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Predicted and measured transmission and diffraction by a metallic
mesh coating
Jennifer I. Halman*a
, Keith A. Ramseya
, Michael Thomasb
, Andrew Griffinb
a
Battelle, 505 King Avenue, Columbus, Ohio 43201
b
Spica Technologies Inc., 18 Clinton Dr #3, Hollis, NH 03049
ABSTRACT
Metallic mesh coatings are used on visible and infrared windows and domes to provide shielding from electromagnetic
interference (EMI) and as heaters to de-fog or de-ice windows or domes. The periodic metallic mesh structures that
provide the EMI shielding and/or resistive electrical paths for the heating elements create a diffraction pattern when
optical or infrared beams are incident on the coated windows. Over the years several different mesh geometries have
been used to try to reduce the effects of diffraction. We have fabricated several different mesh patterns on small
coupons of BK-7 and measured the transmitted power and the diffraction patterns of each one using a CW 1064 nm
laser. In this paper we will present some predictions and measurements of the diffraction patterns of several different
mesh patterns.
Keywords: mesh, grid, diffraction, shielding effectiveness
1.0 INTRODUCTION
Metallic mesh coatings are used on visible and infrared windows and domes to provide shielding from electromagnetic
interference (EMI) and as heaters to de-fog or de-ice windows and domes. Battelle has developed processes to apply
metallic mesh coatings to many sizes and shapes of windows and domes. The windows may be flat or curved (simple
and complex) and vary in size from several millimeters to several meters.
Metallic mesh coatings create a diffraction pattern when optical or infrared beams are incident on the coated windows.
For highly coherent radiation, the transmittance in the main lobe of the diffraction pattern of a square mesh, as shown in
Figure 1 (left), with line widths l and line spacing g is equal to the square of the ratio of the unobscured area, or mesh
open area, to the total area of the mesh.1
The total transmittance of the mesh is equal to the ratio of the unobscured area
to the total area, but the transmittance in the main lobe of a square mesh is
(1)
The remaining transmitted energy is distributed into the higher-order diffraction lobes. The secondary diffraction lobes
are separated by Δθ, where
(2)
*
halman@battelle.org, phone: 614-424-7791

2. 2
The separation between the main lobe and the secondary lobes will be less for mesh patterns with greater line separation.
A non-randomized square mesh, shown in Figure 1 (left), results in a strong diffraction pattern in the shape of a cross
when a laser is pointed at the window.
One of the goals of this study was to determine whether or not the square of the ratio of the mesh open area to the total
area can be used to predict the energy transmitted through the main beam of mesh geometries other than non-randomized
square meshes.
Figure 1 Photo of Non-randomized square mesh (left), line width: 6 µm, line spacing: 200 µm (center-to-center); Predicted
diffraction pattern (right)
The second goal of this study was to predict and measure the diffraction pattern of several different mesh geometries and
determine which geometry results in the lowest side lobe amplitudes. For coherent radiation the intensity of the main
beam cannot be increased, but the maximum intensity of the side lobes can be reduced by randomizing the distances
between the lines and circles in the patterns. The randomization reduces the side lobe peaks, redistributing the energy
between the side lobes. Randomized mesh patterns have been used to reduce the side lobe peaks in the diffraction
pattern and redistribute the energy more uniformly.
For this paper we analyzed and fabricated several different mesh patterns and measured the main beam transmittance and
the diffraction patterns of each.
2.0 APPROACH
A number of different mesh geometries have been used to reduce the effects of diffraction of metallic mesh coatings on
windows and domes. For this study, we fabricated several different mesh patterns on small coupons of BK-7. We
predicted the diffraction patterns of each mesh pattern, and then measured the main beam transmittance and the
diffraction patterns of each one using a CW 1064 nm laser.
2.1 Sample Descriptions
Four different mesh patterns were fabricated and tested for this study: non-randomized square mesh, randomized hub-
and-spoke mesh, randomized hexagon mesh, and randomized overlapping circle mesh. The line widths for all of the
patterns were nominally 6 µm. The percent of open area, or the area not obscured by the opaque metal mesh, is
approximately the same for each of these patterns. Photos of the mesh coatings on the BK-7 coupons are shown in
Figures 1 through 4. We coated three coupons with each of the four patterns.

