Free-Space Optical Propagation Noise Suppression by Fourier Optics Filter Pinhole

Transcription

1 International Journal of Optics and Applications 05, 5(): 7-3 DOI: 0.593/j.optics Free-Space Optical Propagation Noise Suppression y Fourier Optics Filter Pinhole Purnomo Sidi Priamodo,*, Ucuk Darusalam,, Eko Tjipto Rahardjo Department of Electrical Engineering, Universitas Indonesia, Depok, Indonesia Department of Informatics Engineering, Faculty of ICT, Universitas Nasional, Jakarta, Indonesia Astract Terrestrial free-space optical communications (FSOC) is potential to e applied in microcellular networks to provide larger andwidth and higher cellular access. However, the terrestrial propagation quality degrades due to atmospheric asorption and turulence. Turulence-induced noise degrades signal to noise ratio (SNR) and increases it error rate (BER), which finally degrades the overall signal quality at the receiver. In this paper, we propose to develop a method and conduct a laoratory experiment to suppress turulence noise y using a pinhole as Fourier optics low-pass filter. It is shown that pinhole can improve BER very significantly from 0-7 down to 0 -, even in strong noisy medium propagation. Keywords Free-space optical communications, Optical turulence, Noise propagation, Noise fading, Optical filters, Spatial Fourier transforms, Pinhole, Signal-to-noise ratio, Bit-error-rate, Noise suppression. Introduction FSOC is very promising to e applied in the future for deep-space and terrestrial communications [-]. It is very attractive due to its large andwidth, close to fier optics and flexiility of point to point communication such as microwave systems. Moreover, the most interest is due to its low cost investment. Beside of thus promising points, however, FSOC technology has major weaknesses that have to e overcome, which are the existence of static attenuation and temporal or dynamic intensity fluctuation. Static attenuation is caused y asorption and light scattering due to various atmospheric gases and particles in atmospheric propagation medium, while, the dynamic intensity fluctuation is caused y atmospheric turulence, which is due to temporal and spatial temperature gradient in atmosphere. The atmospheric turulence produces various distriutions of pockets of non-homogeneity optical medium as refraction zones. These refraction zones act as multiple lens effects. If the size of turulences is only aout a several wavelengths of the light, then it is called as micro turulences that cause optical scattering and attenuation, where the optical axis path is considered remains the same. The temporal micro turulences produce high frequency intensity fluctuation noise at the receiver. If the size of turulences are sufficiently large or called as macro turulence, these cause eam wandering effect, which lead to shift optical axis from * Corresponding author: p.s.priamodo@ieee.org (Purnomo Sidi Priamodo) Pulished online at Copyright 05 Scientific & Academic Pulishing. All Rights Reserved transmitter (TX) to receiver (RX). The eam wandering causes slow intensity fluctuation at RX, it is called as turulence-induced fading. The overall effects, high frequency fluctuation noise and fading limit propagation distance and andwidth of FSOC [3-6]. Turulence-induced noise and fading at RX has een studied and investigated extensively. Several techniques have een developed to model Turulence-induced noise and fading [7-9]. There are at least (two) important statistical parameters related to turulence-induced noise and fading, i.e. () d 0, the correlation length of random intensity fluctuation and () τ 0, the correlation time of random intensity fluctuation [0]. Several improvements on detection techniques have een developed ased on statistical properties of turulence-induced noise and fading y temporal or spatial-domain technique approaches. In temporal domain technique approach, RX should e designed such that RX oservation interval T 0 > τ 0, where turulence-induced noise can e much reduced y temporal-averaging method at the RX. In the same way, for spatial domain technique approach, RX aperture diameter D 0 > d 0, such that turulence-induced fading can e much reduced y spatial-aperture averaging method at RX. Another improvement on spatial-aperture averaging method is in the form of spatial diversity method that is applying multi TXs and multi RXs, which is called multi-input multi-output (MIMO) and comined with Q-ary pulse-position modulation (QPPM) []. Several research groups have achieved developing FSOC for middle distance up to -km with 0-Gps it rate []. In this paper, we propose to overcome the turulence-induced noise on FSOC y using a different way. Instead of suppressing the turulence-induced noise y using

