Horizontal white light flat-topped beams produced by the diffraction mask

The flat-topped beam is a special beam with wide applications in the directional backlight autostereoscopic display, and it is used as a directional backlight in the horizontal direction. However, it is still challenge to white light flat-topped beams with the traditional flat-topped beam shaper. In this paper, it is proposed that diffraction mask with butterfly-shaped hole arrays and cylindrical lens be used to produce the horizontal flat-topped white beams. The surface of the LCD backlight mask is covered by a layer of diffraction mask, where the butterfly-shaped holes are arranged in line along the vertical direction. Simultaneously, the height and width, hole center height are kept identical, and the ratio between the center depth and the perimeter of butterfly-shape hole is defined as the concavity. A flat convex cylindrical lens is placed in front of diffraction mask gaplessly. The uniform light field from LCD backlight is transformed into the white light flat-topped beams and projected on the receiving screen by the diffraction mask and cylindrical lens. Based on the Huygens-Fresnel diffraction integral, the intensity distribution formula of diffraction of the single wavelength light source on the receiving screen is derived. Furthermore, the intensity distribution formula on the screen is derived by super positioning the multiple wavelengths. The proposed method is verified by both numerical simulation and experimental validation. Numerical simulations elucidate the effects of the different transmission distance and butterfly hole concavity on the white light flat-topped beam flat-topped factor. The stimulated results show that the propagation distance does not influence the white light beam transverse intensity distribution characteristics of flat top. With the beam propagation distance increasing, the horizontal width of flat-topped beam becomes larger. When the concavity of the butterfly hole decreases, light intensity distribution shifts from Gaussian to flat type. However, the flat-topped factor decreases when the butterfly concavity is too small. The optimal concavity varies from 0.4 to 0.6, where the flattened factor of the transverse flat-topped beams reaches 0.89. In the experiments, films are produced with the diffraction of butterfly hole array mask. The height and width of butterfly are both 48 μm, and the concavities of the butterfly are 1, 0.83, 0.66 and 0.83 respectively. The cylindrical lens adopts PMMA cylindrical lens grating plate, with a thickness of 8 mm, a grating density for 18 line/inch, and the cylindrical lens curvature radius R is 2.67 mm. The experimental results show that the beam transmission is consistent with the result of numerical simulation. When concavity of the butterfly is 0.5, the flat factors of the white light horizontal of flat-topped beams are higher than 0.89 in a range from 500 mm to 2000 mm. Moreover, we also discuss the dispersion effects of shaft flat-topped beams and off-axis flat-topped beams, showing that the refraction and dispersion of the cylindrical lens can cancel out each other, so that the horizontal flat-toped white beams is basically dispersionless.