The goal of this research is online monitoring of functional electrical properties, e.g., resistance, of electronic devices made using aerosol jet printing (AJP) additive manufacturing (AM) process. In pursuit of this goal, the objective is to recover the cross-sectional profile of AJP-deposited electronic traces (called lines) through shape-from-shading (SfS) analysis of their online images. The aim is to use the SfS-derived cross-sectional profiles to predict the electrical resistance of the lines. An accurate characterization of the cross section is essential for monitoring the device resistance and other functional properties. For instance, as per Ohm’s law, the electrical resistance of a conductor is inversely proportional to its cross-sectional area (CSA). The central hypothesis is that the electrical resistance of an AJP-deposited line estimated online and in situ from its SfS-derived cross-sectional area is within 20% of its offline measurement. To test this hypothesis, silver nanoparticle lines were deposited using an Optomec AJ-300 printer at varying sheath gas flow rate (ShGFR) conditions. The four-point probes method, known as Kelvin sensing, was used to measure the resistance of the printed structures offline. Images of the lines were acquired online using a charge-coupled device (CCD) camera mounted coaxial to the deposition nozzle of the printer. To recover the cross-sectional profiles from the online images, three different SfS techniques were tested: Horn’s method, Pentland’s method, and Shah’s method. Optical profilometry was used to validate the SfS cross section estimates. Shah’s method was found to have the highest fidelity among the three SfS approaches tested. Line resistance was predicted as a function of ShGFR based on the SfS-estimates of line cross section using Shah’s method. The online SfS-derived line resistance was found to be within 20% of offline resistance measurements done using the Kelvin sensing technique.

References

References
1.
Parekh
,
D. P.
,
Cormier
,
D.
, and
Dickey
,
M. D.
,
2015
, “
Multifunctional Printing: Incorporating Electronics Into 3D Parts Made by Additive Manufacturing
,”
Additive Manufacturing
,
A.
Bandyopadhyay
and
S.
Bose
, eds.,
CRC Press
,
Boca Raton, FL
, p.
215
.
2.
Christenson
,
K. K.
,
Paulsen
,
J. A.
,
Renn
,
M. J.
,
McDonald
,
K.
, and
Bourassa
,
J.
,
2011
, “
Direct Printing of Circuit Boards Using Aerosol Jet
,”
27th International Conference on Digital Printing Technologies (NIP27) and Digital Fabrication Conference
, Minneapolis, MN, Oct. 2–6, pp.
433
436
.
3.
Huang
,
Y.
,
Leu
,
M. C.
,
Mazumder
,
J.
, and
Donmez
,
A.
,
2015
, “
Additive Manufacturing: Current State, Future Potential, Gaps and Needs, and Recommendations
,”
ASME J. Manuf. Sci. Eng.
,
137
(
1
), p.
014001
.
4.
Seifert
,
T.
,
Sowade
,
E.
,
Roscher
,
F.
,
Wiemer
,
M.
,
Gessner
,
T.
, and
Baumann
,
R. R.
,
2015
, “
Additive Manufacturing Technologies Compared: Morphology of Deposits of Silver Ink Using Inkjet and Aerosol Jet Printing
,”
Ind. Eng. Chem. Res.
,
54
(
2
), pp.
769
779
.
5.
Salary
,
R.
,
Lombardi
,
J. P.
,
Tootooni
,
M. S.
,
Donovan
,
R.
,
Rao
,
P. K.
,
Borgesen
,
P.
, and
Poliks
,
M. D.
,
2017
, “
Computational Fluid Dynamics Modeling and Online Monitoring of Aerosol Jet Printing Process
,”
ASME J. Manuf. Sci. Eng.
,
139
(
2
), p.
021015
.
6.
Rao
,
P. K.
,
Liu
,
J. P.
,
Roberson
,
D.
,
Kong
,
Z. J.
, and
Williams
,
C.
,
2015
, “
Online Real-Time Quality Monitoring in Additive Manufacturing Processes Using Heterogeneous Sensors
,”
ASME J. Manuf. Sci. Eng.