2 8 Purnomo Sidi Priamodo et al.: Free-Space Optical Propagation Noise Suppression y Fourier Optics Filter Pinhole temporal and spatial-domain statistical technique approaches as explained aove, we propose to use Fourier optics filter concept. Atmospheric turulence along the propagation medium produces a high frequency temporal and spatial fluctuated wavefront right in front of the RX lens. The fluctuated wavefront ased on Fourier optics analysis concept, consists of fundamental and higher-order spatial harmonic planar wavefronts. The temporal noise mostly rides on the higher-order ones. Pinhole as a low pass Fourier optics filter and common to e used in interferometric process [3], is used to suppress the higher-order spatial harmonics (consisting noisy signal parts) of the receiving turulence-induced noise. After pinhole filter, the detector receives clean signal, which is the fundamental order of optical carrier modulated y the information signal. In this paper, suppression is limited on high frequency fluctuation noise and not the fading, due to the limitation of our laoratory experiment. The receiving lens works as a spatial Fourier transformer. It transforms the temporal-spatial noisy input wavefront to e spatially harmonic focal points on the focal-point plane. On the focal point plane of the receiving lens exists various focal points of each harmonic planar wavefronts surrounding the center of the fundamental focal point. In this filtering process, pinhole works to lock the higher-order spatial harmonic focal points. Only fundamental order wavefront can pass the pinhole to reach the receiving detector. In this case, pinhole acts as a Fourier optics low-pass spatial filter. It locks higher-order spatial harmonics, which are overridden y temporal noise at focal points.. Noise Suppression Mechanism The received wavefront as noisy information carrier is received y the receiving lens aperture, and focused onto the detector. The light focusing process is an equal gain comining detection process. Ideal condition is the receiver diameter D 0 >> d 0, the equal gain comining detection averages the received noisy signal and can vanish the addition noise on the signal. However, mostly the condition is D 0 < d 0. The limitation of receiving aperture diameter causes RX lens focusing system cannot perfectly average the received noisy wavefront in order to clean the noise. At the focal point, the light eam looks like a waist. For a detector that has an area larger than the eam waist area and located right ehind the focal point, then the overall received signal that consists of temporal noises and the original signal will e detected y detector. This decreases SNR and increases BER. In this paper, we propose that the received noisy wavefront is constructed y superposition of fundamental clean signal and noisy harmonic planar wavefronts, which propagate off the optical axis, as shown on Fig. [3]: U( xy, ) F( νx, νy) exp jπν ( xx νyy) + dνxdν y () ( ) P U x, y dx dy r () where ν x and ν y are the spatial frequencies in x and y directions in x-y plane, respectively and F(ν x,ν y ) is the amplitude of the mixing spatial frequencies and U(x,y) is the total electromagnetic field at point (x,y). The total received power at receiving lens is Pr and the fundamental or clean signal power is P 0. The SNR without filtering can e expressed as, SNR P0 (3) P P r 0 Figure. Pinhole locks higher-order spatial harmonic focal-points [3] Pinhole suppresses the noise and improves the receiving SNR. Only fundamental spatial order that rings clean information signal is expected to e detected y the receiving detector. The SNR y using pinhole will e drastically increased, even though the total receiving power decreases. Fig. may help to riefly elaorate how pinhole can suppress turulence-induced noise, such as illustrated y scheme on Fig.. Fig. (a) shows the mixing clean signal and propagation noise at the detector, a distance from the focal point. Fig. () shows that the pin-hole can suppress higher order spatial harmonics overridden y temporal turulence noise. The detector should e located aout the center, which is clean modulated signal. Fig. (a-) were taken for ilustration ased on a simple Fourier optic filtering y pinhole configuration in the laoratory. (a) Figure. Oservation images on oservation screen, (a) without pinhole and () with pinhole Pinhole is located ehind the focal point, as shown on Fig.3. The pinhole diameter has to e equal or slightly larger than the eam waist, in order that the whole clean signal can e detected, while the higher-order spatial harmonics are locked. The relationship etween receiving lens and eam waist radius at focal-point is formulated in the following ()

