Confocal Microscopy Studies for Plasma Surface Modified 

Films and Fibers 

by Donovan Harris and Daphne Pappas 

ARL-TR-4004 December 2006 

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ARL-TR-4004 December 2006 

Confocal Microscopy Studies for Plasma Surface Modified 

Films and Fibers 

Donovan Harris and Daphne Pappas 

Weapons and Materials Research Directorate, ARL 

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Confocal Microscopy Studies for Plasma Surface Modified Films and Fibers 

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14. ABSTRACT 

The focus of this work is plasma-treated Nylon 6 films and woven fabrics characterization by a confocal laser scanning 

microscope. The purposes of these efforts were the preliminary characterization of vendor-treated materials prior to equipment

installation and the evaluation of instrumentation capability to provide the data required in a time-effective manner. Brief 

technical discussions of the atmospheric plasma process and some of the resultant surface chemistries are presented in 

conjunction with the observed topological changes and related characterization issues. 

Results reveal that after exposure to helium nitrogen and helium acetylene plasmas under atmospheric pressure, polymer surface 

modification is achieved and carbonyl and hydroxyl groups are grafted. Moreover, the surface morphology changes, and 

rougher surfaces are created. These effects result in enhancement of the surface energy of the treated polymers and therefore 

can be used in composite systems with success. The work proves that there is a need for better correlation between the atomic 

force microscopy and the confocal laser scanning microscopy when working with similar materials and processes. 

15. SUBJECT TERMS

atmospheric plasma processing, roughness measurements 

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Donovan Harris 

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iii

Contents 

List of Figures iv

List of Tables v

Acknowledgments vi

1. Introduction 1

2. Background 1

3. Experimental 2

4. Results and Discussion 3

5. Conclusion 12

List of Symbols, Abbreviations, and Acronyms 17

Distribution List 18 
iv

List of Figures 

Figure 1. A section of Spectra woven fabric captured by the Nanoscope focusing camera. 

The camera is zoomed out to allow for rapid searching of the whole weave and for 

selection and alignment on a single fiber for analysis. ..............................................................4 

Figure 2. Two AFM height micrographs with roughness data of woven Spectra fabric fibers. 

(The micrographs were collected prior to any known camera issues.)......................................5 

Figure 3. Two AFM height micrographs showing the progression of effects caused by the 

loosening of the camera. The lack of any scale values, shown in the bottom micrograph, 

was the first indication of a problem. In the top micrograph, the image quality and data 

analysis are clearly affected.......................................................................................................6 

Figure 4. The top image is a two-dimensional (2-D) extended focus of an NIST sinusoidal 

roughness standard. The lower two images are 3-D visualizations with roughness values 

of the Z-stack data subjected to two different analysis criteria. The change in parameters 

affects the appearance of the visualizations and the roughness values......................................7 

Figure 5. Three-dimensional visualizations illustrating the effects of “plane fitting” on the 

appearance of those visualizations and the apparent surface roughness of the Nylon 6 

film.............................................................................................................................................8 

Figure 6. Three 2-D extended focus micrographs taken of nearly adjacent areas of the same 

Nylon 6 film. Notice that the parallel ridge-like features change direction, size, and 

radius of curvature from location to location. Because the only repositioning of the 

sample was done using the x-y stage controls, it is unlikely that those features are real. .........9 

Figure 7. Diagram illustrating the most likely source of the ridge structures presented in 

figure 6.......................................................................................................................................9 

Figure 8. The left image shows a 2-D extended focus micrograph of a Nylon 6 film surface 

and the right, a 3-D visualization of that same data set. The visualization has been rotated 

so the Z-axis extends up out of the plane of the paper. The two are similar in appearance 

but not identical........................................................................................................................10 

Figure 9. Three extended focus micrographs from the same plasma treated Nylon 6 film, at 

different locations. ...................................................................................................................13 

Figure 10. Comparison of the appearances between untreated and treated woven Nylon 6 

fabric fibers. The chevron-like features are artifacts from the Z-stack processing. The 

clarity of the details provided the impetus to attempt using the confocal LSM for 

roughness measurements of these samples..............................................................................14 

Figure 11. Five 3-D visualizations and the one extended focus micrograph, top center, 

illustrate one problem with producing roughness values from the fabric Z-stacks, defining 

a reliable reference plane. ........................................................................................................15 
v

List of Tables 

Table 1. Roughness data initially taken using the confocal LSM system. Only untreated 

