High-end optical manufacturing imposes stringent demands on the irregularity and wavefront error of optical components. The Fizeau interferometer serves as a critical instrument in optical precision metrology, offering high accuracy and 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, fulfilling the dual role 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 minimize errors arising from the uncommon optical path between the reference and test wavefronts. Existing research basically addresses the design challenge of the transmission sphere using isolated metrics-such as wavefront slope, F^\primeC error, and mapping geometry. Owing to the lack of in-depth understanding of the underlying measurement error mechanism, lens design relies on conventional optimization approaches that aim for comprehensive correction of multiple aberrations. This strategy not only increases design complexity but also reduces 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. It reveals the fundamental mechanism by which the F# of the transmission sphere and the radius of curvature of the test object influence pupil aberration, thereby affecting retrace error. A 6-inch F/7.2 transmission sphere is designed, and simulation analyses are performed to validate the relationship among imaging aberrations, intrinsic pupil aberrations, and total pupil aberrations. The correlation between pupil aberrations and retrace errors across different test objects is also demonstrated, with the observed trend closely aligned with stop-shift effects at the theoretical level. Tolerance analysis and prototype assembly are carried out 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 is achieved, exceeding tolerance expectations. Retrace error measurement experiments are conducted by shifting the test objects to generate 10 interference fringes. The retrace error is obtained by subtracting the null measurement result from the non-null measurement result. The test groups are as follows: 1) measurement of a convex surface (R=100\;\mathrmmm) using the self-developed 6-inch F/7.2 transmission sphere; 2) measurement of a convex surface (R=100\;\mathrmmm) using a commercial 4-inch F/3.3 transmission sphere; 3) measurement of a concave surface (R=27.61\;\mathrmmm) using a commercial 4-inch F/3.3 transmission sphere. Based on the theoretical analysis and simulation results, pupil distortion is found to contribute to coma in the retrace error. Statistical analysis of the total pupil distortion coefficient and the Zernike coefficient of the coma component in the retrace error for each test group show strong consistency, confirming that the proposed design methodology grounded in pupil aberration theory can accurately predict retrace errors introduced by transmission spheres. In summary, the design theory proposed in this paper advances the understanding of the interrelationships among imaging aberration, pupil aberration of the transmission sphere, and the corresponding cavity and retrace errors in spherical surface metrology. It facilitates the establishment of reasonable design objectives and efficient optimization strategies for transmission spheres. Moreover, it offers a potential pathway for extreme measurement scenarios such as ultra-high precision and aspheric testing by enabling pupil aberration compensation tailored to specific test objects.