The use of a continuously varying index of refraction provides new degrees of freedom in the design of lens systems. By use of the third-order aberration theory developed by Sands, the effectiveness of these new degrees of freedom in correcting third-order aberrations is determined. After the theory is cast into a form suitable for a computer, two major designs are done. The first is a singlet with an axial gradient that is corrected for third-order spherical and chromatic aberrations and has no third-order distortion. A radial gradient is used in a singlet to correct all third-order monochromatic aberrations except Petzval curvature of field. The results of the study indicate that axial gradients have the same effect as aspheric surfaces for third-order aberrations. The study also shows that radial gradients are more effective in aberration correction than axial gradients and have a greater potential in lens design.
© 1971 Optical Society of America
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