Davis J A, Smith D A, McNamara D E, Cottrell D M, Campos J
Appl Opt. 2001 Nov 10;40(32):5943-8. doi: 10.1364/ao.40.005943.
The fractional derivative spatial-filtering operator is useful for image-processing applications, particularly for examination of phase objects. Experimental implementation is difficult because the mask function combines both amplitude and phase. We present a simple one-dimensional analysis of the fractional derivative operation and note similarities with the fractional Hilbert transform. We demonstrate how to encode these amplitude and phase masks using a phase-only liquid-crystal spatial light modulator and present experimental results. Finally, we introduce a radially symmetric extension of this operation that is more useful for objects having an arbitrary shape.
分数阶导数空间滤波算子在图像处理应用中很有用，特别是在相位物体检测方面。由于掩模函数同时包含幅度和相位，因此实验实现较为困难。我们给出了分数阶导数运算的简单一维分析，并指出其与分数阶希尔伯特变换的相似性。我们展示了如何使用纯相位液晶空间光调制器对这些幅度和相位掩模进行编码，并给出了实验结果。最后，我们介绍了该运算的径向对称扩展，这对于具有任意形状的物体更有用。
