Donald J. Roth

Glenn Research Center, Cleveland, Ohio

Laura M. Cosgriff

Consultant, Lakewood, Ohio

Bryan Harder and Dongming Zhu

Glenn Research Center, Cleveland, Ohio

Richard E. Martin

Cleveland State University, Cleveland, Ohio 

Absolute Thickness Measurements on Coatings 

Without Prior Knowledge of Material Properties

Using Terahertz Energy

NASA/TM—2013-216603

December 2013
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Donald J. Roth

Glenn Research Center, Cleveland, Ohio

Laura M. Cosgriff

Consultant, Lakewood, Ohio

Bryan Harder and Dongming Zhu

Glenn Research Center, Cleveland, Ohio

Richard E. Martin

Cleveland State University, Cleveland, Ohio 

Absolute Thickness Measurements on Coatings 

Without Prior Knowledge of Material Properties

Using Terahertz Energy

NASA/TM—2013-216603

December 2013

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

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Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2013-216603 1 

Absolute Thickness Measurements on Coatings Without Prior 

Knowledge of Material Properties Using Terahertz Energy 

Donald J. Roth 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Laura M. Cosgriff 

Consultant 

Lakewood, Ohio 44143 

Bryan Harder and Dongming Zhu 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Richard E. Martin 

Cleveland State University 

Cleveland, Ohio 44115 

Abstract 

This study investigates the applicability of a novel noncontact single-sided terahertz electromagnetic 

measurement method for measuring thickness in dielectric coating systems having either dielectric or 

conductive substrate materials. The method does not require knowledge of the velocity of terahertz waves 

in the coating material. The dielectric coatings ranged from approximately 300 to 1400 m in thickness. 

First, the terahertz method was validated on a bulk dielectric sample to determine its ability to precisely 

measure thickness and density variation. Then, the method was studied on simulated coating systems. 

One simulated coating consisted of layered thin paper samples of varying thicknesses on a ceramic 

substrate. Another simulated coating system consisted of adhesive-backed Teflon adhered to conducting 

and dielectric substrates. Alumina samples that were coated with a ceramic adhesive layer were also 

investigated. Finally, the method was studied for thickness measurement of actual thermal barrier 

coatings (TBC) on ceramic substrates. The unique aspects and limitations of this method for thickness 

measurements are discussed. 

Introduction 

Thermal barrier coatings (TBCs) and environmental barrier coatings (EBCs) are used to protect 

turbine engine components in high temperature or hostile environments (Ref. 1). Degradation of the TBCs 

or EBCs can lead to exposure of the substrate material to the high temperature, hostile engine 

environments resulting in damage to the substrate and component failure. Therefore, nondestructive 

evaluation (NDE) techniques that are capable of measuring the degradation and thickness of the coating 

materials are imperative to predicting remaining component life and failure (Refs. 1 to 3). TBCs and 

EBCs are applied to hot section engine components in a layer with a thickness that is typically less than 

1 mm. Therefore, NDE techniques that are capable of characterizing coatings of thicknesses below 1 mm 

must be developed. Terahertz radiation wavelengths are on the order of 200 to 1500 m (Refs. 4 to 7), 

making terahertz energy a good candidate for interrogation of coatings. Reflections occur at interfaces 

between materials with dissimilar dielectric properties (differences in indices of refraction). Metallic and 
NASA/TM—2013-216603 2 

conductive materials totally reflect terahertz waves, while nonpolar liquids, dielectric solids, and gases are 

partially transparent to terahertz energy. A significant advantage of terahertz waves for NDE is that they 

do not require a coupling medium (such as for ultrasonics) in order to interrogate a material. Continuous 

wave (narrowband) and pulsed (broadband) terahertz systems exist. This study is based on results from a 

reflection-mode broadband terahertz method with a collinear source-detector (transceiver) configuration 

shown schematically in Figure 1. 

The use of terahertz for characterizing thickness and microstructure in coating materials has been 

previously investigated. The width and shape of the terahertz signal was utilized to monitor a thermally 

grown oxide layer and voids in TBCs that were approximately 300 m thick (Ref. 8). A novel terahertz 

method to simultaneously characterize thickness and microstructural variation in thicker bulk materials 

was developed (Refs. 9 to 11). In the current study, the novel terahertz method was investigated for its 

ability to measure absolute thickness in the 300 to 1400 m thickness range. Additionally, the use of the 

method to characterize global microstructural variation in one coating system independent of thickness is 

explored. The method was tested on a number of different coating systems as described in the experimental section. Limitations related to the use of this method on currently-manufactured TBC/EBC 

systems are discussed. Because TBCs typically consist of a heat-insulating (or dielectric) ceramic top coat 

and are often applied to a superalloy substrate, characterization with terahertz energy would be a very 

practical application. 

Methodology 

In this investigation, the conventional terahertz method of inspecting metal reflector-backed dielectric 

materials is taken advantage of to simultaneously provide microstructure-independent thickness (free of 

microstructure effects) measurements and images in coating materials. Figure 2 shows a schematic of the 

pulse-echo terahertz testing method and resulting waveforms. 

