Real-time three-sensitivity measurements
based on three-color digital
Fresnel holographic interferometry
Patrice Tankam,1Qinghe Song,1,3Mayssa Karray,1Jun-chang Li,1,2,3
Jean Michel Desse,4and Pascal Picart1,2,*
1Laboratoire d'Acoustique de l'Université du Maine (LAUM) and the National Center For Scientific Research (CNRS),
Université du Maine, Avenue Olivier Messiaen, 72085 Le Mans, France
2École Nationale Supérieure d’Ingénieurs du Mans (ENSIM), rue Aristote, 72085 Le Mans Cedex 9, France
3Kunming University of Science and Technology (KUST), Kunming, 650093, China
4Office National d’Etudes et Recherches Aérospatiales (ONERA), 5, Boulevard Paul Painlevé, 59045,
*Corresponding author: pascal.picart@univ‑lemans.fr
Received April 2, 2010; revised May 21, 2010; accepted May 25, 2010;
posted June 2, 2010 (Doc. ID 126474); published June 9, 2010
This Letter presents a method for real-time 3D measurements based on three-color digital holographic interfero-
metry. The optical setup is considerably simplified, since the reference beams are combined into a unique beam.
A convolution algorithm allows the three monochrome images to be superposed to provide simultaneous full-field
3D measurements. Experimental results confirm the suitability of the proposed method.
090.0090, 090.1995, 090.1705, 090.2880, 100.2000, 100.3010.
© 2010 Optical Society of
Digital color holography was recently demonstrated by
Yamaguchi et al. . The authors showed the possibility
ofreconstructingthree-colorimages. Since then,an inter-
est for digital color holography has developed, especially
for full-field contact-less metrology. For example, the use
posed in [2,3] to visualize the flow events in one sighting
direction. On a smaller scale, Kuhn et al.  proposed the
use of two-color digital holography to measure the step
height and the surface profile of a micro-object with a
microscope. Multidimensional mechanical deformation
measurements are topics that have stimulated a lot of
of 3D deformation was first described in . Double-
exposure holograms were recorded and spatially multi-
plexed on a photographic plate and then physically
ysis. Schedin et al. proposed a 3D dynamic deformation
line to destroy the coherence of the laser. The setup was
sional measurement was first proposed recently using a
two-color digital Fresnel hologram . Note that the pro-
blem of reconstructing digital color holograms has been
solved according to different ways [7–9]. The advantage
setup can be considerably simplified compared to a setup
methods, eachreferencewave along eachcolor has suita-
must be adjusted separately. Furthermore, owing to the
spatial multiplexing, the occupation of the useful band-
width cannot be optimal, which thus degrades the spatial
first demonstration of real-time 3D deformation measure-
sensor. The method results in a 3D measurement of the
out any loss of spatial resolution. Three-color holograms
may thus be simultaneously recorded by using a simple
experimental scheme without any need for sequential re-
cording or spatial multiplexing of holograms. To achieve
continuous diode-pumped solid-state lasers (red line R at
λR¼ 671 nm,greenlineGatλG¼ 532 nm,andbluelineB
atλR¼ 457 nm).Thecolorsensorconsistsofacolorcam-
single 8 bit per channel digital output, including ðM;NÞ ¼
ð1060;1420Þ pixels with pitches px¼ py¼ 5 μm. Each la-
beam, which are copolarized for each wavelength. Each
collimated laser beam illuminates the object under inter-
est with θR, θG, and θBangles, respectively, for the red,
green, and blue lines leading to the three sensitivities.
The R and G beams are included in the fx;zg plane,
whereas the B beam is included in the fy;zg plane. The
R, G, and B reference beams are combined into an unique
reflects the B beam and transmits the G beam; the second
one reflects the G and B beams and transmits the R one
(Fig. 1). The smooth plane reference waves are produced
Thus, the three reference beams impact the sensing area
with the same incidence angle. Off-line holographic re-
cording is carried out by translating the object perpendi-
cularly to the optical axis of quantities ðx0;y0Þ to produce
spatial frequencies ðuλ0;vλ0Þ ¼ ðx0=λd0;y0=λd0Þ . The
© 2010 Optical Society of America
June 15, 2010 / Vol. 35, No. 12 / OPTICS LETTERS 2055
mechanical object under interest, sized ΔAx× ΔAy¼
25 × 35 mm2, is placed at a distance d0¼ 1630 nm from
the color sensor. The spatial frequencies and recording
distance are optimized for the blue line to fulfill the Shan-
non theorem for the three holograms . Thus, the
variablesweresetatðx0;y0Þ ¼ ð−56:9 mm;−52:1 mmÞ,gi-
ving ðuR0;vR0Þ¼ð−52:1mm−1;−47:7mm−1Þ, ðuG0;vG0Þ ¼
ð−65:6 mm−1;−60:1 mm−1Þ, and ðuB0;vB0Þ¼ð−76:4mm−1;
square area, sized 40 × 40 mm2, sampled with ðK;LÞ ¼
lows the method described in . The transverse magni-
ficationthatmustbeputintothealgorithmisγ ¼ 0:23;the
curvature radius of the numerical spherical reconstruct-
reconstruction distance is dr¼ −γd0¼ −374:9 mm, for
each wavelength. The reader may look at  for further
details on the reconstruction process.
