Visible reconstruction by a circular holographic
display from digital
holograms recorded under infrared illumination
E. Stoykova,1,3,5,* F. Yaraş,1,4H. Kang,1,3L. Onural,1A. Geltrude,2M. Locatelli,2
M. Paturzo,2A. Pelagotti,2R. Meucci,2and P. Ferraro2
1Department of Electrical and Electronics Engineering, Bilkent University TR-06800 Ankara, Turkey
2Consiglio Nazionale delle Richerche-Instituto Nazionale di Ottica Via Campi Flegrei 34, 80078 Napoli and Largo Fermi 6, 50125 Firenze, Italy
3Currently at Korea Electronics Technology Institute (KETI), 8 Floor, #1599 Sangam-dong, Mapo-gu, Seoul 121-835, South Korea
4Currently at Qualcomm Inc., 100 Burtt Road, Suite 123, Andover, Massachusetts 01810, USA
5Bulgarian Academy of Sciences, 109 Acad. Georgi Bonchev, 1113 Sofia, Bulgaria
*Corresponding author: firstname.lastname@example.org
Received April 5, 2012; revised June 5, 2012; accepted June 5, 2012;
posted June 7, 2012 (Doc. ID 166025); published July 20, 2012
A circular holographic display that consists of phase-only spatial light modulators is used to reconstruct images in
visible light from digital holograms recorded under infrared (10.6 μm) illumination. The reconstruction yields a
holographic digital video display of a three-dimensional ghostlike image of an object floating in space where
observers can move and rotate around it.© 2012 Optical Society of America
OCIS codes: 090.1995, 090.2870, 090.4220, 110.3080.
Multiview capture of holograms together with a holo-
graphic display built from many spatial light modulators
(SLMs) widens the range of applications of digital holo-
graphy [1–3]. A circular holographic display [4,5] puts
less severe requirements to the space–bandwidth pro-
duct of the system and supports full parallax binocular
vision at an increased viewing angle. With such a display
system, observers can see three-dimensional (3D) ghost-
like images floating in space and can move and rotate
around them. Successful dynamic wide-angle optical re-
construction from computer-generated holograms using
a circular holographic display built from nine phase-only
SLMs has been recently reported . However, if the data
fed to the SLMs are retrieved from digitally recorded
holograms, the reconstruction is no longer a trivial task.
The main challenge is the difference in coding param-
eters of the recording and display systems. Here, we de-
monstrate wide-angle optical reconstruction using the
circular holographic display in  under illumination at
0.532 μm from a set of holograms recorded at 10.6 μm.
For such a case, the differences in the pixel geometries
of the light-sensitive areas of the capture and display
systems and between the wavelengths of holographic
recording and optoelectronic reconstruction strongly
alter the reconstruction distance and the lateral and
longitudinal dimensions of the reconstruction volume.
The interest in capturing holograms in the long-
wavelength infrared (IR) range arises from such valuable
features of IR digital holography as shorter recording dis-
tances, larger viewing angles, high output powers of IR
laser sources, and less stringent requirements on the
stability of the interferometric system. Furthermore,
transparency of many materials in the IR range makes
inspection of such components using long-wavelength
IR holograms feasible. The recent advances in digital im-
age sensors, such as pyrocameras and focal plane array
microbolometers with a pixel size of 25 μm and no need
of cryogenic cooling, have further improved IR digital
holography [6–8]. Digital holography at 10.6 μm, both
in transmission and reflection configurations, for optical
reconstruction of objects with sizes of less than 1 mm to
40 cm was recently investigated . A nondistorted single
SLM visualization, at 0.532 μm, from a hologram of a
bronze reproduction of the Benvenuto Cellini Perseus
sculpture with a height of 33 cm was presented in .
The hologram was recorded at 10.6 μm in a Fourier con-
figuration. The statuette was a large object with regard to
the common digital holography restrictions. For compar-
ison, in this work, we used the same test object, but with
We used a 110 W CW CO2laser, emitting at 10.6 μm and
operating at TEM00fundamental mode. We used only a
fraction (30 W) from the full power of the laser. The laser
beam had a waist of 10 mm and a divergence of 2 mrad.
