The influence of the positive and negative defocusing on lensless ghost
imaging
Xue Zeng, Yanfeng Bai
n
, Xiaohui Shi, Yang Gao, Xiquan Fu
College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
article info
Article history:
Received 25 April 2016
Received in revised form
5 July 2016
Accepted 9 July 2016
Available online 20 August 2016
Keywords:
Ghost imaging
Defocusing length
Imaging resolution
Fidelity
abstract
Lensless ghost imaging with fully spatially incoherent source is investigated theoretically and experi-
mentally. The effects of positive and negative defocusing on lensless ghost imaging are studied by using
classical optical theory and a fully spatially incoherent source. Based on the numerical calculation and
experimental results, we find that the negative defocusing has a stronger influence on imaging resolution
when compared with that from the positive defocusing. To explain this phenomenon, the analytical
expression of point spread function with the positive and negative defocusing is presented.
& 2016 Elsevier B.V. All rights reserved.
1. Introduction
Ghost imaging which usually called correlated imaging is a
method to nonlocally image an object through spatial intensity
correlation measurement. Firstly, it was realized by using the en-
tangled photon pairs generated by spontaneous parametric down-
conversion (SPDC) in 1995 [1,2]. One of two entangled photons
travels through a reference optical imaging system, and the other
propagates through a test optical imaging system with an object
located. One can reconstruct the image of the object as a function
of the transverse position of the reference photon by measuring
the coincidence rate of these photon pairs at the reference and test
detector. Since then, the observation of this phenomenon was
studied theoretically and experimentally with entangled photons
[3–5] for the great potential applications in quantum metrology,
lithography, and holography [6–10]. These results have evoked
many controversies about whether it is necessary to realize cor-
related imaging by using quantum entanglement. Soon Bennink
et al. presented that it is not necessary by their experimental re-
sults and believed that ghost imaging with classical light is just a
point-by-point, shot-by-shot projection [11]. Gatti et al. demon-
strated theoretically that ghost imaging with truly incoherent light
can be realized [12]. Based on classical statistical optics, coin-
cidence interference with a complete incoherent light and without
lenses was studied by Cheng and Han [13]. Soon, Valencia et al.
confirmed experimentally that ghost imaging can be realized with
quasi-thermal light [14], and the group of Lugiato performed the
experiment of ghost imaging and ghost diffraction with classical
quasi-thermal light [15]. In recent years, because ghost imaging
with classical thermal light provided more potential applications
than that under an entangled source, classical correlated imaging
has been studied extensively, both theoretically and experimen-
tally [16–24]. Especially, Karmakar et al. firstly demonstrated
lensless ghost imaging with sunlight [25].
Lensless imaging system has attracted much interest in recent
years because the correlation result can be obtained without the
use of a lens anywhere in this system [16,17]. Note that the group
of Cheng investigated theoretically the effects of the source para-
meters, detector size and defocusing length on imaging quality in
a lensless ghost diffraction system [26], while the results in a
lensless ghost imaging system were not mentioned. As we all
know, the two imaging systems are similar except that the test
detector is used as a bucket detector in a lensless ghost imaging
system (while the detector is treated as a pixel-like detector in a
lensless ghost diffraction system). In this paper, intrigued by this
work, we theoretically and experimentally study the effects from
the defocusing length on imaging resolution in a lensless ghost
imaging system with incoherent light source. Based on classical
optical theory, the analytical expression describing the point
spread function (PSF) of lensless ghost imaging system with de-
focusing effect is derived. The resolution of ghost imaging is de-
pendent on the width of PSF. It is shown theoretically and ex-
perimentally that the influence of positive defocusing and nega-
tive defocusing are quite different, and the effect from the negative
defocusing is bigger. One can obtain good imaging resolution by
controlling the defocusing length. This result can also be
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journal homepage: www.elsevier.com/locate/optcom
Optics Communications
http://dx.doi.org/10.1016/j.optcom.2016.07.023
0030-4018/& 2016 Elsevier B.V. All rights reserved.
n
Corresponding author.
E-mail address: yfbai@hnu.edu.cn (Y. Bai).
Optics Communications 382 (2017) 415–420