The object is illuminated from three directions, which
produces three sensitivity vectors and, subsequently, a
three-sensitivity measurement. The relation between the
displacementvectorU ¼ uxi þ uyj þ uzkandtheillumina-
ting geometry is Δφλ¼ 2πU · ðKλe− KoÞ=λ for each wave-
length, where Keis the illuminating vector (depending on
θR,θG,θB)and Kotheobservation vector.In the setup,we
have Ko≅ k, KRe¼ sinθRi − cosθRk, KGe¼ −sinθGi
−cosθGk,andKBe¼ −sinθBi − cosθBk.Invertingthesca-
lar product leads to each individual displacement compo-
gital color holograms according to Eq. (1):
1 þ cosðθGÞ
−1 − cosðθRÞ
sinðθGÞð1 þ cosðθBÞÞ=sinðθBÞ
sinðθRÞð1 þ cosðθBÞÞ=sinðθBÞ
beams. In the setup, the angles are adjusted to θR¼ 31°,
θG¼ 31°, and θG¼ 45°. Figures 2(a)–2(c) show, respec-
volution algorithm with the previous reconstruction
parameters. The convolution algorithm adapts the size
of the objects so that the superposition of the three holo-
construction of a three-color image or the reconstruction
image obtained by averaging the individual R, G, and B in
pared to a raw monochrome image. To validate the
suitability of the proposed method, holograms with only
R, G, and B lights were recorded. For the first mechanical
α ¼ sinðθRÞð1 þ cosðθGÞÞ þ sinðθGÞð1 þ cosðθRÞÞ
loading, we recorded six holograms: three holograms for
R-G-B sequential illuminations and three holograms for
RGB simultaneous illuminations. The same process was
putation of the 2 × 6 holograms, six phase changes along
the R, G, and B channels were computed and unwrapped.
Figures 3(a)–3(c) show, respectively, the R, G, and B
wrapped phase changes computed between two recon-
structed RGB color holograms at two different loadings.
Figure 3(d) shows the G wrapped phase change issued
from the two monochrome G holograms. A good corre-
spondence with Fig. 3(b) can be seen, including simply a
computed first with thefull simultaneousRGB holograms
ror maps were obtained by subtracting for each displace-
ment component the three-color measurements from the
one-color ones. For the applied loading, Fig. 4(d) shows
the measured error probability density for the three dis-
placement components fux;uy;uzg, superposed to a
fitting of the curves with a Gaussian modeling. Standard
deviations are found to be σux¼ 0:13 μm (2.94%), σuy¼
0:17 μm(2.34%),andσuz¼ 0:03 μm(0.73%).Theprobabil-
ity density plots are quite close to the Gaussian fitting.
These results show that the standard deviation is quite
SF,spatialfilter;d0¼ 1630 nm;x0¼ −56:9 mm;y0¼ −52:1 mm.
(Color online) Experimentalsetup:M1–M5,flatmirrors;
2056 OPTICS LETTERS / Vol. 35, No. 12 / June 15, 2010
along the x and y components, although the standard de- Download full-text
fields. These results validate the method.
In conclusion, this Letter presents a three-color digital
holographic method for real-time 3D deformation mea-
surements. The setup is considerably simplified, because
a unique reference beam can be used to simultaneously
record the three-color digital holograms, without any
images may be superposed. Furthermore, a high-quality
image of the object can be obtained by averaging the in-
dividual monochrome images. The application of the
method to real-time 3D measurement shows satisfactory
results compared with a pure sequential monochrome
measurement, which validates the concept. To the best
of our knowledge, this Letter proposes the first demon-
on three-color digital Fresnel holography.
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objects using convolution algorithm. (d) Monochrome image
obtained by averaging the individual R, G, and B images.
(Color online) (a) R, (b) G, and (c) B reconstructed
changes computed using three-color holograms. (d) G-only
wrapped phase change.
(Color online) (a) R, (b) G, and (c) B wrapped phase
obtained form the set of data. (d) Measured probability density
error for the real-time 3D measurement: solid curve,experimen-
tal; dashed curve, Gaussian fit.
(Color online) (a)–(c) displacement field fux;uy;uzg
June 15, 2010 / Vol. 35, No. 12 / OPTICS LETTERS 2057