A pulse-echo terahertz thickness measurement is made by sending terahertz energy via a transceiver 

(device that has both a transmitter and a receiver) into and through a dielectic coating backed by a 

material substrate that reflects the terahertz energy back to the transceiver. The terahertz transceiver is 

separated from the dielectric coating by an air path. 
NASA/TM—2013-216603 3 

Pulse-echo imaging involves mapping variations in the time-of-flight of a terahertz echo peak, or 

mapping the time delay between echoes off of a top surface of the coating (FS) and top surface of the 

underlying material substrate (BS) echoes, across a scanned sample. This scanning implementation 

concerns itself more with mapping thickness or global microstructural variation (such as physical density 

variation) as opposed to discrete flaw detection. Time delay between the front surface coating echo and 

material substrate top surface echo (2) is directly affected by thickness variation (d) and terahertz 

velocity (V) in the coating according to: 

 

V

2d 2  (1) 

Here the designations 2and 2d (versus and d) are used since the terahertz echo travels through twice 

the coating thickness in the pulse-echo mode. Terahertz velocity is affected by variations in a volumetric 

microstructural property such as physical density, similar to the way ultrasonic velocity responds to 

microstructural variation (Refs. 12 to 14). Determining the relationship between terahertz velocity and 

density allows actual density maps to be obtained from velocity maps (Refs. 9 to 11). Variations in part 

thickness and/or lateral microstructural character will result in variations in maps of 2. Analogous to a 

complex number having real and imaginary parts, 2images can be thought of as having thickness and 

microstructural components if both thickness and microstructural variation are present. 

Thickness Determination 

The novel pulse-echo method described here for measuring coating thickness on an underlying 

material substrate uses time delay relationships between echoes off of the coating top surface (FS in 

Fig. 2), material substrate top surface with (BS in Fig. 2) and without (M” in Fig. 2) the coating present. 
NASA/TM—2013-216603 4 

The following steps show how thickness (d) is determined without needing prior knowledge of 

coating velocity. With the coating present between the transceiver and the material substrate, the pulse 

that travels from the transceiver through the coating to the material substrate (equivalent to the coating 

back surface position or the interface of the coating and material substrate) and back to the transceiver is 

labeled BS and will be observed at time t' where: 

'   2  2 1 t t (2) 

where 2t1 and 2are the pulse-echo time delays of the terahertz pulse from the transceiver to the coating 

front surface and from the coating front surface to the material substrate, respectively. Depositing the 

dielectric coating on the material substrate slows down the terahertz pulse as compared to its travel time 

in air. Thus, with the coating removed, the pulse that travels from the transceiver to the material substrate 

and back to the transceiver is labeled M” and will be observed at an earlier time t" where: 



	


 




  

c

d

t" 2t

1 2 (3) 

where c is the velocity of terahertz energy in air and d is the air gap equal to the coating thickness. The 

velocity of light at standard temperature and pressure was used as in c in this investigation and is equal to 

0.02997055434 cm/psec. Subtracting Equation (3) from Equation (2) gives: 

c

d

t't" t  2  2 (4) 

Rearranging Equation (4) to solve for coating thickness (d) gives: 

 

2

c 2 t d     (5) 

which allows the calculation of absolute material thickness of the coating without prior knowledge of 

velocity. When this is extended to multiple measurements across the coating for imaging, sample 

microstructure variation effects are eliminated in the image allowing a true mapping of coating thickness 

variation. For conventional thickness mapping (rearranging Eq. (1) to solve for d), microstructure 

variation effects would corrupt the evaluation of thickness variation—thus the new methodology allows 

true characterization of thickness variation in a coating with non-uniform microstructure. 

Velocity Determination 

Similar logic can be used to solve for true velocity (V) in the coating as shown below. 

Rearranging Equation (1) to solve for 2d gives: 

2d    2 V (6) 

Solving Equation (6) for d and substituting the result into Equation (4) gives: 

C

V

t

     2 2 (7) 
NASA/TM—2013-216603 5 

Rearranging Equation (7) to solve for V gives: 



	


 








   2

1 t V c (8) 

As seen from Equation (8), coating thickness (d) is not a variable in the equation. Thus, this method does 

not require prior knowledge of coating thickness. If extended to multiple measurements across the coating 

(imaging), coating thickness variation effects are eliminated in the image allowing a true picture of 

microstructural variation in the coating for types of microstructural variation (such as density variation) 

that correlate with and will be revealed by velocity variation. For conventional time-of-flight imaging 

(Eq. (1)), thickness variation effects would corrupt the evaluation of microstructural variation—thus the 

new methodology allows true thickness independent characterization of microstructural variations in the 

coating. Equation (9) shows how the terahertz velocity in a dielectric coating will be reduced fractionally 

from that in air by the factor: 



	


 








  2

1 t (9) 

A key point of the methodologies presented in this section are that both thickness-independent velocity 

and microstructure-independent thickness images can be derived from the same set of scan information. 

In practice, 2is experimentally obtained from the pulse-echo time delay between the first front surface of 

the coating surface (FS) and material substrate echo (BS). t is the pulse-echo time difference between 

the echo off the material substrate with and without the coating present, respectively. Either the time 

difference from peak locations or cross-correlation of the two echoes can be used to obtain the time delays. 

Materials 

Table 1 summarizes the substrate material—coating systems interrogated by THz in this study. 

Additional details on the material samples are described following the table. 