Nylon 6 film was tested. The change in roughness values with increase in magnification 

mimics trends generally seen with stylist profilometers, but is the inverse of previous 

experiences.................................................................................................................................8 

Table 2. All the confocal LSM data generated using a 1-airy pinhole and a 10× objective is 

presented here for comparison, with discussions following. File no. 16 is physically 

larger than the available ram for the system, which consistently failed to generate any 

values for this data set..............................................................................................................11 
vi

Acknowledgments 

This research was supported in part by an appointment to the Research Participation Program at 

the U.S. Army Research Laboratory (ARL) administered by the Oak Ridge Institute for Science 

and Education through an interagency agreement between the U.S. Department of Energy and 

ARL. 
1

1. Introduction 

This report addresses the analyses of a surface roughness done in preparation for the installation 

of two atmospheric pressure plasma systems. The studied surfaces were Spectra∗

 fabric and 

Nylon 6 fibers and films, plasma treated under atmospheric pressure conditions. The plasma 

exposure results in chemical modification and activation of the surface and interesting 

morphological changes. In our case, He-N2 was utilized, and an increase of the surface 

roughness was expected. The roughness measurements were performed using contact and 

noncontact instrumentation—atomic force microscopy (AFM) and confocal microscopy. The 

report describes instrumental and sample preparation issues affecting the test data and roughness 

analysis. These methods, when coupled with surface analytical tools like x-ray photoelectron 

spectroscopy and water contact angle measurements, can give a complete picture of the plasmasurface interactions occurring during the treatment of the polymeric material and are therefore 

particularly interesting. 

2. Background 

High-strength organic fibers including polyaramid, polyamide, and polypropylene are used as 

reinforcements in polymer composite materials. However, their more widespread use is limited 

by poor interfacial adhesion to some polymer matrix materials, relative low thermal resistance, 

and low mechanical strength. Fiber-matrix adhesion in advanced composites depends on the 

physical and chemical interactions at their interface. The adhesion between the fabric and other 

materials such as epoxies, other polymers, and metals can be improved by grafting new chemical 

groups on the surfaces that will act as bridges with the other material. Moreover an increased 

roughness of the surface through a process will increase the reactive area.1 Compared to fabrics, 

polymer films also have poor adhesion properties but are easier to modify due to their geometric 

uniformity and can be used as model surfaces. 

Plasma treatment of organic materials is a technique employed to modify their surfaces and 

enhance properties such as adhesive bonding, durability, wettability, biocompatibility, and 

adhesion of dyes.2 One of the main advantages of the method is that it is a surface-oriented 

method—impact is profound at a shallow depth of the polymer surface, leaving the bulk 

practically unaffected. Plasma treatment is an alternative method to wet chemical treatments, 

 ∗

Spectra is a registered trademark of Bally Ribbon Mills. 

1Brown, J.; Mathys, Z. Plasma Surface Modification of Advanced Organic Fibres, Part V: Effects on the Mechanical 

Properties of Aramid/Phenolic Composites. J. Mater. Sci. 1997, 32, 2599. 

2

Wertheimer, M.; Fozza, A.; Hollander, A. Industrial Processing of Polymers by Low Pressure Plasmas. Nucl. Instr. Meth. 

Phys. Res. B 1999, 151, 65. 
2

provides a uniform modification, is environmentally friendly, and requires short process times. 

The energetic electrons, ions, excited atoms, molecules, and UV photons present in the gas phase 

are responsible for the surface modification, but their role in the interaction with the polymer 

surfaces is yet not fully understood due to the complexity of the gas phase and the polymer 

structure. When a polymer surface is exposed to plasma, it is bombarded by the plasma active 

species just described and leads to chain scissions and polymer degradation. If a plasma reactive 

gas is used, the appearance of new functional groups on the surface is expected. Until recently, 

low-pressure glow discharges were used to perform the modification process, requiring complex 

vacuum equipment, limited sample size, and longer process times. 

Atmospheric plasma systems are gaining popularity nowadays in order to scale up and make the 

method appealing to industrial applications. Throughput is high, reinforced by the high species 

flux obtained from high-pressure operation. 

