Optics Communications 228 (2003) 271–278

www.elsevier.com/locate/optcom

Superresolution technology for reduction of thefar-field diffraction spot size in the laser

free-space communication system

Jia Jia *, Changhe Zhou, Liren Liu

Shanghai Institute of Optics and Fine Mechanics, Academia Sinica, P.O. Box 800-211, Shanghai 201800, PR China

Received 21 May 2003; received in revised form 29 August 2003; accepted 14 October 2003

Abstract

In the free-space laser communication there is sometimes a strong need for reduction of the diffraction spot size in

the far field. In this paper, instead of the usage of the larger size aperture lens in the free-space laser communication

system, we introduce diffractive superresolution technology to design and fabricate a cheap pure-phase plate for re-

alizing the smaller spot size than the usual Airy spot size, which can decrease the weight and size of the emitting lens.

We have calculated 2, 3, 4, 5 circulation zones for optimizing the highest energy compression (Strehl ratio) with the

constraint of the First zero ratio value G¼ 0.8. Numerical results show that the 2- or 3-circular zone pure-phase plate

can yield the highest Strehl ratio ðS � 0:59Þ with the constraint of G¼ 0.8, but the 4, 5 circular zone binary phase (0,pÞplates are calculated to yield the result of S � 0:57 with G¼ 0.8. We have fabricated 2- and 3-circular zone binary phase

plate with binary optics technology. Finally, we have established an experimental system for simulation of the free-

space laser communication to verify the advantage of the superresolution phase plate. Detailed experiments are pre-

sented.

� 2003 Elsevier B.V. All rights reserved.

PACS: 42.30.Kq; 42.40.Jv; 42.79.Cj; 42.79.Sz; 42.82.Cr

Keywords: Fourier optics; Computer-generated holograms; Zone plates; Optical-communication systems; Lithography

1. Introduction

In the free-space laser communication applica-

tion, the intensity at the far field is the Fraunhofer

* Corresponding author. Tel.: +86215991-1214; fax:

+86216991-8800.

E-mail address: jia_joseph@hotmail.com (J. Jia).

0030-4018/$ - see front matter � 2003 Elsevier B.V. All rights reserv

doi:10.1016/j.optcom.2003.10.011

diffraction of the incident light, which is also the

Fourier transform of the intensity of the incident

light. The size of the diffraction spot in the receive

port in the free-space laser communication system

can also be calculated by the well-known Airy

pattern: x ¼ 1:22ðkL=DÞ [1,2], where D is the ap-

erture of the emitting lens and L is the distancebetween the emitting lens and the receiver and k is

the wavelength of the laser. In the specific array

ed.

272 J. Jia et al. / Optics Communications 228 (2003) 271–278

laser communication applications, as shown in

Fig. 1, there is need for a technology that can

decrease the size of the diffraction spot in the re-

ceiver port because in the free-space laser com-

munication a smaller diffraction spot in the receive

port makes the transmit data more secure. Thewavelength of the laser and the distance between

the emitting lens and the received are usually fixed.

So a larger aperture lens is often employed to

realize the small far-field spot. However, a larger-

sized lens is very expensive, and worse, a larger-

sized lens is usually not available due to the

fabrication technology.

Superresolution technology provides an attrac-tive approach to this application. Superresolution

technique is one of the methods that realize the

diffraction spot smaller than the Airy spot when a

superresolution pure-phase plate is employed. The

first significant study of superresolution was put

forward by Francia [3]. Much attention was de-

voted to the design of the superresolution phase

plate for its applications in enhanced resolutionconfocal system [4], increased storage in optical

disk system [5], etc. More sophisticated methods

based on continuous amplitude transmittance

function have also been developed [6]. Hybrid

Receiver 1

Receiver N

x

Laser 1

Laser 2

1

2

Distance L

Receiver 2

Laser N

Fig. 1. Illustration of an arrayed laser communication system

for the multi-channel increased transmitting capacity. Each

laser should generate its Frauhofer diffraction in the far field. 1,

2 means the intensity distribution in the laser 1, 2 diffraction

field. The signal channels should not disturb the nearby channel

for the diffraction effect of each channel. The receivers can be

put at an optimized closer distance when a superresolution

phase plate is used without resorting to a larger aperture laser

emitting lens.

