Holographic generation of beam spot array with high uniformity have been extensively investigated while existing methods cannot combine high quality and tunability. This paper demonstrated a method to generate beam spot array by using phase-only liquid crystal on silicon (LCOS) device. The proposed method is highly flexible and tolerant to the defects within the LCOS device. The uniformity deviation of the speckle array can be limited to within ±5% in the numerical simulation and the experimental results agreed well with the simulation results.

Generation of beam spot array with high uniformity has been extensively investigated due to its wide range of applications including optical data storage [

In the diffraction regime, the Dammann grating [

In this paper, we propose a method to compose the beam splitting holograms by a series of sinusoid functions with different periods. In this way, the holograms for the spot array generation can be described by a few parameters, i.e., the amplitudes and the periods of the sinusoid functions. While the periods of the sinusoid functions determine the pitch within the generated spot array, the amplitudes affect the power distribution between the spots. In addition, the defects within the LCOS device can also be compensated by fine-tuning the amplitude of each sinusoid component. More importantly, this parametric way of describing the complex beam splitting holograms significantly reduced the number of variables for optimization, leading to a faster and more effective optimization process. In a proof-of-concept experiment, we successfully demonstrated that the proposed method was able to generate highly uniform spot array within a few iterations.

In this work, the holograms for the spot array generation are based on a series of sinusoid functions. The phase profiles of the holograms, i.e.,

The operation principle of this type of holograms is illustrated in the

By combining multiple sinusoid functions in the way described in Equation (1), the number of spots can be increased. The example given in

In this scheme, the number of variables for the optimization was proportional to the number of spots within the target array instead of the number of pixels within the holograms. As a result, the number of variables that require optimization was significantly reduced. This enabled the use of the standard small-scale optimization algorithm for the automated generation of the

The merit function used in this optimization process was based on the Pearson correlation coefficient

In order to evaluate the feasibility of the proposed method, a simulation was carried out to generate 1 × 9 and 1 × 15 spot arrays, respectively.

Subsequently, we increased the size of the target spot array to 1 × 15 in order to evaluate the scalability of the proposed method. In this case, eight sinusoid series were used to describe the hologram. The intensity profiles of the generated spot array were plotted in

The optical system shown in

In the experiment, the initial holograms were generated through the simulation process, which was described in the above. Therefore, the spot array generated by the initial hologram can be closer to the target profile, potentially leading to a faster optimization process. Nevertheless, there still would be some discrepancy between the simulation and experiment since the simulation cannot cover every aspect of the actual optical system, including the misalignment of the optical system, manufacturing errors within the lens, depolarization effect and the phase flicker within the LCOS device, etc. It should be noted that the impact of the depolarization effect of the LCOS device was particularly strong, especially when a large spot array was required. In this case, the intensity of the central spot within the array would be higher than expected. As a result, the target intensity of the central spot was intentionally suppressed for the initial hologram generation through the simulation. During the experimental optimization process, the target intensity level of each spot within the array can be modified adaptively based on the progress of the optimization.

The progression of the optimization process was plotted in

In this work, we proposed a novel method to describe the complex beam splitting holograms by a series of sinusoid functions. This significantly reduced the search dimensions for the beam splitting holograms from hundreds of thousands to fewer than 10. As a result, a rapid and effective generation of the beam splitting holograms can be realized for different spot counts and pitches. The proposed method was validated through both the simulation and experiments by using the standard gradient descent algorithm. It was successfully demonstrated that the proposed method was able to generate a uniform spot array within 15 iterations. More advanced optimization algorithm can be used to further improve the uniformity and the optimization speed.

Conceptualization, H.Y.; methodology, H.Y.; software, Y.L.; validation, Y.L., X.Z. and H.Y.; data curation, Y.L., X.Z. and H.Y.; writing—original draft preparation, Y.L.; writing—review and editing, H.Y.; visualization, Y.L.; project administration, H.Y. and D.C.; funding acquisition, H.Y. and D.C. All authors have read and agreed to the published version of the manuscript.

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

The authors declare no conflict of interest.

Holograms and the corresponding profiles of the generated spot array based on one sinusoid function with different amplitudes (

The hologram (

Flow chart of the optimization process.

Optical setup for the simulation.

The initial and optimized 1×9 (

Optimized holograms for (

Progression of the optimization for (

Experimental setup for the online spot array generation.

The original and result generated beam spot array for 1 × 9 (

2D profiles of the experimentally generated 1 × 9 (

Progression of the experimental optimization for 1 × 9 (