TABLE 1.—MATERIAL SYSTEMS INTERROGATED BY THz

Material 

System 

Substrate Coating Coating thickness range, 

μm 

Coating density, 

g/cm3

Coating 

porosity, 

percent 

Notes 

1 Metal plate Silicon Nitride 3200 to 3500 5.9 to 6.1 2 Bulk sample 

on top of metal 

reflector plate 

2 Nickel-base 

Superalloy 

Paper 190 to 1440 ~0.8 Undefined Adhesivebacked “sticky 

notes” 

3 Nickelbased 

Superalloy 

Teflon 580 to 1200 2.2 Undefined Adhesivebacked Teflon 

4 Glass Teflon 580 to 1200 2.2 Undefined Adhesivebacked Teflon 

5 Alumina Sieved MgOZrO2 based 

ceramic 

adhesive 

489 to 514 ~2.65 to 3.32 41 Sieved ceramic 

adhesive 

applied with a 

doctor blade 

6 Alumina As received 

MgO-ZrO2

based ceramic 

adhesive 

465 to 523 ~1.74 to 1.98 48 As received 

ceramic 

adhesive 

applied with a 

doctor blade 
NASA/TM—2013-216603 6 

Material 

System 

Substrate Coating Coating thickness range, 

μm 

Coating density, 

g/cm3

Coating 

porosity, 

percent 

Notes 

7 Alumina Sieved MgOZrO2 based 

ceramic 

adhesive 

489 to 514 ~2.65 to 3.32 41 Sieved ceramic 

adhesive 

applied with a 

doctor blade 

8 Alumina Sieved MgOZrO2 based 

ceramic 

adhesive and 

carbon black 

417 to 521 ~1.42 to 1.62 74 Sieved ceramic 

adhesive and 

carbon black 

applied with a 

doctor blade 

9 Nickel-base 

superalloy 

8YSZ 249 to 485 5.9 to 6.10 Undefined 8YSZ coating 

applied with an 

air plasma 

spray process 

The first “coating” sample listed in Table 1 is a bulk silicon nitride dielectric sample which is 

approximately 3 by 1.5 cm. This silicon nitride sample, shown in Figure 3, has thickness varying from 

3.2 to 3.5 mm and a small density variation of 2 percent due to porosity variation. 

This sample was previously investigated using the novel terahertz method on another terahertz system 

(Ref. 9). It was important to be able to duplicate the previous results in order to validate the method on the 

system used in this study. 

To simulate dielectric-coated samples, thin adhesive-backed paper samples (i.e., “sticky notes”) were 

layered to create varying thicknesses on an electrically-conducting, nickel-based superalloy substrate. The 

total thicknesses of the layered sticky notes varied from 190 to 1440 m. This is the second material 

system listed in Table 1. 

The third and fourth material systems on Table 1 represented another set of simulated coatings 

consisting of adhesive-backed Teflon. First, rectangles consisting of three different thicknesses from 

approximately 580 to 1200 m of Teflon were adhered to the nickel-based superalloy substrate. A 

schematic illustrating the layout of the three thicknesses is shown in Figure 4. 

Then, to further investigate the method’s capabilities in interrogating dielectric coatings on dielectric 

substrates, Teflon rectangles were adhered to a glass substrate. 

Two sets of three 1 by 1 in. alumina substrates with a MgO-ZrO2 based ceramic adhesive coating 

were also evaluated. The first set of three samples was created to have uniform material/density but 

different thicknesses and is the fifth material system listed in Table 1. To create the coatings for the first 

set of samples with the same density, the larger grains were first sieved from the MgO-ZrO2 based 

ceramic powder using a 100 mesh sieve allowing grains smaller than the mesh opening of 6 mil 

(0.152 mm) to pass through. The sieved powder was then combined with water and applied to the surface 

of the alumina substrate using a doctor blade. After the coating was cured in a 126 C (259 F) oven for 

several hours, the coated samples were placed in a 700 C (1292 F) degree oven to remove any 

impurities. The coatings were then polished, attempting to create a uniform surface area on each coated 

sample to be evaluated with terahertz. Coating thickness ranged from ~480 to 493 m on the first sample, 

~492 to 519 m on the second sample, and ~663 to 682 m on the third sample. 

A second set of three 1 by 1 in. alumina substrates with a MgO-ZrO2 based ceramic adhesive coating 

samples were manufactured with different densities but approximately the same thickness in order to 

evaluate the terahertz method for characterizing microstructural variation in coatings. These are the 6, 7, 

and 8 material systems listed in Table 1. First, the same sieved MgO-ZrO2 based ceramic adhesive 

coating used for material system 5 was applied to an alumina substrate using a doctor blade. Then, carbon 

black was added to the sieved MgO-ZrO2 based ceramic adhesive to create additional porosity in the 

coating. To create a third material/density difference, the as-received, unsieved MgO-ZrO2 based ceramic 

powder was combined with water and applied to the alumina substrate. After the coatings cured in a 

126 C (259 F) oven for several hours, the coated samples were placed in a 700 C (1292 F) degree 
NASA/TM—2013-216603 7 

oven to eliminate the carbon and any additional impurities. The coatings were then polished to 

approximately the same thickness, attempting to create a uniform surface area on each coated sample to 

be evaluated with terahertz. Coating porosities were found using Archimedes’ method to be 48 percent for 

the as received ceramic adhesive, 41 percent for the sieved ceramic adhesive, and 74 percent for the 

sieved ceramic adhesive with carbon black. 

Finally, 1.9 by 1.9 cm square Nickel-based superalloy substrates were coated with 8-YSZ (yttriastabilized zirconia) using an air plasma spray (APS) process. Eight samples with coating thicknesses varying 

from 249 to 485 m were investigated with terahertz. This is the ninth material system listed in Table 1. 
NASA/TM—2013-216603 8 

Figure 4.—Schematic of the Teflon rectangular samples adhered to a circular 

Nickel-based superalloy substrate disk. The thickness of each Teflon section is 

shown in the schematic. 