amplitude-phase elements with two zones, as well

as elements for use in optical pick-up heads have

been studied [7]. Various superresolution com-

pression parameters such as Strehl ratio (S), First

zero (G), have been defined to describe the super-

resolution effect. The Strehl ratio is defined as theratio between the intensity of the superresolution

pattern and the intensity of the Airy pattern, both

calculated at the origin. The First zero is defined as

the ratio between the first zero position of the

superresolution pattern and the first zero position

of the airy pattern. For more details of superres-

olution technology and its applications, one can

see [6–9]. The widely used Full-width-half-maxi-mum (FWHM) is closely related with the first zero

position (G), and the central-lobe energy percent-

age, the ratio of the central lobe energy at the zero

order to the whole energy at all diffraction orders,

is closed related with the Strehl ratio (S). As the

diffraction efficiency is the most important pa-

rameter for practical applications, we will present

the superresolution scheme of the pure-phase platein this paper because of high diffraction efficiency.

As to the best of our knowledge, no one has

pointed out the possibility that superresolution

technology can be applied in the free-space laser

communication system. We introduce the super-

resolution technology into the free-space laser

communication system to compress the far-field

diffractive spot size. With this proposed technol-ogy, we typically place a filter at the exit pupil of

the system and thus the smaller diffraction spot

can be obtained with the same aperture lens. In

this paper, we prescribe the criterion of G6 0:8,while S should be as large as possible for practical

application. If G is too small, such as G6 0:6, themainlobe in the diffraction spot is too small to be

applied in practice. If G is too large such as G ffi 1,the too small reduction of the diffraction spot size

is not interesting for practical use.

In this paper, we have calculated the 2, 3, 4, 5

circular zones for optimizing the highest Strehl

ratio with the constraint of the First zero value

G ¼ 0:8, and have found the optimized radius and

phases of the phase plate. Finally, we have set up

an experimental system for simulation of theFourier transform in the laser long-distance com-

munication. The experimental results have verified

J. Jia et al. / Optics Communications 228 (2003) 271–278 273

the numerical results and confirm the effectiveness

of the superresolution phase plate.

2. Review of superresolution theory

In a traditional sense, the Airy resolution is

defined by the distance from the first zero position

of the main peak intensity spot. Superresolution

technology means that we can realize a smaller

diffraction spot than an Airy diffraction spot. A

pure-phase plate that is put before (or after ) the

diffraction-limited lens is involved to realize the

superresolution effect, as is shown in Fig. 2.According to the superresolution diffractive

theory [6] the normalized field measured at the

observation plane is given by:

uðm; lÞ ¼Z 1

0

P ðqÞ expð�jlq2=2ÞJ0ðmqÞqdq; ð1Þ

m ¼ kr sinðaÞ;

l ¼ 4kzðsinðaÞ=2Þ2;

k ¼ 2p=k; sinðaÞ ¼ NA;

where l, m are the axial and radial coordinates,

P ðqÞ is the pupil function (which is also called the

diffractive phase plate). From Eq. (1), we can get

uðm; 0Þ ¼Z 1

0

PðqÞJ0ðmtÞdt; ð2Þ

where l ¼ 0 in the focal plane

Collimated

laser beam (λ)

Superresolution

pure-phase plate

Fig. 2. The superresolution experimental system for simulation of th

munication system.

uð0; lÞ ¼Z 1

0

P ðqÞ expð�jlq2=2Þdq; ð3Þ

where m ¼ 0 in the axial plane.So in the focal plane, the radial amplitude dis-

tribution is the Hankel transform of the pupil

function, while the axis amplitude distribution isthe Fourier transform of the pupil function. In the

superresolution field, there are many methods to

design the pure-phase plate. Due to ease of fabri-

cation, we choose the circular binary phase-only

plate in this paper. The structure of the 3 zone

circular binary phase-only plate is shown in Fig. 3.

