This paper presents a field curvature correction method of designing an ultrashort throw ratio (TR) projection lens for an imaging system. The projection lens is composed of several refractive optical elements and an odd polynomial mirror surface. A curved image is formed in a direction away from the odd polynomial mirror surface by the refractive optical elements from the image formed on the digital micromirror device (DMD) panel, and the curved image formed is its virtual image. Then the odd polynomial mirror surface enlarges the curved image and a plane image is formed on the screen. Based on the relationship between the chief ray from the exit pupil of each field of view (FOV) and the corresponding predescribed position on the screen, the initial profile of the freeform mirror surface is calculated by using segments of the hyperbolic according to the laws of reflection. For further optimization, the value of the high-order odd polynomial surface is used to express the freeform mirror surface through a least-squares fitting method. As an example, an ultrashort TR projection lens that realizes projection onto a large 50 in. screen at a distance of only 510 mm is presented. The optical performance for the designed projection lens is analyzed by ray tracing method. Results show that an ultrashort TR projection lens modulation transfer function of over 60% at 0.5 cycles/mm for all optimization fields is achievable with f-number of 2.0, 126° full FOV, <1% distortion, and 0.46 TR. Moreover, in comparing the proposed projection lens' optical specifications to that of traditional projection lenses, aspheric mirror projection lenses, and conventional short TR projection lenses, results indicate that this projection lens has the advantages of ultrashort TR, low f-number, wide full FOV, and small distortion.

An iterative optimization algorithm is introduced to address the surface iterative errors as well as source extension issues in a freeform illumination system for producing satisfactory illumination distribution. A unique two-parameter coordinate system is utilized to represent the emitted ray directions. Then, the direction vector for the incident rays, which propagate through several surfaces, is obtained using ray-tracing techniques. Based on the mapping between the incoming rays and a target grid, a freeform surface is generated as a good starting design. An iterative optimization strategy is further employed to alleviate the deterioration of illumination distribution on the target region, and the uniformity of the illumination system is evaluated during optimization. Very few variables are demanded, and more flexibility in the design of the freeform surface is offered. Successive iterations can be performed until the desired result is attained. An optical system is used as an example to demonstrate the validity of the proposed method, and numerical simulations are carried out to evaluate the optical performance. The simulation results show that a small angular intensity distribution and prescribed rectangular illumination pattern can be achieved simultaneously.

Allowing natural scenes as well as maximizing field of view (FoV) can benefit from the minimization of distortion for the wide-angle camera. The wide-angle camera utilizing freeform surfaces for mitigating distortions, either barrel distortion or pincushion distortion, is therefore of interest. In this paper, the designs of using all-aspherical surfaces and aspherical surfaces combined with freeform surfaces are investigated. To minimize the deviation before and after converting from aspherical surfaces to freeform surfaces, a mathematical conversion scheme is derived. By applying it to the design example, the methodology is shown to be effective in the case of an optical system with a large number of aspherical/freeform surfaces. Additionally, custom freeform analysis tools are developed for quantitative analysis and visualization of the critical characteristics of optical performance, namely, a 2D lateral color field map, 2D relative illumination field map, 2D spot radius field map, and 2D average modulation transfer function (MTF) field map. Compared to classical all-aspherical design, simulation results show that freeform design has the capability to reduce distortion, and other performances such as relative illumination, spot size, and MTF can also be improved, even though there are some compromises on the peripheral FoV. The design approach will have potential important research and application values for lens systems utilized in miniature camera lenses, especially the wide FoV capability.

A scanning laser-based back light three-dimensional (3D) display capable of rendering full-resolution, low crosstalk, and vivid 3D depth perception has been developed by incorporating time-sequential multiplexing and eye-tracking technologies. This system includes three main subsystems: a scanning laser module, a relay transfer unit created by combining multiple transmissive-type electrically addressed ferroelectric liquid crystal spatial light modulators (FLC-SLMs), and a dual-directional transmission screen (DDTS) unit that can produce different angular magnification factors in both the tangential and sagittal planes. The light beam is directed by the DDTS after transmission through FLC-SLMs, and left and right eye viewing zones are produced sequentially in accordance with the locations of clear apertures in the FLC-SLM that are controlled based on data from the eye-tracking system. Owing to the persistence of human vision, 3D images are formed as a result of the high-speed scanning backlight and fast response characteristics of the FLC-SLM. A prototype of the proposed 3D display was designed and built, and experiments were carried out. The experimental results verify the feasibility of the proposed scheme, and full-resolution images with natural 3D perception are demonstrated by the prototype.

A time-sequential autostereoscopic three-dimensional (3D) display using a set of cylindrical optical elements (COEs) as the backlight steering is proposed. The operation principle of the system and its detailed design are described. In our system, the COEs control the direction of the backlight for the proposed system of the user's right and left views. Additionally, the displayed images can be observed under ambient lighting by implementing the high density light-emitting diode (LED) arrays. Compared to the first-generation array display, the image resolution is greatly improved by the addition of the time multiplexing technique. A prototype system using a set of COEs, LED arrays, two linear Fresnel lenses, and an elliptical diffuser is constructed. Here, the directional backlight beams are synchronized with the right and left images alternately displayed on the liquid crystal display (LCD) screen, and two convergent viewing zones are formed alternately in front of the user's eyes; then 3D images are perceived because of persistence of the vision of human eye. The experimental results show that the proposed method is a potential technology for 3D applications such as 3D television.