Multimode optical fiber core measurement by speckle correlation Rodrigo Henao Juan A. Pomarico Nelida Russo Roberto D. Torroba, MEMBERSPIE Marcelo Trivi Centro de Investigaciones Opticas (CIOP) Casilla de Correo 124 La Plata 1900, Argentina E-mail: postmaster@ ciop.edu.ar and Universidad National de La Plata Faculty of Engineering La Plata 1900, Argentina Abstract. The modal distribution at the output of a multimode optical fiber behaves as a speckle pattern. Further, a speckle pattern carries information on the pupil diameter of the optical system exit aperture. Pupil measurements by speckle size determination may not be an easy task, because of the statistical nature of the speckle phenomena. The measurement of a multimode fiber core is proposed using a speckle autocorrelation algorithm to obtain the minimum speckle diameter pres- ent in the pattern generated by the fiber. Both computer simulations and actual pupils are used to test its performance. Core diameter measure- ments are carried out showing good agreement with the specifications supplied by the fiber manufacturer. 1 Introduction Measuring the final core diameter of an optical fiber is not done during fabrication, as is the case for the outer fiber diameter, which is usually controlled continuously.’ Considering step-index fibers, the core diameter can be defined by the step change in the refractive index at the core- cladding interface. Therefore the techniques employed for determining the refractive index profile (interferometric, near-field scanning, refracted ray, etc.z) can be used to mea- sure the core diameter. There are reports in the literature on the measurement of the core for the case of single- and multimode fibers. These approaches rely on interferometric and imaging techniques? and the speckle generated by a diffuser placed at the free end of the fiber.4 A speckle pattern carries information about several char- acteristics of both surfaces and optical systems. Thus, optical pamrneters, such as contrast, speckle size, and correlation degree, can be used in metrological applications to determine roughness, deformations, motion, pupil diameter, etc.s-’” These speckle patterns are usually generated by the scattering of coherent light from a rough surface. There exist, however, alternatives to this phenomenon, such as, for instance, the intensity distribution observed at the output of a multimode 1] The presence of speckle is caused step-index optical fiber. by mutual interferences of the modes being propagated. In particular, we are concerned with the measurement of the Subject terms: speckle correlation; speckle metrology; fiber optics. Optical Engineering 35(l), 26–30 (January 1996). Popcr ARC-04 rcceiwJ Dec. 15. 1994; rwisecl manuscript received Apr. 12. 1995; xccp[ul for puhliu[ ion Apr. 17. 1995. ~} 19c)6Socic[y O! pi,olo-op[ic~d Insmmemotion Engineers. 0(191-3286/96/$6.00. fiber core by relying on the fact that the pupil diameter of an optical system is directly related to the speckle size of the resulting speckle pattern. But, in spite of being a classical problem in optics, it is not simple to measure the size of the speckles present in the pattern. We developed an algorithm to compute the minimum speckle size present in a given pattern. Such speckle pattern is detected by a linear photodiode array (LPDA). Digital simulations and measurements of calibrated circular pupils are carried out for testing the performance of the algorithm. Finally, it is applied to actual multimode fibers to determine their core diameter. 2 Description of the Algorithm Let us assume a one-dimensional speckle pattern, obtained by intersecting a speckle diagram with a linear array of N identical photodiodes. At position i within the array, an in- tensity I(i) will be registered. The minimum speckle size is supposed to be large enough compared with the dimension of a single detector (pixel), so as to illuminate several of them. In this way, each speckle can be considered to be well- sampled by the array. To obtain the minimum speckle size present in the dia- gram, the following autocorrelation algorithm is proposed: 1. The vector I(i), containing the N intensity values reg- istered by the elements of the array, is stored. An ex- ample is shown in Fig. 1(a). 2. The discrete autocorrelation of vector I(i) is given byzyxwvutsrqpo N A(x) = ~ ,~[) I(i) I(i + x) . 1 (1) 26/ OPTICAL ENGINEERING / January 1996 /Vol. 35 No. 1 Downloaded From: http://spiedigitallibrary.org/ on 08/29/2012 Terms of Use: http://spiedl.org/terms