ABSTRACT
In this paper, a novel, to the best of our knowledge, method is proposed to design a freeform off-axis three-mirror reflective imaging system. A special algorithm is demonstrated to calculate the data points on the unknown freeform surface using the rays from the pupil of the center field. Then the three-dimensional shape of the freeform surface is solved by these characteristic points, which serves as a good starting point for further optimization. The benefit of this design method is demonstrated by designing a freeform off-axis three mirror imaging system with high performance. The final system operates at F/2 with an entrance pupil diameter of 400 mm and a field of view of 2.4∘×2.4∘. The modulation transfer function (MTF) value of the system reaches 0.6 at 100 lp/mm or higher at all fields of view.
ABSTRACT
With the development of space optics, optical freeform surfaces have gradually been utilized in reflective optical imaging systems in recent years. Freeform surfaces not only bring many benefits to the optical imaging system, but also present many challenges to their manufacture. Regardless of the machining method used, machining errors during the fabrication of freeform surfaces will exist, which limits the accuracy of freeform surface machining. In this paper, the deviation root mean square (RMS) of a freeform surface from the reference aspheric surface is proposed to evaluate the manufacturability of the freeform surface by using single-point diamond turning. Then the deviation RMS of freeform surfaces is added to the design process of the optical system as a manufacturing constraint. Subsequently, an off-axis three-mirror system and an off-axis two-mirror system with and without manufacturing constraints are designed, respectively. Then the imaging quality of these optical systems and the linear interpolation error RMS of freeform mirror are analyzed. It can be concluded that, on the basis of reaching the imaging quality requirements, the machining difficulty of a freeform mirror can be reduced when adding manufacturing constraints to the design process.
ABSTRACT
A key challenge in tailoring compact and high-performance illumination lenses for extended non-Lambertian sources is to take both the étendue and the radiance distribution of an extended non-Lambertian source into account when redirecting the light rays from the source. We develop a direct method to tailor high-performance illumination lenses with prescribed irradiance properties for extended non-Lambertian sources. A relationship between the irradiance distribution on a given observation plane and the radiance distribution of the non-Lambertian source is established. Both edge rays and internal rays emanating from the extended light source are considered in the numerical calculation of lens profiles. Three examples are given to illustrate the effectiveness and characteristics of the proposed method. The results show that the proposed method can yield compact and high-performance illumination systems in both the near field and far field.
ABSTRACT
Freeform optics offers more degrees of freedom to optical design that can benefit from a compact package size and a large field of view for imaging systems. Motivated by the advances in modern optical fabrication and metrology, freeform optics has been found in many applications. In this paper, we will describe the challenging optical design, fabrication, metrology, and assembly of an all-aluminum unobscured two-mirror freeform imaging telescope. The telescope has a large field of view of 20∘×15∘. The freeform aluminum mirrors are manufactured by diamond turning based on a feedback modification strategy. The freeform mirrors are measured by a computer-generated hologram-based interferometric null test method. All-aluminum configuration has the advantages of being athermal and cost-effective.
ABSTRACT
A method is presented for the fast design of a smooth freeform lens to tailor a collimated light beam with an arbitrary contour. This method begins by calculating an initial surface based on a simplified ray mapping. Then the surface is fitted by a system of Zernike polynomials, whose weights are treated as the optimization variables for further optimization. In the optimization, the objective function is analytically calculated using a partial differential-equation-based approach. To validate the effectiveness of the proposed method, a freeform lens is designed for a collimated Gaussian beam with a spline contour to form a uniform illumination distribution with another spline contour, which takes only 26 s. A freeform lens is also fabricated and experimented, and its practical performance approaches the design.
ABSTRACT
A design method is proposed to generate smooth freeform illumination optics for a point light source based on the L2 optimal transport (LOT) mapping. In this method, the LOT mapping between an assumed circular planar source and a prescribed target is first obtained by solving a polar-type LOT problem. Then, the mapping calculated for the circular source is applied for a point light source. Finally, the freeform optical surface is generated by a geometric construction method to realize the ray mapping. As examples, a series of smooth-surface freeform lenses are designed for a point light source to form uniform and complex illumination patterns on rectangular targets. The ray-tracing results show that all the designs achieve excellent performance with the light utilization efficiency η over 0.87 (Fresnel loss considered) and the relative standard deviation (RSD) of the simulated illumination distribution less than 0.051 simultaneously.
ABSTRACT
The freeform optical system plays a key role in illumination engineering, and several methods have been reported to manage the design of such system. In this paper, an approach to generate the polar-grids based flux transportation mapping for an arbitrarily-shaped target is proposed based on the conventional variable separation method. The source emitting grid is divided along the azimuth angle and the zenith angle respectively under the spherical coordinate system. Then, the target grid is achieved by solving the flux integral equations in polar coordinates using separation of variables method. When establishing the target grid along the polar radius, a strategy based on uniformly scaling down the external contour of the target is introduced. According to the mapping, a smooth freeform surface is then generated using the geometric construction method according to Snell's law. Finally, an iterative feedback process is adopted to compensate the deterioration of the target distribution caused by surface construction errors and the extension of a real source. Based on this method, a series of freeform lenses are designed for a 1 × 1 mm(2) LED source to generate uniform, Gaussian and multiple-rings illumination distributions within different target regions. High-performance optical systems with the light utilization efficiency η over 0.8 and the relative standard deviation (RSD) of the simulated illumination distribution less than 0.1 are obtained simultaneously for all the cases.
