The simplistic way to calibrate the PCI system is to
- mount the surface calibration reference,
- make a scan through it and
- from the recorded surface spike get R, that single number, the responsivity, which wraps in it the contribution of the whole system with its multiple parameters to the calibration.
Here are how many errors may happen with this approach:
- you scanned through a bad point,
- the Inconel layer lost homogeneity over years,
- pump or probe develop an interference pattern,
- the pump is damaging the Inconel layer while the scan is going because the power is too big.
The suggested calibration routine is to
- make that scan,
- stop at the location of the maximum, look if the signal is time-dependent, reduce the power if the signal gradually goes down,
- make a few mm-long vertical or horizontal scan to address inhomogeneities and possible interference fringes,
- calculate the median value of R.
This routine will be supported as a semi-automatic feature in the upcoming software update. Meanwhile, it is a good idea to avoid bad points at least and check for time dependence and interference.
The scan above is for the calibration reference with independently measured absorption of 19.6%. Averaging over ripples gives exactly this number but local values are scattered between 17% and 23%. One-point calibration could have 20% relative error.
A way to get absorption of the Inconel layer on the spot
Instinctively, the Inconel-coated surface is placed to face the pump. It is an undisputed, standard way to calibrate. But there is one surprising feature that makes the reverse position special: the reflection from the substrate-Inconel interface is very weak. Experimental estimate for the visible and NIR is <0.5%. Calculations with some reasonable values of the complex refractive index of Inconel support this observation.
There are two benefits that follow:
- virtually no probe-related interference effects for any angular positioning of the calibration piece;
- a simple way to characterize absorption of the Inconel layer just from transmission data and the refractive index of fused silica.
The exact formula for the transmission with no interference involved is
where the uncoated air-substrate boundary reflectivity R1 is about 3.5%, R2 corresponds to the weak reflection from the substrate-Inconel interface, A is the absorption of the Inconel layer. For the typical measured value of T 67% and R2 = 0.5% the strict formula gives A = 30.03%. But if we just neglect this weak reflection then we get A = 30.36%. The resulting error is as small as about 1% relative: 30.36/30.03 = 1.011.
The corresponding calibration technique is as follows:
- Mount the calibration piece in reverse.
- Measure T moving the piece in and out of the pump beam.
- Calculate R1 for the pump wavelength using the refractive index of fused silica (Google “fs refractive index” to get to the webpage on refractiveindex.info as a first option where the reflectivity is calculated for you).
- Calculate A from the simplified formula A = (1 – R1 – T)/(1 – R1) and type it into the corresponding PCI software control.
- Run the calibration routine using this number to get the responsivity. Job done.
- Do not forget to correct the pump power for the front, uncoated surface reflection. If the power meter sensor sits after the sample the additional pump power correction factor is (1 – R1) which is 0.965 if R1= 3.5%.
The reversed position of the calibration piece could be used all the time or the data could be transferred to the standard position. For that do the calibration routine again for the front position of the Inconel-coated surface, get the responsivity which will be wrong and then lower the value of A until you get the same responsivity as for the reversed position. This lower value of A is the single-pass absorption value for the regular position of the piece.
One example of the difference between those two A’s is 23.8% and 34.8% for one fresh, just received FRQ-ND02 filter from Newport. That 11% difference is the reflectivity of the Inconel coating in the front position. In reverse the reflection disappeared and so all the difference was absorbed to keep the transmission same.