We investigated the pupil functions of specific-shaped apertures generated by Lambertian illumination with a rectangular light pipe to derive the corresponding optical transfer functions (OTFs) in aberration-free and defocused optical systems. The semianalytical results indicate that the curves of the OTF of the optical system vary with the form of the shaped apertures that are generated by illumination with different geometric structures of light pipes and light sources. It was found that the OTF values of even-peak frequencies decrease when the Lambertian light source decreases. If there are a total of n X n individual apertures within a pupil, then n near-periodical peaks will appear on the OTF curve. It is evident that the values of the OTF remain almost unchanged even when the lengths of the light pipes are different. Furthermore, the geometric structure of the light pipe does not affect the resolution limit of the optical system, and under the condition of a larger defocused coefficient (omega)_(20), the results of the defocused system can coincide with those of the aberration-free systems.
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机译：我们研究了用矩形光导管通过朗伯照明产生的特定形状孔径的光瞳函数，以得出无像差和散焦光学系统中的相应光学传递函数（OTF）。半分析结果表明，光学系统的OTF曲线随形状不同的孔的形状而变化，这些形状的孔是通过用不同的光导管和光源的几何结构进行照明而生成的。发现当朗伯光源减小时，偶峰频率的OTF值减小。如果在一个瞳孔内总共有n X n个独立的光圈，那么OTF曲线上会出现n个近周期的峰值。显然，即使光导管的长度不同，OTF的值也几乎保持不变。此外，光导管的几何结构不影响光学系统的分辨率极限，并且在较大的散焦系数ω_（20）的条件下，散焦系统的结果可以与像差的结果一致。免费系统。
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