3. 3
Figure 2 Randomized hub-and-spoke mesh, line width: 6 µm, hub outer diameter: 250 µm,
hub spacing: 400 ± 10% (center-to-center)
Figure 3 Randomized hexagon mesh, line width: 6 µm, hexagon Spacing: 225 µm (center-to-center), location of vertices
randomized ± 10%
Figure 4 Randomized overlapping circle mesh, line width: 6 µm, circle diameter: 900 µm, circle spacing: 600µm ± 10%
(center-to-center)

4. 4
2.2 Predictions
The diffraction patterns of a periodic array of rectangular holes or circles can be predicted analytically using Fraunhofer
diffraction and diffraction grating theory.2
The diffraction patterns of meshes of arbitrary geometries that may or may
not be periodic can be found from the Fourier transform of the aperture distribution function.3
The aperture distribution
function is a two-dimensional array of points in the aperture plane whose value is either 1 or 0 depending on whether or
not the aperture exists at each point in the plane.
Battelle’s diffraction prediction program creates the aperture function of an area of the mesh pattern equal to the area of
the collimated beam. It performs a two-dimensional Fast Fourier Transform on the aperture function to approximate the
diffraction pattern of each mesh pattern. Due to memory constraints on the computer we used, the beam diameter
modeled was limited to 1 mm. The predicted diffraction patterns are shown in Figures 9 through 12 along with the
corresponding measured diffraction patterns. The color scales on the predicted patterns are linear but the scale
maximum is adjusted to emphasize the side lobes.
3.0 RESULTS
We measured the power transmitted through the main beam and the diffraction pattern of each of the 12 samples.
3.1 Main beam Transmittance
We calculated the main beam transmittance by dividing the total power of the main beam by the total power incident on
the part. The transmittance of the blank substrate was 92%. The following charts show the predicted and measured main
beam transmittance corrected for reflection losses due to the substrate. In all but one measurement, the difference
between the measured and predicted main beam transmittance is less than 0.8%. The estimated uncertainty of the
measured value is +/-0.4%. The predicted open area is based on two line width measurements on each part and the
known geometry of the mesh. The effects of randomization of the mesh are not included in the predicted open area
calculation. The good agreement between the measured and predicted data confirms that the main beam transmittance is
approximately equal to the square of the ratio of the mesh open area to the total area, regardless of the mesh geometry.
Main BeamTransmittance - Square Mesh
Corrected for Substrate Losses
75.0%
80.0%
85.0%
90.0%
95.0%
100.0%
4-SQ 5-SQ 6-SQ
Part Number
Transmittance
Predicted using Open Area Squared
Measured (+/-0.4%) at 1.064 micron
89.0% 89.0%89.0%87.0% 88.8% 88.4%
Figure 5 Main beam transmittance of non-randomized square mesh

5. 5
Main Beam Transmittance - Hub and Spoke
Corrected for Substrate Losses
75.0%
80.0%
85.0%
90.0%
95.0%
100.0%
1-HS 2-HS 3-HS
Part Number
Transmittance
Predicted using Open Area Squared
Measured (+/-0.4%) at 1.064 micron
90.1% 89.2% 89.9%89.6% 89.3% 89.5%
Figure 6 Main beam transmittance of randomized hub-and-spoke mesh
Main Beam Transmittance - Hexagons
Corrected for Substrate Losses
75.0%
80.0%
85.0%
90.0%
95.0%
100.0%
10-HX 11-HX 12-HX
Part Number
Transmittance
Predicted using Open Area Squared
Measured (+/-0.4%) at 1.064 micron
89.8% 89.6% 89.8%89.1% 89.4% 90.4%
Figure 7 Main beam transmittance of randomized hexagon mesh

