| Author | Message | ||
     Bob Jordan (jordan) Junior Member Username: jordan Post Number: 6 Registered: 3-2003 |
Thanks guys - just the support I needed. I had in fact consulted both books referred to. I had missed your NIR News post. In that the A(R.T) curve is so like our response that it is not funny. Much more dramatically asymptotic than an exponential. Although on scanning the pic and fitting the curve I think it probably is exponential. Cannot quite see the curve's algebraic form in the text. I wonder if our rectangular hyperbola comes from the baseline correction that is discussed. Will have to leave this till next year now - mid summer here and work closes up for the year in a couple of hours. Fascinating and many thanks to you both for your thoughts. Bob J. | ||
| Howard Mark (hlmark) Senior Member Username: hlmark Post Number: 465 Registered: 9-2001 |
Bob - first let me welcome you to the NIR discussion forum: Welcome, Bob! Next, let me tell you that you're in exactly the right place. Modern NIR analysis grew up out of a need to analyze scattering samples. In fact it's only relatively recently that analysis of non-scattering samples came to be of interest. Thirdly, let me inform you that Don Dahm, who posted his answer to your question, is the forum's guru on the optics of scattering materials and probably the contemporary world expert on the subject, so you can't get a better response than what he gave you. Finally, let me point you to a fairly recently-discovered fact, that C, the concentration that yo uso casually put into your equations, isn't what it seems to be. It turns out that the units matter; different measures of concentration behave differently, are not linearly related to each other, and may not even have a one-to-one correspondence to each other. This was (moderately) recently published, in Applied Spectroscopy, 64(9), p.995-1006 (2010). The bottom line of that article is the the interactions between EM radiation and the absorbers in the sample depend on their volume fractions, and use of other units for concentration create a built-in nonlinearity between the concentration and the spectroscopy. So the bottom line is that it matters what units the concentration is expressed in. Howard \o/ /_\ | ||
| Donald J Dahm (djdahm) Senior Member Username: djdahm Post Number: 71 Registered: 2-2007 |
Well, the reviewer is full of crap. It is generally well known by those of us who worry about such things that in diffuse transmission the non-linear part of the absorbance curve is at lower absorbance values. This is stated on page 28 of our book "Interpreting Diffuse Reflectance and Transmittance - A Theoretical Introduction to Absorption Spectroscopy of Scattering Samples", where it says: Interestingly, in measurements of diffuse transmission, the departures from linearity in the Absorbance curve due to the causes we are discussing tend to be at the very low Absorbance levels. There is also a non-linearity introduced due to �stray light�. You should take a look at the pictures in Chapter 1 on the Handbook: Near-Infrared Technology: In the Agricultural and Food Industries, Phil Williams and Karl Norris (Editors). You will see the ball of light you are talking about forming as more and more milk is added to water. The equations that govern this phenomenon are fairly well known for the case where there is no absorption by the continuous phase, as was the case in the above mentions photos where visible light was being used. The theory is less well developed for the case where there is absorption in the continuous phase. [I wrote about oil in water emulsions in a column in NIR News, Volume 21, Issue, 3 Pages 9�14 (2010) Speaking theoretically� �Understanding confusing phenomena in remission spectra�. However that was about remission data, and it was particle size rather than concentration that was changing.] The spectrum obtained from an Absorbance spectrum by subtracting the absorbance at a place of zero absorption is called "Truncated Absorbance". (Such corrections are a favorite of Analytical Chemists because it looks like a �baseline correction�.) Your equation has a truncated absorbance term in it. That is usually considered a good thing in a model of the kinds of systems you are looking at. I assume that one could do theoretical calculations rather straightforwardly to help evaluate the model, but the absorption and scatter parameters would have to be reasonable for the system to make one believe in the analysis. | ||
| Bob Jordan (jordan) New member Username: jordan Post Number: 5 Registered: 3-2003 |
Apologies if this is a little off topic but there does seem to be the expertise in this forum space to help. I looked through the archives and there are many relavent comments but none specifically target this question. A colleague has developed and is in an advanced stage of publishing an improved Lowry method of protein analysis. I was asked to help with the maths of the response. Measurements are made of transmitted light through the wells of a 96 well microtitre plate and are highly non-linear, plateauing at about 1.7 absorbance units. On analysing the curve, it appears to have a rectangular hyperbola form and there does seem to be some precedence for this in the literature. A number of other forms have been tried (powers, exponentials etc) but none seem as good as the Rec Hyp form. One of the referees suggested that the measurements should be done at reduced absorbance where the response 'would' be linear and the use of 'unreliable' equations would not be required, but our initial tests suggest that the curvature starts very early in the response and that measurements are more reliable at the higher absorbance. It appears one is best to use the form: A=A0+(Am-A0)*Conc/(Conc+C50) where the terms define zero abs, plateau abs and Conc for 50% Abs. This curve has a rapidly changing slope at a conc near zero and does not approximate a linear equation well in that region. In fact between Concs of 0 and C50 (absorbance between 0.1 and 0.8) it reduces by a factor of 4. This is supported by observation of the data as well. My theory is that absorbance is in fact not a major component of the light loss, and that the light is scattered off the protein/detergent particles to increasing levels (with increasing concentration) until it reaches the state where there is a 'ball' of scattered light which then produces the plateau level as a sort of background light. Measurements seem reliable and repeatable and the lack of absorbance (if indeed that is the problem) does not seem to invalidate the method. In checking the pattern of the absorbance over the visible range of the spectrometer it seemed very broad starting from low values around 300 and peaking around 700nm. I am not sure if this gives a clue to the form of the light loss - absorbance or scatter. 680nm is used for routine measurements. SO I wonder - is there any theory or work that readers are aware of that justifies an equation of this sort? Sounds a nice case to explore the 'layers' of the well solutions - if one had the skills to do that. Again sorry for a slightly non-NIR question. Bob J. |