3. Experimental 

In this work, polyamide (Nylon 6) and ultra high molecular weight polyethylene (Spectra) fibers 

and nylon films were treated under atmospheric pressure glow discharges. The effects on the 

morphology and chemistry of the material were also studied. The plasma-induced changes in 

surface chemistry, topology, and roughness were documented using x-ray photoelectron 

spectroscopy (XPS), field emission-environmental scanning electron microscope, AFM, and 

confocal laser scanning microscopy (LSM). The scope of this report is confined to the last two 

techniques, AFM and LSM, while wettability and XPS results are presented elsewhere.3, 4

The atmospheric plasma system used for the surface treatments was a Sigma Technologies large 

scale plasma system. The two electrodes of the system incorporate a porous metallic layer with 

pores of average size within one order of magnitude of the mean free path of the plasma gas at 

atmospheric pressure. The gases in this case, N2-He and C2H2-He, were injected into the 

electrode at atmospheric pressure and allowed to diffuse through the porous layer, forming a 

uniform glow discharge. Helium is typically used to initiate and generate the plasma at 

atmospheric pressure before another gas is introduced to the system. The operating frequency 

was 90 kHz, with an operating power of 850 W. 

The average diameter of Nylon 6 and Spectra fibers was 20 and 100 μm, respectively, and 

Nylon 6 films (Goodfellow) were 100 μm thick. The polymers were exposed to the plasma 

created between this electrode and a second electrode covered by a dielectric layer. All fabric 

 3Pappas, D.; Bujanda, A.; Demaree, J. D.; Hirvonen, J. K.; Kosik, W.; Jensen, R.; McKnight, S. Atmospheric Plasma 

Treatment of Polyamide Films. Proceedings of the 49th SVC Ann. Techn. Conference, Washington, DC, 22–27 April 2006. 

4

Pappas, D.; Bujanda, A.; Demaree, J. D.; Hirvonen, J. K.; Kosik, W.; Jensen, R.; McKnight, S. Surface Modification of 

Polyamide Fibers and Films Using Atmospheric Plasmas. Accepted to appear in Surf. Coat. Technol. 
3

samples were cut into 7- × 25-mm rectangular pieces. Single fiber tests were not preferred 

because the extraction of a single fiber may have resulted in an uneven distribution of finishes, 

coatings, and sizing. 

The plasma modified surfaces were subsequently treated with colloidal silica to increase surface 

roughness of the fibers. The colloidal silica particles were coupled to the modified surfaces 

using traditional organofunctional silane chemistry (3-glycidoxytrimethoxysilane, GPS).5

 

Surface roughness measurements were needed to complete a quantitative characterization of the 

effects of the different process parameters. First roughness measurements were made on plasma 

treated woven fabrics using a Digital Instruments Nanoscope IV atomic force microscope. A 

loose spring washer rendered the instrument unusable. Although Nylon 6 films were plasma 

treated by the instrument vendor, it was decided to attempt to use a Zeiss confocal laser scanning 

microscope for the balance of these initial roughness measurements. Once the roughness values 

for the films were analyzed, the plasma-treated woven fabrics were analyzed with the LSM; 

however, the outcome was unsuccessful. 

4. Results and Discussion 

AFM scans of the woven Spectra fabrics were performed in tapping mode using a tip with a 

nominal radius of 10 nm. This style of tip had worked well on glass fiber tows to measure the 

roughness differences among sizing treatments of woven mats. The plasma treatment of the 

weaves dictated using the full sample and not extracting tows for examination. An image of the 

weave crest of a single tow captured by the AFM camera at minimum magnification is shown in 

figure 1. 

The measurements were made using only the top-most fibers to avoid any possible interactions 

between the counter lever and adjacent fibers. The first results appeared to be good, as 

illustrated in figure 2. 

Figure 3 shows the first indications of the camera problem with the AFM. The nature of the 

problem was unclear at the time and unresolved until a service technician examined the system. 

The loose lock washer caused the camera zoom lens to remain at an arbitrary position between 

full in and full out, producing a false Z value for the interval between tip focus and surface focus. 

While it was possible to image, the results were nonsensical, e.g., Zμn. It became impossible to 

engage the tip. The Zeiss confocal laser scanning microscope was used with the nylon film 

samples until the AFM was repaired. 

 5

Pappas, D.; Kosik, W.; Bujanda, A.; Demaree, J. D.; Hirvonen, J. K.; Jensen, R.; McKnight, S. Wettability of Nylon Fibers 

Modified via Atmospheric Plasma Treatment and Surface Roughness. Proceedings of the 29th Ann. Meeting Adh. Soc., 

Jacksonville, FL, 19–22 February 2006. 
4

Figure 1. A section of Spectra woven fabric captured by the Nanoscope 

focusing camera. The camera is zoomed out to allow for rapid 

searching of the whole weave and for selection and alignment on a 

single fiber for analysis. 

