382 Optical Fiber Measurement advances in digital signal processing and high-sensitivity CCD technology greatly simplified the processing and analysis of digital images, allowing real-time obser- vation of the far-field and near-field images [10]. In principle, the far-field and the near-field are related and they are all deter- mined by the optical field distribution E(r) on the fiber cross section. In practice, near-field measurement requires a lens with large magnification, which may intro- duce image distortion for the measurement. In comparison, far-field measurement is more straightforward which only requires a scanning probe. If mechanical scan- ning stage is stable enough far-field measurement can potentially be more accurate with better signal to noise ratio and dynamic range, which can be observed by comparing Figure 4.2.6 with Figure 4.2.8 [9]. There are a number of alternative techniques to measure fiber mode-field diam- eter, such as the transverse offset method, the variable aperture method, and the mask method. The details of these methods can be found in [11]. 4.3 FIBER ATTENUATION MEASUREMENT AND OTDR Optical attenuation in an optical fiber is one of the most important issues affecting all applications that use optical fibers. A number of factors may con- tribute to fiber attenuation, such as material absorption, optical scattering, micro or macro bending, and interface reflection and connection. Some of these factors are uniform, whereas some of them vary along the fiber, especially if dif- ferent spools of fibers are fusion-spliced together. Characterization of fiber attenuation is fundamental to optical system design, implementation, and per- formance estimation. 4.3.1 Cutback Technique In early days, the cutback technique was often used to measure fiber attenu- ation. As illustrated in Figure 4.3.1, the cutback technique measures fiber trans- mission losses at different lengths. Suppose the attenuation coefficient a is uniform; the power distribution along the fiber is PðzÞ ¼ P 0 e Àaz . With the same amount of optical power coupled into the fiber, if the output power measured as P 1 , P 2 , and P 3 at the fiber lengths of L 1 , L 2 , and L 3 , respectively, the fiber attenuation coefficient can be calculated as a ¼ ½lnðP 2 =P 1 Þ=ðL 1 À L 2 Þ or a ¼ ½lnðP 3 =P 2 Þ=ðL 2 À L 3 Þ. For a single-mode fiber, there are only two orthogonal fundamental modes and the difference in their attenuations is generally negligible. For a multimode fiber, on the other hand, there are literally hundreds of propagation modes and