Complementary computer generated holography for
aesthetic watermarking
Christophe Martinez,* Olivier Lemonnier, Fabien Laulagnet,
Alain Fargeix, Florent Tissot and Marie Françoise Armand
CEA, LETI, MINATEC campus, DOPT, SIONA, 17 rue des Martyrs, Grenoble, 38054, France
*
christophe.martinez@cea.fr
Abstract: We present herein an original solution for the watermarking of
holograms in binary graphic arts without unaesthetic diffractive effect. It is
based on the Babinet principle of complementary diffractive structures
adapted to Lohmann-type computer generated holograms. We introduce the
concept and demonstrate its interest for anti-counterfeiting applications with
the decoding of a hidden data matrix. A process of thermal lithography is
used for the manufacturing of binary graphic arts containing complementary
computer generated holograms.
2011 Optical Society of America
OCIS codes: (090.1760) Computer holography; (220.3740) Lithography; (050.5080) Phase
shift; (050.1220) Apertures.
References and links
1.
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4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
A.W. Lohmann, and D.P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6,
1739-1748 (1967).
D. Leseberg, and O. Bryngdahl, “Computer-generated rainbow holograms,” Appl. Opt. 23, 2441-2447
(1984).
M. Gerspach, S. Noehte, and S. Borsmüller, “Holographic polymer data storage medium as a security
label,” Photonik International., 30-32 (2009).
J.H.M. Neijzen, E.R. Meinders, and H. van Santen, “Liquid immersion deep-UV optical disc mastering for
Blu-Ray disc read-only memory,” Jpn. J. Appl. Phys. 43, 5047-5052 (2004).
E.R. Meinders, R. Rastogi, M. van der Veer, P. Peeters, H. El Majdoubi, H. Bulle, A. Millet, and D. Bruls,
“Phase-transition mastering of high-density optical media,” Jpn. J. Appl. Phys. 46, 3987-3992 (2007) .
Y. Usami, T. Watanabe, Y. Kanazawa, K. Taga, H. Kawai, and K. Ichikawa, “405 nm laser thermal
lithography of 40 nm pattern using super resolution organic resist material,” Appl. Phys. Express 2, 126502
(2009).
K. Kurihara, C. Rockstuhl, S. Petit, Y. Yamakawa, and J. Tominaga, “Plasmonic devices with controllable
resonances - an avenue towards high-speed and mass fabrication of optical meta-materials,” J. Microsc.
229, 396-401 (2008).
K. Kurihara, Y. Suzuki, K. Suto, N. Shiba, T. Nakano, and J. Tominaga, “Wettability control using largearea nanostructured film,” Microelectron. Eng. 87, 1424-1427 (2010).
C. Martinez, A. Fargeix, O. Lemonnier, B. Martin, M. Armand, and R. Templier, “Blu-Ray mastering
process applied to the manufacturing of computer generated holograms,” in Digital Holography and ThreeDimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWD5.
http://www.opticsinfobase.org/abstract.cfm?uri=DH-2009-DWD5
B. R. Brown, and A.W. Lohmann, “Complex spatial filtering with binary masks,” Appl. Opt. 5, 967-969
(1966).
W.H. Lee, “Binary computer-generated holograms,” Appl. Opt. 18, 3661-3669 (1979).
P. Chavel, and J.P. Hugonin, “High-quality computer holograms - problem of phase representation,” J. Opt.
Soc. Am. 66, 989-996 (1976).
J.P. Allebach, “Representation-related errors in binary digital holograms: a unified analysis,” Appl. Opt. 20,
290-299 (1981).
G. Tricoles, “Computer generated hologram: an historic review,” Appl. Opt. 26, 4351-4360 (1987).
L.B. Lesem, P.M. Hirsch, and J.A. Jordan, “Kinoform - a new wavefront reconstruction device,” IBM J.
Res. Develop. 13, 150-155 (1969).
C.B. Burckhardt, “Use of a random phase mask for the recording of Fourier transform holograms of data
masks,” Appl. Opt. 9, 695-700 (1970).
17. N. C. Gallagher, J. C. Angus, F. E. Coffield, R. V. Edwards, and J. A. Mann, “Binary phase digital
reflection holograms : fabrication and potential applications,” Appl. Opt. 16, 413-417 (1977).
18. A. W. Lohmann, and S. Sinzinger, “Local Babinet effect,” J. Opt. Soc. Am. A 9, 1154-1158 (1992).
19. J. Chatelain, and G. Priuli, “Vieux objets en bois de la montagne,” Ed. Glenat (2004).
1. Introduction
In addition to the intrinsic vibratory nature of light propagation, an image can be seen as a
harmony of spatial vibrations. As in music, coding techniques based on frequency
decomposition can be elaborated to produce and reproduce images. The development of
digital technologies has allowed a large implementation of this concept, for example in image
compression such as jpeg coding. Computer generated holography is another singular
example of image coding techniques that was elaborated at the very beginning of the digital
era [1]. In computer generated holography, the spatial vibrations of an image are coded
according to their occurrences. While this coding is done through numerical algorithms based
