The two-dimensional spatial image transmission characteristics of the optical graded-index fiber with a refractive index distribution including fourth and sixth order terms in the core region are investigated. Since the GRIN fiber for image transmission has a large core radius, the most field is tightly confined to the center of the core. The effect of the core-clad interface on the image transmission characteristics is approximately evaluated. Therefore the GRIN fiber is assumed to have an infinitely-extended index profile. The propagation constants and the electric field distributions in the core region are strongly affected by the coefficient of the fourth order term, D4, but, are only slightly affected by the sixth order term. The optimum value of D4 is found to be 0.8, because the deviation of the difference between the propagation constants of the two consecutive modes becomes minimum. For the graded-index fiber with D40.8, the on-axis and off-axis transmission characteristics show that the two dimensional image can be transmitted for a length of more than 50 m and the beam waist of the output image becomes 1.3 times of that of the input for spatial impulse image signal.

Degradation of the two-dimensional images transmitted through a graded-index (GRIN) optical fiber is evaluated by considering the fourth and sixth order terms of the refractive index distribution, and the spatial inverse filter and Wiener filter are investigated in order to restore the degraded images. When a point image is transmitted through a practical GRIN fiber, the output image is degraded by the modal dispersion, i.e. the phase differences between the modes. This degraded image at the output plane of the GRIN fiber is restored by the spatial inverse filter and Wiener filter which are designed so that the filtered coherent transfer function of the GRIN fiber has almost flat spatial frequency spectrum. The transform function of the inverse filter is calculated by using only the on-axis point spread function (PSF) of the fiber and is found to be effective in a region near the propagation axis, because the fiber is space-invariant around the axis. By considering the difference between the on-axis and off-axis PSFs, the transfer function of the optimum Wiener filter is obtained. The optimum Wiener filter restores the off-axis PSF as well as that of the on-axis. The waists of the main peaks at which the intensities of the filtered on-axis and off-axis PSFs become 1/e2 of their maximum values, are 0.75 and 0.52 of those without filtering. The resolution of the PSFs corresponding to the point images transmitted in the range of 0-25 µm are increased. The levels of the small peaks in the field intensity distributions of the filtered on-axis and off-axis PSFs are also reduced and these peaks are low enough to obtain high contrast images at the output for the considered range.

Spatial color image transmission characteristics in the optical graded-index (GRIN) fibers are investigated in order to transmit two-dimensional spatial images. Color images can be transmitted through the GRIN fibers, when lasers of primary colors with adjusted powers are used at the input of the GRIN fiber and an achromatic optical system is applied at the output. The transmitted images through the GRIN fibers are degraded due to the refractive index profile aberration and chromatic aberration at the wavelengths of the primary colors λ10.442µm (He-Cd laser), λ20.532µm (the second harmonic of the YAG laser) and λ30.694µm (Ruby laser). The profile aberration is related to the coefficient of the fourth order term D4 of the refractive index profile of the GRIN fiber and the color aberration is ascribed to the wavelength dependence of the on-axis refractive index, n0, and the focusing parameter, lt, of the fiber. The minimum focusing depth, i.e. the profile aberration, is achieved for the minimum mode dispersion of a GRIN fiber with D40.8 at each wavelength of the primary colors. Also the minimum distance between the longitudinal positions of the on-axis (χiyi0) and off-axis (χi50µm, yi0) point images in the fiber (D40.8) becomes identical value of about 52µm at three different wavelengths of λ1, λ2, and λ3 for a transmission length of 51.965 m. For the GRIN fiber with D40.8, the longitudinal color aberrations for the on-axis and off-axis point image transmission are almost equal and the fiber does not have lateral aberration for the considered transmission length. The number of propagation modes in a GRIN fiber is different at each wavelength, so that, the intensities of the transmitted images at λ2 and λ3 are smaller than those at λ1. Therefore, the powers of the lasers which are used as of the sources of the primary colors should be adjusted in order to obtain output images with almost equal intensities at the wavelengths. The compensation of the longitudinal aberration for two-dimensional spatial color image transmitted through the GRIN fiber with D40.8 can be achieved using more than two rod lenses of different materials.