124 CAOL 2003. 1 t-20 September 2003. Alurhla. Cdmea. Ukraine

CORE POSITION IDENTIFICATION AT THE OPTICAL FIBERS CONNECTION BY AN AUTOCONVOLUTION METHOD

A. I. Filipenko, I. Sh. Nevludov

Kharkiv National University of Radio Electronics, depart. TAPR, 14, Lenin av., 61166, Kharkiv, Ukraine. Tel: (+380-57) 7021486

The precision positioning of optic fibers and component details is a main problem in fiber connectors and fiber splicing. As it is known, the exceeding of allowable misalignments of optical fibers has influence on the significant growth of insertion optical losses. Therefore the determination of a positioning objects space disposition relatively base coordinates is an important moment. The ferrule axes, the core axes of adjacent optical fibers or the technologic equipment base axes can act as this co'ordinates. The solution of this problem is achieved by the development of special automated methods ensuring errors, which are not exceeding of inspected values percent units, which lie in the region of the micrometer tenth path. Most of these methods are based on optical methods of image perception and' analysis. The coordinates deterimination optical methods can be realized under the scheme of optical fiber sounding by longitudinal or transversal (to an fiber axis) rays. The longitudinal sounding is usudly used when optical fibers are terminated by ferrules, and transversal - at the fiber splicing operations and other positioning operations of unterminated fibers. In both variants the standard setup scheme of the typical position identification system realize of a near field method and contain the light source with uniform intensity distribution, optical system &h high aperture, multi-element photoreceiver, more often charge coupled devices (CCD- sensors), and processing computing unit (personal computer). The difference is, that in the first case the mode field of the optic fiber core radiation is analyzed and in the second one - the optical field, as result of a focusing operation of transversally lighting fiber. However the refraction index profile has significant influence on field distribution in both cases.

Taking into account features of switching fiber-optical components, basic of which the small geometric sizes, complexity and. transformation of mode structure in traveling optical fields, availability of noise sources there are certain problems in a pattem recognition and forming of the conclusion about an optical fibers space disposition. Traditional methods of processing including sequential operations of an image filtration, solution of return problems and the determination of optical field distribution centers do not always satisfy contradictory requirements of productivity and accuracy. The overcoming of the indicated problems requires search and creation of the near approaches in improvement of methods and modeling of experimental data processing algorithms.

From features of optic .fiber structure it is known, that generally (when unacceptable defects are absent) the field intensity distribution has a symmetrical character concerning a core axis. The same feature t&es place for polarized mounting fibers, when the field modification along any polarization axes (slow or fast) is considered. The images obtained with longitudinal and transversal sounding of optical fibers and appropriate to them of field intensity distributions in one-dimensional variant on orthogonal axes are represented in fig. 1 a n d 2 '

When the object is accurating positioned the field distribution center is combined with the base center (for example, central element of the photoreceiver). At the decentration this picture has a side displacement.

From Figures it is .visible, th.at the signal is symmetrical and represents an even function conceming an axis taking place through a symmetry center and conterminous to a required core optical axis without displacement. Therefore the problem of transversal (radial)

0-7803-7948-9/03/$17.00 02003 IEEE

CAOL 2003. 16.20 September 2003, Alushta. Crimea, Ukraine 125

displacement monitoring is reduced to determination of a side shift of a signal symmetry center. This operation in the computing unit is expedient for executing with principle of a matched filtering in the autoconvolution form.

Figure 1

The signal model in a cut of optic field intensity distribution has a kind

w,P)=I(x,P)+n(x), (1)

Figure 2

where I ( x ) - the intensity distribution function, n ( x ) - the add.itive noise with zero average value, p - the transversal displacement.

The matched filter is an optimum filter minimizing RMS (root-mean-square) error of useful component I ( x ) selection from a mixture with a noise <(x), and the impulse performance of a matched filter with accuracy to constant factor should represent a conversion copy of useful component, namely

h(x) = aI(-x). (2 )

The output signal of a matched filter is determined by a convolution integral

D; 2

-D.'2 s(2) =&x)*h(x) = j ~ ( x ) h ( z - x ) d x ,

where D - registration region. If we substitute (2) in (3) and a = 1 in a point z = 0 we shall receive

(3)

126 CAOL 2003. 16-20 September 2003. Alushta. Crimea. Ukraine

D, 2 s(O)= J 1 2 ( x ) & + R , ; ( 0 ) = R R , ; ( O ) ,

-D, 2 (4)

where the evaluation of mutual covariance noise and signal function is close to zero owing to their statistical independence. Thus, the output signal of a matched filter corresponds to auto covariance function useful component I(x) and achieves a maximum at the moment of exact identification by this component.

The use of the matched filter generally assumes the knowledge of a signal model. Let's show, that the determination of a signal symmetry center displacement p is possible without a priori knowledge of signal parameters.