,
137
(
6
), p.
061007
.
7.
Rao
,
P. K.
,
Kong
,
Z.
,
Duty
,
C. E.
,
Smith
,
R. J.
,
Kunc
,
V.
, and
Love
,
L. J.
,
2016
, “
Assessment of Dimensional Integrity and Spatial Defect Localization in Additive Manufacturing Using Spectral Graph Theory
,”
ASME J. Manuf. Sci. Eng.
,
138
(
5
), p.
051007
.
8.
Tootooni
,
M. S.
, Dsouza, A., Donovan, R., Rao, P., Kong, Z., and Borgesen, P.,
2017
, “
Classifying the Dimensional Variation in Additive Manufactured Parts From Laser-Scanned 3D Point Cloud Data Using Machine Learning Approaches
,”
ASME J. Manuf. Sci. Eng.
, epub.
9.
Arciniegas
,
A. J. R.
,
Esterman
,
M.
, and
Cockburn
,
J. C.
,
2015
, “
Toward the Control of the EP3D Printed Surface
,”
ASME J. Manuf. Sci. Eng.
,
137
(
2
), p.
021012
.
10.
Salary
,
R.
,
Lombardi
,
J. P.
,
Tootooni
,
M. S.
,
Donovan
,
R.
,
Rao
,
P. K.
, and
Poliks
,
M. D.
,
2016
, “
In Situ Sensor-Based Monitoring and Computational Fluid Dynamics (CFD) Modeling of Aerosol Jet Printing (AJP) Process
,”
ASME
Paper No. MSEC2016-8535.
11.
Sun
,
H.
,
Wang
,
K.
,
Li
,
Y.
,
Zhang
,
C.
, and
Jin
,
R.
,
2017
, “
Quality Modeling of Printed Electronics in Aerosol Jet Printing Based on Microscopic Images
,”
ASME J. Manuf. Sci. Eng.
,
139
(7), p.
071012
.
12.
Elhabian
,
S. Y.
,
2008
, “
Hands-On Shape From Shading
,” Computer Vision and Image Processing (CVIP) Laboratory, University of Louisville, Louisville, KY, Technical Report No.
SFS08
.http://www.sci.utah.edu/~gerig/CS6320-S2015/Materials/Elhabian_SFS08.pdf
13.
Horn
,
B. K.
, and
Brooks
,
M. J.
,
1989
,
Shape From Shading
(Artificial Intelligence Series),
MIT Press
,
Cambridge, MA
.
14.
Paragios
,
N.
,
Chen
,
Y.
, and
Faugeras
,
O. D.
,
2006
,
Handbook of Mathematical Models in Computer Vision
,
Springer Science & Business Media
,
New York
.
15.
Pentland
,
A.
,
1989
, “
Shape Information From Shading: A Theory About Human Perception
,”
Spat. Vision
,
4
(
2
), pp.
165
182
.
16.
Ping-Sing
,
T.
, and
Shah
,
M.
,
1994
, “
Shape From Shading Using Linear Approximation
,”
Image Vision Comput.
,
12
(
8
), pp.
487
498
.
17.
Abada
,
L.
, and
Aouat
,
S.
,
2013
, “A Machine Learning Approach for Shape From Shading,”
Second International Conference on Signal, Image, Vision and Their Applications
(
SIVA
), Guelma, Algeria, Nov. 18–20, Paper No. arXiv:1607.03284.https://arxiv.org/pdf/1607.03284.pdf
18.
Wang
,
G.
, and
Cheng
,
J.
,
2016
, “
Three-Dimensional Reconstruction of Hybrid Surfaces Using Perspective Shape From Shading
,”
Optik-Int. J. Light Electron Opt.
,
127
(
19
), pp.
7740
7751
.
19.
Zheng
,
Q.
, and
Chellappa
,
R.
,
1991
, “
Estimation of Illuminant Direction, Albedo, and Shape From Shading
,”
IEEE Computer Society Conference on Computer Vision and Pattern Recognition
(
CVPR
), Maui, HI, June 3–6, pp.
