航空共形光学窗口的外表面形状由空气动力学要求确定，常常是某种非对称的自由曲面，它在光路中会引入大量像差。通过将窗口内表面面形优化设计成适当的自由曲面，可以实现对外表面引入像差的校正。研究了适用于共形窗口的自由曲面的特点。给出了自由曲面共形窗口的具体设计方法。分别针对在窗口后加入的不同光学设计参数的中波红外光学系统设计相应共形窗口，设计结果表明，使用这种方法设计完成的自由曲面共形窗口校正了窗口外表面引入的大量像差，且对其后相应光学系统的成像质量影响很小。

The outside surface shape of the aerial conformal optical window is determined by the aerodynamic requirement and is often an asymmetric free-form surface which produces a large number of aberrations. The aberrations can be reduced by appropriate inner surface shape of conformal window after design and optimization. The characteristics of free-form surface which is applied to the conformal optical window are studied. The specific design method of aerial conformal optical window is given. The conformal optical windows are designed for corresponding medium-wave infrared optical systems which are placed behind them. And the design results show that the conformal optical windows through design and optimization with this method reduces the aberrations in large quantities produced by the free-form outside surface. And the conformal optical windows have small influence on the image quality of corresponding optical systems when these optical systems are placed behind the corresponding conformal optical windows.