1. Physics 114: Lecture 17 More Fitting to Arbitrary Functions
John F. Federici
NJIT Physics Department

2. Star Wars quotes and jokes….

3. The problem…
A current problem with applying paint to vehicles such as automobiles, planes, buildings, etc. is the need to monitor the thickness and composition of paint layers. For example, to paint a car, one typically requires at least four layers
Primer – this acts as an adhesive layer to the metal (or composite) body so that subsequent layers stick
Color layer – This gives the ‘color’ to the body of the car.
Top Coat – This usually is a protective layer to protect the color layer underneath. For example, it usually has TiO2 (essentially sunscreen) to prevent UV radiation from dulling the color.
Color
metal
TopCoat
Primer
Primer

4. The problem … Cont.
Of course, there are also other types of coatings which automobile manufacturers use… Rust inhibitors, Corrosion protection coatings (particularly on the undercarriage of the car).
And of course the Military has ‘other’ types of coatings which is uses to enhance the ‘stealthy’ properties of its aircraft and helicopters and ground vehicles.
The key point is that in order to get the proper performance out of the coatings its is important to control the THICKNESS of the various layers as they are deposited. Essentially, variations in thickness can lead to variations in performance of the coatings.
As a simple example, if the corrosion protection layers are too thin, then the car corrodes to quickly. If the layers are too thick, you just used too much paint…. Multiply the wasted cost in the paint times the number of parts you have to spray to make ~million cars per year and it turns into a non-negligible loss.

5. Monitoring thicknesses of Paint layers
How can you measure the thickness of paint layers NON-INVASIVELY?
Electromagnetic probing a good choice!
Can not use ANY color of light since these paints are generally opaque in the visible range.
Let’s use THE FORCE LUKE!
Sorry, I don’t know how to use the FORCE, but I can use TERAHERTZ Radiation.

6. Terahertz Time-Domain Data – Recall the basic experimental layout
Think of THz pulses of radiation as similar to a Radar pulse
HOWEVER, THz radiation will NOT propagate through metal substrate which is painted. Experiment MUST be done in reflection.

7. Transmission Vs. Reflection

8. Methods and Materials
The basic method is to illuminate the multilayer coating with a short pulse (several picoseconds) of THz radiation. Whenever there is a refractive index change from one layer to another layer, a portion of the THz pulse is reflected from the boundary.
The total reflectance includes contributions from each layer of the coating: FRESNEL reflections from each boundary.

9. Thick and Thin Paint
For THICK Paint layers, Reflection from BACK and FRONT Interface are WELL SEPARATED in time.
But for thin layers, the reflected pulses overlap in time and you can not separate them easily. Pulses INTERFERE with each other

10. Frequency Domain Analysis
For a single paint layer on a substrate material.
Complex Refractive Index
Fourier Transformed Reflected THz electric field from Sample
Fourier Transformed Reflected THz electric field from Reference
Frequency of THz wave

11. Results – Single Paint layers
FFT
The (left) time domain and (right) frequency dependent reflectivity plots for the rain erosion coating layer on the aluminum substrate before any degradation occurred. A fit to the measured reflectivity using the reflectivity equation on previous slide gives a best fit of
for an assumed thickness of mil.

12. Results – Multilayer stack
Acquire a THz image of sample coupon by scanning sample pixel by pixel.
real refractive index
imaginary refractive index
In analysis, it is assumed that thickness of sample is FIXED.
Variation in refractive index over coupon due to changing THICKNESS of paint
Optical Path Length

13. Class Exercize
Your OVERALL GOAL (it will be in final project) will be to create a 2D map of the thickness of painted sample. You will extract the optical path length from experimental data. From the 2D map of thickness you will then determine the AVERAGE thickness of the pain.
As a first step, let’s develop a code which extracts a best fit refractive index from the experimental data.
Download the REFERENCE file and SAMPLE file from WEEK 13 (in-class project)
Convert data from time domain to frequency domain…. Lecture 09.
The data which you will fit will be the magnitude of the reflectivity.
Assume a thickness of mils, fitting parameters are the REAL refractive index and the IMAGINARY refractive index