According to the expression (1) and, taking into account, that the useful signal is an even function shifted concerning a beginning of coordinates in the region of an explanatory variable on value p we can note

where f ( x ) = f ( - x ) .

relatively vertical axis of coordinates, namely

I (x , P) = f ( x - P) > ( 5 )

This property allows to use in (2) copy of input signal distribution inverted

h(x) = 4(-x - p) . (6)

The substitution (6) in (3) results in expression

D 2 0 2 s(z) = J<(X - p)S(x + p -. z)& = J I ( x ) I ( x + 2p - z)& + 0; , (7)

-D 2 -D 2 .I

defining operation of an autoconvolution. Property of an autoconvolution function, which satisfies to a condition ( 5 ) , is the

dependence from a displacement parameter p . An autoconvolution integral (7) for arbitrary signal I(x) under p = 0 is transformed into

D 2 s(2) J l ( x ) l ( z - X)&.

-D 2

In case if the condition (5) is observed and in (8) z = 2p , then the maximum of an autoconvolution is reached ..

which coincides value of the matched filters response (4). Therefore, the identification of a symmetry center position of optical field intensity distribution is reduced to execution of an autoconvolution of this signal and determination of a maximum position of resulting function. Let's underline, that the equations (7) - (9) are obtained without any a priori restrictions for the input signal excluding condition (5).

The executed consideration allows to create algorithm of the measured optical field distribution computer processing by an autoconvolution method. These operations are registration of the sequence of the signal discrete value, forming the second sequence with a return renumbering of elements, multiplication of element values of these sequences in

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-Init ial field pairs and summation of amplitude obtained products under

varied shift parameter z. To maximum resulting value of the obtained sum there corresponds such a shift of the second sequence conceming first, for which their concurrence on a criterion of a minimum RMS-error is observed.

Figure 3 The possibilities of algorithm were researched by modeling on the computer. Two kinds of field distribution - a gauss type (fig.3) and the so-called W-type, which characteristic

. of multilayer optical fibers (fig.4) were researched. In fig.3 and 4 the initial field amplitude distributions with

-100 -75 -50 -25 0 25 50 75 100 125 additive 10% - noise and Point coordinate calculated autoconvolutions

Figure 4 are indicated. The image digitization step with

allowance for fiber performances, matrix CCD and optical system magnification makes 0.1 p n . The coordinate of initial field distribution center settled account in the

correspondence with an

center of field distribution ' '

function

convolution

-150 -125 -100 -75 -50 -25 n 25 50 75 100 125 150 Point coordinate

I:? 7 Normalized . lC,,=101 ~ -Measured field equation, defining gravity

amplitude

convolution 012

jwdx

J 4 x W . (10)

- 012 xc = ,312

-012

-. .. .... .. In figures k,,, - a

an autoconvolution Figure 5 maximum.

The similar procedures were made for real optical fields obtained on the measuring equipment, realizing a near field method [ I , 21. Input fiber radiation distribution with a step-index profile (see fig.1) and it an autoconvolution are represented on fig.5. The initial optic field distribution in transversal plane to fiber axis created by a single mode fiber under transversal sounding (see fig.2) and it an autoconvolution are represented in fig.6.

-300 -200 -100 0 100 200 300 400 500 pixel number appropriate to Point coordinate

128 CAOL 2003, 16-20 September 2003, Alushta. Crimea, Ukfaine

.

-200 -150 -100 -50 0 50 100 150 200 Point coordinate

Figure 6 The researches show, that the autoconvolution calculation outcome depends on the

length of processed signal realization, background and noise level. This feature is appreciable in fig.6 and is showed in growth of autoconvolution value outside of informative component field distribution area. However even with availability of significant measurement errors there is an obviously expressed autoconvolution maximum, which allows to determine positioning errors with a high accuracy. In the same time, the using for fiber position determination of equation (IO) with allowance for within the integration limits of uninformative signal area results to roughest errors reaching several tens of pixels.

'The research outcomes of offered algorithm accuracy are represented in the table. The equation (IO) was applied to distributions for account of initial field displacementp. The measured data were subjected previously to the filtration by a sliding average method, elimination of background and noise component outside of informative signal area. From the analysis of the table it is visible, that the error in all cases does not exceed two pixels. The reached error values of optic fiber positioning identification ensure design- technological requirements to allowable displacements generated on the base of the optical losses level.

Table

REFERENCE 1. Filipenko A.I. Method for fiber optic radiation analysis // Radiotekhnika. All-Ukr. Sci.

Interdep. Mag. 1997. N 103. P.26-30. 2. Malik B.A. Filipenko A.I. Precision measurement system of fiber-optic components details in data transmission systems // Radiotekhnika. All-Ukr. SCI. Interdep. Mag. 1997. N 103. P.31-34.