Reduction of the defocusing effect in lensless
ghost imaging and ghost diffraction with
cosh-Gaussian modulated incoherent sources
CHAO DUAN,YANFENG BAI,* LINGLI TANG,SUQIN NAN,QIAN SHEN, AND XIQUAN FU
College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
*Corresponding author: yfbai@hnu.edu.cn
Received 3 August 2017; revised 26 September 2017; accepted 9 October 2017; posted 9 October 2017 (Doc. ID 304033);
published 2 November 2017
The inhibition effect from the cosh-Gaussian modulated incoherent source on the defocusing effect is investigated
theoretically in lensless ghost imaging (LGI) and ghost diffraction (LGD) systems. The corresponding numerical
simulations are presented to show the influen ce of the cosh-Gaussian incoherent source on the defocusing effect in
LGI and LGD. Compared with the widely used Gaussian incoherent source, it is shown that the defocusing effect
in LGI and LGD can be greatly weakened by properly adjusting the modulation parameter ω of the cosh-
Gaussian source. To explain this phenomenon, the analytical expression for point spread function of the
LGI system with the cosh-Gaussian source is derived.
© 2017 Optical Society of America
OCIS codes: (110.1650) Coherence imaging; (030.1640) Coherence; (100.2960) Image analysis; (140.3300) Laser beam shaping.
https://doi.org/10.1364/AO.57.000B20
1. INTRODUCTION
Ghost imaging (GI), also known as correlated imaging, is a
method to nonlocally image an object through spatial intensity
correlation measurement. Ghost interference and GI were first
observed in 1995 by using entangled photon pairs arising from
spontaneous parametri c downconversion (SPDC) [1,2]. These
results led to a very lively debate on the question of whether or
not quantum entanglement is necessary to realize correlated im-
aging. Soon, Bennink et al. first demonstrated experimentally
that it was not necessary [3]. The theoretical demonstration of
GI with truly incoherent light was reported by Gatti et al. [4].
A great advantage of using an incoherent source is that it can be
used to image without a lens, which is very useful in many ap-
plications. Cheng and Han first investigated coincidence inter-
ference with a completely incoherent light and without a lens,
which can be applied to x-ray diffraction [5]. A year later,
Valencia et al. confirmed experimentally that GI could be
realized with pseudothermal light [6]. And Ferri et al.
performed the experiments of GI and ghost diffraction with
classic pseudothermal light in the same year [7]. Compared
with an entangled source, GI with classical thermal light
provides more potential practical applications. That is why
many works have been focused on GI with thermal sources.
In recent years, many different aspects of GI have been studied,
such as computational GI [8], compressive GI [9], differential
GI [10,11], high-order GI [12], and normalized ghost imaging
(NGI) [13].
The defocusing effect is an inevitable phenomenon
during the optical imaging process. According to previous stud-
ies, the existence of the defocusing effect can highly degrade
imaging quality [14–16]. However, the method of reducing
the defocusing effect in a lensless imaging system is rarely
mentioned. As we know, a glass rod is inserted into a longer
arm, and the clear image can be formed by designing the length
of the glass rod [17]; however, one needs to know the length
difference between the two arms. Thus, how to weaken the
defocusing effect should be restudied. In this paper, we present
a detailed discussion about the effect of the cosh-Gaussian
modulated incoherent source on the defocusing effect in
lensless ghost imaging (LGI) and lensless ghost diffraction
(LGD) systems. Based on the classical optical theory, the
analytical formula of the point spread function (PSF) of an
LGI system with the cosh-Gaussian source is derived. It is
shown that the cosh-Gaussian modulated incoherent source
can significantly improve imaging quality of LGI and
LGD under the condition of existing defocusing. Especially,
by properly increasing the modulation parameter ω, the quality
of ghost-image and ghost-diffraction patterns under the
defocused condition can be improved better than that under
a nondefocused condition. Therefore, a cosh-Gaussian source
B20
Vol. 57, No. 7 / March 1 2018 / Applied Optics
Research Article
1559-128X/18/070B20-05 Journal © 2018 Optical Society of America