Instrumental Deviations from Beer-Lambert Law
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:
Creating a Calibration Curve
Limits to Beer's law
No longer linear when the molar absorptivities differ
Instrumental Deviations from Beer-Lambert law
Polychromatic Radiation rather than Monochromatic IR
Sample cross-examination of CFS expert on university textbook dealing with deviations from linearity - deviations from Beer-Lambert Law. CFS takes the position, without empirical evidence, that such deviations will never be gross deviations:
MR. BISS: Q. Mr. Palmentier, this is a...
A. Skoog an 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.
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?
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:
"...is 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.
Q. And then it says down at the next paragraph
"Computerizing numerical data analysis has largely
replaced graphical calibration methods..."
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.
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. 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.
Q. Right. Talking about instrumental deviations,
if we could move ahead, please, to page 671.
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.
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...
Q. ...an optical filter...
Q. ...to isolate a band of wavelengths
surrounding 9.4 microns.
A. Or 3.4 micrometres, yes.
Q. All right. On page... it's covered up by the
staple, but 672.
Q. Halfway down the page it says, "As shown in
A. Sorry. Sorry. Sorry. As... 672?
Q. Page 672.
A. Okay. Sorry. There. "In addition"?
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
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
Do you understand that?
A. So this is referring to... where are E prime
and E double prime referred to.
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...
Q. ...to 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.
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.
Q. All right. Let's look at the next paragraph
A. Which page are we on now?
Q. We're on 67...
A. Oh, okay.
Q. "If the band of wavelength selected for
spectrophotometric measurements corresponds to a
region of the absorption spectrum in which the
molder absorptivity of the analyte is essentially
constant, departures from Beer's law will be
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?
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 slide slope of the valley or the
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.
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.
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 sustem (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: