## OD Thickness Measurement

### Quick Start

If your coating absorbs some relevant wavelength of light sufficiently strongly, it is easy to convert optical density into thickness. The app is not about that trivial fact. It's about analysing the best wavelength for readout and thinking through what the scale of the errors would be given an estimate (say 0.5%) of the accuracy of the measurement of OD. This depends on the absorption peak, the reference wavelength and on the thickness/extinction coefficient combination.

### OD

_{max}

_{max}nm

_{ref}nm

_{meas}nm

When light passes through an absorbing coating, a certain fraction, T, is transmitted and the rest is absorbed. Doubling the coating thickness more than halves T because T=10^{-εl} where ε is the extinction coefficient specific to that absorbing medium and wavelength and l is the thickness. Because of this non-linearity it is more usual to report the OD (Optical Density), defined as -log_{10}T which, because of the log() term is linear in thickness. So "all" that is needed is a light source, detector and conversion to OD. If ε is known, or if the system can be calibrated from known thicknesses of coating, in principle there is a very easy thickness monitor ready for use.

As always, the problems are in the details.

- Any scattering from the absorber sends light away from the detector, so unless the detector has a very broad collection angle small changes in scattering can give apparent changes in absorption
- For these transmissive detectors, T doesn't depend only on absorption. Light reflected from any interface (air/coating, coating/substrate, air/substrate) cannot be distinguished from light absorbed
- Any fluctuation in the light source will appear as fluctuation in coating thickness
- It is very easy to be lulled into a false sense of accuracy. If OD changes from 1 to 2 clearly thickness has increased by 2/1. If OD changes from 2 to 3, thickness has increased by 3/2 and so forth. But an OD of 1 means that 90% of the light has been absorbed and an OD of 2 means that 99% of the light has been absorbed. At OD=3 it is 99.9% of the light. So the shift of OD 1-->2 is a reduction of 9% of the light, but from 2-->3 it is just 0.9%. Obviously accuracy must suffer at some point.

There is not much to be done about the scattering problem if the detector is already installed. Just be aware of the problem. For the other problems the answer is to use a spectrometer wisely. Using a wavelength far from the absorption of the coating it is easy to get a reference %T that captures reflections from the substrate and variations in the light source. Choosing a measurement wavelength that, for your thickness, is comfortably in the 0.5-1.5 OD range guarantees that the detector has plenty of photons to work on while also having enough absorption to make it easy to differentiate thickness changes. A final refinement is to avoid a wavelength that has a very steep absorption change where a measurement depends strongly on the absolute wavelength chosen in the spectrometer which might be out by a few nm.

Play with the extinction coefficient, ε, the thickness, l (the values are artificial to give a relevant OD range), the λ_{max} and Width of the absorption peak, the λ_{ref} for the reference wavelength λ_{meas} for the measurement wavelength (hint - move it away from λ_{max} if the OD is too high) and an assumed error in the measurement of light intensity. The estimated error is then calculated.

As you play with the values you quickly find the limits of the method. The key lies in the Error value. If, at the measurement wavelength, the OD is too high then the absolute amount of light getting through may only be 0.1% so a 0.05% error in the %T is a huge error in calculated OD. And if the absorption spreads to the reference wavelength then the measured OD gains an extra error.

Of course, in a real system things are more complicated, but the app gives you a good idea of the trade-offs involved in OD measurements. These are:

- For very thin coatings or low ε there isn't enough absorption to give a good signal.
- For very thick coatings or high ε there may be too much absorption, though it is often easy to choose a different measurement wavelength.
- If the absorption band is too wide there might not be a reference wavelength free from absorption, though there are workarounds if the light from the source can be fed to a separate spectrometer or simple photodiode.

### Summary

- Accuracy: Broad areas of high accuracy with obvious areas of low accuracy.
- Size: Medium
- Safety: Safe
- Scanability: Easy to scan, and to use in spot mode
- Cost: Medium
- Wet/Dry: Works on both.
- Big limitations: Needs relevant ε in measurement wavelength range; is highly subject to scatter unless a large collection angle is used.