For capture from different perspectives, the object was
rotated with an angular step of 3°. The holograms were
acquired by means of an ASi (amorphous silicon) thermal
camera (Thermoteknix MIRICLE 307K) with nx× ny?
640 × 480 pixels with Δ1? 25 μm pixel period. The max-
imum angle, θmax, between the reference and the object
beams to satisfy the Wittaker–Shannon sampling require-
ment for a given Δ1is found from sin
IR holograms .
(Color online) Experimental setup for the recording of
3120OPTICS LETTERS / Vol. 37, No. 15 / August 1, 2012
0146-9592/12/153120-03$15.00/0© 2012 Optical Society of America
λ1is the wavelength of recording. The minimum distance
between the object and the sensor, which is proportional
to Δ1D∕λ1if the object lateral size D is much greater than
the sensor size, decreases substantially in the long-
wavelength IR range. For the scheme in Fig. 1, the
distance between the object and the camera was z0?
880 mm. The expanding reference beam had a spherical
wavefront R1?x;y? ? exp
curvature r1? z0∕2. Here, (x ? pΔ1, y ? qΔ1, p ?
1…nx, q ? 1…ny) are the coordinates in the plane of
the sensor aperture. All spherical waves are given in
In the case of reconstruction with a SLM with a pixel
period Δ2, the recorded hologram undergoes a linear
stretching with a coefficient m ? Δ2∕Δ1. At illumination
with a wavelength λ2, the value of the angle θmaxremains
unchanged, if Δ1∕Δ2? λ1∕λ2is fulfilled. This would re-
quire Δ2? 1.25 μm for a reconstruction at 0.532 μm. For
illumination at λ2with a spherical wavefront with a ra-
dius of curvature r2, the distance ziat which the recon-
structed image is in focus is given by1
where μ ? λ1∕λ2[10,11]. For the scheme in Fig. 1, the
formula gives zi? 1.78 m for a reconstruction with
Δ2? 8 μm at illumination with a plane wave (r2→ ∞)
with longitudinal magnification Mlong?dzi
magnification, given by Mlat?μ
m ? 0.32 for plane wave illumination. Figure 2 presents
the optical reconstruction under plane wave illumination
for one of the recorded holograms. We applied spatial
filtering to suppress the zero-order and twin-image terms
 and retrieved the object wave by a multiplication
of the filter output in the spatial domain with a numerical
reference wave R?
pΔ2, η ? qΔ2, p ? 1…Nx, q ? 1…Ny) are the coor-
dinates in the plane of the SLM, and r0
The asterisk denotes the complex conjugate. The phase
of the retrieved object wave was fed into a Holoeye HEO-
1080P phase-only liquid-crystal-on-silicon (LCoS) SLM
with Nx× Ny? 1920 × 1080 pixels and Δ2? 8 μm. The
retrieved phase distribution with nx× ny? 640 × 480
with a radius of
μ. The lateral
zo, is equal to Mlat?
λ2? 2.04, where we substitute zi? zom2
2?ξ;η? ? exp
. Here, (ξ ?
pixels was placed at the center of the SLM. The phase
hologram to focus the rays reflected by them outside
the viewing zone. Figure 2 gives the photographs
of the reconstruction observed on a diffuse screen and
of the 3D image floating in space.
The multiview optoelectronic reconstruction of the
recorded nine holograms was made with a holographic
video display system built from nine phase-only Holoeye
HEO-1080P SLMs that formed a circular configuration
. Elimination of the gaps between the SLMs was pro-
vided by a beam splitter to tile them side by side (Fig. 3)
 and to achieve a virtual alignment with a continuous
increased field of view. To position the reconstructed 3D
image slightly above the display setup and to avoid block-
ing of the observer’s vision by the display’s components,
the SLMs were also tilted up at a small angle. Negligible
reduction in the quality of the reconstructions for a tilted
illumination of up to 20° has been shown by experiments
and subjective test results . All SLMs were illumi-
nated with a single astigmatic expanding wave by means
of a cone mirror :
2?ξ;η? was added to the SLM’s pixels around the
W?ξ;η? ? exp
where k2? 2π ∕λ2, Dhis the distance between the axis
of the cone mirror and the SLM, hSLMis the height of
the SLM, and Dsis the distance between the apex of
the cone mirror and the point source of the wave posi-
tioned on the line of the cone mirror axis.
