### Fast calculation of computer generated hologram based on single Fourier transform for holographic three-dimensional display

Author(s):

Chang, Chenliang; Zhu, Dongchen; Li, Jiamao; Wang, Di; Xia, Jun & Zhang, Xiaolin

Abstract:

“We present an efficient method for the fast calculation of computer generated hologram (CGH). The 3D object is split into sub-layers according to its depth information. A 2D all-in-focus image is generated by sequential tiling all the layers in one plane. A Fourier hologram that contains all the information of 3D object is calculated from the fast Fourier transform (FFT) of the reassembled 2D image. By multiplying a pre-calculated multifocal off-axis digital phase mask (DPM) to the Fourier hologram, the content of each layer is axially relocated to different depth in the Fourier transform optical system to reconstruct the 3D object. The computation speed of the proposed method is greatly improved with only single FFT calculation process. Both of simulation and experimental results proves the validation of the proposed method.”

Publication: Displays
Issue/Year: Displays, Volume 69; Pages 102064; 2021
DOI: 10.1016/j.displa.2021.102064

### Recognizing fractional orbital angular momentum using feed forward neural network

Author(s):

Jing, Guoqing; Chen, Lizhen; Wang, Peipei; Xiong, Wenjie; Huang, Zebin; Liu, Junmin; Chen, Yu; Li, Ying; Fan, Dianyuan & Chen, Shuqing

Abstract:

“Fractional vortex beam (FVB) possessing helical phase can be applied in the shift-keying communication due to its fractional orbital angular momentum (FOAM) mode, which theoretically allows an infinite increase of the transmitted capacity. However, the discontinuity of spiral phase makes FVB more likely to be disturbed in turbulence environment, and the precise measurement of distorted FOAM modes is crucial for practical FOAM-based communication application. Here, we proposed a FOAM mode recognition method with feedforward neural network (FNN). Employing the diffraction preprocessing of a two-dimensional fork grating, the original optical features of FVBs can be extended along the far-field diffraction order, endowing FNN more feature information and saving calculation time, and enlarging the detection range to conjugate FOAM modes. The simulation results show that the 9-layer FNN can identify FOAM mode with interval of 0.1 with an accuracy of 99.1% under the turbulences of $$C^n_2=1×10^{–14}m^{–2/3}$$ and Δz=10m. Furthermore, we experimentally constructed a 102-ary FOAM shift-keying communication link to transmit gray image, and the signals are successfully demodulated by the FNN model with the pixel-error-rate of 0.07160. It is anticipated that the proposed FNN-based FOAM recognition method will break the limitation of precision measurement under turbulence environment in practical FOAM applications.”

Publication: Results in Physics
Issue/Year: Results in Physics, Volume 28; Pages 104619; 2021
DOI: 10.1016/j.rinp.2021.104619

### Experimental investigation in Airy transform of Gaussian beams with optical vortex

Author(s):

Xu, Yi-Qing; Li, Xia; Zhou, Lu; Zhou, Yi-Min; Wang, Fei & Zhou, Guo-Quan

Abstract:

“The Airy transform was first introduced for a Gaussian beam, and the output beam is an Airy beam. When the Gaussian beam is extended to the Gaussian beam with optical vortex, what kind of output beam will be achieved by executing the Airy transformation. Therefore, the experimental research on Airy transformation of a Gaussian beam with optical vortex is carried out, including the generation of Gaussian beams with optical vortex, the realization of Airy transform, and the related measurements of the output beams. The phase pattern is indirect measured and is recovered from the intensity pattern which is the interference result of a plane wave and the output beam. The experimental measurement results of the light intensity and the phase patterns of transformed Gaussian beams with the optical vortex are consistent with the corresponding numerical simulation results.

