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### 高对比度各向异性边缘增强技术无阴影效应的研究 #### 一、研究背景与意义本文介绍了一种高对比度各向异性边缘增强技术，该技术在图像处理领域具有重要意义。边缘增强技术广泛应用于工业检测、天文观测以及指纹识别等领域。传统的边缘增强方法，如傅里叶滤波法和希尔伯特变换方法，虽然能够实现一定的边缘增强效果，但在实际应用中存在一些局限性，比如暗场方法由于部分吸收导致大部分功率被衰减。为了解决这些问题，研究人员提出了一种新的方法——基于贝塞尔类复合涡旋滤波器的高对比度各向异性边缘增强技术。 #### 二、研究内容本研究的主要内容包括设计一种新型的贝塞尔类复合涡旋滤波器，用于实现高对比度且功率可控的各向异性边缘增强，同时避免了阴影效应，并降低了背景噪声。通过抑制系统点扩散函数的旁瓣，有效地减少了背景噪声，提高了图像边缘的对比度至0.98。通过保持滤波过程中的径向对称性彻底消除了阴影效应，使边缘更加清晰，提升了图像分辨率。此外，通过引入两个相反涡旋滤波器组件之间的加权因子，使得边缘增强的功率变得可控。 #### 三、研究方法与结果 - **滤波器设计**：研究人员设计了一种贝塞尔类复合涡旋滤波器，它能够实现高对比度的各向异性边缘增强，同时避免了阴影效应。滤波器的设计考虑了径向对称性和功率控制。 - **背景噪声抑制**：通过优化滤波器的设计，特别是抑制系统点扩散函数的旁瓣，有效减少了背景噪声，提高了图像的质量。 - **阴影效应消除**：通过保持滤波过程中的径向对称性，完全消除了阴影效应，使得边缘更加清晰，增强了图像的整体效果。 - **功率可控**：引入一个加权因子来调整两个相对涡旋滤波器组件之间的关系，从而实现了边缘增强功率的可控性。 - **实验验证**：通过数值模拟和实验验证，证明了所提出的滤波器能够实现更高的对比度边缘增强，适用于相位对比和幅度对比的对象。 #### 四、研究贡献 1. **技术创新**：提出了一种新颖的贝塞尔类复合涡旋滤波器，克服了传统边缘增强技术的局限性。 2. **性能提升**：通过抑制背景噪声和消除阴影效应，显著提高了图像边缘的对比度和清晰度。 3. **应用广泛**：该技术不仅适用于工业检测和天文观测等专业领域，还可以扩展到其他需要高质量图像处理的应用场景。 #### 五、结论与展望本研究成功地开发出了一种高对比度各向异性边缘增强技术，能够在不产生阴影效应的情况下提高图像边缘的对比度。通过抑制背景噪声和保持滤波过程中的径向对称性，该技术有效地解决了传统边缘增强技术存在的问题。未来的工作将探索该技术在更多领域的应用潜力，并进一步优化滤波器的设计，以满足不同应用场景的需求。

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Research Article

Vol. 58, No. 34 / 1 December 2019 / Applied Optics G351

High-contrast anisotropic edge enhancement free

of shadow effect

Zhongzheng Gu,

Da Yin,

Shouping Nie,

Shaotong Feng,

Fangjian Xing,

Jun Ma,

3,4

AND Caojin Yuan

1,2,

Jiangsu Key Laboratory for Opto-Electronic Technology, School of Physics and Technology, Nanjing Normal University, Nanjing, 210023, China

Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing, 210023, China

School of Electronic Engineering and Optoelectronic Techniques, Nanjing University of Science and Technology, Nanjing, 210094, China

e-mail: majun@njust.edu.cn

*Corresponding author: yuancj@njnu.edu.cn

Received 26 June 2019; revised 20 October 2019; accepted 21 October 2019; posted 22 October 2019 (Doc. ID 371110);

published 21 November 2019

We propose a Bessel-like composite vortex ﬁlter to perform high-contrast and power-controlled anisotropic edge

enhancement with shadow-effect-free and low background noise. The background noise, which is commonly

found and strongly decreases the ﬁltered image quality in previous anisotropic vortex ﬁlters, is effectively reduced

by suppressing the side lobes of the system point spread function, thereby increasing the image edge contrast to

0.98. The shadow effect is totally eliminated by keeping the radial symmetry of the ﬁltering process, which makes

edges sharper and improves image resolution. By introducing a weighting factor between two opposite vortex

ﬁlter components, the power of edge enhancement becomes controllable. Numerical simulations and experimen-

tal results prove that the proposed ﬁlter achieves higher-contrast edge enhancement for both phase-contrast and

https://doi.org/10.1364/AO.58.00G351

1. INTRODUCTION

Edge enhancement techniques have been widely employed

in industrial inspection [1,2] astronomical observation [3,4],

and ﬁngerprint identiﬁcation [5,6]. Fourier ﬁltering and

Hilbert transform methods are often used to implement edge

enhancement. The dark-ﬁeld method related to Fourier ﬁlter-

ing operations attenuate most power owing to being partially

absorptive [7]. Vortex ﬁltering based on Hilbert transform has

attracted increasing attention for its sensitivity to the gradient of

the complex refractive index of an object, which leads to strong

edge contrast enhancements for both phase-contrast [8,9] and

amplitude-contrast objects [10,11]. Isotropic edge enhance-

ment [12,13], which enhances the object edges regardless of its

orientation, is always adopted to demonstrate the effect of scalar

vortex ﬁlter. For biomedical and condensed matter samples and

objects, a vector vortex ﬁlter is used to perform edge enhance-

ment [14,15]. However, in practical applications, where the

local features of some edges are of more interest than those of

others, anisotropic edge enhancement techniques should be

employed to emphasize these edges.

