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Thesis (Ph. D.)--University of Rochester. Institute of Optics, 2000.
The incorporation of gradient-index (GRIN) material into optical systems offers novel and practical solutions to lens design problems. However, widespread use of gradient-index optics has been limited by poor correlation between gradient-index designs and the refractive index profiles produced by ion exchange between glass and molten salt. Previously, a design-for-manufacture model was introduced that connected the design and fabrication processes through use of diffusion modeling linked with lens design software. This project extends the design-for-manufacture model into a time-varying boundary condition (TVBC) diffusion model. TVBC incorporates the time-dependent phenomenon of melt poisoning and introduces a new index profile control method, multiple-step diffusion. The ions displaced from the glass during the ion exchange fabrication process can reduce the total change in refractive index (An). Chemical equilibrium is used to model this melt poisoning process. Equilibrium experiments are performed in a titania silicate glass and chemically analyzed. The equilibrium model is fit to ion concentration data that is used to calculate ion exchange boundary conditions. The boundary conditions are changed purposely to control the refractive index profile in multiple-step TVBC diffusion. The glass sample is alternated between ion exchange with a molten salt bath and annealing. The time of each diffusion step can be used to exert control on the index profile. The TVBC computer model is experimentally verified and incorporated into the design-for-manufacture subroutine that runs in lens design software. The TVBC design-for-manufacture model is useful for fabrication-based tolerance analysis of gradient-index lenses and for the design of manufactureable GRIN lenses. Several optical elements are designed and fabricated using multiple-step diffusion, verifying the accuracy of the model. The strength of multiple-step diffusion process lies in its versatility. An axicon, imaging lens, and curved radial lens, all with different index profile requirements, are designed out of a single glass composition.