The Zeiss LSM topography module can perform several surface roughness measurements using 

the image data from a Z-stack. The plasma-treated nylon films and the untreated control sample 

were examined using 10×, 20×, and 50× objectives and 458-, 514- and 543-nm lasers. The 

composite in figure 4 illustrates the operation of the LSM topography module. The image at the 

top is the 10× micrograph of a National Institute for Standards and Technology (NIST) standard 

reference material (SRM) 2073A sinusoidal roughness standard, Ra = 3.044 ± 0.034 μm. The 

images immediately below that image are the three-dimensional (3-D) projections of the data. 

The first visualization and data set is the calculated roughness using only the “CENTER” 

function topography correction. The apparent Ra, PSa, equals 4.351 μm. The second has had 

additional processing; the PSa roughness is 2.988 μm. The SRM data was generated at 10× and 

453 nm. 
5

Figure 2. Two AFM height micrographs with roughness data of woven Spectra fabric fibers. (The 

micrographs were collected prior to any known camera issues.) 
6

Figure 3. Two AFM height micrographs showing the progression of effects caused by the loosening 

of the camera. The lack of any scale values, shown in the bottom micrograph, was the 

first indication of a problem. In the top micrograph, the image quality and data analysis 

are clearly affected.

 
7

Figure 4. The top image is a two-dimensional (2-D) extended focus of an 

NIST sinusoidal roughness standard. The lower two images 

are 3-D visualizations with roughness values of the Z-stack 

data subjected to two different analysis criteria. The change in 

parameters affects the appearance of the visualizations and the 

roughness values. 

Based upon the full roughness standards data, table 1 shows inconsistent Nylon 6 film control 

results and unrealistic roughness values. The magnification vs. roughness relationship was the 

inverse of previous experiences with the LSM. Initially, the 514-nm laser used was based on 

having the best low power signal return. 

Fastened only at the ends, the film samples in figure 5 bowed. Efforts to use an adhesive 

covering the entire underside and flatten the specimen were unsuccessful; however, applying the 

“Cylinder Fit” function in place of the “Plane Fit” corrected the problem. 
8

Table 1. Roughness data initially taken using the confocal LSM system. Only untreated Nylon 6 

film was tested. The change in roughness values with increase in magnification mimics 

trends generally seen with stylist profilometers, but is the inverse of previous 

experiences. 

File No. Magnification Z-Stack 

(μm) 

PSc 

(μm) 

PSa 

(μm) 

PSq 

(μm) 

Pin Hole

(μm) 

Control Nylon 6 Film; 514-ηm Laser 

1 10× 30.10 15.04 0.876 1.131 139.000 

2 20× 20.30 10.146 0.537 0.676 84.000 

3 50× 6.10 3.032 0.211 0.279 131.000 

Average — — 9.406 0.541 0.695 —

Standard deviation — — 6.038 0.333 0.426 —

Figure 5. Three-dimensional visualizations illustrating the effects of “plane fitting” on the appearance of 

those visualizations and the apparent surface roughness of the Nylon 6 film. 

The 2-D extended focus surfaces shown in figure 6 contain a series of apparent ridges similar to 

those of the roughness standard shown earlier. Initially, they were identified as machining scores 

generated at the time of manufacture, but comparing adjacent areas proved that could not be the 

case. The specimen has a single orientation for all the Z-stacks collected—how could machine 

lines change direction? The most probable explanation is that the film bow caused the 

generation of those ridges. Figure 7 illustrates how the bowing of the nylon film sample would 

generate the ridge lines. 
9

Figure 6. Three 2-D extended focus micrographs taken of nearly adjacent areas of the same Nylon 6 film. 

Notice that the parallel ridge-like features change direction, size, and radius of curvature from 

location to location. Because the only repositioning of the sample was done using the x-y stage 

controls, it is unlikely that those features are real. 

Figure 7. Diagram illustrating the most likely source of the ridge structures presented in figure 6. 

Another problem was the slippage or movement of the film during the collection of the Z-stacks. 

In the 6–13 min it took to generate a stack, the film often slipped lower than the Z interval 

defined for collection. Because LSM utilizes an inverted microscope, it was not possible to 

monitor the film or adhesive tape during data generation. Keeping the pinhole equal to 1 airy 

appeared to minimize any effects on the film roughness measurements. 

