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Optik 125 (2014) 1423– 1426

Contents lists available at ScienceDirect

Optik

jou rn al homepage: www.elsev ier .de / i j leo

n optimum structure design for Cassegrain optical system

iaojun Ma, Huajun Yang ∗, Bing Wang, Ping Jiang, Mingyin Yu, Yuchun Huang, Shasha Kechool of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China

r t i c l e i n f o

rticle history:eceived 12 April 2013ccepted 1 September 2013

a b s t r a c t

Because the energy loss caused by the secondary mirror of Cassegrain antenna is seriously, an optimumstructure is designed to improve the transmitting energy of Cassegrain optical system. It is made upof Cassegrain antenna and Double pyramidal system. The parameter of Cassegrain antenna has been

eywords:assegrain antennaaussian beam theoryptimum structure

analyzed, and it has been revealed that relationship between the Double pyramidal system and Cassegrainantenna. Finally, the relationship between the optimum parameters of Cassegrain and the transmittingefficiency has been researched. Through this optimum structure, the emitting power can be achieved to91.5%.

Crown Copyright © 2013 Published by Elsevier GmbH. All rights reserved.

ouble pyramidal system

. Introduction

With the development of the times, the optical communicationechnology has been developed rapidly. Because of large aperture,o chromatic aberration and the wide range of available band [1–5],he Cassegrain antenna is widely used in satellite communicationstations and single-pulse radars. For application of the laser beamn the atmosphere, Cassegrain telescopes, for beam expansion andow-speed focus control, are often used as transmitters. To receive

ore of the laser beam’s power, and then shrink it with a laser beamontrol system, Cassegrain telescopes are often used as receivers6]. Obviously, the optical antenna is the most important compo-ent of the optical system.

In this paper, a Double pyramidal system in Cassegrain systemas been designed, meanwhile an optical system software has beenet up to analyze the performances of the traditional Cassegrainntenna and the performances of this optical antenna.

. Structure for optical antenna

The Cassegrain system consists of two reflecting surfaces, a con-ave parabolic main dish and a convex hyperbolic secondary dishhich is shown in Fig. 1.

The wavelength of laser is 1550 �m, by the optical design soft-are Ze-MAX, we have designed a pre-collimation optical lenses

ystem, which is shown in Fig. 2. It includes two aspheric cylinderenses, which are perpendicular with each other for the generatorf the cylinder lens.

∗ Corresponding author.E-mail address: yanghj@uestc.edu.cn (H. Yang).

030-4026/$ – see front matter. Crown Copyright © 2013 Published by Elsevier GmbH. Attp://dx.doi.org/10.1016/j.ijleo.2013.09.021

3. Analysis of Cassegrain optical antenna

3.1. Gaussian model for Cassegrain antenna

By theoretical analysis [7], the electric field distributing ofGaussian beam can be described as

E(r) = A exp

(− r2

ω2(z)

)exp

(jk

r2

2R

)(1)

where

A = C

ω(z), k = 2�

�,

ω(z) = ω0

√1 + [�z/�ω0

2]2,

R = z

[1 +

(�ω0

2

�z

)2]

A is a constant coefficient, ω(z) is the radius of Gaussian beam, ω0is the beam waist, � is the wavelength of laser beam.

3.2. The energy loss caused by Cassegrain antenna

In Cassegrain optical system, the beam emitted by the

Cassegrain antenna is parallel beam with tiny beam divergence, thebeam is firstly reflected by the secondary mirror and then reflectedby the primary mirror. The whole process is shown in Fig. 3, dottedline part is obscured, these energy cannot be emitted by antenna.

ll rights reserved.

1424 X. Ma et al. / Optik 125 (2014) 1423– 1426

4321

Fig. 1. The structure of Cassegrain system. (1) Laser, (2) pre-collimation lenses sys-tem, (3) primary mirror and (4) secondary mirror.

so

p

p

p

wbs2

a

tti

iAgod

g

Fig. 4. The relationship between a, b and �.

Fig. 2. Pre-collimation lenses system.

At first, assuming that the primary mirror is full of laser beam,uppose that the radius of primary mirror is b, the radius of sec-ndary mirror is a.

=∫ 2�

0

∫ ∞

0

[∣∣E1(r)∣∣]2

rdrdϕ (2)

a =∫ 2�

0

∫ a

0

∣∣E1(r)∣∣2

rdrdϕ (3)

out = pb =∫ 2�

0

∫ b

a

[∣∣E2

∣∣2]

rdrdϕ (4)

here E1 is the electric field of laser beam 1, p is power of signaleam, pa is reflecting power of the secondary mirror, pb is the emis-ion power of the primary mirror. E2 is electric field of laser beam, pout is the emission power of the optical antenna.

Considering a and b are variable, the relationship between a, bnd the antenna efficiency � is shown in Fig. 4.

Taking account into the parameter of the Cassegrain antenna,ransmitting efficiency and the manufacturing cost. The radius ofhe primary mirror is b = 150 mm and the radius of secondary mirrors a = 30, then the antenna efficiency is 81.5%.

