QC 351 A7 no. 39 / Optical systems known as "null correctors" are often required to test certain aspheric optical surfaces. This report classifies these systems on the basis of their first -order geometry and analyzes the merits of each type. The behavior of optical aberrations, especially spherical aberration, in these systems is examined in the context of computer optimization techniques, particular attention being given to some design problems unique to null correcting systems. Orthonormal concepts are applied to the problem of reducing spherical aberration in null correctors. It is shown that exceedingly simple merit functions may be constructed to streamline the optimization process. These merit functions are composed of simple linear sums of the angular spherical aberration coefficients B1, B3, B5, and B7. Thus, minimizing the following sums will improve nearly diffraction - limited systems: ( - 13 B1 + 1 B3 - g' B5 - B7) , ( 4.131 - B3 - B5) , ( - 2B1 - B3) , and ( - B1) /1-5- 3/7 3 or ( 120 B3 + 960 B5 + 840 B7 ) , ( 840 B5 + 2520 B7) , and ( 840 B7) Non -diffraction - limited systems may be optimized by minimizing the sums ( 6 B3 + 5 B5 + 5 B7) , ( p B5 + 3 B7) , and ( 1 0 B7) To demonstrate the effectiveness of the techniques discussed, the process of designing a specific null correcting system is followed in detail.