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. 2017 Dec 21;7:18011. doi: 10.1038/s41598-017-18147-7

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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(a) Experimental beam generated by SPP with p = 1, ℓ = 1. Brightness and colours refer to intensity (experimental) and phase (theoretical) respectively. (b) Input image entering the optimization loop. (c) On the left: diffracted pattern window (DPW) on the object plane, including the signal window (SW) where the image is formed. At each step of the algorithm, a replacement of the output signal amplitude with the desired image amplitude within the SW is imposed, while free phase is left on the whole DPW. On the right: corresponding hologram phase pattern after 200 iterations. On the hologram plane, direct amplitude-elimination and partial phase-quantization are performed at each step. Evolution of diffraction efficiency η (d) and signal-to-noise ratio (SNR) (e) during algorithm convergence to an optimized design of the computer-generated hologram for illumination with an OAM beam with indices (p = 1, ℓ = 1) (a–c).