Based on the first and the second moments of light intensity, the centroid and the beam size are measured. According to the hyperbolic law of the beam width along the axial propagation distance, the propagation factor of the output beam is measured. The influences of the Airy coefficients and the topological charge on the intensity pattern, the phase pattern, the centroid, the beam size, and the propagation factor of transformed Gaussian beams with optical vortex are experimentally investigated, respectively. The intensity pattern, the phase pattern, the centroid, the beam size, and the propagation factor of a transformed Gaussian beam with optical vortex are also compared with those of the corresponding transformed Gaussian vortex beam. This experiment fully proves the effect of the optical vortex on the Airy transformation of Gaussian beams. Meanwhile, this study offers an optional method to generate Airy-like beams from Gaussian beams with optical vortex, which is beneficial to the applications of Gaussian beams with optical vortex.”

Publication: Results in Physics
Issue/Year: Results in Physics, Volume 28; Pages 104588; 2021
DOI: 10.1016/j.rinp.2021.104588

### Wide angle holographic video projection display

Author(s):

Chlipała, Maksymilian; a; Kozacki, Tomasz; Yeom, Han-Ju; Martinez-Carranza, Juan; Rafał; Kukołowicz; Kim, Jinwoong; Yang, Jong-Heon; Choi, Ji Hun; Pi, Jae-Eun & Hwang, Chi-Sun

Abstract:

“Holographic projection displays provide high diffraction efficiency. However, they have a limited projection angle. This work proposes a holographic projection display with a wide angle, which gives an image of size 306mm×161mm at 700 mm and reduced speckle noise. The solution uses single Fourier lens imaging with a frequency filter and hologram generation utilizing complex coding and nonparaxial diffraction. The experiment was performed with a 4K phase-only spatial light modulator (SLM) to prove the high efficiency of the developed numerical tools. Optical reconstruction shows high resolution and high image quality achieved from a single frame. Hence, displaying video at a full frame rate of the SLM is possible.”

Publication: Optics Letters
Issue/Year: Optics Letters, Volume 46; Number 19; Pages 4956; 2021
DOI: 10.1364/ol.430275

### Experimental estimation of the longitudinal component of a highly focused electromagnetic field

Author(s):

Maluenda, David; Aviñoá, Marcos; Ahmadi, Kavan; Martínez-Herrero, Rosario & Carnicer, Artur

Abstract:

“The detection of the longitudinal component of a highly focused electromagnetic beam is not a simple task. Although in recent years several methods have been reported in the literature, this measure is still not routinely performed. This paper describes a method that allows us to estimate and visualize the longitudinal component of the field in a relatively simple way. First, we measure the transverse components of the focused field in several planes normal to the optical axis. Then, we determine the complex amplitude of the two transverse field components: the phase is obtained using a phase recovery algorithm, while the phase difference between the two components is determined from the Stokes parameters. Finally, the longitudinal component is estimated using the Gauss’s theorem. Experimental results show an excellent agreement with theoretical predictions.”

Publication: Scientific Reports
Issue/Year: Scientific Reports, Volume 11; Number 1; 2021
DOI: 10.1038/s41598-021-97164-z

Author(s):

Yasuki, Daiki; Shimobaba, Tomoyoshi; Makowski, Michal; Suszek, Jaroslaw; Kakue, Takashi & Ito, Tomoyoshi

Abstract:

“Holograms are computed by superimposing point spread functions (PSFs), which represent the distribution of light on the hologram plane. The computational cost and the spatial bandwidth product required to generate holograms are significant; therefore, it is challenging to compute high-resolution holograms at the rates required for videos. Among the possible displays, fixed-eye-position holographic displays, such as holographic head-mounted displays, reduce the spatial bandwidth product by fixing eye positions while satisfying almost all human depth cues. In eye-fixed holograms, by calculating a part distribution of the entire PSF, we observe reconstructed images that maintain the image quality and the depth of focus almost as high as those generated by the entire PSF. In this study, we accelerate the calculation of eye-fixed holograms by engineering the PSFs. We propose cross and radial PSFs, and we determine that, out of the two, the radial PSFs have a better image quality. By combining the look-up table method and the wavefront-recording plane method with radial PSFs, we show that the proposed method can rapidly compute holograms.”