ABSTRACT
A two-step optimization method is proposed to design a compact single-surface far-field illumination system, satisfying the requirements of illuminance uniformity and light control efficiency with h/D less than 3:1. In the first step, the conventional tailored edge-ray design (TED) method is employed to generate prescribed illumination distribution for the rotationally symmetric optical system, and an optimization process is added to reach a balance between illuminance uniformity and light control efficiency. Based on the improved TED method, we can construct an initial optical system more accurate than that obtained by point source assumption. In the second step, an iterative feedback modification process is employed to optimize the initial optical system, so that the degradation of performance due to insufficient control of skew rays is mitigated. Because the initial optical system constructed in the first step is accurate enough, the second-step feedback modification can converge to a satisfactory result within several iterations. As an example, a free-form rotationally symmetric lens with the height of h = 25 mm is designed for a discoidal LED source with the diameter of D = 10 mm. Both high illuminance uniformity of 0.75 and high light control efficiency of 0.86 are obtained simultaneously. The method can be further used to achieve more complex non-uniform illumination distributions. The design of an optical system with h/D = 2.5:1 and a circular linear illumination distribution is demonstrated.
ABSTRACT
A two-step optimization method is proposed to design a compact single-surface far-field illumination system, satisfying the requirements of illuminance uniformity and light control efficiency with h/D less than 3:1. In the first step, the conventional tailored edge-ray design (TED) method is employed to generate prescribed illumination distribution for the rotationally symmetric optical system, and an optimization process is added to reach a balance between illuminance uniformity and light control efficiency. Based on the improved TED method, we can construct an initial optical system more accurate than that obtained by point source assumption. In the second step, an iterative feedback modification process is employed to optimize the initial optical system, so that the degradation of performance due to insufficient control of skew rays is mitigated. Because the initial optical system constructed in the first step is accurate enough, the second-step feedback modification can converge to a satisfactory result within several iterations. As an example, a free-form rotationally symmetric lens with the height of h = 25 mm is designed for a discoidal LED source with the diameter of D = 10 mm. Both high illuminance uniformity of 0.75 and high light control efficiency of 0.86 are obtained simultaneously. The method can be further used to achieve more complex non-uniform illumination distributions. The design of an optical system with h/D = 2.5:1 and a circular linear illumination distribution is demonstrated.
ABSTRACT
Designing an illumination system for a surface light source with a strict compactness requirement is quite challenging, especially for the general three-dimensional (3D) case. In accordance with the two key features of an expected illumination distribution, i.e., a well-controlled boundary and a precise illumination pattern, a two-step design method is proposed in this paper for highly compact 3D freeform illumination systems. In the first step, a target shape scaling strategy is combined with an iterative feedback modification algorithm to generate an optimized freeform optical system with a well-controlled boundary of the target distribution. In the second step, a set of selected radii of the system obtained in the first step are optimized to further improve the illuminating quality within the target region. The method is quite flexible and effective to design highly compact optical systems with almost no restriction on the shape of the desired target field. As examples, three highly compact freeform lenses with ratio of center height h of the lens and the maximum dimension D of the source ≤ 2.5:1 are designed for LED surface light sources to form a uniform illumination distribution on a rectangular, a cross-shaped and a complex cross pierced target plane respectively. High light control efficiency of η > 0.7 as well as low relative standard illumination deviation of RSD < 0.07 is obtained simultaneously for all the three design examples.
Subject(s)
Algorithms , Computer-Aided Design , Lenses , Lighting/instrumentation , Semiconductors , Computer Simulation , Equipment Design , Equipment Failure Analysis , Light , Models, Theoretical , Scattering, RadiationABSTRACT
Taking color quality scale (CQS) as color rendering assessment criterion, the parameters including each color LED's peak wavelength λi and fractional radiant flux Ii are optimized using genetic algorithm to maximize the luminous efficacy of radiation (LER) of the spectral power distributions (SPDs) of multi-color white light source with 3 to 7 components while maintaining the deviation of its color and color-rendering capability from that of the reference light source within the specified scope. Then the wavelength dependence of these SPDs is analyzed. It is shown that to achieve a Q(a) greater than 95 (5-color LEDs) or even close to 100 (7-color LEDs), the spectral energy could be concentrated in the range of 410~675 nm, indicating that this wavelength range makes a major contribution to high color rendering properties. Spectra filtering experiments show that spectrum around 580nm is harmful to color rendering. To obtain a white light source composed of 3-color LEDs with CQS Q(a) ≥ 80 and correlated color temperature (CCT) within 2700-6500K, the energy ratios among 410-495nm, 495-595nm, and 595-675nm intervals, can be simplified as that of the reference source with the same CCT.
