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OPTICAL SIGNAL PROCESSING Interferometric Methods for Suppressing Additive Noise V. M. Nikitin1*, V. A. Sautkin2**, V. N. Fomin3***, and A. B. Tserevitinov3**** 1National Research University “Belgorod State University”, ul. Pobedy 85, Belgorod, 308015 Russia 2JSC “Krasnogorsky Zavod”, ul. Rechnaya 8, Krasnogorsk, Moscow Oblast, 143403 Russia 3Prokhorov General Physics Institute, Russian Academy of Sciences, ul. Vavilova 38, Moscow, 119991 Russia Abstract— Interferometric methods for signal processing, which make it possible to obtain a better noise protection of information laser and optoelectronic systems during detection and processing of optical fields under conditions for external additive noise, are proposed based on the results of analysis of the specific features of field formation in passive and active optical interferometers. The possibility of reducing the effect of external factors on the efficiency of additive-noise suppression by supplementing an interferometer with a stimulated-Brillouin-scattering fiber mirror is investigated. The technical feasibility of the methods proposed is shown and their efficiency is experimentally confirmed. DOI: 10.3103/S1541308X14020058 1. INTRODUCTION full measure. Thus, there is a wide area of activity for researchers and experts in this field. Here, The rapid progress of laser and optoelectronic we consider one of applications of interferometric technologies in all fields of fundamental and applied methods aimed at improving the noise protection of research gave a new impetus to the development laser and optoelectronic information systems applied of optical interferometry and made it possible to in detection and processing of optical fields under expand significantly its application range. Currently, conditions of external additive noise. interferometric methods are an actively developing line of research in physical and applied optics, which 2. SPATIAL AND TEMPORAL uses the latest achievements of laser technique, opto­ SELECTION OF NOISE electronics, and fiber optics and is applied in various IN A PASSIVE INTERFEROMETER fields. Currently, double-beam interferometers (such 2.1. Formation of Fields in a Passive Interferometer as Mach—Zehnder interferometer and its various modifications) are widely used in designing highly Let us consider some specific features of field for­ sensitive precise optical sensors and gyroscopes and mation at outputs of a passive optical interferometer. in other important fields of science and technology, Generally, interferometer arms are characterized by including astrophysical systems for observing dis­ some relative temporal and spatial mismatch, which tant objects and systems for diagnostics of various is caused by various factors. The spatial wave mis­ physical processes (see, for example, [1—8]). The match (Аж) in the interferometer arms characterizes constant interest in the transformation of optical their angular mismatch, while the temporal mismatch fields by interferometric methods is related to the A t is characteristic of the optical lengths of different possibility of implementing direct optical processing interferometer arms. We assume that a plane coher­ of optical fields and controlling their spatial and ent monochromatic wave E (an additive mixture of temporal structure. At the same time, an analysis signal and noise) arrives at the interferometer input. of the modern state of the problems related to the de­ In this case, the amplitude \ E\ is related to the arrival velopment and application of interferometric methods rate of signal and noise photons. Note that the re­ shows that their unique potential for various applied sults obtained in this study for monochromatic waves problems has not been realized and implemented in can be expanded to optical fields of complex spectral composition [9] and that the term “coherent” does E-mail: [email protected] not necessarily imply limited consideration of only E-mail: [email protected] laser sources, because partially coherent light can be E-mail: [email protected] formed by sources of other types, emitting in a wide E-mail: [email protected] spectral range. I l l 112 NIKITIN etal. The complex wave amplitudes in the first and second interferometer arms can be found from the relation [ 10] \Ег\ = \E2\ = \E\/V2. (1) Mixing of waves with the amplitudes \En \ = | E\21 = |s2i| = 1^221 = E/V 2 (2) occurs at the interferometer outputs. The total light intensity at the first output of the interferometer is found from the relation lp x = l^ E n (x ,t) + E 2\(x + A x ,t + A t)] [E h (x ,t) + E 2\(x + Ax, t + A t)f = (EnE*n ) + (E 21E*21) + 2R e (^Ец{х, t) E*2l{x + A x ,t + A t)), (3) in which the first two terms describe the energy of the interacting beams Е ц and E 2\ and the third term is the result of their interference in the form of spatial and temporal correlation