The hologram computation for each of the SLMs con-
sisted of two steps: (i) retrieval of the phase distribution
Ψ?ξ;η? in the complex amplitude a?ξ;η?exp?ik2Ψ?ξ;η?? of
the object field from the recorded off-axis 8 bit encoded
digital hologram; (ii) compensation for the nonsymmetri-
cal illumination with the cone mirror and adjustment of
the reconstruction volume position. The first step implied
spatial filtering, and then we discarded the amplitude
a?ξ;η? as we used phase-only SLMs. Improvement of im-
age reconstruction was observed if the spectrum of the
phase-only term exp?ik2Ψ?ξ;η??R2?ξ;η? was filtered
again with the same filter, as presented in Fig. 2. Finally,
we multiplied the second filter output by R?
spatial domain to obtain the object field as H?ξ;η? ?
exp?ik2Ψ?ξ;η??. The distance between the reconstruction
volume and each SLM was 35 cm. To compensate for the
nonsymmetrical illumination, we computed the phase of
H?ξ;η?W??ξ;η?. Under plane wave illumination, ziex-
2?ξ;η? in the
0.532 μm of the hologram captured at 10.6 μm projected on a
diffuse screen. Right, ghostlike SLM optical reconstruction of
the same hologram.
(Color online) Left, SLM optical reconstruction at
nine phase-only SLMs, denoted as 1…9. Right, illumination of a
single SLM .
Circular holographic display. Left, arrangement of the
August 1, 2012 / Vol. 37, No. 15 / OPTICS LETTERS3121
ceeded 35 cm, and we introduced a digital converging
lens term L1?ξ;η? ? exp?ik2?ξ2? η2?∕ρ1? with a focal
distance ρ1? 43.5 cm. To separate the image from the
strong nondiffracted beam due to the pixelated nature
of SLMs (Fig. 2) , we multiplied the hologram area with
P?η? ? exp?ik2η sin θt?, where θt? 2°. The holograms
were placed at the centers of the SLMs (Fig. 4). A con-
verging lens term L2?ξ;η? ? exp?ik2?ξ2? η2?∕ρ2?, with
ρ2? 35 cm, was introduced in addition to W??ξ;η? for
the pixels outside the hologram to gather the light re-
flected from them below the reconstructed image. The
magnification of the reconstruction volume in the long-
itudinal and lateral directions was more or less the same:
Mlong? 0.078 and Mlat? 0.062. Figure 5 presents the re-
construction at 12° and the video showing the ghostlike
image captured with a camera that rotates around it
(Media 1). An optical lens was used to blend reconstruc-
tions more smoothly. The quality of the image is good,
especially in view of the small number of pixels in the
recorded holograms. Rather small details are easily
recognizable with a smooth parallax within a viewing
angle of 24°.
In conclusion, we obtained an optical reconstruction
with a circular display consisting of nine Holoeye LCoS
spatial light modulators (pixel period 8 μm) under illumi-
nation with a 0.532 μm wavelength. The reconstruction is
obtained from a set of nine holograms, which were
captured at a 20 times larger wavelength. The results
show good quality reconstructed ghostlike images for
a continuously varying parallax within a 24° viewing an-
gle, paving the way for a reliable multiview IR-recording/
holographic display can be used for virtual museum
applications; it may also lead to holographic 3D displays
for terahertz imaging.
This work is supported by the European Community
(EC) within the Seventh Framework Programme (FP7)
under Grant 216105 with the acronym Real 3D, and
the Programma Operativo Nazionale (PON) project
IT@CHA funded by the Italian Ministry of Education,
University and Research (MIUR).
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andthe noninformativezone; theobject wavefocuses abovethe
focus of rays from the noninformative pixels under illumination
with the astigmatic wave W.
Front and side views of each SLM with the hologram
struction at 0.532 μm from holograms captured at 10.6 μm. Left,
view at 12°. Right, image from a video taken with a camera that
rotates around the reconstructed image (Media 1) .
(Color online) Ghostlike SLM multiview optical recon-
3122OPTICS LETTERS / Vol. 37, No. 15 / August 1, 2012