Fast reconstruction of digital holograms for
extended depths of field
P. W. M. Tsang
1,
*, T.-C. Poon
2
,T.Kim
3
, and Y. S. Kim
3
1
Department of Electronic Engineering, City University of Hong Kong, Tat Chee Avenue,
Kowloon, Hong Kong SAR, China
2
Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, VA 24061, USA
3
Dept of Optical Engineering, Sejong University, 209, Neungdong-ro, Gwangjin-gu, Seoul, South Korea
*Corresponding author: eewmtsan@cityu.edu.hk
Received March 21, 2016; accepted May 5, 2016; posted online June 13, 2016
Past research has demonstrated that a static, three-dimensional (3D) object scene can be directly recorded as a
complex digital hologram. However, numerical reconstruction of the object scene, which may comprise multiple
sections located at unknown distances from the hologram, is a complicated and computation-intensive process.
To the best of our knowledge, we propose, for the first time, a low complexity method that is capable of recon-
structing a complex hologram, such that sections at different depths in the 3D object scene can be automatically
reconstructed at the correct focal distances and merged into a single image for an extended depth of field. We
demonstrate an order of magnitude increase of the depth of field for binary objects. With the use of a graphical
processing unit, the reconstruction of a 512 × 512 complex hologram can be accomplished in about 100 ms,
equivalent to around 10 frames per second.
OCIS codes: 090.0090, 090.1995, 090.1760.
doi: 10.3788/COL201614.070901.
Digital holography
[1]
is a powerful technique that enables
a three-dimensional (3D) object scene to be recorded as
a complex digital hologram. Phase-shifting holography
(PSH) and optical-scanning holography (OSH) are the
common methods used to obtain complex holograms
[2,3]
.
However, PSH is a coherent technique, whereas OSH can
either be configured to operate in a coherent mode or
an incoherent mode. OSH has been applied in many
disciplines, such as remote sensing
[4]
, fluorescence micros-
copy
[5,6]
, and 3D image recognition
[7]
. In any case, a complex
digital hologram obtained by PSH or OSH can be recon-
structed with a filter matched to a particular depth to pro-
vide an in-focus image that is located at a particular depth
distance or a depth section from the hologram. However,
apart from the capturing range (which is determined by
the setting of the digital holographic system), in general,
there is no prior information on the location of the object
points in the 3D space. Hence, methods that assume a cer-
tain geometrical distribution in the object scene, such as a
tiled plane approach
[8]
, are not applicable. The rest of the
object scene that does not reside in the reconstructed sec-
tion will appear as a de-focused haze. An effective method
to overcome this problem, which is referred to as “ blind
sectional image reconstruction,” has been reported in
Refs. [
9,10]. In this approach, filters matched to a range
of depth distances are applied to reconstruct the discrete
image sections from the hologram at regularly spaced,
focal distances. Each section corresponds to a physical
plane of the object scene that is either empty or housing
at least one object point. Next, edge detection and analy-
sis are performed to associate a non-empty object plane
with one of the reconstructed sections. This process is
known as “focus estimation.” Finally, an in-focus image
of the object points represented in each section is recon-
structed through an iterative optimization process.
Integrating the reconstructed images in all the sections
result in a view of the 3D object scene with an extended
depth of field. Recently, the optimization process has
been simplified with an iterative shrinkage-thresholding
algorithm
[11]
. Despite the success achieved in Refs. [9–11],
the iterative optimization process is complicated and
computationally intensive. A faster, non-iterative method
is reported in Ref. [
12]. Instead of employing the iterative
optimization process, the edge analysis technique is ap-
plied to extract the in-focus image in each reconstructed
non-empty section. The downside of the method in
Refs. [
9,10,12] is that edge analysis is employed in focus
estimation, based on the assumption that the edge count
in a local region is weakest when an image area is in
focus. However, edge detection and analysis are sensitive
to the image content, and the effectiveness is affected by
the correct choice of parameters, such as the threshold
value for deciding the existence of an edge point. The
problem is even more severe in Ref. [
12], as a similar
strategy is employed to select the in-focus image contents
from the correct non-empty sections.
In this Letter, we report a novel technique to recon-
struct a 3D image of the object scene with an extended
depth of field from a complex hologram generated by
OSH. Our method can be divided into 2 stages. First, a
sequence of uniformly spaced discrete image sections, each
corresponding to a vertical plane of the object scene
located at a unique distance from the hologram, is recon-
structed. Second, a decision rule is applied to select, for
COL 14(7), 070901(2016) CHINESE OPTICS LETTERS July 10, 2016
1671-7694/2016/070901(4) 070901-1 © 2016 Chinese Optics Letters
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