The 1-airy pinholes did not fully eliminate the laser-generated pseudo ridges, as can be seen in 

both the 2-D extended focus images, and the data projections or visualizations (figure 8). Any 

effects from the pseudo ridges on the roughness values appear to have been rendered nominal by 

using the 1-airy pinholes, as document by the roughness data presented in table 2. 

Table 2 shows the roughness values for three different sets of nylon films—the control sample, 

the plasma treated under He-N2 plasma, and the plasma treated film with a deposited silicon 

oxide coating. This data appears to be an accurate reflection of the variation of surface 

topography. 
10

Figure 8. The left image shows a 2-D extended focus micrograph of a Nylon 6 film surface and the right, 

a 3-D visualization of that same data set. The visualization has been rotated so the Z-axis 

extends up out of the plane of the paper. The two are similar in appearance but not identical. 

We expect an activation process and mild surface etching due to plasma exposure. As the 

dissociation of molecular nitrogen is unfavorable, it is expected to impose Penning ionization to 

other molecules present. The role of helium is to remove any surface residing impurities and, 

through energy transfer mechanisms, cause chain scission and formation of crosslinked layers on 

the polymer surfaces. Crosslinked layers provide stability to the material and act as a barrier to 

surface changes. 

XPS results reveal that the modified surfaces exhibit a surface rich in oxygen-containing groups. 

The oxidation was also confirmed by the atomic concentration of oxygen on the surface that 

increased from 9.88% for the untreated nylon film to 13.49% for the film that was exposed to 

N2/He plasma for 4.8 s. The ratio N1s/C1s remained almost constant for all the samples treated 

under different treatment times. Similar results were observed for Nylon 6 films treated with 

nitrogen and for low-pressure treatments of polyamide fibers with oxygen plasma. In our case, 

the O1s/C1s ratio increased from 0.115 for the control film to 0.177 for the nylon film treated for 

4.8 s. It is suggested that the plasma treatment induced the formation of carboxylic species on 

the surface, either in the hydrocarbon or carbonyl groups, which finally enhanced the 

hydrophilicity of the polymer. The oxygen uptake can be attributed to the presence of atomic 

oxygen during the process, resulting from the dissociation of atmospheric O2, and the reaction of 

the resulting “active” surface obtained after the plasma modification. It is known that the plasma 

treatment is responsible for chain scission on the polymer surface and thus can react with the 

environment prior to reaching equilibrium. 
11

Table 2. All the confocal LSM data generated using a 1-airy 

pinhole and a 10× objective is presented here for 

comparison, with discussions following. File no. 16 is 

physically larger than the available ram for the system, 

which consistently failed to generate any values for this 

data set. 

File No. PSc 

(μm) 

PSa 

(μm) 

PSq 

(μm) 

Pin Hole 

(μm) 

Control 2; 543-ηm Laser 

31 9.676 1.118 1.434 73.000 

32 8.992 1.445 1.818 73.000 

33 5.889 1.506 1.862 73.000 

Average 7.783 1.312 1.648 —

Standard Deviation 2.678 0.274 0.303 —

Treated Nylon 6 Film; 543-ηm Laser 

16 — — — 73.000 

17 24.130 1.908 2.855 73.000 

18 24.141 1.908 2.850 73.000 

Average — 1.908 2.853 —

Standard Deviation — 0.000 0.004 —

Si-Treated Nylon 6 Film; 543-ηm Laser 

34 5.972 1.481 1.837 73.000 

35 1.952 1.545 1.952 73.000 

36 26.900 3.041 3.939 73.000 

37 27.053 3.635 4.161 73.000 

38 57.056 9.838 11.802 73.000 

39 8.993 1.479 1.957 73.000 

40 8.904 2.305 3.258 73.000 

41 44.973 5.893 7.575 73.000 

42 59.998 5.980 7.489 73.000 

43 44.959 3.194 4.008 73.000 

44 38.980 2.416 3.138 73.000 

45 35.971 5.115 6.618 73.000 

46 15.017 2.545 3.174 73.000 

47 32.997 3.472 4.827 73.000 

Average — 3.710 4.695 —

Standard Deviation — 2.318 2.796 —

Therefore, the observed increased roughness (1.908 μm) after plasma treatment compared to the 

control sample (1.312 μm) can be attributed to the degradation of the polymer surface and the 

etching effect due to the presence of atomic oxygen, as the process takes place in open air. The 

further increase of roughness after the deposition of the silica coating is a proof of the formation 

of a nonconformal coating on the plasma-treated nylon film. The average roughness is measured 

to be 3.710 μm, but the standard deviation is 2.318 μm. Therefore, the coating seems to not have 

the same thickness over the entire area. 
12

The large variation of the silicon-bead plasma treatment roughness data is reflected in the 

Z-stack visualizations showing a surface transformed to a series of heterogeneous zones by the 

plasma process. One series of adjacent zones and the accompanying changes in surface 

roughness is presented in figure 9. 