TABLE 2.—DIELECTRIC CONSTANTS, k 

[At standard temperature and pressure, 

relative to vacuum.] 

Material k 

Vacuum 1 

Air 1.0059 

Paper 2 

Silicon Nitride 4.2 

Teflon 2.1 

Glass 3.7 to 10 

Alumina 4.5 

Cement (powder) 5 to 10 

8YSZ 24 

Water (68 F) 80.4 

Table 2 lists the room temperature dielectric constants for some of the coating and substrate materials 

used in this study (Refs. 15 to 17). Materials with a low dielectric constant, close to 1, are transparent or 

near transparent to terahertz energy, while materials with dielectric constants larger than 1 will reflect 

some fraction of the incident terahertz energy. As the dielectric constant approaches that of water (80.4), 

more of the Terahertz energy is reflected. Highly conductive materials, such as metals, have very high 

dielectric constants and reflect all of the terahertz energy. The dielectric constants for a vacuum, air and 

water are included in the table for reference. The dielectric constant for the nickel-based superalloy is 

unavailable because it is such a conductive material, reflecting all of the Terahertz energy. A difference in 

dielectric constant, or dielectric mismatch, between two layered materials, will result in some terahertz 

energy being reflected from and some being transmitted into the layer that the terahertz energy is incident 

upon. The greater the mismatch, the greater the amount of reflected energy. 

Terahertz Scanning 

Two scans were obtained for each sample studied with the THz system shown in Figure 5 before and 

after applying a simulated or actual coating material to the material substrate. 

The THz signalis generated by the pulsed THz controller, which contains the laser, power supplies, and 

other components of the system. A lensed, collinear reflection transceiver was used to send and receive the 

THz signal into the dielectric coating material. Each acquired waveform consisted of 400 points over an 

80 psec time window. The resulting time domain resolution is 0.2 psec per acquisition point. The THz 

Nickel-based superalloy 

substrate 
NASA/TM—2013-216603 9 

Figure 5.—Photograph of the THz system utilized in this study. 

bandwidth of the pulse is 0.01 to 2 THz. To maximize the signal amplitude, the transceiver was focused at 

the substrate at the lens focal length of 76.2 mm (3 in.). The focal spot size was 2 mm which is 

approximately the limit of lateral resolution. 

For each material system interrogated, a baseline scan of the underlying material substrate without the 

coating present, yielding the M” echo, and a scan with the coating present, containing the FS and BS 

echoes, was acquired. For example, the bulk silicon nitride wedge sample was placed on an aluminum 

plate within the scan system hardware. A baseline scan was obtained from the aluminum plate, without 

the silicon nitride sample present, and yielded the M” echo. A second scan was then performed with the 

sample placed on the aluminum plate to obtain the FS and BS echoes. 

For the coated samples, first, a baseline scan from the uncoated material substrate was obtained and 

yielded the M” echo. The second scan with the coatings present provided the FS and BS echoes. The FS 

echo reflected off the top surface of the coating, while the BS echo represents a reflection off of the 

material substrate top surface. The scan and step increments were 0.5 by 0.5 mm. 

The time delays 2and t were measured using the negative peak times (valleys) of the FS, M”, and BS 

echoes (Fig. 2). For the samples in this study, FS, M”, and BS echoes were in phase with each other and had 

distinct single negative peaks. Waveform data from the substrate only and substrate with coating scans were 

used to create a “Fused” data file using the NDE Wave and Image Processor (Ref. 18). This merged data 

contains the FS, BS, and M” at each scan location and is used for all subsequent data analysis. 

Results and Analysis 

Silicon Nitride Wedge 

To validate the current terahertz system and to determine the novel THz method’s ability to measure 

thickness and density variation, the silicon nitride wedge sample with thickness and density variation was 

scanned using the methodology described above. Figure 6 shows the fused THz waveform with the front 

surface (FS), back surface (BS), and M” echoes labeled. 

The results in Figure 7 show that the terahertz thickness measurements agree with the thicknesses as 

measured with a micrometer. In fact, the THz thickness measurements were within 4 percent of the 

micrometer measured thickness. In addition, these results were in agreement with previously published 

terahertz thickness results on the same sample (Ref. 9), hence verifying the method for thickness 

measurement. The echoes obtained for this material are of extremely high signal-to-noise ratio with wellformed valleys from which time-of-flight was extracted. 
NASA/TM—2013-216603 10 

Figure 6.—Fused THz waveform from the two scans of the silicon nitride sample with the front surface (FS), back 

surface (BS), and M” echoes. 

Figure 7.—Terahertz thickness map from the silicon nitride ceramic 

sample. Thickness as measured with a micrometer is shown on the left. 

Thickness as measured with THz is shown in the scale on the right. 

(a) Velocity map (b) Density map

Figure 8.—Velocity map (a) and the density map (b) for the silicon nitride wedge. Density map obtained from the 

relationship between density and terahertz velocity in silicon nitride from prior work (Ref. 10). 

Figure 8 shows the THz velocity map (a) and the terahertz-derived density map (b) for the silicon 

nitride wedge. The velocity values were converted to density values using the best linear curve fit 

reported in previous work (Ref. 10). The density variation shown in Figure 8(b) corresponds well with the 

variations shown by optical microscopy (Fig. 3). These density results also agree with previously 

published results (Ref. 10), thus validating the method for thickness and density variation 

characterization. 

