RESUMO
Two methods to measure the cladding diameter of single-mode fibers are presented. The first method is based on an interference fringe measurement technique. Interference fringe spacing at two different planes is measured to determine the cladding diameter of the fiber. The theory of the fringe formation in the interferometeric arrangement using single-mode fibers is discussed. It is theoretically shown that the far-field overlapping Gaussian field distribution from the fibers shifts the position of the fringe maxima and minima. As a special case of unit fringe visibility the minima positions do not shift, whereasthe maxima positions are shifted. In the case of a Lloyd mirror arrangement it is shown that fringes can be obtained from a rough surface as well. A lens is used in the second method to image the two identical point sources that cause the interference. Through the use of the magnification and spacing of the images, the cladding diameter is estimated. It is shown that the accuracy of the fiber cladding-diameter measurement can be enhanced by generating multiple point sources. Consistent results of the fiber cladding diameter have been obtained with the proposed methods. Fiber cladding-diameter measurements with a standard error of less than 0.15 µm can be achieved.
RESUMO
Spatial differentiation can be performed by imaging an input pattern with a binary optical element consisting of Fresnel lenses having identical focal lengths but different center locations. Each of these lenses forms an image of the object at a different transverse location in the image plane. If the two lenses have a phase shift of pi rad, the two images will be subtracted, resulting in an image that is differentiated in the direction of the shifted lens positions. We show experimental results in which the optical element is written onto a programmable magneto-optic spatial light modulator.