Auto-stereoscopic display, which can present three-dimensional images with spatial depth information to observers without cumbersome eyewear [[1], [2], [3], [4]], is recognized as an important development direction in the future display field. In recent years, various efforts have been devoted to improving the performance of auto-stereoscopic displays [[5], [6], [7], [8], [9], [10], [11], [12], [13]]. In recent research, researchers have optimized the divergence angle of the light beam by lens design to achieve smooth motion parallax in 3D light field display, the lens is reversely designed based on the results of the views-fitting optimization algorithm [10]. Moreover, a vertically spliced tabletop light field cave display with extensional depth of field and separate optimization of compound lens array was proposed [11]. Additionally, a large viewing angle integral imaging 3D display system based on a symmetrical compound lens array (SCLA) has been proposed. The symmetrical structure of the SCLA enables a reduced focal length and the elimination of lateral aberration, improving the viewing angle and the 3D image resolution simultaneously [12]. Furthermore, a color liquid crystal grating based color holographic 3D display system with large viewing angle has been proposed, the color liquid crystal grating allows performing secondary diffraction modulation on red, green and blue reproduced images simultaneously and extending the viewing angle in the holographic 3D display system [13].

Among the various auto-stereoscopic displays, binocular parallax 3D display stands out as the simplest and most mature [14,15]. Projection technology is also widely used in binocular parallax 3D display, it can provide full resolution and full size 3D images [16,17]. Retro-reflective structure is commonly utilized in projection stereoscopic displays to form views [18]. However, projection based binocular parallax 3D displays usually have a fixed optimal viewing distance [19,20]. While observers situated at the optimal viewing distance can observe correct parallax images without crosstalk, any displacement towards the back or front from this optimal viewing distance will introduce crosstalk [21,22]. Furthermore, the fixed optimal viewing distance limits the position of the observer, thereby limiting the application of 3D display. In this paper, a non-coaxial optical screen based projection 3D display with extended viewing distance range is proposed. Each view area of the proposed 3D display is a linearly shaped region covering from back to front, thereby the proposed 3D display can extend the viewing distance range.