Objective Due to the inability of flat display technology to meet people's desire to perceive three-dimensional depth information, and the inability of bulky display devices in head mounted 3D display products to meet portability requirements, glasses-free 3D (three-dimensional)display technology has become a highly promising development direction. Although significant progress has been made in the development of glasses-free 3D displays based on cylindrical barriers or microlens arrays utilizing the principles of geometric optics. However, the inherent defects of geometric optics lead to issues such as reduced image brightness, poor fusion performance, and significant waste of pixel resources. In contrast, the glasses-free 3D display technology based on diffraction optics has largely solved these problems. At present, the implementation methods using diffraction gratings and traditional diffraction optical elements still exhibit drawbacks such as low brightness, significant color difference, and complex design and manufacturing processes. Therefore, in order to improve light efficiency and image clarity, and reduce design and manufacturing difficulties, a phase modulation panel has been designed. By aligning the array of harmonic diffraction subunits with the pixel level of the LCD panel, a good glasses-free 3D visual experience can be provided.

Methods A phase modulation panel consisting of four interleaved arrays of harmonic diffraction subunits was designed. In TracePro software, nearly 10 000 light rays were vertically incident on two individual pixels located in the horizontal direction of the phase modulation panel to verify the convergence effect of light rays (Fig.2), simplifying the complexity of designing and manufacturing harmonic diffraction structures. To meet the binocular parallax attribute, a display effect with a 32 mm horizontal interval for dual views and uniform distribution of four viewpoints has been achieved. At the same time, the effect of oblique incidence of light sources on the total luminous efficiency was studied under different step approximations (Tab.3).

Results and Discussions Compared with ordinary diffraction structures that require three RGB diffraction subunits, harmonic diffraction optical elements have the same optical power and high diffraction efficiency at multiple high diffraction levels, and can use the same harmonic diffraction structure to modulate the three RGB outgoing rays, thereby reducing design complexity and manufacturing difficulty, improving optical efficiency and image clarity. Within the range of 384.2-402.8 mm, bright color 3D parallax images can be seen over a length of approximately 18.6 mm. In addition, when the incident angle is 0°, the total luminous efficiency of the 16th order approximate harmonic diffraction microstructure can reach 60.65%, and there is little change in the total luminous efficiency when the incident angle is within 10°. By combining with LCD display panels to achieve pixel by pixel light modulation, a naked eye 3D display system with high brightness, low color difference, and low design and manufacturing difficulty is ultimately obtained.

Conclusions Due to the characteristics of harmonic diffraction optical elements having the same focal length and high diffraction efficiency at multiple high diffraction levels, a phase modulation panel consisting of four interlaced arrays of discrete harmonic diffraction subunits was designed. Combined with a 4.3-inch (1 inch=2.54 cm)LCD panel with 800 pixel×480 pixel resources, the display effect of a horizontal four point distribution with a horizontal spacing of 32 mm and a single image resolution of 400×240 was achieved. By modulating the three outgoing RGB rays through the same harmonic diffraction structure, the design complexity and manufacturing difficulty are reduced. The light modulation effect of two individual pixels in the horizontal direction of the phase modulation panel was simulated using Tracepro software at three harmonic wavelengths of R=638.4 nm, G=532.0 nm, and B=456.0 nm. This provides a simple verification method for the light modulation effect of the entire phase modulation panel. Finally, a naked eye 3D display effect was obtained with two viewing angles, a viewing angle interval of approximately 9.4°, the optimal viewing position being approximately 384.2-402.8 mm away from the screen, and the optimal viewing range being approximately 18.6 mm. In addition, considering the difficulty of manufacturing and design, it is determined that the incident angle of the light source should be less than 10° to ensure a total luminous efficiency of over 60% at the 16th order approximation. The simulation results show that the designed harmonic diffraction structure has the characteristics of low processing difficulty, high design degrees of freedom, and strong optical modulation ability.