Volume 11 Issue 4
Jul.  2018
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HU Qi, WANG Zhe, LIU Hong-shun, XUE Zhi-wen, DENG Jia-chun. Step diffraction algorithm based on single fast Fourier transform algorithm[J]. Chinese Optics, 2018, 11(4): 568-575. doi: 10.3788/CO.20181104.0568
 Citation: HU Qi, WANG Zhe, LIU Hong-shun, XUE Zhi-wen, DENG Jia-chun. Step diffraction algorithm based on single fast Fourier transform algorithm[J]. Chinese Optics, 2018, 11(4): 568-575.

# Step diffraction algorithm based on single fast Fourier transform algorithm

##### doi: 10.3788/CO.20181104.0568
Funds:

National Natural Science Foundation of China 11604243

National Natural Science Foundation of China 11504268

National Natural Science Foundation of China 11204213

Natural Science Found Project of Tianjin 16JCQNJC01600

More Information
• Corresponding author: WANG Zhe, E-mail:snowleoperd@126.com
• Received Date: 14 Dec 2017
• Rev Recd Date: 10 Feb 2018
• Publish Date: 01 Aug 2018
• 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.

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