6. 6
Main Beam Transmittance - Overlapping Circles
Corrected for Substrate Losses
75.0%
80.0%
85.0%
90.0%
95.0%
100.0%
7-OV 8-OV 9-OV
Part Number
Transmittance
Predicted using Open Area Squared
Measured (+/-0.4%) at 1.064 micron
89.8% 89.5% 89.6%89.4% 89.4% 89.3%
Figure 8 Main beam transmittance of randomized overlapping circle mesh
3.2 Diffraction Patterns
The diffraction pattern of each sample was measured using a 7 mm diameter beam of a CW 1064 nm laser. The
diffraction pattern screen was located 157 cm down the table from the test site. A hole was cut in the screen allowing the
main laser beam to propagate through the screen rather than saturating the sensor and obscuring the diffracted
component of the laser beam. A CCD camera and commercial camera lens was used to observe the diffraction. The
image was captured using a laser beam profiling camera and associated software. The diffraction pattern was observed
from the front of the screen, and the color scale in the graph represents magnitude of the pixel counts. An image with no
diffractive sample in the beam was used as a reference and subtracted from all of the subsequent images of the
diffraction patterns to reduce the background noise on the target from scattered laser light, providing stunning images of
the diffraction. Figures 9 through 12 show the resulting diffraction patterns. Figure 13 indicates the size of the pattern.
The screen was 157 cm from the sample, so the angular range of each image shown is about +/- 0.04 radians or +/-2.54º.
Figure 9 Diffraction pattern of non-randomized square mesh, line width: 6 µm, line spacing: 200 µm (center-to-center), (left=
measured, right=predicted)

7. 7
Figure 10 Diffraction pattern of randomized hub-and-spoke mesh, line width: 6 µm, hub outer diameter: 250 µm, hub
spacing: 400 ± 10% (center-to-center) , (left= measured, right=predicted)
Figure 11 Diffraction pattern of randomized hexagon mesh, line width: 6 µm, hexagon Spacing: 225 µm (center-to-center),
location of vertices randomized ± 10%, (left= measured, right=predicted)
Figure 12 Diffraction pattern of randomized overlapping circle mesh, line width: 6 µm, circle diameter: 900 µm, circle
spacing: 600 µm ± 10% (center-to-center), (left= measured, right=predicted)

8. 8
Figure 13 Diffraction screen with scale
4.0 CONCLUSIONS
With respect to the diffraction patterns, the side lobe amplitudes of the randomized hub and spoke and randomized
overlapping circle patterns are much lower than the non-random square mesh. The energy of the side lobes has been
redistributed so that the peaks of the higher-order side lobes are reduced. It is difficult to determine from the measured
diffraction patterns whether the overlapping circle or the hub and spoke results in lower side lobe levels. The predicted
images seem to indicate that the side lobes from the overlapping circle pattern may be slightly more randomly arranged.
In some applications this may mean the overlapping circle pattern may be more desirable.
The randomized hexagon pattern is not much of an improvement over a randomized square mesh. Although we did not
measure a randomized square mesh in this study, we know from previous experience that it is similar to the randomized
hexagon pattern shown here, although the side lobes are distributed over two axes for a square mesh and three axes for a
hexagonal pattern.
As far as the percent of coherent light transmitted in the main lobe is concerned, the measured values are very close to
square of the ratio of the mesh open area to the total area for each of the four patterns studied, as expected.
Finally, the most common reason to use mesh coatings on windows is to provide radio frequency (RF) and microwave
shielding. There is always a tradeoff between shielding effectiveness and UV/visible/infrared transmittance. In most
cases it is desirable to have high shielding effectiveness and high optical and IR transmittance. In some cases low side
lobe levels are also important. The overlapping circle pattern seems to have low side lobes and the most randomly
arranged side lobes. One remaining question is whether or not there is any penalty for using the overlapping circle
pattern over the more commonly used hub-and-spoke pattern. Is the shielding effectiveness of the overlapping circles
equivalent to the hub-and-spoke if the line widths are equal and the percent open area is the same in both cases? We
hope to demonstrate the answer to this question in a future effort.
[1] Kohin, M., Wein, S.J., Traylor, J.D., Chase, R.C., Chapman, J.E., ”Analysis and Design of Transparent Conductive Coatings and
Filters”, Optical Engineering 32(5), 911-925 (1993).
[2] Elmore, William C. and Heald, Mark A., [Physics of Waves], Dover Publications, New York, Chapter 10 (1969).
[3] Goodman, Joseph W., [Introduction to Fourier Optics], McGraw-Hill Book Company, New York, 61 (1968).
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