Future commercialization of glasses-free holographic real 3D displays requires not only appropriate image quality but also slim design of backlight unit and whole display device to match market needs. While a lot of research aimed to solve computational issues of forming Computer Generated Holograms for 3D Holographic displays, less focus on development of backlight units suitable for 3D holographic display applications with form-factor of conventional 2D display systems. Thereby, we report coherent backlight unit for 3D holographic display with thickness comparable to commercially available 2D displays (cell phones, tablets, laptops, etc.). Coherent backlight unit forms uniform, high-collimated and effective illumination of spatial light modulator. Realization of such backlight unit is possible due to holographic optical elements, based on volume gratings, constructing coherent collimated beam to illuminate display plane. Design, recording and measurement of 5.5 inch coherent backlight unit based on two holographic optical elements are presented in this paper.