Micrometer Thickness (um) Terahertz Thickness (um) 
NASA/TM—2013-216603 11 

Layered Paper on Ceramic Substrate 

The novel THz scanning method was next applied to simulated coating systems consisting of layered 

thin paper samples (i.e., “sticky notes”) of varying thicknesses on a ceramic substrate. The thicknesses of 

the layered paper samples, as measured by a micrometer, ranged from 190 to 1440 μm. Three thicknesses 

of layered paper were applied to the ceramic substrate for an individual scan. This was done for three 

different thickness ranges of papers to provide three sets of scan results. A typical fused waveform from 

the layered paper on a nickel-based superalloy material systems is shown with the FS, M”, and BS echoes 

labeled in Figure 9. Since the paper samples all had uniform microstructure, it was expected that paper 

coating velocity would be almost constant regardless of the coating thickness. The THz thickness and 

velocity results from the THz scan with the thickest set of layered paper sections are shown in Figure 10. 

Figure 9.—Typical fused waveform from the 490 μm thick layered paper on a 

nickel-based superalloy with the front surface (FS), back surface (BS), and 

uncoated substrate (M”) echoes labeled. 

(a) Photo of disk with layered 

paper 

(b) THz thickness (c) THz velocity map 

Figure 10.—Photograph and THz results from the paper layers ranging from 1050 to 1440 μm thickness on a nickelbased superalloy. Thickness values shown are the mean calculated from five locations (center and four quadrants 

for each thickness). 
NASA/TM—2013-216603 12 

TABLE 3.—THICKNESS MEASUREMENTS OF LAYERED PAPER ON A NICKEL-BASED SUPERALLOY SUBSTRATE 

[All values shown are the mean of five locations (center and four quadrants for each thickness).] 

Micrometer measured 

thickness, 

μm 

THz thickness, 

μm 

Percent difference, 

thickness 

THz velocity, 

cm/sec 

1440 1412 1.9 2.00E+10 

1250 1250 0.0 2.02E+10 

1050 1058 –0.8 2.01E+10 

480 520 –8.3 2.07E+10 

380 419 –10.3 2.10E+10 

290 311 –7.2 2.02E+10 

390 498 –27.7 2.52E+10 

290 396 –36.6 2.61E+10 

190 318 –67.4 3.12E+10 

Figure 11.—Photograph and THz results from the paper layers ranging from 290 to 480 μm thickness on a nickelbased superalloy. Thickness values shown are the mean calculated from five locations (center and four quadrants 

for each thickness). 

Table 3 summarizes the THz results from all the layered paper samples with each listed measurement 

representing the average of five locations. The percent difference in thickness between micrometermeasured and terahertz-measured thickness was calculated using the formula: 

 

A

A  T  100 * Percent Difference (11) 

where A is the micrometer measured thickness and T is the THz thickness. 

The mean THz thicknesses from the three thickest paper layers were 1058, 1250, and 1412 m, which 

represents a –0.8, 0, and 1.9 percent, difference from the micrometer measured thicknesses of 1050, 1250, and 

1440 m. The THz thickness and velocity results from another set of layered paper are shown in Figure 11. 

The nearly-uniform gray scale color of the velocity maps in Figures 10 and 11 indicate that the THz 

velocity is relatively uniform as expected, regardless of thickness. The variation of the THz velocities 

found from the 1050, 1250, and 1440 m thicknesses is low with the total standard deviation 

approximately 0.5 percent of their means. However, as the thickness of the three paper layers scanned 

decreased, the percent difference between all of the velocities increased and the standard deviation of the 

THz velocities also increased. For the thinnest paper layers of 190, 290, and 390 m, the percent 

difference was as high as 67.4 percent and the standard deviation of the THz velocities from the three 

thicknesses was 11.7 percent of the mean of the three THz velocity values. This is likely related to FS, 

BS, and M” waveforms interference reducing the precision of true peak (valley) detection. Interpolation 

of the waveforms by a factor four times (increasing point density by four times) was used in an attempt to 

improve the precision of valley detection for better thickness accuracy but it did not help. 

(a) Photo of disk with layered 

paper (b) THz thickness map (c) THz velocity map 
NASA/TM—2013-216603 13 

(a) Waveform from the 190 μm thick section (b) Waveform from the 290 μm thick section

Figure 12.—Fused THz waveforms from the thinnest paper layers on a ceramic substrate illustrating the 

decrease in separation between FS, BS, and M” echoes. The amplitude scale is the same for both 

waveforms.

Figure 12 shows the decrease in separation between the echoes of the fused waveform. It became 

difficult to unambiguously detect the valley needed for time-of-flight extraction. Therefore, analysis of 

these layered samples helped define a practical thickness limit of 350 m for the method. This limit will 

depend upon the velocity of terahertz in a material (lower velocity provides greater FS and BS echo 

separation), but it was consistently observed for the samples in this study. A minimum coating thickness 

of 350 m provides enough separation in time between FS and BS and prevents overlap of FS, BS, and 

M” echoes during the gating, fusing and analysis process. When analyzing layers thicker than 350 m, the 

accuracy improves considerably. 

