# Inline thickness measurement by optical transmission (Beer-Lambert law)

I am wondering how effective would be an inline system for thickness measurement of diffuse plastic samples based on light attenuation. Sample thickness woud be in the order of a few mm. I know that there are several other optical solutions for thickness measurement on the market, but I did not find solutions employing this method.

The idea would be shining a laser light straight onto the sample, and measuring the transmitted light with a photodiode on the other side of the sample. According to Beer-Lambert law I expect the absorbance is $$A=ln(I/I_0)=-\alpha\cdot t$$, where $$I$$ is the transmitted intensity, $$I_0$$ is incident intensity, $$\alpha$$ is the absorption coefficient, and $$t$$ is object thickess. $$A$$ is measured directly by a photodiode. I was thinking about measuring $$\alpha$$ by measuring $$A$$ on samples of different known thicknesses and fitting the resulting straight line.

Of course, one big issue is scattering. One way would be to use an integrating sphere on the detector side so to collect all transmitted light, including the scattered one.

I searched around the internet and found virtually no systems or experiments that use this method. The only paper I found using it was this one. Is it because the result would be unreliable? What is the accuracy that one could reach with such method?

• And would the color of the item being measured make a difference? what about surface finish like glossy, mat etc May 15 at 8:58
• Yes, for sure it would make a difference in the result, depending on the chosen laser wavelength. The surface finish would be mainly glossy May 15 at 10:03
• I could see it working within a batch of material, but needing calibration batch-to-batch. There are off-the-shelf laser or diode type "triangulating" distance sensors, designed for factory automation, which can quickly do inline "height measurement" from which thickness can be determined (either one-sided application with opposite side restrained against a fixed location, or two-sided application if that is not possible). For really fine measurements, several other optical techniques exist May 15 at 14:32