## 1 Introduction  
Light-emitting diodes (LEDs) offer advantages such as high efficiency, a high color-rendering index, energy saving, and environmental protection [1; 2; 3]. Therefore, they have been widely applied as the light source in desk lamps [4]. However, the luminous flux and unified glare rating (UGR) of desk lamps affect the comfort of the human eye. At the same luminous flux, a smaller light-emitting area has more serious glare problems. Converting a point light source into a light source with a larger, uniform area and adjusting the appropriate light beam angle can suppress UGRs effectively. Because of their light-emitting characteristics, LEDs are point light sources; therefore, they must first be converted into planar light sources.  
Some studies have discussed how to convert LED point light sources into a planar light source to reduce the UGR index. In 2015, a hollow light guide with edge-lit LED sources was proposed. A hollow-type planar light source with reflecting, scattering, and multiple point light sources along at least one side plane was proposed to build a planar light source module [5]. A hollow light guide comprising LEDs with an asymmetric light field was proposed to transform an LED point light source into a planar light source without a light guide plate, so that it had 40% lower weight than a solid light guide module [6]. Another study developed a light guide plate with LEDs with an asymmetric light distribution and a light guide plate with a printed diffusion reflection on the bottom surface to achieve a circular large-area light source [7]. A light source module with adjustable diffusion includes an array of illumination elements and a light-diffusing material [8]. A light regulation device includes a first light guide structure with an incident light, a second light guide structure with a light-emitting surface, and a light deflection sheet with a first light deflection layer [9]. In industrial applications, some design methods have been proposed to achieve sufficient and uniform luminance over the entire surface--which is irradiated with light--of a light guide plate, and to achieve uniform luminance over an entire range to be irradiated with light [10; 11; 12]. A linear light source device was developed with a rectangular-shaped wiring substrate and a wiring pattern on it, and multiple light-emitting elements were arranged on the wiring substrate to achieve a linear light source device and a planar light source device [13]. A planar light source device with an illumination apparatus was developed to realize a planar light source device that can provide planar, uniform, and high-quality planar illumination [14; 15; 16; 17].  
The UGR value is an important function for evaluating the suitability of desk lamp lighting for the human eye. The lighting-driven spatial light field distribution can affect the perception of the human eye. Overly bright light sources can cause glare, which may impair visual efficiency. Luminaire designers use multiple structures to reduce glare; for instance, reflective matrix bars can improve the UGR and illumination uniformity and simultaneously achieve adequate illuminance. However, this causes a large loss in luminaire efficiency. Therefore, we proposed luminous intensity field optimization for an antiglare LED desk lamp without a second optical element. This study used DIALux evo 8.2 for simulations.