Fourier analysis is a key tool in physics and engineering in the broadest sense and is particularly used in the field of optics to design and study the properties of advanced imaging systems. Fourier optics as a distinct topic is usually taught in final-year undergraduate or first-year postgraduate studies, and a wide range of teaching approaches have been used to describe and explain its key concepts. Concerning practical work to accompany classroom lectures, the simplest laboratory experiments are based on studying how the properties of some diffracting aperture (pupil) are related to the corresponding Fraunhofer diffraction pattern, but this approach usually does not consider in detail the concepts of the optical transfer function and spatial frequencies. We here describe a simple experimental setup that fills this particular gap and that illustrates the spatial frequency-domain response of a simple optical system using incoherent light. The Modulation Transfer Function is directly measured for several different pupil geometries and shows very good agreement with theoretical calculations. This experiment clearly demonstrates spatial transfer function concepts in Fourier optics, complementing and extending other studies of Fourier transforms in physics that may consider similar ideas in a time and frequency signal-processing context.

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说明傅立叶光学中空间传递函数概念的本科实验

傅里叶分析是最广泛意义上的物理学和工程学的关键工具，特别用于光学领域，以设计和研究先进成像系统的特性。傅立叶光学作为一个独特的主题通常在本科最后一年或研究生一年级学习中教授，并且已经使用了广泛的教学方法来描述和解释其关键概念。关于伴随课堂讲授的实际工作，最简单的实验室实验是基于研究某些衍射孔径（瞳孔）的性质与相应的夫琅禾费衍射图案如何相关，但这种方法通常没有详细考虑光学传递的概念功能和空间频率。我们在这里描述了一个简单的实验装置，它填补了这个特殊的空白，并说明了使用非相干光的简单光学系统的空间频域响应。调制传递函数是针对几种不同的瞳孔几何形状直接测量的，并且与理论计算非常吻合。该实验清楚地展示了傅立叶光学中的空间传递函数概念，补充和扩展了物理学中傅立叶变换的其他研究，这些研究可能会在时间和频率信号处理环境中考虑类似的想法。