Based upon the LSM roughness results with the films, using the LSM to measure changes in the 

surface roughness of woven fibers was attempted. The initial raw data appeared promising, as 

illustrated by the two Z-stack extended focus images in figure 10. 

The visualizations in figure 11 show the processed data used for the roughness determinations, 

which do not approximate the actual surface. The upper left and right visualizations were 

generated using the same analysis parameters as for the nylon films. The resultant images have 

significant void areas. Using the “Fill Holes” function in the analysis software corrects the voids 

problem but generates additional features and changes the roughness data. The obvious solution 

would have been to crop the stack along the length of any single fiber. The post-processing 

software only allows a user to define rectangle extraction from the stack without any rotation. 

Only the capture software allows for rotation during the Z-stack generation process. Attempting 

to derive an analysis technique using the available functions without the AFM for support 

appeared to be an open-ended effort. Because the AFM repair was only 2 weeks away, these 

analyses were not rerun. 

5. Conclusion 

The objectives for the initial phase of the atmospheric plasma treatment program were to first 

obtain a practical working understanding of the plasma process parameters. Second was to 

establish how well our instrumentation could detect, document, and analytically quantify any 

plasma-induced changes in the materials of interest. Both of these objectives were met, but with 

varying levels of success. 

Nylon fibers and films were plasma treated with nitrogen, helium, and acetylene under 

atmospheric pressure conditions. Results revealed the improvement of the wettability of the 

surfaces, accompanied with an increase of their surface tension. The modified materials showed 

an alteration of their surface composition resulting mainly from the oxygen uptake, as confirmed 

by XPS analysis. The modified surfaces were rougher and therefore ideal for advanced 

composite systems requiring enhanced adhesive properties. 

The analysis results from the confocal LSM are the reverse of what had been anticipated. The 

10× objective produced reliably repeatable data for the nylon film samples. The 50× objective 

produced imagery clearly documenting plasma-induced changes in the woven fabrics, but could 

not provide any roughness values. For reasons presented earlier, the accuracy of the confocal 

LSM roughness values cannot be accepted as reliable as those from an AFM. 
13

Figure 9. Three extended focus micrographs from the same plasma treated Nylon 6 film, at different locations. 
14

Figure 10. Comparison of the appearances between untreated and treated woven Nylon 6 fabric fibers. The chevron-like features are a

processing. The clarity of the details provided the impetus to attempt using the confocal LSM for roughness measurements 
15

Figure 11. Five 3-D visualizations and the one extended focus micrograph, top center, illustrate one problem with producing roughness 

Z-stacks, defining a reliable reference plane. 
16

The confocal LSM proved to be the more time efficient of the two methods and thus is better 

suited to maintain the required time line for testing and analysis. An upgrade of the confocal 

LSM system will provide a 100× objective; hopefully, this will enable the relative roughness 

differences of the fabrics to be documented. The AFM will then be reserved for providing more 

accurate roughness measurement data for a select number of samples. 
17

List of Symbols, Abbreviations, and Acronyms 

Roughness 

PSc = mean height z. 

1

[1/[ * ]]* * * ( , ). = == ∑ ∑

Nx Ny

ij j

Sc Nx Ny z xi yj

Psa = arithmetic mean deviation. 

=1 1

[1/[ * ]]* * *[ ( , ) ]. == − ∑ ∑

Nx Ny

x y

i j

Sc N N z x yj Sc i

PSq = root mean square deviation. 

2

1 1

[1/ * ]]* * *[ ( , ) ] . = == ∑∑ −

Nx Ny

x y ii c i j

Sq N N z x y S

Z-stack = a series of micrographs uniformly spaced along Z-axis and stored as a single file. 

Airy Unit 

1.22* 1 . λ

AU = NA

AU = airy unit. 

NA = numerical aperture. 

λ = wavelength. 
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