Teflon on Glass and Nickel-Based Superalloy 

Adhesive-backed Teflon was adhered to glass and to a Nickel-based superalloy in the next set of tests 

with the novel terahertz method. A glass substrate, representing a dielectric/insulating material, and a 

Nickel-based superalloy substrate, representing a conductive material, was used to compare the 

capabilities of the system for investigating material systems having dielectric versus conductive 

substrates. The results shown here represent Teflon thicknesses measured with a micrometer ranging from 

approximately 590 to 1100 m. A fourth Teflon thickness of approximately 330 m was also measured. 

However, this thickness was deemed too thin to evaluate as its inclusion in the analysis caused large 

percent differences in the thickness measurements and large variations in the velocity measurements. This 

result further defined the practical thickness limit of 350 m for the THz method discussed above. For 

thicknesses below 350 m, interference between front surface and back surface echoes resulted in 

difficulty obtaining accurate time-of-flight values needed for velocity and thickness calculation. 

The fused waveform from Teflon on a glass substrate is shown in Figure 13. The FS, M”, and BS 

echoes are labeled, along with an additional echo further in time, labeled fixture echo. The fixture echo is 

thought to be the echo from the interface of the back surface of the glass and the support fixture where the 

Teflon and glass material system sample is placed and did not influence the thickness or velocity analysis 

or the calculations. More of the Terahertz penetrated the dielectric glass material than has been observed 

in other material systems. This makes sense since glass is non-electrically-conducting. Figure 14 shows 

the THz thickness and velocity scan results from the Teflon adhered to the glass substrate. 

As shown in Table 4, THz thickness measurements of the Teflon layers on the glass substrate were 

within 3 to 5 percent of the measured thickness. Each thickness and velocity value listed in the table 

represents an average of five locations in each thickness region. Velocity varied across all of the samples 

by ~1.5 percent, regardless of thickness. 
NASA/TM—2013-216603 14 

Figure 13.—Fused THz waveform from the 1136 μm thick section of adhesive-backed Teflon on a glass substrate 

with the FS, M”, BS, and an additional fixture echo labeled. 

(a) THz thickness map 

(b) THz Velocity map 

Figure 14.—Thickness map (a) and velocity map (b) for adhesive-backed Teflon on a glass substrate. 

TABLE 4.—THICKNESS MEASUREMENTS OF TEFLON ON GLASS SUBSTRATE 

[All values shown are the mean of five locations (center and four quadrants for each thickness).] 

Micrometer measured 

thickness, 

m 

THz thickness, 

m 

Percent 

difference 

thickness 

THz velocity, 

cm/sec 

588 568 3.4 1.93E+10 

818 790 3.4 1.94E+10 

1136 1078 5.1 1.96E+10 
NASA/TM—2013-216603 15 

A representative fused waveform from Teflon on the nickel-based superalloy is shown in Figure 15 

with the resulting THz thickness map shown in Figure 16. 

As shown in Table 5, THz thickness measurements of the Teflon layers from the nickel-based 

superalloy substrate were within 4 percent of the thickness measured with a micrometer. Each thickness 

and velocity value listed in the table represents an average of five locations in each thickness region. The 

image in Figure 16(a) shows that the thickness was uniform over each region. The image in Figure 16(b) 

shows that the THz velocity and material density was also uniform. 

It appears that the THz results from the two systems with material substrates having different 

dielectric properties are very similar. Although the amplitude of the THz signal was slightly larger from 

the nickel-based superalloy substrate versus the glass substrate, the percent differences between the 

micrometer-measured and THz-measured thicknesses were both  ~5 percent. Velocity varied across all 

of the samples by ~3.5 percent, regardless of thickness. 

Figure 15.—Fused THz waveform from the 1128 μm thick section of adhesive-backed Teflon on nickel-based 

superalloy with the FS, M”, and BS echoes labeled. 

(a) Thickness map (b) Velocity map 

Figure 16.—Thickness map (a) and velocity map (b) from the adhesive-backed Teflon samples on a conductive 

nickel-based superalloy substrate. 

TABLE 5.—THICKNESS MEASUREMENTS OF TEFLON ON NICKEL-BASED SUPERALLOY 

[All values shown are the mean of five locations (center and four quadrants for each thickness).] 

Micrometer measured 

thickness, 

μm 

THz thickness, 

m 

Percent 

difference 

thickness 

THz velocity, 

cm/sec 

596 574 3.7 1.95E+10 

814 814 0.0 2.02E+10 

1128 1110 1.6 1.98E+10 
NASA/TM—2013-216603 16 

Ceramic (MgO-ZrO2) Adhesive on Alumina Substrate 

To further investigate the capabilities of the method to characterize thickness and material density on 

actual coatings, ceramic adhesive was applied to alumina substrates. For the first set of samples the 

thickness was varied, while attempting to keep the material/density the same (Table 1, material 5). For the 

second set of samples attempts were made to keep the thickness uniform, while varying the material 

density (Table 1, materials 6 to 8). 

Figure 17 shows the THz thickness and velocity maps from the ceramic adhesive with varying 

thickness. Due to machining difficulties, a uniform thickness was not obtained for these samples. 

Therefore, instead of averaging the thicknesses from the center and four quadrants, as was done for the 

analysis of the previous coating systems, single thickness and velocity values from the five individual 

locations were calculated. Table 6 lists the THz thickness and velocity measurements from the five 

locations on each of the three samples. 

THz thickness measurements were obtained with percent differences between micrometer- and THzmeasured thicknesses up to 31 percent. The THz velocities varied by 13 percent, perhaps indicating that 

the microstructures were not uniform. Figure 18 shows a waveform with the FS, M”, and BS echoes 

labeled. The peak from the BS echo is not as sharp as it is for some other materials (like Teflon, as shown 

in Fig. 15). The dullness of the BS echo peak may make it difficult to find the correct time of flight 

measurements for calculating thickness. 

