Measuring Turbidity

Turbidity defines in a quantitative way how cloudy a solution is. It increases with the number of particles in suspension but also depends on the nature of the particles (such as their size). Usually, it is measured by illuminating a sample and check how light is scattered in various directions. Because light can also be absorbed by the sample, it is important to track the ratio between transmitted light and scattered light to prevent spurious results with samples that may contain optically-absorbent chemicals. It should be noted that turbidity is given by the direct ratio of transmitted light and scattered light and not by the log of the ratio, such as in the Beer-Lambert absorption law.

The largest issue with turbidity is that it is difficult to compare samples of different nature (for example, a mixture of solvents with a suspension of particles in waste-waters etc.). Results should always be compared with standard solutions whose preparations are given at the end of the post. In this way, and only this way, it will be possible to draw conclusions about the turbidity of a solution.

Here, I will present a specific case of turbidity measurement related to nephelometry where the scattering sensor is placed at 90° from the source. The overall concept is presented on Figure 1 where two light sensors at 90° and 180° are used to compute the turbidity of a sample.

Because it is troublesome to get a precise ratio calculation through electronics, I will use a trick that consists of maintaining the transmitted light constant by increasing/decreasing the current in the light source through a feedback loop. It is mathematically equivalent to computing the ratio of both light sensors but, in practice, it is thought to be more accurate because the sample is always illuminated the same way, independently of absorption effects.

The circuit schematic is given on Figure 2 and consists of two different parts. The first part (bottom of schematics) uses a phototransistor in photoconductor mode with a follower op-amp to adapt impedance of V_out. The second part of the circuit (top of schematics) is a feedback loop which read the value of the second phototransistor (also used in photoconductor mode) and compares it with a fixed value. The difference is sent to a low-pass circuit limited to a 5.1 Volts that drives a current source for the light. Because of the 5.1 Volts zener diode, the maximum current flowing into the light source is of 5.1V/R₃. The value of R₃ should then be selected accordingly to the light source maximum current specifications.

A small note should be made on the low-pass circuit. Its sole purpose is to make the feedback loop stable because there is a small low-pass effect in the sensor response. If the action on the current driver is faster than the output response of the sensor, the circuit will become unstable. To prevent this, a strong low-pass filter is inserted in the command to be sure that the frequency bandwidth of the command is smaller than the one of the sensor. It's not a big deal if you don't understand it fully; just remember that it is necessary. I will probably cover the topic of feedback loops and stability in a later post when I have time.

The gain of the photoreceptors are set by R₁ and R₂ and their ratio will give you access to several ranges of turbid media. Indeed, we know that the photo-current is linearly proportional to the light intensity, so we have:

The ratio is then equal to:

Because I₂/I₁ is dependent on the turbidity of the medium, α, and the voltage V₁ is fixed by the potentiometer, we have:

which is clearly proportional to the turbidity and the R₂/R₁ ratio. Also, we should always maximize V₁ such that the light source is just below its maximum current (you may monitor it with a fourth op-amp, it works well!).

I have built two prototypes which are shown on Figure 3. The first one (left) was made from a polypropylene cylinder and uses a thick-walled test tube with either a red LED or a 650 nm laser diode. The second one (right) was an attempt to make it more integrated and easier to build with a 3D printer and uses an IR LED with extremely thin-walled test tubes. In all cases, special care was taken to protect the photoreceptors from the ambient light by gluing them with an opaque epoxy resin.

The setups were then tested with standard solutions ranging from 0 to 200 NTU (see end of the document for a procedure). The results for a 10 cd red LED are given on Figure 4, the results of a 650 nm 5 mW laser diode on Figure 5 and the results with a TSFF5210 IR LED are given on Figure 6.

I have drawn two conclusions from these results. First, the former prototype has a non-linear relationship in its turbidity response while the latter is much more linear. I believe that this effect is due to the thickness of the walls of the tubes which conduct a part of the light a bit like an optical fiber. Using thin-walled tube is then a good idea. Second, the latter prototype seems to be less reproducible than the former. Moreover, the best results were obtained with the laser prototype, probably because the test tube focuses the laser light to the centre of the sample.

As a consequence, I would now suggest using the second prototype which is more compact and easy to build but to substitute the IR source with a laser diode. This should take benefits of the thin-walled vs. thick-walled tube issue and the focusing property. From these results, and by applying the recommendation, I think it would be possible to have a linear signal from 0 to 200 NTU with less than 2% error and, if required, to increase the range up to 1000 NTU.

Standard solutions preparation

There exists a wide variety of standards for turbidity measurements but here is one that is recognized as an ISO standard: formazine. Formazine is a suspension of polymer microspheres which range from 0.1 µm to 10 µm and is obtained by mixing two equal volumes of 10 g/l hydrazine sulphate (hazardous, take care!) and 100 g/l hexamethylenetetramine (a.k.a.: methenamine, hexamine, urotropine...). The resulting solution is firmly shaken and left to polymerize for 48 hours in the dark at a stabilized 25°C temperature. The polymerization reaction is given on Figure 7.

The formazine solution obtained is defined as a 4000 FTU/NTU (Formazine/Nephelometric Turbidity Unit) standard. Other standard solutions can then be obtained by successive dilutions of the mother standard. Through careful procedure, the reproducibility of formazine solutions is about 1% and they should be used immediately although the mother solution can remain stable for a few weeks.