## 1 Introduction  
In recent years, white LEDs based on phosphor conversion have constituted a considerable proportion of the LED market because of their many advantages, such as long lifetime, high reliability, environmental protection, safety, and multiple applications [1]. To meet the requirements of sustainable development, continual enhancement of the luminous efficiency of LEDs is crucial. A remote phosphor package that separates the phosphor layer from the chip to suppress reabsorption is an efficient method for enhancing luminous efficiency. Remote phosphor white LEDs with the LED chip and phosphor layer at the bottom and top of a reflector cup were investigated [2]. The experimental results showed that the backscattered photons can be extracted and the efficacy can be significantly increased by separating the phosphor layer from the chip. For white LEDs with a diffuse reflector cup, the numerical and experimental results showed that light extraction efficiencies were enhanced by 75% and 15.4%, respectively [3]. The optimization investigation on packaging configuration for remote phosphor white LEDs comprising the LED chip, the phosphor layer, a diffuse reflector cup, and a hemispherically shaped encapsulation is presented. The numerical and experimental results show that luminous efficiencies can be enhanced by up to 50% and 15.4% over conventional packages, respectively [4]. A remote phosphor packaging was numerically and experimentally investigated. The results prove that this separate packaging can prevent the heat of the LED chip from transferring to the phosphor layer and improve the luminous efficiency and color characteristic stability of the white LED [5]. However, in typical remote phosphor white LEDs, the phosphor-scattered blue light and phosphor-emitted yellow light have different radiant intensity distributions. Therefore, the angular color distribution becomes non-uniform, and a yellow ring phenomenon appears in the illuminating plane. Several research studies have focused on the improvement of angular color distribution for remote phosphor white LEDs. A simulation analysis of color distribution for white LEDs with five phosphor packaging methods was presented [6]. The results showed that, for the effects of angular color distribution, the most important issue was the packaging method, followed by the reflector cup, and the minor was the separation distance between the phosphor layer and the LED chip. Among these methods, the angular color uniformity for the types with a plane phosphor layer was poor and that of the types with a convex phosphor layer was better. Based on ray-tracing simulations, [PERSON] et al. showed that the uniformity of angular correlated color temperature (CCT) was enhanced by optimizing the color conversion element geometries and material compositions [7]. [PERSON] et al. proposed that the remote phosphor of fully patterned sapphire provides a much better CCT uniformity than that obtained in the cases of planar sapphire and partially patterned sapphire [8]. [PERSON] et al. demonstrated that adding a silicone layer with ZrO\({}_{2}\) particles onto the surface of the remote phosphor layer could enhance the capability of light scattering [9]. The structure enhanced the uniformity of angular CCT and increased the luminous efficiency by a small amount. [PERSON] et al. proposed a patterned remote phosphor structure in which not spraying phosphor on a window region could improve CCT uniformity and luminous efficiency, as compared with the conventional remote phosphor coating structure [10]. [PERSON] et al. proposed the addition of a micro-patterned array optical film into the packaging configuration for remote phosphor white LEDs [11]. The numerical and experimental results showed that this optical film could improve the uniformity of angular CCT. [PERSON] et al. proposed the effects of melamine formaldehyde resin and CaCO\({}_{3}\) diffuser-loaded encapsulation on the correlated color temperature uniformity of phosphor-converted LEDs [12].