The manufacturing technique of aspherical surfaces relies on the assistant optical test design. The paper introduces the typical methods of classic test and null compensation test. Based on the third order spherical theory, the aplanatic expression of classic test and null compensation is derived. In order to realize the aspherical test of large diameter and large relative aperture, and even super large diameter and super large relative aperture. In this paper, the new theory and concept of conjugate correction aspheric test is proposed for the first time. The test is applicable to convex and concave aspheric surface. The principle of conjugate correction test is explained. The basic theory of conjugate correction is established. The analytical mathematical expressions of spherical aberration for three kinds of conjugate correction test configurations are explored. Optical designs of three self-collimating conjugate correction lenses and Offner null test are given. The difference of conjugate correction test is compared with classic test or null compensation test. According to theory analysis, the mathematical expression of conjugate correction aspherical test includes the cases of classic aspheric test and null compensation aspheric test. And the mathematical expression of classic aspheric test and null compensation aspheric test is a special case of the conjugate correction aspheric test.
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