使用局部角-时间扩展函数滤波恢复Rotman透镜近场图像

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"该文探讨了基于局部角-时间扩展函数(Angle-Time Spread Function, ATSF)的滤波方法在解决Rotman透镜近场图像复原问题中的应用。Rotman透镜作为一种实时微波/毫米波成像技术，由于近场目标散射导致的非平面波散焦现象，使得成像质量下降，图像出现模糊。为解决这一问题，文中提出了使用ATSF滤波技术来减少离焦模糊，以此提高图像的角分辨率和径向分辨率。通过模拟和实际测量验证，该方法能显著改善Rotman透镜的近场成像效果。此外，文中引用了多个关于功率分配器设计和微波技术的研究，进一步支撑了所提方法的技术背景。" 本文详细阐述了基于局部角-时间扩展函数的滤波方法在Rotman透镜近场成像系统中的应用。Rotman透镜因其独特的并行多波束特性，被广泛视为实时微波/毫米波成像的一个潜在解决方案。然而，在近场成像时，由于来自目标的散射波不再是平面波，导致Rotman透镜的束端口出现模糊，严重影响成像质量。为了克服这个挑战，研究者提出了利用ATSF滤波技术来处理这一问题。ATSF是一种可以有效定位和分析信号在角度-时间空间分布的工具，通过这种滤波方法，可以有针对性地减少由非平面波散射引起的离焦模糊，简化图像去模糊过程。通过这种方法，不仅能够提升恢复图像的清晰度，还能同时增强角度和径向方向上的分辨率。文章中列举了若干篇关于微波和光学技术的研究文献，如可变功率分配器、紧凑型三端口功率分配器、频率补偿的rat-race耦合器以及可重构的微带贴片天线等，这些文献反映了滤波技术和微波元件设计的最新进展，为理解所提方法提供了必要的理论和技术支持。通过模拟和实验结果的对比，文章证明了使用ATSF滤波方法可以显著提升Rotman透镜近场图像的复原质量，从而提高了成像系统的性能。这一成果对于微波成像领域，特别是Rotman透镜的应用具有重要意义，为优化近场成像效果提供了新的思路和技术手段。

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 63, NO. 5, MAY 2015 2353

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Near-Field Image Restoration for Rotman Lens

by Localized Angle-Time Spread Function-Based

Filtering Method

Min Yu, Deshuang Zhao, Yuanwei Jin, and Bing-Zhong Wang

Abstract—Rotman lens is a prospective device for real-time

microwave/millimeter-wave imaging by virtue of its parallel multi-

beam functionality. For imaging purposes, a Rotman lens intrinsically

requires that the scattered waves arriving at the array be plane waves.

However, this requirement cannot be met in near-ﬁeld imaging appli-

cations, as the scattered waves from targets in the near ﬁeld defocus at

the beam ports of the lens because of the nonplane wave scattering. As

a result, out-of-focus blurs appear in the near-ﬁeld images, thus leading

to degradation of picture quality. To address this problem, we propose

a localized angle-time spread function (ATSF)-based ﬁltering method to

reduce out-of-focus blurs. With the proposed method, the deblurring pro-

cess becomes simple for a Rotman lens. Both simulations and experiments

were performed. The results show that the proposed method signiﬁcantly

improves the quality of near-ﬁeld images with enhanced resolutions in

both angular and radial directions.

Index Terms—Image restoration, near-ﬁeld imaging, out-of-focus blur,

Rotman lens.

I. INTRODUCTION

Rotman lens is generally r egarded as a low-cost beam-forming net-

work for designing parallel multibeam arrays [1]–[3], retro-directive

arrays [4], and spatial Fourier transform devices [5]. Due to the parallel

Manuscript received December 08, 2013; revised February 02, 2015;

accepted February 16, 2015. Date of publication February 27, 2015; date of cur-

rent version May 01, 2015. This work was supported by the National Natural

Science Foundation of China under Grant 61371106, Grant 61331007, and

Grant 61201089). The work of Y. Jin was supported in part by the U.S. National

Science Foundation under Grant CMMI-1126008 and in part by the Army

Research Ofﬁce under Grant W911NF-11-1-0160. (Corresponding author:

D. Zhao.)

M. Yu, D. Zhao, and B-Z. Wang are with the School of Physical Electronics,

University of Electronic Science and Technology of China, Chengdu 610054,

China (e-mail: dszhao@uestc.edu.cn).