If we put the circular phase-only plate into the

optical system, the diffractive field can be describedas

wðnÞ ¼XNj¼1

expði/jÞ½a2j2J1ðajnÞ=ajn

� a2j�12J1ðaj�1nÞ=aj�1n�; ð4Þwhere aj and /j represent the radius and phase of

the jth zone, respectively. If the binary phases are

chosen to be only 0 and /, we can rewrite Eq. (4)

as

wðnÞ ¼ 2J1ðnÞ=n� ½1� expði/0Þ�ð�1ÞNþ1

�XN�1

j¼1

ð�1Þj � a2j2J1ðajnÞ=ajn: ð5Þ

In numerical simulations, we will apply Eq. (5) tocalculate the 2, 3, 4, 5 circular zones of the phase

plate. According to the compression criterion, we

will find the optimized parameters: the radius and

phase value of each zone.

focal plane

D

CCD

camera

e far-field diffraction in the long-distance free-space laser com-

0

0

a b

1.0

Φ

Fig. 3. The normalized structure of the 3 zone binary pure-

phase plate, a, b are the radii of the phase-transition circles

between the phase 0 and U.

274 J. Jia et al. / Optics Communications 228 (2003) 271–278

3. Optimization algorithms and numerical results

We have used the global searching algorithms in

our computer simulations. The global searching

algorithm is to find the optimized result in the

whole searching areas with changing each radius at

a minimum searching step. The advantage of this

algorithm is that it can find the optimized result,

but the searching time is quite long.Numerical results of the Strehl ratio (S) and

First zero ðS ¼ 0:8Þ and the central-lobe energy

percentage with the radius (a) and the phase are

given in Table 1. From Table 1, we know that the

largest Strehl ratio S ¼ 0:5911, which is the Strehl

ratio of the 2 zone phase plate. From numerical

results of the First zero and Strehl ratio with two

radius a and b of the 3 zone phase plate, we findthe best optimized result under the constraint

Table 1

Numerical result of the multi-zones superresolution phase plate with

Zone no. Search step Optimized numerical result

Normalized radius

2 0.01 a¼ 0.34

3 0.03 a¼ 0.09, b¼ 0.36

4 0.08 a¼ 0.16, b¼ 0.24,

c¼ 0.40

5 0.10 a¼ 0.1, b¼ 0.2, c¼ 0.4,

d ¼ 0.9

See Fig. 3 for the meaning of the normalized radius a, b.

of G ¼ 0:8 as: a ¼ 0:09; b ¼ 0:36;U ¼ 0:9p;G ¼0:7979; SMAX ¼ 0:5835. The central-lobe energy

percentage that is closely related with the Strehl

ratio is calculated and given in Table 1. The

maximum central-lobe energy percentage is 39% in

Table 1 while it is 84% for the Airy diffractiondistribution. The far-field intensity distribution of

this optimized numerical result is shown in Fig. 4.

From Fig. 4, we can see that the superresolution

technology can yield a smaller diffractive size in

the far field than that in the Airy spot.

We have also studied the effect of the multiple

phase modulation for the 3 zone plate with the

same optimized two radius a ¼ 0:09 and b ¼ 0:36.The inner zone phase is always assumed to be zero.

The optimized phases are as follows: /1 ¼ 0:00p;/2 ¼ 0:06p;/3 ¼ 0:86p, and the Strehl ratio

Smax ¼ 0:5905. Note that this optimized Strehl ra-

tio S ¼ 0:59 with the multiple phases is a little

higher than the optimized S ¼ 0:5835 with the bi-

nary phases. This result illustrates that the multi-

ple-phase modulation can indeed improve theperformance but at a much higher cost for fabri-

cation than the binary phase modulation.