on mathematical and physical concepts, decoding is performed via physical phenomenon of
light diffraction. In this respect, it differs both from digital holography that uses the inverse
process of physical recording and digital recovery and from optical holography based on light
propagation for coding/decoding.
The complexity in designing, manufacturing and decoding of computer generated
holograms (CGHs) has driven this technology to security applications. For example, rainbow
holograms are commonly used in credit cards and bank-notes and allow a direct visual control
of the product authenticity [2]. As the counterfeiter's capacities improved, more and more
sophisticated CGH solutions were elaborated. Furthermore, new configurations that need
specific decoding instruments have been presented recently [3].
All current hologram-based anti-counterfeiting technologies have the common point of
using diffraction grating based components. As a result, the visual aspect of the anticounterfeiting marks exhibits rainbow color effects that can both degrade the aesthetic of the
product to be protected and betray the location of the marks. Here we present an original
solution that overcomes both these problems. It is based on the traditional Lohmann type
CGH and allows an invisible watermarking of a hologram in aesthetic graphic artworks.
First, we explain in section 2 a direct laser thermal lithography process used to
manufacture anti-counterfeiting marks. Then we describe in section 3 the basic concepts of
Lohmann type CGH with special focus on an elliptical cell encoding technique. The principle
of complementary holography that allows the watermarking of certification data into graphic
artworks is described in section 4. Finally, section 5 is devoted to experimental results,
followed by the conclusion.
2. Thermal lithography
Since beginning of the 2000s, advanced lithographic technologies have been developed for
Blu-ray read only memory mastering [4, 5]. The structuring of the pits at a scale below the
optical diffraction limit is necessary for this purpose and is particularly difficult to implement
when high production throughput is required. The use of phase transition material has rapidly
appeared as a good alternative as it avoids the cumulative photoreaction effects encountered in
photo resist and allows super-resolution through the non-linear thermal response of the
material [6]. This technology has also been employed for various applications [7, 8]. Recently,
we have demonstrated its interest for CGH manufacturing [9].
Figure 1 introduces the principle of thermal lithography. A Phase Transition Material
(PTM) is thermally modified by a laser exposure. The modified part of the layer is then etched
by an appropriate etching agent. Figure 1c shows an AFM view of a PTM layer after exposure
of various laser scans with 200 nm period. The quasi instantaneous thermal change of the
layer allows the fabrication of structures smaller than the spot size at a laser linear velocity as
high as Vlin = 25 m/s [6].
Fig. 1. Principle of thermal lithography on PTM: (a) PTM modification under laser exposure,
(b) PTM layer after etching, (c) AFM view of a PTM layer after various laser exposure scans,
before etching.
The writing setup used in our work is shown in the Fig. 2. We have modified a Laser Beam
Recorder dedicated to Blu-ray mastering to allow 2D maskless lithography. A 405 nm high
speed modulated laser (frequency modulation up to 500 MHz) is focused on the surface of a
wafer through a high numerical aperture lens (0.9 NA). To achieve repeatable exposure the
focus depth is controlled to +/- 50 nm.
The lens is translated slowly upon the rotating wafer so that the laser spot follows a spiral
trajectory with a period y smaller than the minimum feature size. A high precision linear
optical encoder gives a precision of a few nanometres on the translation of the lens. A
constant angular velocity is monitored by 50 000 pulses per round trip optical encoder.
A monitoring computer calculates real-time, once per revolution of the wafer, the laser
pulse sequence corresponding to the watermarking of the image I in the graphic artworks G.
Fig.2. Schematic view of the Laser Beam Recorder used to manufacture graphic artworks with
embedded holograms. The images G and I, visually and holographically reproduced for
demonstration are shown on the left.
3. Computer generated holography
3.1. Generality
Computer generated holography was first described in a significant paper of Brown and
Lohmann in 1966 [10]. Their approach was intuitive with a basic concept of great clarity. This
concept was formulated in a more analytical form in 1967 [1] and widely studied since then
[11-14].
