Freeform surfaces have been widely used in various imaging applications. The selection of the initial structure is particularly critical in the optical design of freeform imaging systems due to the significantly expanded solution space. Here, we introduce a method to identify an initial point for the optical design of four-mirror freeform reflective imaging systems. The initial design method for four-mirror freeform imaging systems leverages the optical property of conical surfaces and the linear-astigmatism-free condition, which is computationally simple, easily accessible and theoretically supported. The initial configurations prioritize the elimination of field-constant aberration and linear astigmatism, providing a robust foundation for subsequent optimization of freeform imaging systems. We generalize the design method for linear-astigmatism-free confocal systems to four-mirror confocal off-axis systems with “double-pass surface”. We present a design example in which the field-constant aberration and the linear astigmatism are eliminated, showcasing the effectiveness of the proposed method. The proposed approach proves capable of delivering a promising starting point for the development of four-mirror freeform off-axis reflective imaging systems.
Specially designed backlight systems can cast information from display screen to designated zone. Here we introduce an ultra-thin multi-directional backlight system. The main components of the system include microlens arrays, a Fresnel lens and a high-brightness liquid crystal display (LCD) panel. The proposed backlight system allows us to control the light propagation in a desired manner, and could be applied to three dimensional (3D) display.
With the development of display technology, augmented reality (AR) devices have a wide range of application scenarios in many fields. The optical performance, volume and cost of the device are the main factors restricting the development of AR technology. As a traditional structure for optical combiner, birdbath faces challenges in achieving both a large field of view (FoV) and a lightweight, compact design. In this study, we introduce a novel off-axis configuration by replacing the polarized beam splitter (PBS) with a freeform holographic optical element (HOE). The system achieves a 46° FoV with a total thickness of 8.42mm, representing a 17.5% reduction in size compared to conventional PBS-based structures. Due to the wavefront manipulation by uniquely designed HOE, this approach significantly reduces system volume while maintaining high imaging performance. The proposed system holds potential for future AR applications where compactness, lightweight structures, and image quality are important factors.
Freeform surfaces are optical surfaces without linear or rotational symmetry. Their flexible surface geometry offers high degrees of freedom, which can be employed to avoid restrictions on surface geometry and create compact yet efficient designs with better performance. Therefore, freeform surfaces can endow beam shaping with more new functions and satisfy the ever-growing demand for advanced beam-shaping systems. The Monge-Ampère (MA) equation method converts the design of freeform beam-shaping optics into an elliptic MA equation with a nonlinear boundary condition. The MA method can automatically satisfy the integrability condition and be implemented efficiently. In this talk, we will introduce the principles behind the MA method and reveal the mathematical essence of illumination design based on ideal source assumptions. Also, several interesting beam-shaping systems will be provided to show the effectiveness of the MA method in a wide variety of applications.
The edge-emitting laser diodes (EELs) are widely used due to their superior performance, however, the strongly asymmetric beam profile along the fast and slow axes presents a big challenge in the beam shaping of EEL. Traditional optical devices mainly focus on adjusting the asymmetric divergence angle of the fast and slow axes of the EEL, and it is difficult to achieve flexible and precise control of the luminous distribution of the EEL due to the limited freedom of the conventional beam-shaping elements. In this article, we employ freeform lenses to flexibly reshape EEL beams and develop an approach to tackle the obstacles caused by the strongly asymmetric beam profile by generalizing the Monge– Ampère method to tailor freeform beam-shaping lenses for EELs. Three typical but challenging beam-shaping tasks show that both the intensity and wavefront of an EEL beam can be reshaped in a desired manner by the use of a single compact freeform lens without any symmetric restrictions on the architecture of the beam-shaping system.
Designing a general method of freeform optics for illuminating hard-to-reach areas is a challenging but rewarding issue. Most of the current designs of freeform illumination optics are valid in the applications in which the region of interest is easily accessible. However, there are some applications in which the region of interest is inaccessible due to the obstacles that cannot be removed and high-quality illumination is still needed (this is usually the case in endoscopic lighting). In this paper, we present a general formulation of designing freeform lenses for illuminating hard-to-reach areas. In this method, the freeform lens consists of two elaborately designed surfaces, by which both the irradiance distribution and wave-front of the light beam are manipulated in a desired manner. The light beam after refraction by the freeform lens is further guided through a light-guiding system to produce a prescribed illumination on a target plane which is inaccessible. Here, the light-guiding system can be a light-guiding element [e.g., a gradient refractive index (GRIN) lens] or an optical system that consists of several optical components. The properties of the light-guiding system are taken into account in the tailoring of the freeform lens profiles to guarantee the prescribed illumination on the target plane. The result shows that the design of freeform optics for illuminating hard-to-reach areas in the presence of a light-guiding system can still be formulated into an Monge–Ampère equation (MA) with a nonlinear boundary condition. Two examples are given to demonstrate the elegance of this method in designing freeform optics for illuminating hard-to-reach areas.
Freeform surfaces are widely used in optical design, due to the high design degree of freedom. The aberration theory of freeform optics can better lead designers to obtain a good structure. However, the existing aberration theory of freeform optics is only suitable for the optical system with a relatively small field of view (FOV). In this case, each field area (footprint) shows approximately the same shape and size, and positions of footprints across a surface have a linear relationship with fields. A wide FOV freeform optical system is analyzed in this paper. Parameters of all fields based on real-ray trace and non-linear interpolation can be employed to calculate the aberration generated by freeform terms. Then, to correct aberrations, coefficients of freeform terms are calculated using the least-square fitting method. By bringing back the coefficients to the optical system, the result shows great performance when using non-linear interpolation.