The numerical simulation results of the 4 and 5

zone phase plates give the maximum S � 0:57 with

G ¼ 0:8. We realized from our numerical result

that the S could not be increased with the increase

of the zone numbers. Numerical comparison of the

2- and 3-zones plate in Table 1 is given in Fig. 4.From Fig. 4, we can see that FWHM (Superre-

solved) is smaller than the FWHM (Airy). If the

maximum intensity of the superresolved pattern is

normalized from 0.59 to 1, the FWHM keeps un-

changed because of the fixed first zero position.

the prescribed First zero (G ¼ 0:8)

U ðpÞ Strehl ratio Central lobe energy (%)

1.0 0.5911 38.83

0.9 0.5835 36.06

0.9 0.5645 35.06

0.9 0.5587 13.16

0 0.5 1.0 1.5 2.0 2.5 3.00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9superresolved pattern(3-zones)superresolved pattern(2-zones)Airy pattern

Relative radial distance

1/2FWHM (Airy)

1/2FWHM (Superresolved)

No

rmal

ized

Inte

nsi

ty

Fig. 4. Theoretical far-field intensity distribution of the Airy (solid line) and the superresolution diffraction (dashed line) patterns with

the 2- and 3-zones plates in Table 1. The superresolution pattern generated by the 2- and 3-zones plates are quite close to each other.

The receiver 2 can be at the first zero position of the superresolution pattern that is 0.8 times closer to receiver 1 than the Airy pattern.

FWHM is the Full-width-half-maximum of the diffraction distribution. We can see that the FWHM (Superresolved) is smaller than the

FWHM (Airy).

J. Jia et al. / Optics Communications 228 (2003) 271–278 275

Thus, the FWHM of the superresolved distribu-

tion is indeed reduced compared with the FWHM

of the Airy distribution. From Fig. 4, we can also

see that there is little difference between 2- and 3-

zones plates. Fabrication of the three zone phase

plate can demonstrate the capability that we can

also fabricate the 2-zone phase plate. So we choose

the 3-zone binary phase plate for the experiment,which is given in the next section.

4. Fabrication and experimental results

VLSI techniques have been adopted in our ex-

periment to obtain the phase plate. The mask is

made with electro-beam writing method. We havefabricated two three-zone mask with the apertures

of 2 and 20 mm that are designed from Table 1 as

follows: a ¼ 91:3 lm, b ¼ 360 lm, r3 ¼ 1 mm; and

a ¼ 913 lm, b ¼ 3600 lm, r3 ¼ 10 mm, respec-

tively. The phase plate of the aperture size of 2 mm

can generate a larger central diffraction spot that is

more easily captured by the CCD camera than that

with the aperture size of 20 mm. Larger-sized

phase plates can also be fabricated in principle.

Then a thin layer of photoresist is spun onto a

glass substrate. We transfer the mask pattern into

photoresist through photolithographic technology.

In our experiment, the photoresist is Shipley

S1818. The contact copy error is within 0.5 lm.

We use the wet chemical etching (WCE) method

[10,11] to transfer the photoresist pattern into theglass substrate.

The glass substrate has a refractive index of

n ¼ 1:52. The expected etching depth correspond-

ing to 0.9p in Table 1 is 548 nm. We use the Taylor

Hobson step height standand to measure the sur-

face relief profile of the phase plate. The surface

relief profile of the superresolution phase plate is

shown in Fig. 5. The measure depth is 518 nm, thephase error is smaller than 5%.

We have set up an experimental system, as

shown in Fig. 2, to simulate the far-field diffraction

free-space laser communication. The He–Ne laser

with a wavelength of 633 nm is used as the light

source. A diffraction-limited lens with a focal

length f ¼ 550 mm is used to yield the Airy dif-

fraction pattern in its focal pattern that is captured

Fig. 5. The surface relief profile of the fabricated superresolution phase plate of the 3-zones plate in Table 1.

276 J. Jia et al. / Optics Communications 228 (2003) 271–278

by a CCD camera and shown in Fig. 6(a). When

the fabricated phase plate of Fig. 5 is inserted and

aligned with the aperture of the lens, a superreso-lution diffraction pattern is generated, which is

shown in Fig. 6(b). Comparison of the Airy pat-

tern and the superresolution pattern is done off-

line in the computer and shown in Fig. 7. From

Fig. 7, we can see that the experimental results are

in good agreement with the theoretical results, and

that the fabricated superresolution phase plate do

generate a smaller central spot ðG � 0:8Þ thanthe Airy spot. This result demonstrated the possi-

bility that a superresolution phase plate can be

incorporated in free-space laser communication

system for reduction of the far-field diffraction

spot size.

