立方角反射镜衍射孔径计算与分析

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"Song Li, Bei Tang, Hui Zhou. Calculation on diffraction aperture of cube corner retroreflector. Chinese Optics Letters, Vol. 6, No. 11, November 10, 2008, Pages 833-833. doi:10.3788/COL20080611.0833." 这篇论文关注的是立方角反射器（CCR）的衍射孔径计算方法。立方角反射器是一种光学元件，因其独特的光学特性，常被用于激光测量系统中作为合作目标。它具有将入射光束沿原路反射回去的能力，这在卫星激光测距（SLR）等高精度空间测量技术中至关重要。作者提出了一个新的理解和计算立方角反射器在两种不同形式下衍射孔径的方法。衍射孔径是光学系统中一个重要的参数，它决定了光波通过系统后的分布特征。在本文中，研究了六种不同反射顺序和入射角组合下的衍射孔径与入射光之间的关系。入射角和方位角是决定光波在反射器上反射方式的关键因素，不同的角度会改变衍射图案的形态。通过对立方角反射器进行不同条件下的远场衍射模式分析，论文提供了丰富的实验结果。远场衍射图案是理解光束经过反射器后在空间分布情况的重要手段，它能揭示反射器对光束传播的影响。这些结果对于优化和设计使用立方角反射器的系统，尤其是那些需要精确控制光束传播特性的应用，如激光通信、遥感和导航等领域，具有重要意义。论文的关键词包括：角反射器、衍射孔径、入射角、方位角，以及相关的光学分类代码050.1220、050.1940、050.1960，这些代码通常用于标记和检索光学领域的专业文献。通过这篇研究，读者可以深入理解立方角反射器的衍射特性，并能据此进行更精确的光学系统设计和性能评估。

November 10, 2008 / Vol. 6, No. 11 / CHINESE OPTICS LETTERS 833

Calculation on diffraction aperture of

cube corner retroref lector

Song Li (

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), Bei Tang (

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), and Hui Zhou (

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)

School of Electronic Information, Wuhan University, Wuhan 430079

Received April 8, 2008

On the basis of optical property of cube corner retroreflector (CCR), a new perception and calculation

approach for diffraction aperture of CCR in two different forms is presented. The relationship between

diffraction apertures and incident light with six different combinations of reflection order and incident

angle is established. Far-field diffraction patterns of CCR under various incident conditions are also

provided.

OCIS codes: 050.1220, 050.1940, 050.1960.

doi: 10.3788/COL20080611.0833.

Retroreflector has been widely used in various laser mea-

surement systems as a cooperative target based on its

direct reflecting

[1,2]

. Satellite laser ranging (SLR) which

is a high-precision space measurement technology comes

forth in the 1960s. The laser cooperation target in SLR

system is laser cube corner retroreflector (CCR) or laser

retroreflector array which is installed on the surface of

the satellite. The orbital altitude of satellite is generally

several hundred kilometers to tens of thousands of kilo-

meters. Therefore, the SLR system can be regarded as a

Fraunhofer diffraction optical system. On the one hand,

CCRs on the satellite directionally reflect the laser pulse

which comes from the observing station; on the other

hand, CCRs diffract and redistribute energy of the laser

pulse as diffraction aperture. The light field distribution

diffracted by CCRs is of great significance for the laser

ranging system to receive laser pulse echo correctly and

to accomplish the ranging function exactly.

The most important parameter which influences the

far-field diffraction characteristics of CCR is the inte-

gral region of diffraction aperture. However, previous

researches into the far-field diffraction of CCR take the

diffraction aperture as a whole. We want to explore the

deeper reason what makes the light field distribution of

CCR be taken on like that and why the certain part of

light spot is much better than other parts of light spot

for the reception. In this paper, the diffraction aperture

theory of oblique incidence on the CCR is established.

The CCR consists of three mutually orthogonal planar

surfaces and one flat bottom surface. The light which en-

ters the CCR through the bottom surface is reflected by

the three planar surfaces in turn. There are six different

reflection orders of light as three reflective surfaces have

six different sequences of arrangements

[3]

. The reflection

order of light depends on the incident direction and co-

ordinates of light on the bottom surface of CCR. Take

the vertex of CCR as the origin and three edges of CCR

as X, Y , Z axes to establish the coordinate system, as

shown in Fig. 1. Without regard to refraction, for an

incident light with any direction (a, b, c), the light direc-

tion converts to (−a, −b, −c) after being reflected by the

three reflective surfaces respectively.

As shown in Fig. 2, taking the midpoint of bottom sur-

face as the origin o, the bottom surface as x-y plane, and

the direction of light which comes out of the CCR after

being reflected by the three reflective surfaces sequently

as z-axis, we establish the oxyz coordinate system. Draw

a vertical line to one of the bottom surface borders across

point O in X-Z plane, with the foot of the perpendicular

labeled as point T . It is assumed that the angle between

line OT and z-axis is ϕ, and the angle between line OT

and line Oo is ω. These two sets of coordinates are pro-

vided with coordinate transformation matrix as

[4]

M =

cos ϕ − sin ϕ sin ω − sin ϕ cos ω

0 cos ω − sin ω

sin ϕ cos ϕ sin ω cos ϕ cos ω

. (1)

Fig. 1. Cartesian coordinates of CCR.

Fig. 2. Schematic diagram of coordinate transformation of

CCR.

1671-7694/2008/110833-04

 2008 Chinese Optics Letters

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