This idea uses Fraunhofer diffraction to generate an image I from a hologram structure
defined by the function h. As Fraunhofer diffraction can be described by Fourier
transformation, function h has to be related to the complex Fourier transform of the image.
The inverse problem to be solved involves the design of an appropriate structure that
introduces the needed phase and amplitude modification of the optical beam.
The technological process presented in this paper is based on the structuring of a thin
metallic layer deposited on a glass wafer. Our technology enables the realization of binary
amplitude holograms. We thus leave out of the scope of the present paper all the phase
holograms like kinoform [15].
Two general options are possible when dealing with binary amplitude holograms [14].
First is to consider the hologram as a binary interferogram built with elementary gratings or
fringe elements (nondetour phase holograms) [11]. This solution presents some drawbacks
for our application as shown in section 4. The second option comprising the original Lohmann
detour phase holograms was preferred.
In detour phase holograms, h function is divided into elementary cells that contain a
diffraction pattern C. Each cell diffracts an elementary wave with the phase and the amplitude
tuned by the offset d and the size wx, wy of the pattern C with respect to the cell size  (Fig.
3). The hologram can be seen as a 2D pattern grating with "defects" in the x pattern location,
so that diffraction has vanished on the corresponding diffraction orders [10]. Randomly
distributed defects would produce a ghost shadow on these diffraction orders. In the case of
computer generated holography, the pattern offsets are calculated to form the image I.
Fig. 3. (a) Principle of the coding of phase and amplitude of a hologram by the size and the
location of an elliptical pattern in a cell of size . (b) Principle of the manufacturing of a
hologram pattern with direct laser writing system.
3.2. Hologram recovery
The hologram recovery is based on Fraunhofer diffraction with the use of a Fourier lens. In
the scope of our watermarking control application, the accessibility of the hologram must be
as easy as using a mobile reader. Hence, we have chosen a reflection configuration for the
recovery. The optical setup is shown on Fig. 4. A cube beam splitter directs the laser beam
towards the hologram and redirects the diffracted signal towards the Fourier lens. An image
sensor is placed at focal distance of the lens so that the signal on the sensor is the Fourier
transform of the hologram.
When a plane wave is incident on the hologram, each pattern diffracts an elementary
wave. Due to the periodic structure of the hologram, the signal interferes in phase in the
diffraction orders of the grating.
Fig. 4. Optical setup used to read the hologram
Figure 5 shows an illustration of the hologram recovery of the image I. The central
focused laser beam corresponds to the zero order diffraction 0/0 contribution of the hologram.
It is represented by an Airy function. As no phase perturbation is introduced in the y direction
of the patterns, the diffraction orders 0/-1 and 0/+1 in the y direction also lead to focused spots
separated from zero order by f/, with f being the Fourier lens focal length and  being the
laser wavelength.
The hologram recovery is performed in the x diffraction orders +1/0 and -1/0. Due to the
discrete form of the hologram function h, the image I is periodically distributed on a f/ grid.
The numerical aperture of the optical beam fixes the resolution /2NA on the image sensor.
As the hologram recovery is valid for the two conjugated diffraction orders, two symmetrical
images distributions are superimposed around zero order.
The detection of the recovered image I on the image sensor is constrained by various
factors. First of all is the presence of a focalized bright central spot, corresponding to zero
order. The useful image must be located as far as possible from this noise generator and from
the secondary spots corresponding to 0/-1 or 0/+1 grating diffraction orders. Another
limitation comes from the imaging field, reduced by the numerical aperture of the Fourier lens
(NA 0.2 here). To optimize the detection, an offset dx, dy is introduced in the hologram
design.
3.3. Hologram design
CGH with detour phase are generally designed with a rectangular pattern [14]. In our case we
used elliptical patterns with sizes wx and wy that are easy to implement in our laser writing
system. A binary hologram function H is expressed in the hologram plane (xh,yh) by the sum
of the N x N patterns distribution on a  periodic grid:
 x  n  d nm   yh  m  
H  xh , yh    Cnm  xh , yh    D 2 h
,2

