We present a simple freeform lens design method for an application to LED collimating illumination. The method is derived from a basic geometric-optics analysis and construction approach. By using this method, a highly collimating lens with LED chip size of 1.0 mm × 1.0 mm and optical simulation efficiency of 86.5% under a view angle of ± 5 deg is constructed. To verify the practical performance of the lens, a prototype of the collimator lens is also made, and an optical efficiency of 90.3% with a beam angle of 4.75 deg is measured.

Freeform lens design for LED collimating illumination

Freeform optics constitutes a new technology that is currently driving substantial changes in illumination design. It liberates designers and engineers from restrictions of optical surface geometry, enabling them to achieve compact, lightweight, and efficient illumination systems with excellent optical performance. Freeform optics is currently used widely for both fundamental research and practical applications. This Review focuses on the design of freeform illumination optics, which is a key factor in advancing the development of illumination engineering. The design methods of freeform illumination optics can be divided into two groups: zero-´etendue algorithms based on ideal source assumption and design algorithms for extended light sources. The zero-´etendue algorithms include ray mapping method, Monge–Ampere equation method, and supporting quadric method. The algorithms for extended sources include illumination optimization, feedback design, and simultaneous multiple surfaces method. The characteristics and limitations of these design methods are illustrated and a summary of these methods with future outlooks is also given.

Design of Freeform Illumination Optics

We present a glasses-free 3D display design with the potential to provide viewers with nearly correct accommodative depth cues, as well as motion parallax and binocular cues. Building on multilayer attenuator and directional backlight architectures, the proposed design achieves the high angular resolution needed for accommodation by placing spatial light modulators about a large lens: one conjugate to the viewer's eye, and one or more near the plane of the lens. Nonnegative tensor factorization is used to compress a high angular resolution light field into a set of masks that can be displayed on a pair of commodity LCD panels. By constraining the tensor factorization to preserve only those light rays seen by the viewer, we effectively steer narrow high-resolution viewing cones into the user's eyes, allowing binocular disparity, motion parallax, and the potential for nearly correct accommodation over a wide field of view. We verify the design experimentally by focusing a camera at different depths about a prototype display, establish formal upper bounds on the design's accommodation range and diffraction-limited performance, and discuss practical limitations that must be overcome to allow the device to be used with human observers.

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Focus 3D: Compressive accommodation display

This paper presents a novel hybrid Fresnel-based concentrator with improved uniformity irradiance distribution on the solar cell without using secondary optical element (SOE) in the concentrator photovoltaic (CPV) system to overcome the Fresnel loss and to increase the solar cell conversion efficiency. The designed hybrid Fresnel-based concentrator is composed of two parts, the inner part and the outer part. The inner part is the conventional Fresnel lens, while the outer part is double total internal reflection (DTIR) lens. According to the simple geometrical relation, the profile of the proposed hybrid Fresnel-based concentrator is calculated as an initial design profile. To obtain good irradiance uniformity on the solar cell, optimal prism displacements are optimized by using a simplex algorithm for collimated incident sunlight based on different prism focus on different position principles. In addition, a Monte-Carlo ray-tracing simulation approach is utilized to verify the optical performance for the hybrid Fresnel-based concentrator. Results indicate that the hybrid Fresnel-based concentrator designed using this method can achieve spatial non-uniformity less than 16.2%, f -number less than 0.59 (focal length to entry aperture diameter ratio), geometrical concentrator ratio 1759.8×, and acceptance angle ±0.23°. Compared to the conventional Fresnel-based lens and the traditional hybrid Fresnel-based lens, the optimized concentrator yields a significant improvement in irradiance uniformity on the solar cell with a wide solar spectrum range. It also has good tolerance to the incident sunlight.

Optimization design of hybrid Fresnel-based concentrator for generating uniformity irradiance with the broad solar spectrum

A quartic phase retardation function is described that reduces the variation of the intensity of the focal point of incoherent imaging systems suffering from primary third-order aberrations limited to coma and astigmatism. Corresponding modulation transfer functions are shown to remain practically invariant for moderate amounts of coma and astigmatism.

Circularly symmetric phase filters for control of primary third-order aberrations : coma and astigmatism

Most of the previous imaging characteristics analysis of the wavefront coding system has been carried out within the frequency domain. In this paper, the stationary phase method is employed to perform the analysis within the spatial domain. The approximate expression of point spread function (PSF) in the presence of defocus aberration is derived for the system with a cubic phase mask, which shows a good agreement with the Fast Fourier Transform (FFT) approach. Based on this, the PSF characteristics are analyzed in terms of the boundaries, oscillations and sensitivities to defocus, astigmatism and coma.

Point spread function characteristics analysis of the wavefront coding system.

A slope angle-based reflector profile optimization method is introduced at the first time. Compared to the traditional profile-based optimization method, better optimization results are obtained with this method. Design examples of reflectors for general lighting applications are given to compare both types of optimization methods. Disadvantages, such as range definition, range overlapping, and parameter-dependent problems, which existed in the traditional profile-based optimization method can be totally overcome with the proposed method.

Free-form reflector optimization for general lighting

Approximate expressions of the ray aberrations for off-axis collimated beams and free form phase plates with a small derivative magnitude are derived with the defocus aberration taken into account. The cubic phase plate, which is one of the most commonly used phase plates in wavefront coding imaging systems, is illustrated as an example. The approximate expressions for the upper and lower boundaries of ray map, and the spot size in the vicinity of the focal plane are derived. The sensitivity to the defocus aberration and the variation of the induced aberrations with respect to the field positions are analyzed with derived approximate expressions as well. Some characteristics unmentioned before are derived, showing a good agreement with the exact aberrations. Finally some useful guidelines are given for the design of imaging systems with phase plates.

Ray aberrations analysis for phase plates illuminated by off-axis collimated beams.

The point spread function (PSF) of a wavefront coding (WFC) system with a cubic phase mask is analyzed with a wide viewing angle based on physical optics for what is believed to be the first time. Two coordinate transformations are made to generate a pupil function, from which we obtain the encoded PSF of the WFC system with defocus parameters W020 and object angles α and β. The encoded PSFs are further side extended as the object angles get wider. When αβ 0, Φ will skew to an acute angle. Furthermore, the effect of skew and side extension is even symmetric about W020. As a result, the wide viewing angle has a bad effect on the imaging quality of the WFC system.

Wide viewing angle skewed effect of the point spread function in a wavefront coding system

The point spread function (PSF) is asymmetric in a wavefront coding (WFC) system with cubic phase mask (CPM). The image formation of the WFC system is described as the generalized Sylvester matrix equation. With Tikhonov regularization, a global generalized minimal residual method (Gl-GMRES) algorithm is used to obtain the restored sharp image. For this large-scale, linear, and discrete, ill-posed problem, we introduce a Kronecker product approximation of the blurring operator to reduce the computation consumption. To eliminate ringing effect, four boundary conditions (BCs) are considered in the image restoration: periodic BCs, zero BCs, reflective BCs, and antireflective BCs. Analysis and numerical results show that the antireflective BCs provide better results than others. The experiment results show that the Gl-GMRES algorithm with antireflective BCs is more effective than the classic Wiener filter.

Wenzi Zhang

Papers

Point spread function characteristics analysis of the wavefront coding system.

Free-form reflector optimization for general lighting

Ray aberrations analysis for phase plates illuminated by off-axis collimated beams.

Wide viewing angle skewed effect of the point spread function in a wavefront coding system

Image restoration based on generalized minimal residual methods with antireflective boundary conditions in a wavefront coding system