外-内传播模型提升圆柱计算机全息图衍射计算效率

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本文探讨了"基于外-内传播模型的圆柱计算机全息图的快速衍射计算"这一主题，发表在2017年的《光学通信》(Optics Communications)第403期，296-303页。该研究论文聚焦于利用先进的显示技术，即圆柱计算机全息图(Cylindrical Computer-Generated Hologram, CCGH)，来实现具有360度视场的全视角显示器。传统的圆柱全息图采用的是内-外传播模型，然而，这存在两个主要缺点：有限的对象尺寸限制和有效的重构方法的缺乏。为了克服这些问题，作者提出了一个创新的解决方案，即运用外-内传播模型，与传统模型相反，通过改变光的传播路径，以解决图像再现的局限性。这种方法的关键在于逆转了内-外模型的传播方向，从而使得全息图能够处理更大范围的对象，并且可能提供了更高效的图像重建算法。文章的主要贡献包括新的衍射计算公式，它基于这个外-内传播模型，旨在优化圆柱计算机全息图的性能，特别是在全息显示方面。这不仅提升了图像的扩展性和清晰度，还可能对全息成像技术的未来发展产生积极影响，例如在虚拟现实(VR)、增强现实(AR)和3D显示等领域。总结来说，这篇研究论文深入分析了圆柱计算机全息图的衍射计算问题，并提出了一种创新的方法，通过改变传播模式来改进其在宽视野显示中的应用。这对于提高全息显示的效率和灵活性具有重要意义，是光学通信和计算机图形学领域的重要研究成果。

Optics Communications 403 (2017) 296–303

Contents lists available at ScienceDirect

Optics Communications

journal homepage: www.elsevier.com/locate/optcom

Fast diffraction calculation of cylindrical computer generated hologram

based on outside-in propagation model

Jun Wang

, Qiong-Hua Wang

*, Yuhen Hu

School of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China

Department of Electrical & Computer Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA

a r t i c l e i n f o

Keywords:

Diffraction theory

Computer generated hologram

Cylindrical CGH

Holographic display

a b s t r a c t

Cylindrical computer-generated hologram is a promising approach to realize a display with 360

◦

field of view.

However, conventional cylindrical hologram employs an inside-out propagation model and suffers from two

main drawbacks: limited object size and lack of effective reconstructed method. Previously, we proposed to fix

these problems using an outside-in propagation model with reversed propagation direction of the inside-out

model. We also derived corresponding diffraction calculation formula for the outside-in propagation model. In

this work, we investigate a non-constant obliquity factor in the outside-in propagation model, and show that

it is the projection of the unit complex amplitude in the propagation direction onto the outer normal of the

observation point. We then propose to apply fast Fourier transform to accelerate the convolution operation

needed for diffraction calculation. We conducted experiments on inverse diffraction and reconstruction of the

cylindrical objects. Very encouraging results demonstrate the validity of this proposed approach.

1. Introduction

Holography is a promising three-dimensional (3D) display technique

because it can record and reproduce wholistic 3D information such as a

motion parallax, a convergence, an occlusion, an accommodation, and

so on. Usually holograms are made on flat surfaces which limit the

viewing angles. This limitation can be alleviated if holograms are made

on cylindrical surfaces [1–3]. Beside a 3D display, a cylindrical geometry

is also preferred for 3D volumetric imaging, such as computed tomog-

raphy, magnetic resonance images, and integral-floating display [4].

A cylindrical computer generated hologram (CGH) can provide 360

◦

horizontal field of view (FoV) as opposed to the limited FoV offered by

the conventional planar CGH. Furthermore, the amount of data needed

in a curved hologram is smaller than that in a planar hologram for the

same range of FoV [5]. With the developments of curved display and

recording devices, a cylindrical CGH with a ‘‘look around property’’ has

attracted much attention recently.

Sakamoto et al. [6] proposed a fast calculation method for the cylin-

drical hologram of a planar object using the angular spectrum of plane

wave and the fast Fourier transform (FFT) algorithm which exploits

the rotational shift invariance property between a planar surface and

a cylindrical surface. Continue on this work, Kashiwagi and Sakamoto

generated a cylindrical hologram of 3D object by slicing it into planar

Corresponding author.

E-mail address: qhwang@scu.edu.cn (Q.-H. Wang).

segments [7]. Sando et al. [8] demonstrated the propagation from

cylindrical surface as cylindrical waves by defining wave propagation in

cylindrical coordinates. By choosing the object also to be a concentric

cylindrical surface with the hologram, the shift invariance was pre-

served, and the FFT algorithm is applicable. Jackin et al. [9] define wave

propagation in the spectral domain in cylindrical coordinates, hence one

fewer FFT operation is needed. By applying this approach, they reported

successful reconstruction of a simple 3D object [10]. For a complex 3D

object, an algorithm of wavefront recording surface for fast calculation

of cylindrical CGH was proposed by Kim et al. [11]. Different from the

previous approaches, Yamaguchi et al. [12] generated the cylindrical

holograms by segmenting the cylindrical surface into elemental plane

surfaces. They also developed a computer generated cylindrical rainbow

hologram using the same method [13]. Above mentioned methods

consider wave propagation from the inner object surface to the outer

cylindrical observation surface using an inside-out propagation (IOP)

model. Due to the limited observation or hologram surface area, the

size of object may be limited. Moreover, the IOP model also needs to

calculate the diffraction distribution, which is propagated from outside

to inside cylindrical surface, during the reconstruction process.

Previously, by placing the object surface on the outer cylinder and

observation surface on the inner cylinder, we proposed an outside-

in propagation (OIP) model [14] with opposite propagation direction

http://dx.doi.org/10.1016/j.optcom.2017.07.045

Received 8 June 2017; Received in revised form 15 July 2017; Accepted 16 July 2017

Available online 2 August 2017

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