In the inter-satellites laser communication, high gain is the mostmportant. The loss caused by the secondary mirror is a big problem.s the electric field distributing of Gaussian beam, the antenna’sain would deviate from the ideal value. Assuming that differencef antenna between the actual gain and ideal gain is gr, it can beefined as the antenna gain factor, which can be represented as [7]

r = 2˛2

[exp(−˛2) − exp(−˛2ε2)]2

(5)

Fig. 3. Cassegrain antenna.

Fig. 5. The plot of antenna gain factor.

where ̨ = Dp/2ω, ε = Ds/Dp, Dp is the primary mirror diameter, Ds isthe secondary diameter, ε is the system block rate.

Therefore, the relation between the system block rate � and theantenna gain factor in the case of ε = 0.1, ε = 0.2, ε = 0.3 have beenobtained, shown in Fig. 5

3.3. Optimum structure of Cassegrain antenna

Though a Cassegrain configuration is widely used for expend-ing the beam in a reflecting mirror system, the loss caused bythe secondary mirror is seriously, which would affect the effectof transmission [8]. Therefore, the traditional structure have beensubstituted by an improved structure made up of two pyramid,which is shown in Fig. 6. In this antenna, the primary mirror is justfull of laser beam 2.

The Double pyramidal system is shown in Fig. 7. Gaussian beamhave been reshaped as hollow beam, it has been researched that

the existence of hollow laser beam has been assured under therefraction disciplines.

Because laser beam is parallel beam 2 with tiny divergence andthe radius of beam waist is near to the antenna, the beam radius

Fig. 6. Optimum structure of Cassegrain antenna.

X. Ma et al. / Optik 125 (2014) 1423– 1426 1425

L

d2R

Fig. 7. Double pyramidal system.

nwa

p

o

m0

I

i

I

w

I

I

ω

ω

R

Fig. 9. The relationship between R and L, �.

Fig. 8. The relation of �′ and the radius.

ear the antenna approximately equal to the radius of the beamaist. By theoretical analysis, the emitted power p′

out is describeds follow:

′out =

∫ 2�

0

∫ d

0

[∣∣E1(r)∣∣2

]rdrdϕ (6)

The relation of transmission efficiency �′ with the parameter df optimum structure have been discussed, as shown in Fig. 8.

Considering proper size of optimum structure, d = 0.03 m is theost efficient, so the radius d of optimum structure is devised to

.03 m.The light intensity of Gaussian beam can be described as [9]:

(r, z) = 2p

�ω2(z)exp

[− 2r2

ω2(z)

](7)

Through ray tracing, the intensity of hollow beam can be approx-mately expressed as the sum of two Gaussian beams:

(r, z) = I+(r, z) + I−(r, z) (8)

here

+(r, z) = p

�ω+(r, z)exp

[−2(r − R/2)2

ω+2(r, z)

]

−(r, z) = p

�ω−(r, z)exp

[−2(r + R/2)2

ω−2(r, z)

]

+(r, z) = ω0

√1 + [z + (r − R/2)/tan(�/2)]2

z02

−(r, z) = ω0

√1 + [z + (r + R/2)/tan(�/2)]2

z02

= L

2sin �(1 − sin(�/2)√

n2 − cos2(�/2))

Fig. 10. Hollow beam after transmission through Cassegrain antenna.

where p is the laser power, L is the length of Double pyramidalsystem, � is apex angle, 2R is the diameter of the hollow beam. Therelationship between R and L, � have been shown in Fig. 9, when� = �/2, R is the extreme value.

When the size of the primary mirror is b = 150 mm and the diam-eter of secondary mirror is a = 30, the System block rate ε = 0.2. Byusing the optimum structure, it makes that 2R = εa = 0.006 m, thetransmitting efficiency have been added up to 91.5%. The beamshape through Cassegrain antenna has been tested by the exper-iment, which is shown in Fig. 10.

According to the result of experiment, the Gaussian beam havebeen converted into hollow beam, it is feasible to covert the beaminto hallow beam under optimization structure and use Cassegrainantenna to transform information, which is available from theoryanalysis.

4. Conclusion

Because laser beam represent Gaussian distribution, the energymainly focus on center laser spot. The loss caused by secondarymirror induce transmitting efficiency. It has been analyzed that theassociation between the parameter of Cassegrain and the trans-mitting efficiency and the paragraph about gain of antenna underdifferent system block rate. An optimum structure of Cassegrainantenna have been proposed to in crease transmitting efficiency.Double pyramidal system could generate hollow beam, the rela-tionship between the radius of hollow beam and the parametersof Double pyramidal system have been discussed. This optimumstructure efficiently avoid the loss caused by secondary mirror,which makes the transmitting efficiency add up to 91.5%.

Acknowledgement

This project research is supported by the National Natural Sci-ence Foundation of China (No. 61271167).

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