Figure 19 shows the THz thickness and velocity maps from the ceramic adhesive with intentionallyvarying density. Attempts were made to create a uniform thickness from sample to sample, but due to 

machining difficulties, a uniform thickness was not achievable. Therefore, single thickness and velocity 

values from the center and the four quadrant locations were calculated individually. Table 7 summarizes 

these THz thickness and velocity measurements from these samples. The estimated porosity is included 

on the table for reference. 

(a) Thickness map (b) Velocity map

Figure 17.—THz thickness map (a) and velocity map (b) from the ceramic adhesive with varying thicknesses but the 

same material (sieved ceramic adhesive). 
NASA/TM—2013-216603 17 

TABLE 6.—THz THICKNESS AND VELOCITY MEASUREMENTS OF 

CERAMIC ADHESIVE OF VARYING THICKNESS

Micrometer 

measured thickness, 

μm 

THz thickness, 

μm 

Percent 

difference 

thickness 

THz velocity, 

cm/sec 

487 582 30.2 1.00E+10 

482 612 23.2 1.13E+10 

480 552 22.9 1.09E+10 

493 462 31.0 1.07E+10 

486 522 23.9 1.10E+10 

518 400 22.8 1.06E+10 

519 400 22.9 1.03E+10 

512 370 27.7 1.03E+10 

492 340 30.9 1.00E+10 

495 340 31.3 1.03E+10 

663 550 17.0 1.13E+10 

681 550 19.2 1.13E+10 

671 490 27.0 1.13E+10 

666 520 21.9 1.11E+10 

682 550 19.4 1.09E+10 

Figure 18.—Typical fused waveform from the sieved ceramic adhesive on alumina. 

(a) Thickness map (b) Velocity map 

Figure 19.—THz thickness map (a) and velocity map (b) from the ceramic adhesive with varying material/density but 

the similar thicknesses. 
NASA/TM—2013-216603 18 

TABLE 7.—THICKNESS MEASUREMENTS OF VARYING CERAMIC ADHESIVE 

ON AN ALUMINA SUBSTRATE 

Micrometer measured 

thickness, 

m 

THz thickness,

m 

Percent difference 

thickness 

THz velocity, 

cm/sec 

Estimated porosity, 

percent 

489 428 12.5 1.30E+10 41 

504 458 9.1 1.25E+10 41 

504 428 15.1 1.33E+10 41 

510 428 16.1 1.30E+10 41 

514 458 10.9 1.30E+10 41 

465 428 8.0 1.63E+10 48 

488 428 12.3 1.46E+10 48 

489 338 30.9 1.45E+10 48 

505 458 9.3 1.58E+10 48 

523 488 6.7 1.42E+10 48 

417 338 18.9 1.45E+10 74 

428 338 21.0 1.45E+10 74 

475 368 22.5 1.45E+10 74 

480 368 23.3 1.52E+10 74 

521 309 40.7 1.58E+10 74 

(a) As received ceramic adhesive (b) Sieved ceramic adhesive with carbon 

Figure 20.—Typical fused waveforms from (a) the as-received ceramic adhesive on alumina (estimated porosity 

48 percent) and (b) the sieved ceramic adhesive and carbon black on alumina (estimated porosity 74 percent). 

Figure 20 shows the fused waveforms from the as-received ceramic adhesive on alumina (estimated 

porosity 48 percent) and the sieved ceramic adhesive and carbon black on alumina (estimated porosity 

74 percent). 

Thickness differences between micrometer- and terahertz-measured thicknesses ranged from 

7 percent up to 40 percent. The coating with the highest porosity of 74 percent also had the highest 

percent differences in thickness ranging from 19 to 41 percent. Figure 20 shows representative waveforms 

from these two material systems with the FS, M”, and BS echoes labeled. For the material system with 

the highest porosity, the valley from the BS echo (shown in Fig. 20(b)) is not as sharp as it is for some 

other materials (like Teflon, as shown in Fig. 15). The dullness (wideness and flatness) of the BS echo 

valley may make it difficult to find the correct time of flight measurements for calculating velocity. The 

average THz velocity for the material system with the sieved ceramic coating with an estimated porosity 

of 41 percent was 1.30E+10 cm/sec. This represents the average of the first five locations listed in 

Table 7. The average THz velocity for the material system with the as-received ceramic coating with an 

estimated porosity of 48 percent was 1.51E+10 cm/sec which was ~13 percent greater than the mean 

velocity for the 41 percent coating illustrating the greater velocity for a coating with more air as would be 

expected. However, this trend did not remain consistent when comparing the 48 percent porous coating 

with the 74 percent porous coating. The average THz velocity for the material system with the estimated 

porosity of 74 percent was 1.49E+10 cm/sec, approximately the same as for the 48 percent porous coating. 
NASA/TM—2013-216603 19 

8YZS Coated Nickel-Based Superalloy Samples 

The method was studied on actual thermal barrier coating (TBC) systems consisting of 8YSZ (Yttriastabilized Zirconia) coating applied to a nickel-based superalloy. The coating thicknesses, as measured by 

a micrometer, ranged from 249 to 485 m. Table 8 lists the THz thickness and velocity results from the 

eight 8YSZ-coated nickel-based superalloy samples. 