It is a meaningful but challenging issue that designing illumination optics for extended sources directly. A number of direct design methods developed specifically to deal with prescribed intensity designs usually fail to produce satisfactory illumination in the near field where the influence of lens size on the irradiance distribution cannot be ignored. In this paper, a direct method of designing aspherical lenses for extended sources is introduced to achieve specified irradiance characteristics. And various types of prescribed irradiance distributions are shown in this paper to verify the broad applicability and high efficiency of the direct design method, especially two examples of producing discontinuous irradiance distributions are analyzed in detail.
KEYWORDS: Light sources, Light sources and illumination, Direct methods, Near field optics, Near field, Lens design, Geometrical optics, Light, Energy efficiency, Aspheric lenses
Direct design of illumination optics for extended light sources is challenging but rewarding. Most of the current direct methods, which are developed specifically for the treatment of prescribed intensity designs, usually cannot yield acceptable illumination in the near field where the influence of lens size on the irradiance distribution cannot be ignored. Here, for the first time, to the best of our knowledge, we develop a direct method for designing aspherical illumination lenses with prescribed irradiance properties for extended sources in 3D geometry. The proposed method is valid in both near field and far field. The proposed method is numerically and experimentally evaluated. The results obtained show the effectiveness of the proposed method.
Freeform surfaces are optical surfaces without linear or rotational symmetry. Their high degrees of design freedom liberate designers and engineers from restrictions on optical surface geometry, yielding compact and lightweight imaging systems with excellent optical performance. Freeform optics have become a competitive tool in the design of optical seethrough head-mounted display (OST-HMD) systems. In this paper, we present two different OST-HMD systems which have different optical different configurations and both employ freeform optics to correct and balance optical aberrations. In the optimization design of the two OST-HMD systems, we start from a spherical imaging system with an on-axis configuration, and then tilt and decenter each optical surface to find a starting point. In the final state of optimization, the order of each XY polynomial used to represent the freeform surface is gradually increased. The modulation transfer functions of the two OST-HMD systems are evaluated and the three-dimensional models of the two systems are also presented.
Spectral confocal technology is an important three-dimensional measurement technology with high accuracy and non-contact; however, traditional spectral confocal system usually consists of prisons and several lens whose volume and weight is enormous and heavy, besides, due to the chromatic aberration characteristics of ordinary optical lenses, it is difficult to perfectly focus light in a wide bandwidth. Meta-surfaces are expected to realize the miniaturization of conventional optical element due to its superb abilities of controlling phase and amplitude of wavefront of incident at subwavelength scale, and in this paper, an efficient spectral confocal meta-lens (ESCM) working in the near infrared spectrum (1300nm-2000nm) is proposed and numerically demonstrated. ESCM can focus incident light at different focal lengths from 16.7 to 24.5μm along a perpendicular off-axis focal plane with NA varying from 0.385 to 0.530. The meta-lens consists of a group of Si nanofins providing high polarization conversion efficiency lager than 50%, and the phase required for focusing incident light is well rebuilt by the resonant phase which is proportional to the frequency and the wavelength-independent geometric phase, PB phase. Such dispersive components can also be used in implements requiring dispersive device such as spectrometers.
Metasurfaces are expected to realize the miniaturization of conventional refractive optics into planar structures; however, they suffer from large chromatic aberration due to the high phase dispersion of their subwavelength building blocks, limiting their real applications in imaging and displaying systems. In this paper, a high-efficient broadband achromatic metasurface (HBAM) is designed and numerically demonstrated to suppress the chromatic aberration in the continuous visible spectrum. The HBAM consists of TiO2 nanofins as the metasurface building blocks (MBBs) on a layer of glass as the substrate, providing a broadband response and high polarization conversion efficiency for circularly polarized incidences in the desired bandwidth. The phase profile of the metasurface can be separated into two parts: the wavelength -independent basic phase distribution represented by the Pancharatnam-Berry (PB) phase, depending only on the orientations of the MBBs, and the wavelength-dependent phase dispersion part. The HBAM applies resonance tuning for compensating the phase dispersion, and further eliminates the chromatic aberration by integrating the phase compensation into the PB phase manipulation. The parameters of the HBAM structures are optimized in finite difference time domain (FDTD) simulation for enhancing the efficiency and achromatic focusing performance. Using this approach, this HBAM is capable of focusing light of wavelengths covering the entire visible spectrum (from 400 nm to 700 nm) at the same focal plane with the spot sizes close to the diffraction limit. The minimum polarization conversion efficiency of most designed MBBS in such spectrum is above 20%. This design could be viable for various practical applications such as cameras and wearable optics.
Two freeform surfaces provide more degrees of freedom in designing illumination optics and can yield a better solution. The existing methods for point-like sources are mostly valid in designing one freeform surface. Designing two freeform surfaces for point-like sources still remains a challenging issue. In this letter we develop a general formulation of designing two freeform lens surfaces for point-like sources. The proposed method is very robust in designing freeform lenses with two elaborately designed surfaces. The examples clearly show that using two freeform surfaces yields better solutions to challenging illumination problems with ultra-high energy efficiency.
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