Y. Jin is with the Department of Engineering and Aviation Sciences,

University of Maryland Eastern Shore, Princess Anne, MD 21853, USA.

Color versions of one or more of the ﬁgures in this communication are

available online at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TAP.2015.2408362

multibeam formation functionality, researchers have recently found

that Rotman lens is a promising candidate for real-time microwave

or millimeter-wave imaging applications [6]. Real-time imaging has

important applications in many ﬁelds. However, these lens systems are

typically limited to far-ﬁeld imaging, because their parallel multibeam

formation is based on the condition that the scattered waves arriving at

the array are plane waves. In the near ﬁeld, the nonplane waves scat-

tered from a near-ﬁeld target will spread across several beam ports of

the Rotman lens. As a result, out-of-focus blurs appear in the near-ﬁeld

images.

In optical imaging systems, out-of-focus blurring is a common

problem. For image deblurring, ﬁltering is usually employed to restore

the images by utilizing point spread function (PSF) to model the out-

of-focus signals [7], [8]. PSF is deﬁned as the spatial response of an

imaging system to a point source. This function can characterize the

out-of-focus blurring of ideal point objects. However, when it comes

to modeling the blurs in the near-ﬁeld images by a Rotman lens using

PSFs, two important factors must be considered: the blurs are time-

angle-dependent and the blurs vary along the radial distance. These

two factors are quite different from the blurring effects that occur in

optical imaging systems, thus posing challenges to Rotman lens.

Furthermore, the performance of a real-time imaging system is

often limited by computational time. Most of the existing algorithms,

such as back-propagation [9], [10], virtual-echo projection [11], and

propagation back-propagation [12], can be applied to near-ﬁeld imag-

ing problems in principle. However, the high computation cost of

calculating the Green’s functions for these algorithms make the sys-

tems unsuitable for the real-time applications [13], [14]. Here, we

attempt to facilitate the Rotman lens with simultaneous real-time near-

ﬁeld and far-ﬁeld imaging capability. Therefore, fast algorithms are

desired for the imaging systems.

In this communication, a fast ﬁltering method is developed for that

purpose. This method is based on a Weiner ﬁltering approach devel-

oped by the localized angle-time spread functions (ATSFs). Although

other ﬁlters such as the direct inverse ﬁlter, the geometric mean ﬁlter,

and the constrained least-square ﬁlter can be utilized, our preliminary

results show that the direct inverse ﬁlter works poorly as the noise

levels increase. The other two ﬁlters have a better performance than

the direct inverse ﬁlter, but their design procedure is more complex.

Due to space limitation, we present only the results by the Weiner

ﬁltering methods. To verify our method, we conduct both simula-

tions and experiments using a fabricated microstrip Rotman lens and

demonstrate its superior performance in image deblurring.

II. F

AR-FIELD IMAGING PRINCIPLE OF ROTM A N LENS

Fig. 1 shows the photograph of a fabricated microstrip Rotman lens

used for this study. The lens is fabricated on a 1.5-mm-thick FR4

substrate with a size of 300 mm × 320 mm. The relative dielectric con-

stant of the substrate is 4.5. The frequency range is from 3 to 8 GHz.

The lens consists of a lens cavity, 14 antenna ports, 11 beam ports,

and 4 dummy ports. The lens cavity is used to focus the incident

waves on the beam ports. The antenna ports (A1–A14) are for physical

connection to a 273-mm aperture array with a uniform inter-element

spacing of 21 mm. The beam ports (B1–B11) are for receiving the sig-

nals from the lens cavity. The dummy ports (D1–D4) are terminated

with loads for absorbing inter-cavity reﬂections. The delay lines are

designed to compensate for the phases of the incoming waves from

different angles. A comprehensive description of Rotman lens design

can be found in [15] and [16].

See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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