Currently, anisotropic edge enhancement is commonly

achieved by introducing fractional topological charge [16,17],

off-axis vortex [18,19], and vortex phase with astigmatism [20].

It is worth noting that an apparent shadow effect appears in the

output plane once the radial symmetry of the ﬁltering process is

broken. Therefore, the results obtained by the above methods

are always not satisﬁed. A superposed vortex ﬁlter made up of

the superposition of two opposite vortices is also proposed to

perform anisotropic edge enhancement [21]. However, the side

lobes by the diffraction light from the line dislocations and the

sharp aperture edge of the superposed vortex ﬁlter will worsen

the image quality. Although side lobes causing background noise

have been partially eliminated in isotropic ﬁlters by Laguerre–

Gaussian spatial ﬁlter (LGSF) [22] and Airy spiral phase ﬁlter

(AiSF) [23], those in anisotropic ﬁlters still need to be solved.

Additionally, the vector vortex ﬁlter shows good performances

in anisotropic edge enhancement [24,25], but the superﬂuous

side lobes still exist, and the polarization state needs to be care-

fully regulated [26–28]. Therefore, it is necessary to design an

anisotropic ﬁlter to obtain high-contrast edge enhancement

with shadow-effect-free and low background noise.

In this paper, we propose a Bessel-like composite vortex

ﬁlter (BLCVF), which can be used to achieve high-contrast

anisotropic edge enhancement for phase-contrast and

amplitude-contrast objects. By modifying amplitude distri-

bution with Bessel-like function, the side lobes of the ﬁlter

are almost completely suppressed, according to the numerical

analysis of the point spread function (PSF). Moreover, without

G352 Vol. 58, No. 34 / 1 December 2019 / Applied Optics

Research Article

breaking the radial symmetry of the ﬁeld, the proposed ﬁlter

achieves high-contrast anisotropic edge enhancement in dif-

ferent directions. Innovatively, the edges in different directions

can be independently enhanced in varying power. Compared

with previous anisotropic edge enhancement with vortex ﬁl-

ters, the proposed BLCVF can achieve higher-contrast and

power-controlled anisotropic edge enhancement.

2. THEORETICAL ANALYSIS

A typical 4 f -imaging system employed to implement edge

enhancement is shown in Fig. 1, where the object plane,

the Fourier plane, and the image plane are represented by

o(r

, θ

), O(ρ, φ), and o

, θ

), respectively. The object

plane and the Fourier plane are located at the front and the rear

focal planes of the lens L1, respectively. The BLCVF is located at

the Fourier plane. Similarly, the image plane is located at the rear

focal plane of the lens L2.

At the Fourier plane, the object spectrum F [o(r

, θ

)] is

obtained, where the symbol F [] denotes the Fourier transform.

After being modulated by BLCVF at the Fourier plane, the

optical ﬁeld can be written by multiplying the object spectrum

with transmittance function T(ρ, φ) of the ﬁlter. It can be

Fig. 1. Schematic diagram of the 4 f imaging system.

expressed as

O(ρ, φ) = F [o(r

, θ

)] × T(ρ, φ). (1)

The transmittance function T(ρ, φ) of the proposed ﬁlter can

be given by

T(ρ, φ) =

(αρ)

circl





× {c exp[il(φ + φ

)] + exp[−il(φ + φ

)]}, (2)

where J

is the second-order Bessel functions of the ﬁrst kind,

and α denotes the modulation parameter. The item circl(ρ/R

)

describes a circular ﬁlter aperture with radius R

. The value of

the circular aperture function equals to zero when |ρ| is larger

than R

. The last term is the superposition of a positive and a

negative vortex, i.e., exp[il(φ + φ

)] and exp[−il(φ + φ

)],

where the topological charge l is an integer and 0 ≤ φ < 2π.

Via the Fourier transform, the PSF of the 4 f system in polar

coordinates can be written as

t(r

, θ

) = −

2π

λ f



c exp[il(φ + φ

)] − exp[−il(φ + φ

)]



(αρ)J



2πρr

λ f



dρ,

(3)

where (r

, θ

) represents polar coordinates at the image plane,

is the focal length of the lens L2, and J

is the ﬁrst-order

Bessel function of the ﬁrst kind. The orientation of edge

enhancement can be controlled by the initial phase φ

. The

weight ratio of the positive and negative vortex is determined

by the weighting factor c , which controls the edge enhance-

ment power. Edge enhancement power changes as the value of

c changes. When c = 0, isotropic edge enhancement can be

obtained by this ﬁlter.

The ﬁltering characteristics of the proposed and existing

methods are compared by simulating the PSFs of the fractional

Fig. 2. (a1)–2(e1) PSFs of the fractional vortex ﬁlter, off-axis vortex ﬁlter, the conventional superposed vortex ﬁlter, LGSF, and BLCVF.

(a2)–(e2) Amplitude proﬁles in radial section of (a1)–(e1), respectively.

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