know the bandwidth of the filter.

A. I mean, that's going back three to four years.

I seem to recall that there was information that was

obtained. Where that information came from, I thought it

came from the correspondence that I was shown on the stand,

but we've never ever approached CMI, that I can recall, about

asking what the bandwidth of that filter is.

[Excerpt from response by CFS scientists, including this witness, to letter by the cross-examiner, requesting that the CFS make inquiries from the manufacturer as to bandwidth.]

Q. All right. That's my point. The Centre of

Forensic Sciences does not know the bandwidth of those

filters. We don't have good information about the bandwidth

of those filters, and I want to suggest --

A. I don't think anybody does, other than CMI,

the manufacturer of the instrument.

Q. But the problem is -- and usually you and I

are discussing this from the perspective of the specificity.

But in this particular case it becomes really, really

important because the equation, the Beer-Lambert equation, I

would suggest to you, if you are dealing with monochromatic

light, you can contemplate the coefficient of ethyl alcohol

as being a constant. But if you're dealing with

polychromatic light, and you don't know the width of the

filters, the bandwidth of the filters, how big the window is

of the light that's getting through, then you don't have a

constant to work with in terms of absorption coefficient of

ethanol, and that's one of the main reasons why we have to be

concerned always about the issue of linearity in these


A. This is probably something that would be best

answered by an engineer who is responsible for setting up the

instrument and who has a better understanding of the physics

involved in that than I do.

[End of excerpt from cross-examination]

In other words:

  1. The CFS does not have any information about the bandwidth of the filters.

  2. The manufacturer does not publish any information about the bandwidth of its filters.

  3. If the bandwidth is wide, then the IR light received by the detectors is polychromatic.

  4. If the bandwidth is narrow, then the IR light received by the detectors is close to0 monochromatic.

  5. The Beer-Lambert equation described ion the CFS Training Aid assumes monochromatic IR light.

  6. There exists no single absorption coefficient of ethanol if the IR instrument is using polychromatic IR light, rather than monochromatic IR light.

  7. The Beer-Lambert Law as stated in the Training Aid does not therefore apply to quantitative analysis of ethyl alcohol in an Intoxilyzer 8000C.

  8. An expert chemist, physicist, or metrology may therefore assist a defence lawyer in convincing a Court that linearity is suspect, and that single point calibration checks are inadequate.

  9. The problem may be worse as instruments age, without full re-calibration.

With IR instruments the peaks and valleys are very narrow; so if the filter is wide then we have the band B problem illustrated below, for at least part of the bandwidth. Ultimately that means that linearity cannot be assumed. As Mr. Kupferschmidt (a respected chemist and toxicology expert) has often said "IR is notoriously non-linear."

Excerpt graph from the reference:

Please also see the following blog entry on this topic:

Please also see the blog entries:

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