COL 12(6), 060017(2014) CHINESE OPTICS LETTERS June 10, 2014
Data-embedded-error-diffusion hologram
(Invited Paper)
P. W. M. Tsang
1∗
and T.-C. Poon
2,3
1
Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, China
2
Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, VA 24061, USA
3
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
∗
Corresponding author: eewmtsan@cityu.edu.hk
Received April 7, 2014; accepted April 23, 2014; posted online May 28, 2014
This pap er describes a method for converting a complex Fresnel hologram into a phase-only hologram
that can be embedded with large amount of data. Briefly, each row of pixels in the hologram is scanned
sequentially in a left-to-right d irection. The magnitude of each visited pixel is set to a constant, and
its phase is embedded with the data. Subsequently, the error is diffused to the neighborhood pixels.
The phase hologram realized with such means, which is referred to as the data-embedded-error-diffusion
(DEED) hologram, is capable of preserving high fidelity on the content of the hologram and the embedded
data.
OCIS codes: 090.0090, 090.1995, 090.1760.
doi: 10.3788/COL201412.060017.
1. Introd uction
In this paper , we propos e a method to address two im-
portant issues in digital holography. The first one is the
generation of phase-only hologram, a method which is
required to overcome the practical limitation of existing
holographic display. The second issue is, how to embed
large amount of external data into a phase-only holo-
gram. We shall demonstrate that our propose d method is
capable of handling both issues. Regarding the problem
on holography display, it is well known that the thr e e -
dimensional image represented by a digital hologram can
be obs erved visually, if the holog ram can be displayed
with a complex electronic accessible device. However,
existing devices such as a spatial light modulator (SLM)
or a liquid crystal on silicon (LCoS), are only capable
of reproducing either the phase, or the magnitude of a
complex holograms. An effective way of overcoming this
problem, is through the optical integration of a pair of de-
vices for displaying the magnitude and phase (or the real
and imag inary) components of a complex hologram
[1−3]
.
Alternatively, a complex hologram can be converted into
a double phase-only holograms
[4]
, and displayed with a
pair of phase-only devices. Despite the success of this
straightforward approach, the optical setup, which re-
quires precis e alignment of two high-resolution display
devices, could b e rather cumber some. In some recent
attempts, the pair of components of a complex hologram
is presented in non-over lapping partitions on a single
device, and the wavefronts scattered from each partition
are merged with a grating
[5−8]
. Similar to the us e of a
pair of devices, the optical setups of such methods are
complicated, and the display area is reduced by 2 times.
In view of these shortco ming s, research on the generation
of Pha se-Only Hologram (PO H) has been identified as
a potential and viable solution to the above mentioned
problems. The factors that sustain such long term inter-
est are manifolds. Basically, POH can be displayed with
a single, phase-only spatial light modulator. In addition,
the reconstructed image is brighter, and also inherently
free from the zeroth-order diffractio n and the twin im-
age. However, the favorable features of the POH do not
come without a cost, as the removal of the magnitude
component of a hologram c ould lead to severe loss on the
pictorial information it represents.
Other solutions in generating POH include the adop-
tion of iterative steps to adjust the pixe l values (each
leading to a phase change to the illuminating beam that
falls on it) o f the POH progressively, so that the re-
constructed image will ultimately match with a target
image
[9,10]
. Despite the effectiveness, the c omputation
time is generally lengthy, especially if the ta rget im-
age is comprising of multiple depth planes. A complex
hologram can also be directly converted into a POH by
dropping the magnitude component, if random noise is
added to the s ource image prior to the generation of the
hologram. On the downside such approach, which is r e -
ferred to as the One Step Phase Retrieval, requires fa st
display of multiple holograms frames (each representing
the s ame so urce image, but added with different noise
signals) to suppress the effect of the added noise
[11,12]
.
Recently, it has als o be e n reported that a digital complex
Fresnel hologram can be swiftly converted into a POH
with the use of err or diffusion
[13,14]
. In this approach,
the ma gnitude of e ach pixel in the source hologram is
forced to a constant value, and the resulting error dis-
tributed to the neighboring pixels with error diffusion
[15]
.
The reconstructed image of a P OH obtained with this
method when comparing from that obtained from the
original ho logram, is very similar.
In this letter, we have adopted the error diffusion
framework for converting a complex digital hologram
into a phase-o nly hologram, as well as embedding large
amount of external data into the holog ram. Briefly, each
row of pixels in a complex, digital Fresnel hologram is
processed se quentially from the top to the bottom row.
The pixels in each row, in turn, are scanned from a
left-to-right direction. The magnitude of ea ch visited
pixel is forced to a constant value, leaving behind the
phase value of the pixel. Next, the least M digits of the
1671-7694/2014/060017(4) 060017-1
c
2014 Chinese Optics Letters