For the samples with the thinnest layers of coating ranging from 249 to 267 m, the percent 

difference from the THz thickness measurements ranged from 28 to 51 percent with the larger percent 

difference associated with the thinnest coating. These results further confirmed the result suggesting a 

practical inspection limit of 350 m that was observed with the layered paper samples and the adhesivebacked Teflon. When considering only the coating thicknesses  400 m, the micrometer- and THzmeasured thicknesses differed by 20 to 30 percent which was higher than consistently observed for the 

other coating systems. Again, considering only the coating thicknesses  400 m, the velocities varied by 

only 3.9 percent which is consistent with that expected for a uniform coating. 

The 8YSZ coated samples were notably rougher than the other samples utilized in this investigation. 

Surface roughness measurements were collected from some of the 8YZS -coated samples and the Tefloncoated samples to determine if some of the large thickness error variation could be explained by the 

surface variation. The average roughness, denoted by Ra, was calculated over a 2.5 by 1.9 mm area on 

each sample using the following formula: 

    M

j

N

k a Z jk MN

R

1 1

1 (12) 

where Zjk is the height of each pixel after the zero mean is removed and M and N are the x and y 

dimensions of the area. The surface roughness was calculated for the Teflon sample as 448.49 nm (or 

0.448 m), which represents 0.04 percent of the full thickness of 1128 m. A three-dimensional surface 

roughness image for the Teflon sample is shown in Figure 21. 

In comparison, the surface roughness from an 8YSZ coated sample identified was calculated as 

16.27 m, which represents 3 percent of the micrometer-measured thickness of 483 m. For the 267 m 

thick coating, Ra was calculated as 14.61 m, which represents 5 percent of the micrometer measured 

thickness of 267 μm. So, approximately 5 percent of the percent difference of the thickness may be 

explained by the surface roughness of the coating. A three-dimensional surface roughness image for the 

483 m thick 8YSZ coating is shown in Figure 22 with coating thickness peaks being 78 m above the 

zero mean and the valleys being 76 m below the zero mean. 

TABLE 8.—THICKNESS MEASUREMENTS OF 8YZS COATED NICKEL-BASED 

SUPERALLOY SAMPLES 

[All values shown are the mean of five locations (center and four quadrants for each thickness).] 

Micrometer measured 

thickness, 

m 

THz thickness, 

m 

Percent 

difference, 

thickness 

THz velocity, 

cm/sec 

267 342 –28.1 9.56E+09 

254 364 –43.3 1.08E+10 

485 611 –26.0 9.27E+09 

483 592 –22.6 9.25E+09 

249 375 –50.6 1.10E+10 

249 372 –49.4 1.08E+10 

452 566 –25.2 9.19E+09 

447 577 –29.1 9.38E+09 
NASA/TM—2013-216603 20 

Figure 21.—A three-dimensional surface roughness image from a Teflon-coated sample. 

Figure 22.—A three-dimensional surface roughness image from an 8YSZ-coated sample. 
NASA/TM—2013-216603 21 

Figure 23.—A fused waveform from one of the 8YSZ-coated samples with the FS, M”, and BS echoes labeled. 

The accuracy of micrometer measurements for the 8YSZ samples is questionable due to the thickness 

nonuniformity of the coating. The micrometer measurement will always be an overestimate because it 

measures the highest peak within the micrometer gauge, introducing some additional error in the 

thickness measurements. In addition, it is likely that the surface roughness caused scatter in the THz 

signal which would lower the signal to noise ratio and change the morphology of the front and back 

surface echoes. Figure 23 shows the fused waveform from the first 8YSZ-coated sample listed in Table 8. 

The morphology of the BS echo peak is not well defined and is wider than the BS echo for the Teflon 

coating system shown in Figure 15. 

Conclusion 

The applicability of a novel noncontact single-sided terahertz electromagnetic measurement method 

for measuring coating thickness in dielectric coating systems having either dielectric or conductive 

substrate materials was investigated. The method does not require prior knowledge of the material 

properties (terahertz velocity) in the coating material. However, terahertz measurement is required prior 

to coating deposition. The dielectric coatings ranged from approximately 300 to 1400 m in thickness. 

First, the method was validated on a bulk dielectric sample to determine the method’s ability to precisely 

measure thickness and density variation. Then, the method was studied on simulated coating systems. 

One simulated coating system consisted of thin layers of paper samples on a ceramic substrate. Another 

simulated coating system consisting of adhesive-backed Teflon was adhered to electrically-conductive 

and dielectric substrates. This method was proven applicable for a dielectric coating on a dielectric 

substrate. Thus, it can be utilized where eddy current methods for thickness measurement cannot be used. 

Finally, the method was studied for thickness measurement of actual thermal barrier coatings (TBC) on 

conducting ceramic substrates. 

Coating thicknesses measured with terahertz were within 0 to 10 percent of the actual coating 

thicknesses measured by micrometer for the simulated coating systems but showed much greater 

deviation from actual thicknesses for the rough-surfaced TBC-coated samples. It is thought that the rough 

surface and variable microstructure of the TBC coatings caused waveform distortion resulting is less 

accuracy of the method. It was found that use of this terahertz thickness measurement method is practical 

for coatings greater than approximately 350 m (depending on the terahertz velocity in the coating). 

Below that thickness, interference between front surface and back surface echoes resulted in difficulty 

obtaining accurate time-of-flight values needed for velocity and thickness calculation. 
NASA/TM—2013-216603 22 

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