wxnm 
wynm  
n,m
n ,m 
(1)
Where D is the circular aperture function:
D x , y   1
if
 0 if
x2  y 2  1
x2  y 2  1
(2)
Fig. 5. Simulation of the recovered intensity in the plane of the imaging sensor.
Fraunhofer diffraction is described by the Fourier transform of the field located in the
hologram plane. The field diffracted from the hologram is then given on spatial frequencies x
and y as follows:




H  x , y    Cnm  xh , yh  e2 i xh x  yh y dxhdyh
n ,m
(3)
The integral representation of the Bessel function and the properties of dilatation and
translation of the Fourier transform are used to develop Eq. (3) into the following expression:

J    2 i  x d nm   2 i  x n  y m

H  x , y    wxnm wynm 1
e
e
2

n ,m 



(4)
Where J1 is the first Bessel function and   wxnm2  x 2  wynm2  y 2
The diffracted field is calculated at the focal plane of a Fourier lens in the vicinity of first
diffraction order. Spatial frequencies are replaced by discrete spatial coordinate: x = 1/+
k/N and y = k/N, with k, l = 1...N. As a common approximation, the first term in Eq. (4) is
considered as continuous around x = 1/and y = 0 [1]. Equation (4) can then be expressed
as a Discrete Fourier Transform (DFT):
H
   Anme nm e
kl


n ,m 
l
k

2 i  n m 
N
N

(5)
With the following amplitude and phase functions:
A

nm
wynm
J  .wxnm 
1
2
 nm  2 .d nm
(6)
(7)
The diffracted field is associated with an image I coded in the hologram so that equations
for the amplitude and phase of the hologram h are given by:
 I nm 
(8)
 I nm   dx  n  dy  n
(9)

