The first-order quantity of the optical structure can be obtained using the ybar-y diagram and this diagram has a control point quantity. Based on the concept and quantity of the ybar-y diagram, this paper establishes a mathematical model to calculate an optical system’s first-order structure. The aberration is induced by the deflection of the transmission rays. If a first-order structure has a minimal total deflection angle of the first paraxial ray and the second paraxial ray, the higher order aberration will have a small value and the calculated first-order optical structure will be the best. According to the mathematical model, the issue of optical structure calculation is converted to a numerical optimization problem. And the objective function, i.e. the sum of the first and second paraxial ray’s deflection angles, is constructed. After comparison among etween many kinds of numerical optimization algorithms, the particle swarm optimization algorithm is used to solve the problem. Then a calculation program containing graphical user interface (GUI) is developed to calculate the first-order structure quickly and efficiently. The basic design parameters of the optical system are imported into the GUI after some treatments, then the resulting first-order structure is obtained after some clicks of the mouse. The resulting structure is thereafter converted to a practical lens system by the use of commercially available optical design software such as ZEMAX. After a lens optimization process, an actual optical system is accomplished. According to the method proposed in this paper and by the use of the calculation program, a 13 megapixel mobile phone camera lens is designed first. The F# of this lens system is 2.3 and the full field of viewing angle is 70 degree. The system has a total length of 4.5 mm and a distortion of 1.2%. Only four aspheric lenses are used and the other optical performance meets the design requirements as well. In addition, an eyepiece of helmet-mounted display system is designed, in which only two lenses are used and a visual field angle of 90 degree is achieved. The entrance pupil is 5 mm width and the image diagonal length is 65 mm. This system has a total length less than 45 mm and eye relief greater than 12 mm. Other performance of the eyepiece can also meet the requirements. These designs of the two optical systems demonstrate that the proposed method is reliable in calculating the optical structure of the optical system.