High-end optical manufacturing imposes stringent demands on the irregularity and wavefront error of optical components. Fizeau interferometer serves as a critical instrument in the field of optical precision metrology, offering high accuracy and high sensitivity. The transmission sphere is the key component for achieving high-precision measurement of the surface figure of spherical elements and the wavefront error of optical lenses. It serves the double purpose of generating the reference wavefront and collecting the test wavefront. On one hand, it must provide a highly precise transmitted wavefront to suppress cavity-induced measurement error. On the other hand, it should also minimize errors introduced by the uncommon optical path between the reference and test wavefronts. Existing research basically addresses the design challenge of the transmission sphere by individual indicators, such as wavefront slope, F'C error, and mapping geometry. Due to the lack of in-depth understanding of the measurement error mechanism, the lens design follows conventional optimization approaches, aiming for comprehensive correction of various aberrations. The strategy not only increases design complexity but also diminishes cost-effectiveness in engineering due to over-design. Therefore, this paper analyzes the origin of measurement error in Fizeau interferometry and establishes a theoretical model linking pupil aberration and retrace error for the first time. It reveals the underlying mechanism through which the F# of the transmission sphere and the radius of curvature of the testing object affect pupil aberration and influence retrace error further. A 6-inch F/7.2 transmission sphere was designed, and simulation analyses were conducted to validate the relationship between imaging aberrations, intrinsic pupil aberrations, and total pupil aberrations. The correlation between pupil aberrations and retrace errors across different testing objects was also presented. The trend is closely related to the stop-shift effects at the theoretical level. Tolerance analysis and prototype assembly were conducted for this lens. By actively compensating the lens spacing, a transmitted wavefront with a defocus term of 0.03λ and an overall wavefront PV of 0.32λ was achieved, exceeding tolerance expectations. Retrace error measurement experiments were carried out, during which the test objects were shifted to generate 10 interference fringes. The retrace error was obtained by subtracting the null measurement result from the non-null measurement result. The test groups are as follows: (1) measuring a convex surface (R = 100mm) using the self-developed 6-inch F/7.2 transmission sphere; (2) measuring a convex surface (R = 100mm) using a commercial 4-inch F/3.3 transmission sphere; (3) measuring a concave surface (R = 27.61mm) using a commercial 4-inch F/3.3 transmission sphere. From the above theoretical analysis and simulation results, it can be concluded that pupil distortion contributes to coma in the retrace error. The total pupil distortion coeffcient and the Zernike coeffcient of the coma component in the retrace error of each test group were statistically analyzed and showed good consistency. It confirms that the proposed design methodology based on pupil aberration theory can accurately predict retrace errors introduced by transmission spheres. In summary, the design theory proposed in this paper contributes to a deeper understanding of the relationship between the imaging aberration, pupil aberration of the transmission sphere and the corresponding cavity error, retrance error in spherical surface metrology. It facilitates setting reasonable design goals and effcient optimization strategies for the transmission sphere. Moreover, it offers a potential solution for extreme measurement scenarios such as ultra-high precision and aspheric testing by compensating pupil aberration for specific test objects.