Additional hints for worksheet 4.1: How to construct an absorption photometer on your own (3/4)

Precision of measurements

Accidental measurement errors have to be distinguished from systematic ones in all physical measurements.

Accidental errors...

... can emerge from various sources;

  • inaccuracy of the optical alignment through manual interventions such as an exchange of the light source or the sample.
  • drift of the light source's brightness through instable power supply or aging
  • contaminated samples or cuvettes
  • air bubbles on the cuvettes' windows
  • suspended matter in the sample that influences the transparency through light scattering. Suspended matter has to be filtered out before analysis if it is intended to exclusively examine the absorption of dissolved substances.

There are further sources for measurement errors which can not be prevented even by great diligence. For avoiding the major errors some rules should be respected:

  • undesired suspended matter can be discovered by shining through the sample with a laser pointer. The particles scatter the collimated beam which can be easily observed.
  • each measurement has to be repeated with the reference solvent with dispatch.
  • cuvettes are touched only with clean gloves. Transparent disposable gloves of polyethylene (PE) are applicative. Gloves made of tissue or laboratory gloves with talcum on them are unsuited.
  • The obtained data has to undergo a plausibility check already while measuring. Examples:
    • if values stay constant when changing the wavelengths, the electronic signal processing is probably overloaded
    • if data from the sample shows more brightness than the reference data, either the reference solvent has to be polluted, the optical alignment is inaccurate or the brightness of the light source has changed.

 

Systematic errors ...

... are attributable to characteristics of the exponential function in Lambert's law, and the consequences of experimental accuracy which follow. We depict this using the relations of the reference and sample data from the section about the analysis of photometer data:

I ref =G⋅ I o e − a ref x             I probe =G⋅ I o e − a probe x
The log of its quotient has to be found so that after some transformation the absorption coefficient is obtained.

If the sample is only slightly absorbing and the weakening of light in the sample cuvette is in consequence negligibly stronger than the one in the reference cuvette, the quotient approaches 1 and the log of it is close to 0. In those cases, even minor differences in the optical alignment can evoke changes of the instrumental function G, which can overshoot the effects of the slightly different absorption.

However, if the sample is highly absorbing and the measured value Iprobe almost 0, even small variation of that value evoke high numeric changes of the quotient and the corresponding error in the absorption coefficient.

What value of a with given x will produce the smallest systematic error? Or: What length of the cuvette has to be chosen to analyse a sample with a given absorption coefficient while producing the smallest error?

This seems to be a problem of extrema calculus. The oceanographer R.W. Austin depicted this calculation in his article Precision considerations in the measurement of volume attenuation coefficient published by J.E. Tyler in the book Light in the Sea, p. 121-124, to what is made reference here.