Precise algebraic method to solve the noncemented two-lens objective free from the aperture aberrations

An original method to enable the exact solution for the noncemented two-lens objective by means of any number of simultaneous non-linear equations is described. The method is limited to spherical surfaces without decentrations. Separations and refractive indices of glasses are fixed. Ail curvatures of surfaces are indirectly determined in the final stage. The typical meridional aperture aberrations deal with aplanatic and achromatic conditions. Essence of the method relies on formulation functions which contain trigonometric expressions and are nested up to certain depth. The method uses the advanced professional mathematical software which is indispensable for serving the non-linear system of equations. Numerical examples confirm the helpfulness of the method.