Abstract

The radial gradient-index rod lens array with unit magnification called SLA has been widely utilized in copy machines, LED printers, image scanners, and facsimiles as an imaging lens system of unit magnification, but the theoretical resolution limit analysis of SLA has not been defined. A theoretical resolution limit analysis of a radial gradient-index lens element has now been studied. Results of the first-order analysis are as follows: (1) an SLA with higher view angle had a higher resolution limit, (2) the meridional spot size increased in the peripheral zone of an image field because of vignetting. (3) A third-order aberration analysis has been done. In this analysis, not numerical but analytical aberration coefficient polynomials have been successfully obtained based on Moore and Sands.¹ Using these polynomials, the ray intercept curve was calculated without ray tracing through the lens medium. Results of the third-order analysis were as follows: (1) all aberrations were proportional to the square of the view angle; (2) spherical aberration and Petzval curvature were dominant; (3) astigmatism had a small effect for ray error; and (4) by optimizing high-order index coefficients, blur of the peripheral zone of the image field was improved.

© 1989 Optical Society of America