A
 mod  DFT
nm



 nm  arg  DFT
In Eq. (9) normalized coefficients dx and dy are used to tune the image location on the
hologram recovery field as noted above (dx = -0.25 and dy = -0.5 in Fig. 5).
Digital representation h is transferred into the metallic layer by direct laser writing. The
writing resolution is dependent on a longitudinal resolution x in the laser displacement
direction and a radial resolution y in the perpendicular direction (Fig. 3b).
In this work, we used a laser track pitch y = 200 nm and a longitudinal resolution x = 50
nm. With a cell size  = 5 µm and reference ratio wy/wx = 3, the hologram amplitude could be
sampled on 256 values (Fig. 6) and the phase on /x = 100 values.
The hologram function h was calculated with the use of a random phase mask [16]. This
gave a randomly distributed layout of the amplitude with medium value 0.25 as shown on the
amplitude histogram of Fig. 6. The medium pattern was about 8.5% of the cell surface.
Fig. 6. Radius coefficients wx and wy distribution (resp. green and blue curve) and normalized
histogram of the hologram function (orange bars).
4. Complementary holography
4.1. General concept
Lohmann type CGHs are interesting because the patterns C are relatively small as illustrated
before. Consequently they generate very little diffraction visual effects as compared to
nondetour phase holograms. The drawback is a generally low diffraction efficiency for the
hologram recovery.
In order to mix the hologram of an image I and a high resolution graphic artworks G, an
obvious solution would consist in designing a hologram structure H' with opaque cells
corresponding to the black pixels of a superimposed graphics: H' = H x G. However the
recovery of hidden image I with the resulting truncated hologram could be difficult to obtain
due to the decay in the overall diffraction efficiency.
To overcome this drawback we present the concept of complementary holography. The
binary graphics G carries the hologram patterns in both its white and black pixels. To allow
the correct recovery of the watermarked image, the Babinet principle of complementary
diffractive structures was implemented.
4.2 Principle
Figure 7 introduces the general principle of complementary CGH. In the left part of the figure
is presented a hologram cell with its elliptical pattern. The hologram phase coding is
performed via lateral offset d of the pattern as described before. The mapping of the
diffractive opaque patterns is given by the binary transmittance function H1 of the hologram h.
The image on the center of the figure shows the same cell of the complementary hologram
function H2 = 1 - H1.
Fig. 7. (a) CGH cell with an elliptical pattern. (b) Same hologram cell with contrast inversion.
(c) Same hologram cell with contrast inversion and phase correction.
A plane wave E diffracted by the hologram H1 allows the recovery of the image I. This
can be expressed by the straightforward relation:
E xh , yh H1 xh , yh I  xs , ys 
(10)
Same relation is given in the case of the complementary hologram H2:
E  xh , yh H 2  xh , yh  
E  xh , yh 1 H1 xh , yh  
   xs , ys  I  xs , ys     xs , ys  I  xs , ys ei
(11)
The term  is related to the non diffracted part of the wave that gives a Dirac impulse in
the Fourier field. Equation (7) shows that the diffraction of H2 gives the same result than H1
except for a  phase shift as stated in Babinet principle and as pointed out by N. C. Gallagher
et al. for the design of phase digital reflection holograms [17] and by Lohmann et al. on the
study of the local Babinet effect [18].
Let's consider H'', a mix of complementary hologram cells H1 and H2 given by the
graphics analogical function G:
H   H  G  H  1G 
1
2
(12)
This hologram allows the visual rendering of the graphics but the recovery of the hidden
image is jeopardized by a destructive interference between H1 and H2. In practice, the image I
can't be recovered.
To overcome this effect a  phase shift offset is introduced in the hologram by modifying
the location of the diffractive pattern as shown in the Fig. 7c. As a result, the new hologram
function H3 is equivalent to the function H1 in terms of diffraction. This graphic hologram H'''
can be defined by:
H   H  G  H  1G 
1
3
(13)
The hologram H''' theoretically allows both a visual rendering of the graphics G and a
recovery of the hidden image I.
We must underline here the particular interest of detour phase holograms in relation to the
principle of complementary holography that limits its implementation to Lohmann type
holograms. Thanks to the concept of the phase offset d, the structures H2 and H3 diffract with
a  phase shift. On the contrary, the complementary representation of a nondetour phase
hologram does not allow the application of the Babinet principle: due to its sinusoidal
definition, a  phase shifted interferogram diffracts with the same phase as the complementary
interferogram.
5. Experimental results
For the purpose of demonstration, we have chosen a complex binary graphic artworks G
reproduced from the Alpine cultural heritage [19] and an image I, 800x800 pixels, including a
data matrix and logos from our research institute for the watermarking (Fig. 2).
Figure 8a shows a macroscopic photography of the graphic arts viewed in reflection
(reflective PTM part in white, transparent substrate in black). Very little rainbow effects are
observed and the hologram watermarking is not noticeable. The 800x1400 pixels image G
was reproduced with a pixel of 5 µm. Figure 8b shows a microscopic view of the graphic arts
that reveals the embedded complementary hologram with cell size 5 µm.
Fig. 8. (a) Macroscopic photography of graphic arts G. (b) Microscopic view of complementary
hologram structure H'''.
To validate the concept of complementary computer generated holography we fabricated
four hologram structures with the thermal lithographic process presented in section 2. Each
hologram was tested under same conditions, except for the laser intensity, with the setup of
Fig. 4. A data matrix reader was used to test the decoded hologram quality. Figure 9 shows
the image sensor acquisition for all hologram structures.
First hologram (a) is a uniform hologram structure H = H1 without any graphic artwork
superimposed. The recovery of image I is visually good and the data coded in the data matrix
are recovered with a symbol contrast of 45 %.
Second hologram (b) corresponds to the case H' where the hologram structure is erased in
the opaque part of the graphic arts. As explained before, about half of the hologram is
truncated so that the overall diffraction efficiency is dramatically decreased. Image I is hardly
visible and the data matrix can't be decoded even at high laser intensity.
Third hologram (c) represents the hologram structure H'' of Eq. (8). In this case about half
of the hologram structure is out of phase and destructive interferences prevent the image
recovery.
Finally, fourth hologram (d) is the complementary hologram H''' of Eq. (3) where the
diffractive effect of the Babinet principle is anticipated. The visual rendering of the hologram
recovery is as good as in the first case. The data matrix can be decoded with a symbol contrast
of 38 %, very close to the optimal case shown in Fig. 9a.
Fig. 9. Result of hologram recovery on the imaging sensor: (a) uniform hologram H, (b)
truncated hologram H', (c) out of phase hologram H'', (d) complementary hologram H'''.
6. Conclusion
We have demonstrated the application of Babinet principle to the design of Lohmann type
CGH for very discrete watermarking of data in graphic artworks. A quasi random distribution
of small elliptical diffracting micro patterns avoids the visual diffractive effects usually
generated by grating based holograms. The complementary design of the hologram maintains
its diffractive efficiency at a very high level despite the watermarking. Therefore embedded
data such as data matrix can be decoded using a simple reflective optical setup.
This concept has been experimentally demonstrated using a maskless direct laser writing
system based on optical disk mastering technology. A Phase Transition Material was used as a
metallic layer for the thermal lithographic process.
The lithographic process and the patented concept of complementary computer generated
holograms is currently employed by Arnano, a French company dedicated to the design and
the manufacturing of aesthetic anti-counterfeiting marks, in particular for luxury watches
(contact@arnano.fr).
Acknowledgements
This work has been financially supported by Arnano and by regional funding from the
"Région Rhône-Alpes".