function, which can be written for a stationary field in the following form: (^En (x,t) E 2 1 {x + A x ,t + A t)) = B i2(Ax, At). (4) The light transmission through the interferometer is analyzed using the normalized spatial and temporal correlation function 0 ,л (En (x,t)E21(x + Ax,t + At)) адд-дг) = в ' ,5) Having transformed expression (5), we obtain Ipi = hi(Pi) + I21 (-Pi) + 2ReQi2(Aa;, At)\Jhi(Pi) hi(Pi), (6) where / 1 1 ( ^ 1) and I 2i(P i) are the intensities of the Е ц and E 2\ beams at the P\ point (at the first output of interferometer). Similarly, for the second output of interferometer (point P2), we have Ip2 = -^22( ^ 2) + -^12( ^ 2) + 2 R e Q i2(Aa;, A t)\/I22(P2) / 12( ^ 2)- (7) Based on relations (5)—(7) and the energy conservation law, one can write 2 R e Q i2 (Aa;, A t)д/In(P\) I2i(Pi) + 2 R e Q i2 (Aa;, At)\/l22{P2) / 12( ^ 2) = 0. ( 8 ) Having analyzed expression ( 8 ), one can conclude be described in terms of equivalent plane-parallel that, when a plane monochromatic wave passes plate. An analysis of this equivalent scheme leads through a passive interferometer, fields with an to the following important conclusion: there is a inverse spatial and temporal intensity distribution potential possibility of concentrating the entire light are formed at its outputs. When a signal+noise energy at only one of the interferometer outputs. additive mixture arrives at the interferometer input, the result of interaction of these fields is determined The situations differing from that described above by their spatial and temporal coherent properties and have some specific features, which are presented the relative spatial and temporal mismatches (Аж, in Figs. 1—3. These figures show dependences il­ Ay, and At) of interferometer arms. Depending on lustrating the qualitative changes in the normal­ the combination of the aforementioned factors, one ized spatial and temporal correlation functions of can process interferometric signals to solve different the signal+noise additive mixture, Qi2(Ax, At) and problems related to selection of desired signal against Q21 (Аж, A t), as well as their components related to the background of additive noise. When the inter­ ferometer arms are characterized by zero mismatch the signal (QSl2(Ax, At), QS21(A x, At)) and noise (Аж = 0, Ay = 0, At = 0), its optical scheme can (Г2щ2 (Д ж) At), Qmi(Ax, A t)) for different situations: INTERFEROMETRIC METHODS FOR SUPPRESSING ADDITIVE NOISE 113 C \( A x , A t ) (b) S \.( A x ,A t ) Ax Fig. 1. (a) Normalized spatial and temporal correlation functions of radiation at the interferometer outputs and their components determined by (b) a signal from a point object with low temporal coherence and (c) radiation from uniformly spatially distributed noise with low temporal coherence. Q 12(A x, At), Q2)(Ax, A/) QCp(Ax, A/), Qc,,(Ax, A/) Q<Ilp(Ax, А/), Оф^Ах, At) Офр(Л х, At) (C) О ф, (Л х, At) A / Fig. 2. (a) Normalized spatial and temporal correlation functions of radiation at the interferometer outputs and their components determined by (b) a signal from a point object with low temporal coherence and (c) spatially matched point noise with high temporal coherence. (i) observation of a signal from a point object with (ii) observation of a signal from a point object with a low temporal coherence against the background of a low temporal coherence against the background of noise with uniform spatial distribution and low tem­ point noise (spatially aligned with this object) with poral coherence (Fig. 1); high temporal coherence (Fig. 2 ); 114 NIKITIN et al. Q 12(Av, Д/), 0 21 (Ax, ДО Q c (A x, ДО, Q cA A x , At) Оф (Дх, At), Оф (Дх, ДО (Ax, At) (b) A /A-\ О/ ф|1(Лл\ At) \Пф,,(Дх, Д/). 1 \ 1 / 1 / \ \ \\ V , V 1 /\ / / S \ .( A x ,A t ) V V Дх V At Fig. 3. (a) Normalized spatial and temporal correlation functions of radiation at the interferometer outputs and their components determined by (b ) a signal from a point object with low temporal coherence and (с ) a signal against the background of spatially mismatched point noise with low temporal coherence. (iii) observation of signal from a point object withcomponent can be formed at the interferometer out­ low temporal coherence against the background of put. In this case, the useful signal is proportionally spatially mismatched point noise with low temporal distributed between the interferometer arms. This coherence (Fig. 3). result is obtained by tuning the interferometer optical axis to the point noise and introducing a spatial An analysis of the dependences presented in Fig. 1 mismatch of interfering beams by a value exceeding shows the following. When a signal from a point ob­ the spatial coherence length of the signal. ject with low temporal coherence is observed against the background of uniformly spatially distributed noise with low temporal coherence, introduction of 2.2.

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