Gradient-index (GRIN) materials possess an index ofrefraction that varies spatially. By providing additional designvariables, GRIN lenses can improve system performance and reducethe number of lenses while maintaining system performance. In orderto realize these benefits, however, manufacturing tolerances forgradient-index lenses are required. Previous research used atrial-and-error approach applied to the polynomial description ofthe profile. The individual coefficients of the polynomial weretreated as independent parameters, and the tolerances wereunrelated to the manufacturing processes used to create thegradient. The results were neither applicable for other lensdesigns nor practical for manufacturing. Thisresearch describes the first systematic analysis of tolerances forthe index profile in axial GRIN lenses (i.e., the gradient is alongthe optical axis.) Variations in the profile shape and in the tiltbetween the gradient direction and the optical axis are considered.A linear approximation to the true ray trajectory is made. Usingperturbation analysis, the first-order correction to the opticalpath length (OPL) along a ray is calculated from a change in theprofile. This method is computationally fast since rays do not needto be traced through the perturbed system; only data from the raytrace of the nominal system and the perturbation are required. TheOPL is used to calculate the root mean squared wavefront error atbest focus. This form is consistent with common tolerance analysisschemes.