Fig. 6. The experimental image of the diffraction spot of Airy

pattern (a) and the superresolution pattern (b) with the 3-zones

plate of Fig. 5. We can see that the central spot of (b) is smaller

and especially the first ring of (b) is a little wider and brighter

than that of the well-known Airy pattern (a).

5. Conclusion

Reduction of the far-field diffraction size in thefree-space laser communication system is always

interesting. The wavelength, the distance, and the

aperture size of the emitting lens are usually con-

sidered to this end. The wavelength that is related

with the available laser and the distance between

the transmitter and the receiver are usually fixed,

so a larger sized lens has to be fabricated at a much

higher cost and sometimes unavailable due to thelimit of the fabrication technology. The superres-

olution technology can realize the smaller central

diffraction spot size in the far field than the usual

Airy spot size. So the superresolution technology is

very interesting in the free-space laser communi-

cation system. A superresolution phase plate is

much cheaper than the larger aperture lens, which

is the essential motivation of this work.We have calculated the 2, 3, 4, 5 circular zones

for optimizing the highest energy compression

(Strehl ratio) with the constraint of the First zero

value G ¼ 0:8. Numerical results show that the 2-

circular zone pure-phase plate can yield the highest

Strehl ratio (S ¼ 0.59) with the constraint of

G ¼ 0:8. The 3 zone phase plate with 0.9p phase

modulation yields the largest Strehl ratio S ¼ 0:58with the constraint of G ¼ 0:8. The 3-circular zonepure-phase plates with the respective phases of

U1U2U3 have also been calculated. At the same

0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1experimenttheoryAiry pattern

Superresolution pattern

Fig. 7. Experimental comparison of the superresolution diffraction distribution with the Airy diffraction with the superresolution

phase plate of Fig. 6, which are represented by the dotted line (experiments) and the solid line (theory), respectively. Experimental

results verify that a smaller central spot (G�0.8) than the Airy spot has been achieved.

J. Jia et al. / Optics Communications 228 (2003) 271–278 277

time the 4, 5 circular zone binary phase (0,pÞ plateshave been calculated to yield the result of S ¼ 0:57with G ¼ 0:8. We realized from our numerical re-sults that it might be not necessary to calculate

more zone phase plate for a higher Strehl ratio.

The efficiency of the superresolution phase plate

may be enhanced by using a multi-phase modu-

lation, which is the future work.

It should be noted that using a stronger or a

weaker laser intensity should yield the same nor-

malized Airy diffraction pattern in the far field, thefirst zero position will not be changed. Air turbu-

lence, absorption and scattering are not considered

in this paper. The preassumed condition using a

superresolution phase plate is that the emitting lens

should be diffraction-limited. If the emitting lens is

not diffraction limited, it is not necessary to use the

superresolution phase plate proposed in this paper.

In summary, we have studied the superresolu-tion technology for generating the small diffraction

spot size in the far field. We have presented nu-

merical simulation results and we have also given

experimental results as a simulation of reduction

of the far-field diffraction size in the laser free-

space communication system. We have set up an

experimental system to detect such a smaller dif-

fraction spot size in the far field that is generated

by using the superresolution plate above. Two

phase plate with an aperture size of 2 and 20 mm

has been fabricated with the microlithingraphictechnology. We have obtained the experimental

image of the smaller diffraction spot using the su-

perresolution phase plate in this experimental

system. More larger-sized superresolution phase

plate can be fabricated in principle. But the smaller

diffraction spot resulting from the superresolution

technology always causes the energy loss in the

mainlobe. And the lossing energy is transferredinto the sidelobes. Careful avoidance of the in-

tensity in the sidelobes would not cause the serious

communication problem. So this technology can

be applied when the laser energy is not the main

concern in the communication. Experimental re-

sult has verified the possibility that by using a

superresolution phase plate matching the emitting

laser lens, a smaller central diffraction spot can beobtained in the far-field than Airy pattern.

Acknowledgements

The authors acknowledge financial support

from the National Outstanding Youth Foundation

of China (60125512, 60177016).

278 J. Jia et al. / Optics Communications 228 (2003) 271–278

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