3 International Journal of Optics and Applications 05, 5(): Eq.(4) ased on Ref. [3]. D 0 4λ f (4) π D where D is the receiving wavefront diameter right in front of the receiving lens. D 0 is the eam waist diameter at focal point, f is the focal length and λ is the wavelength. In this experiment, the receiving eam diameter is 5-cm and focal distance is 5-cm, then the eam waist diameter at focal point is 3.8λ. Based on experience, the pinhole diameter size of 3.8λ, where λ550-nm, is very difficult for optical alignment, and facing prolem when eam wander exist. To anticipate the difficulty in optical alignment due to eam wandering effect that sometimes occurs in FSOC, it is recommended to locate pinhole not exactly right on focal-point. Pinhole should e shifted from focal point at least aout Rayleigh range or a half of depth of focus [3] and pinhole diameter enlarged at minimum of times as shown on Fig.3. The Rayleigh range (z 0 ) is expressed as, π D0 z0 (5) 4λ For the aove typical example, the pinhole is suggested to e located at distance aout 4πλ from focal point with pinhole diameter at least 5.4λ. Based on our experience, pinhole diameter range from 6 30 λ is good to e exercised. Figure 3. Receiving lens and pinhole alignment Pinhole To estimate the SNR gain due to pinhole effect and to simplify derivation, it needs to assume that the noise power is distriuted equally from low to high spatial frequency noise. SNR gain is defined as an SNR comparison etween different pinhole diameters. Assuming that the fundamental clean signal waist radius is R D 0 at focal plane of receiving lens and R is small and R is large pinhole radii, y recalling Eq.(3), then the SNR gain can e formulated as: R R0 SNRGain (6) R R0 To estimate BEP, it needs to assume that the turulence channelis a log-normal distriution model [4, 5] as a representation of weak-turulence inside the propagation simulator ox. The spatial spectral distriution as a result of Fourier optical transformation y the receiving lens should represent the proaility density distriution of the receiving signal. The modulation is on-off keying (OOK). By assuming that the noise due to turulence is a Gaussian distriution and larger than the receiver noise figure, then the BER improvement or gain formula can e derived from Ref [6]. The proaility of error when receiving a transmitted is: ( '') ( '') P r p r dr π N 0 N0 e ( ) r E / N0 dr x / E e dx Q π N0 The proaility of error when receiving a transmitted 0 is: ( '0') ( '0') P r p r dr π N 0 N0 ( r) e / N0 dr x / E e dx Q π N0 where p(r '') and p(r '0') proaility amplitude error distriution functions for transmission '' and '0' respectively. Q or complementary error function is the tail proaility in a Gaussian random variale, r is random amplitude error. E is the received it energy and N o is noise intensity due to turulence or signal covariance at the focal plane of the receiving lens: Pr P0 N0 σ N (9) π R R0 ( ) where P r is total received power and P 0 is the fundamental clean signal and R and R 0 are radii of eam waist of total signal and fundamental signal, respectively at the focal plane of the receiving lens. Since the signal and 0 are equaly likely to e transmitted, then the overall average proaility of error is ( ) 3 E Pe Pe '' + Pe ( '0' ) Q (0) N0 The proaility of error P e or sometimes is called as it error proaility (BEP) is the expectation value of it error rate (BER). The value of E /N o is simply corresponded with (7) (8)

4 30 Purnomo Sidi Priamodo et al.: Free-Space Optical Propagation Noise Suppression y Fourier Optics Filter Pinhole SNR. Then Eq.(0) can e written as BEP 3 Q SNR () The BEP improvement (BEP Gain ) of the small radius pinhole R in comparison to the large radius pinhole R is written as: BEP Gain 3 Q Q ( SNR ) N π R R 3 Q ( SNR ) E Q Noπ R R 3. Experiment ( ) o 0 ( 0 ) () The experiment set-up shown on Fig.4 is to prove noise suppression y pinhole. This set-up is designed for wavelength of 550-nm, which is the favorite wavelength for terrestrial FSOC propagation. It is intended to prove the improvement of BER performance for FSOC using pinhole filter. The propagation simulator ox as shown, consists of types of propagation channels, one is affected y air turulence due to air flow through ostacles and water vapor (as shown as upper part). The second one is not affected y turulence unless eam divergence less than 5 0 (the lower part). The overall dimension of the ox is 4m x m x 0.5m. The in-flow air has temperature of 4 0 C, while the hot water vapor has temperature of nearly 00 0 C, sufficient to create multiple lens scattering and asorption effects. For this experiment, we assume it is sufficiently to model a weakturulence condition that fit to a log-normal distriution. In order to prove the enhancement on detection quality y using pinhole, the comparison etween non-pinhole and various diameters of pinhole detections are investigated. Various diameters of pinhole are used, i.e. 50-μm, 40-μm, 30-μm, 5-μm and 0-μm, which is located aout 0 5 μm ehind the focal point. To give insight of the measurement values, the following Tale shows the measurement levels for various pinhole diameters. Tale. Average Power Measurement in Reference and Turulence chamers, where TX power (after EDFA) is 3.5 dbm and P i is the received signal power Pinhole (µm) Turulence Pi (dbm) No pinhole No No.5 50 Yes No.0 30 Yes No.5 0 Yes No.0 0 Yes No.3 5 Yes Discussion and Analysis Fig.5 shows the experiment measurement and theoretical results, when various sizes of pinhole are applied. Fig.5 shows oth measurement results and theoretical calculations ased on Eq. (). It shows that when pinhole diameter getting smaller, then the performances of BER is improved (to lower value). It proves our proposed hypothesis that smaller pinhole diameter will lock more higher-order spatial harmonics, which are overridden y temporal noise, in comparison to the larger diameters. It agrees with the theoretical derivation as well. Figure 4. Experiment set-up for filtering turulence-induced noise y pinhole. The set-up uses Erium-doped fier amplifier (EDFA) 6.0 db gain with maximum output 3.5 dbm and JDSU is a rand of Gps full-duplex TX-RX and BER-meter

