基于单次傅里叶变换的分段衍射算法

针对单次傅里叶变换算法(S-FFT算法)受到采样定理的约束,衍射面画幅尺寸和有效内容像素数无法灵活控制,很容易出现衍射面画幅尺寸大小与衍射距离不匹配的情况,本文提出了一种分段衍射算法。首先,在采样数、光的波长、初始衍射面大小确定的情况下,利用拆分的衍射距离比控制最终衍射面画幅尺寸。然后,对单次衍射计算结果与分段衍射计算结果进行了图像相似度对比。实验表明,分段衍射算法可在画面强度分布不变的情况下,提高有效像素数目,数据量增加了2~3个数量级。此外,文章分析了造成误差的一个主要原因来自有效数据分辨率提高后,细节分布与低分辨率像素值之间的差别。在图像细节较丰富时,其差别较大。因此这种差别应视为优于直接计算的一种结果。本算法能够获得更加清晰的图像细节,灵活调整衍射面画幅尺寸,使得S-FFT算法在大衍射距离问题计算中能发挥其算法优势。

Step diffraction algorithm based on single fast Fourier transform algorithm

Due to the constraints of the sampling theorem, it is not possible to flexibly control the diffractive frame size of the single Fourier transform algorithm and the number of effective content pixels and it is highly likely that the size of the diffractive surface frame does not match the diffraction distance. To solve this problem, we propose a step diffraction algorithm. First, in the case of a fixed number of samples, the wavelength of the light, the size of the initial diffraction surface, and the final diffractive frame size can be controlled by the split diffraction distance ratio. Then, the single-diffraction calculation results are compared with the segmented diffraction calculation results for image similarity. Experiments show that the step diffraction algorithm can increase the number of effective pixels and the data volume increases by 2-3 orders of magnitude. In addition, the following conclusion is drawn:one of the main causes of errors is the difference between the distribution of details and the low-resolution pixel values after the resolution of the effective data is increased, and it is also known that the richer the image details, the greater the difference. Therefore, this difference should be regarded as a better result than that of direct calculation. Through this algorithm, clearer image details can be obtained, and the size of the diffraction surface frame can be flexibly adjusted, so that the S-FFT algorithm can exert its algorithm advantage in the calculation of the large diffraction distance problem.