540
545
.
20.
Zhang
,
R.
,
Tsai
,
P.-S.
,
Cryer
,
J. E.
, and
Shah
,
M.
,
1999
, “
Shape-From-Shading: A Survey
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
21
(
8
), pp.
690
706
.
21.
Horn
,
B. K.
,
1990
, “
Height and Gradient From Shading
,”
Int. J. Comput. Vision
,
5
(
1
), pp.
37
75
.
22.
Ikeuchi
,
K.
, and
Horn
,
B. K.
,
1981
, “
Numerical Shape From Shading and Occluding Boundaries
,”
Artif. Intell.
,
17
(
1–3
), pp.
141
184
.
23.
Frankot
,
R. T.
, and
Chellappa
,
R.
,
1988
, “
A Method for Enforcing Integrability in Shape From Shading Algorithms
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
10
(
4
), pp.
439
451
.
24.
Szeliski
,
R.
,
1991
, “
Fast Shape From Shading
,”
CVGIP: Image Understanding
,
53
(
2
), pp.
129
153
.
25.
Malik
,
J.
, and
Maydan
,
D.
,
1989
, “
Recovering Three-Dimensional Shape From a Single Image of Curved Objects
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
11
(
6
), pp.
555
566
.
26.
Lee
,
K. M.
, and
Kuo
,
C.-C.
,
1993
, “
Shape From Shading With a Linear Triangular Element Surface Model
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
15
(
8
), pp.
815
822
.
27.
Leclerc
,
Y. G.
, and
Bobick
,
A. F.
,
1991
, “
The Direct Computation of Height From Shading
,”
IEEE Computer Society Conference on Computer Vision and Pattern Recognition
(
CVPR
), Maui, HI, June 3–6, pp.
552
558
.
28.
Vega
,
O. E.
, and
Yang
,
Y.-H.
,
1993
, “
Shading Logic: A Heuristic Approach to Recover Shape From Shading
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
15
(
6
), pp.
592
597
.
29.
Rouy
,
E.
, and
Tourin
,
A.
,
1992
, “
A Viscosity Solutions Approach to Shape-From-Shading
,”
SIAM J. Numer. Anal.
,
29
(
3
), pp.
867
884
.
30.
Dupuis
,
P.
, and
Oliensis
,
J.
,
1992
, “
Direct Method for Reconstructing Shape From Shading
,”
IEEE Computer Society Conference on Computer Vision and Pattern Recognition
(
CVPR
), Champaign, IL, June 15–18, pp.
453
458
.
31.
Oliensis
,
J.
,
1991
, “
Shape From Shading as a Partially Well-Constrained Problem
,”
CVGIP: Image Understanding
,
54
(
2
), pp.
163
183
.
32.
Oliensis
,
J.
, and
Dupuis
,
P.
,
1993
, “
A Global Algorithm for Shape From Shading
,”
Fourth International Conference on Computer Vision
(
ICCV
), Berlin, May 11–14, pp.
692
701
.
33.
Kimmel
,
R.
, and
Bruckstein
,
A. M.
,
1992
, “
Shape From Shading Via Level Sets
,” Technion-Israel Institute of Technology, Haifa, Israel, CIS Report No. 9209.
34.
Lee
,
C.-H.
, and
Rosenfeld
,
A.
,
1985
, “
Improved Methods of Estimating Shape From Shading Using the Light Source Coordinate System
,”
Artif. Intell.
,
26
(
2
), pp.
125
143
.
35.
Durou
,
J.-D.
,
Falcone
,
M.
, and
Sagona
,
M.
,
2008
, “
Numerical Methods for Shape-From-Shading: A New Survey With Benchmarks
,”
Comput. Vision Image Understanding
,
109
(
1
), pp.
22
43
.
36.
Hedges
,
M.