5 International Journal of Optics and Applications 05, 5(): Figure 5. Bit-error-rate (BER) measurement and theoretical calculations Vs. various pinhole diameters. The theoretical calculations use the following assumptions: E Watt-sec; N o Watt/mm and -Gps it rate However, there is a situation that contradictive with our hypothesis. When pinhole diameter is less than the optimal diameter (in this case the optimal diameter is 6-μm), then the BER degrades to the higher value. The reason of this condition is ecause that the receiving power signal is getting smaller and will compete with the detector noise figure. The weakness of pinhole implementation for optical noise filtering is in the condition when eam wander occurs as the result of atmospheric turulence. Pinhole filtering system is not immune from eam-wander effect, the system will temporally e misalligned and produce fading effect. In order to take the enefits of pinhole advantages in suppressing high-order spatial noises and to avoid the weakness of pinhole from eam-wander effect, our research group, since a year ago has developed detection system y replacing pinhole with charge-coupled device (CCD) array detector and controlled y pinhole signal processing algorithm. The pinhole will e removed in the future, however the function of pinhole in suppressing the noise still exist represented y the pinhole algorithm controlling the receiving CCD array detector. The fading due to eam wander effect is ale to e reduced, since the CCD detector can always detect the receiving moving eam. 5. Conclusions A new idea of propagation noise suppression in FSOC, y using a pinhole as a Fourier optics low-pass filter has een presented. By experiment, it has een proven to improve BER performance in medium turulence-induced fading propagation from 0-7 down to 0 - (up to 0 +4 BER improvement), even more. Furthermore, this proposed filtering method can also e implemented for applications with longer wavelength such as in RF technologies to suppress the propagation noise due to turulence atmosphere. ACKNOWLEDGEMENTS This work is funded y research grant BOPTN Universitas Indonesia 04. The authors declare that there is no conflict of interests regarding to the pulication of this manuscript and this manuscript is original work and never een pulished elsewhere. REFERENCES [] H. Hemmati, A. Biswas, I.B. Djordjevic, "Deep-Space Optical Communications: Future Perspectives and Applications," Proceedings of the IEEE, 99 (0) [] C.C. Davis, I.I. Smolyaninov and S.D. Milner, "Flexile optical wireless links and networks," IEEE Communications Magazine, 4 (003) [3] S. M. Navidpour, M. Uysal and M. Kavehrad, BER Performance of Free-Space Optical Transmission with Spatial Diversity, IEEE Transactions on Wireless Communications, 6 (8), pp , August 007. [4] M. Ijaz, Z. Ghassemlooy, J. Perez, V. Brazda, and O. Fiser, "Enhancing the Atmospheric Visiility and Fog Attenuation Using a Controlled FSO Channel," IEEE Photonics Technology Letters, 5(3), pp.6 65, July 03. [5] H. Kaushal, V. Kumar, A. Dutta, H. Aennam, V. K. Jain, S. Kar, and J. Joseph, "Experimental Study on Beam Wander Under Varying Atmospheric Turulence Conditions," IEEE Photonics Technology Letters, 3(), pp , Novemer 0.

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