A new method to optimize the azimuth angle of elements in a projection lens

In the manufacturing process of high-precision photolithography lens, clocking of lens element is a commonly used and efficient method to compensate the surface figure error. This method obtains the optimal azimuth angles of a lens element. With complex description of the surface figure error, developing a mathematical model to optimize the azimuth angle of the element is difficult. This work expresses the surface figure error and wavefront aberration of a lens system with Zernike polynomials. Results indicate that the surface figure error is linearly correlated with the induced wavefront aberration at any point field of view. Thus, a mathematical model adopting this linear relationship is proposed to optimize the azimuth angles of a lens element. Employing the proposed mathematical model, the optimization keeps good efficiency and precision. The clocking optimization instance confirms that the mathematical model is effective for clocking optimization.