, and
Marin
,
A. B.
,
2012
, “
3D Aerosol Jet Printing-Adding Electronics Functionality to RP/RM
,”
The Fraunhofer Direct Digital Manufacturing Conference
(
DDMC
), Berlin, Mar. 14–15, pp.
14
15
.https://www.optomec.com/wp-content/uploads/2014/04/Optomec_NEOTECH_DDMC_3D_Aerosol_Jet_Printing.pdf
37.
Paulsen
,
J.
,
Renn
,
M.
,
Christenson
,
K.
, and
Plourde
,
R.
,
2012
, “
Printing Conformal Electronics on 3D Structures With Aerosol Jet Technology
,”
Future of Instrumentation International Workshop
(
FIIW
), Gatlinburg, TN, Oct. 8–9, pp.
1
4
.
38.
Verheecke
,
W.
,
Van Dyck
,
M.
,
Vogeler
,
F.
,
Voet
,
A.
, and
Valkenaers
,
H.
,
2012
, “
Optimizing Aerosol Jet Printing of Silver Interconnects on Polyimide Film for Embedded Electronics Applications
,” Eighth International
DAAAM
Baltic Conference Industrial Engineering, Tallinn, Estonia, Apr. 19–21, pp.
373
379
.http://innomet.ttu.ee/daaam_publications/2012/Verheecke_1.pdf
39.
Ahn
,
B. Y.
, and
Lewis
,
J. A.
,
2014
, “
Amphiphilic Silver Particles for Conductive Inks With Controlled Wetting Behavior
,”
Mater. Chem. Phys.
,
148
(
3
), pp.
686
691
.
40.
Goth
,
C.
,
Putzo
,
S.
, and
Franke
,
J.
,
2011
, “
Aerosol Jet Printing on Rapid Prototyping Materials for Fine Pitch Electronic Applications
,”
IEEE Electronic Components and Technology Conference
(
ECTC
), Lake Buena Vista, FL, May 31–June 3, pp.
1211
1216
.
41.
Tait
,
J. G.
,
Witkowska
,
E.
,
Hirade
,
M.
,
Ke
,
T.-H.
,
Malinowski
,
P. E.
,
Steudel
,
S.
,
Adachi
,
C.
, and
Heremans
,
P.
,
2015
, “
Uniform Aerosol Jet Printed Polymer Lines With 30 μm Width for 140 ppi Resolution RGB Organic Light Emitting Diodes
,”
Org. Electron.
,
22
, pp.
40
43
.
42.
Eckstein
,
R.
,
Hernandez-Sosa
,
G.
,
Lemmer
,
U.
, and
Mechau
,
N.
,
2014
, “
Aerosol Jet Printed Top Grids for Organic Optoelectronic Devices
,”
Org. Electron.
,
15
(
9
), pp.
2135
2140
.
43.
Kopola
,
P.
,
Zimmermann
,
B.
,
Filipovic
,
A.
,
Schleiermacher
,
H.-F.
,
Greulich
,
J.
,
Rousu
,
S.
,
Hast
,
J.
,
Myllylä
,
R.
, and
Würfel
,
U.
,
2012
, “
Aerosol Jet Printed Grid for ITO-Free Inverted Organic Solar Cells
,”
Sol. Energy Mater. Sol. Cells
,
107
, pp.
252
258
.
44.
Rodriguez
,
J.
,
Lennon
,
A.
,
Luo
,
M.
,
Li
,
Z.
,
Yao
,
Y.
,
Lu
,
P.
,
Chan
,
C.
, and
Wenham
,
S.
,
2012
, “
Dielectric Patterning Using Aerosol Jet Printing
,”
J. Imaging Sci. Technol.
,
56
(
4
), pp.
40502
40509
.
45.
Vogeler
,
F.
,
Verheecke
,
W.
,
Voet
,
A.
, and
Valkenaers
,
H.
,
2013
, “
An Initial Study Into Aerosol Jet Printed Interconnections on Extrusion Based 3D Printed Substrates
,”
Strojniski Vestn.-J. Mech. Eng.
,
59
(
11
), pp.
689
696
.
You do not currently have access to this content.