泽尼克圆多项式在圆形光瞳的正交性和能够代表经典像差而被广泛应用到波前分析中，用泽尼克圆多项式作为矩形光瞳基底函数，通过推导得到在矩形光瞳上正交的多项式。这个在矩形光瞳上正交的多项式不仅是唯一的，而且也能够表示经典像差，就像泽尼克圆多项式在表示圆形光瞳时具有这样的特性一样。矩形光瞳上正交多项式像泽尼克圆多项式一样即可以用极坐标表示也可以用直角坐标表示。使用正交多项式前 15项在 MATLAB中用最小二乘法拟合窗口干涉数据，从拟合残差的 RMS统计分析的结果来看，能很好描述高质量熔石英材料在窗口方向上的折射率均匀性分布。

Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. Using the circle polynomials as the basis functions for their orthogonalization over rectangle pupil, we derive closed-form polynomials that are orthonormal over it. The polynomials are unique in that they are not only orthogonal across rectangle pupils, but also represent balanced classical aberrations, just as the Zernike circle polynomials are unique in these respects for circular pupils. The polynomials may be given in terms of the circle polynomials as well as in polar or Cartesian coordinates. Using the first 15 items of the rectangle polynomials to fit the data of interferometer of rectangle windows in the least squares method, we can get the conclusion that the first 15 items of the rectangle polynomials can be fit the data very well from the result of statistical analysis.