Luminous Intensity Field Optimization for Antiglare LED Desk Lamp without Second Optical Element

: This study proposes a model of a light module with an optimized luminous intensity ﬁeld for realizing an antiglare light-emitting diode (LED) desk lamp without a second optical element. We simulated di ﬀ erent luminous intensity ﬁeld proﬁles to analyze the uniﬁed glare rating (UGR) and illumination uniformity performance of a desk lamp. The spatial e ﬀ ect of UGR and the illumination uniformity a ﬀ ect eye comfort. The light module was set to di ﬀ erent beam angles without a second optical element, louver structure, and reﬂective element on the luminaire to compare di ﬀ erent UGRs and uniformity values for evaluating human eye comfort. The simulation and experimental results indicated that the luminous intensity curve for a beam angle of 90 ◦ achieved an illumination uniformity of 80% and a UGR of 18.1 at a height of 45 cm, thus realizing a human-friendly antiglare desk lamp.


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 Appl. Sci. 2020, 10 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.

Glare Definition and Spatial Characteristics
The glare calculation method recommended by the International Commission on Illumination (CIE) was used to combine the Einhorn and Hopkinson formulas and the Guth position parameter. The calculated uniform glare index was used to predict the visual impact on the environment from the glare of a light source based on human factors. According to CIE 55-1983 and CIE 119-1995, the CIE Glare Index (CGI) of indoor lighting fixtures is defined as follows [18,19] where E d is the direct vertical illumination of human eyes (direct vertical illuminance, lux), E i is the indirect illumination on human eyes (indirect illuminance, lux), L a is the brightness value of a single lamp in the line of sight of the human eye (luminance, nit), ω a is the solid angle formed by a single lamp on human eyes (steradian, sr), and P a is the Guth Position Index of a single luminaire. The Guth position refers to the position of the lamp and the human eye, and it is defined as follows where EXP is defined as follows where d is the horizontal distance between the luminaire and the human eye divided by the vertical height between the luminaire and the human eye (forward distance of source/height), and S is the horizontal distance between the luminaire and the vertical line of sight divided by the vertical height between the luminaire and the human eye (sideways distance of source/height).
Appl. Sci. 2020, 10, 2607 3 of 13 CIE 117-1995 also defines another uncomfortable glare index called the UGR that considers the effect of background brightness on glare. Therefore, the parameters of the background luminance of the environment L b are added as follows [20] where 8 gives UGR numbers that optimize and range from approximately 5 to 40, the logarithm (log) is used because human eyes react logarithmically to light, and Σ shows that the equation includes all the fittings located within the area, where L b is defined as follows: Here, L b is the value of the background luminance in cd/m 2 , E ind is the vertical indirect illuminance of the viewer's eye, and L is defined as follows: Here, L is the luminance value of the luminous parts of each luminaire in the direction of the viewer's eye in cd/m 2 , I is the luminaire's luminance, A p is the project area, and ω i is defined as follows: Here, ω i is the solid angle of the luminous parts of each luminaire on the viewer's eye in steradian (sr), r is the distance from the light source to the viewer's eyes, and p is the Guth position index for each individual luminaire that corresponds to its displacement from the line of sight and is related to the horizontal and tangent function of the observer to the light source.

Spatial Characteristics
We set up a desk lamp for a study desk, as illustrated in Figure 1a, with a desk length and desk width of L0 and W0, respectively. P1 and P2 indicate the positions of the desk lamp and observer, respectively; the distance between them is D1. As shown in Figure 1b, the observer and desk lamp are positioned at P3 and P4 above the desk surface at height H1 and height H2. The calculation object has a length and width of L1 and W1, respectively. The observer on the edge of the desk indicates a student in front of the desk. We set the desk lamp rotation angles as +θ and −θ. Table 1 shows the simulation setup parameters.
The simulation setup parameters of symbol and characteristics are shown in Table 2.
width of L0 and W0, respectively. P1 and P2 indicate the positions of the desk lamp and observer, respectively; the distance between them is D1. As shown in Figure 1b, the observer and desk lamp are positioned at P3 and P4 above the desk surface at height H1 and height H2. The calculation object has a length and width of L1 and W1, respectively. The observer on the edge of the desk indicates a student in front of the desk. We set the desk lamp rotation angles as +θ and −θ. Table 1 shows the simulation setup parameters. The simulation setup parameters of symbol and characteristics are shown in Table 2.

Specifications Characteristics
Luminous flux 800 lumens Reflection factors of desk surface 50% Desk lamp height (H2) 45 cm

UGR and Uniformity at Beam
Angles of 70-120 • at the Same Height Table 2 shows the DIALux simulation parameters. It has a luminous flux of 800 lm, reflection factors of desk surface of 50% and desk lamp height of 45 cm. Table 3 shows the variation in the UGR with the beam angle of 70-120 • . We can vary the beam angles without changing the height of the desk lamp on the study desk to compare the corresponding UGR values.  Figure 2 shows the isoline and color illumination map (lux) of uniformity under different beam angle conditions.  Figure 2 shows the isoline and color illumination map under different beam angles: 70°, 80°, 90°, 100°, 110°, and 120° respectively. Figure 2c shows the simulation result with a desk lamp beam angle of 90° in the illumination isoline. This result indicates that the 1000-1400 lux isoline is distributed in most of the space and the >1000 lux isoline is at the four corners, as indicated by the orange and yellow regions, respectively. The lux isoline changes with a variation in the beam angle. When the beam angle increases, the isoline distribution becomes more uniform because the light exposure range is wider.
The simulation results were used to calculate the illumination and uniformity for different beam angles. As shown in Table 4, the uniformity had its maximum value of 0.83 for a beam angle of 120°. The average illumination was 1139 lux for a beam angle of 90°; this was higher than the values for beam angles of 100-120°. The illumination value is greater than 500 lux to comply with the regulations for a desk lamp for a study desk.  Figure 3 shows the luminous intensity profile for beam angles of 70-120°.   Figure 2c shows the simulation result with a desk lamp beam angle of 90 • in the illumination isoline. This result indicates that the 1000-1400 lux isoline is distributed in most of the space and the >1000 lux isoline is at the four corners, as indicated by the orange and yellow regions, respectively. The lux isoline changes with a variation in the beam angle. When the beam angle increases, the isoline distribution becomes more uniform because the light exposure range is wider.
The simulation results were used to calculate the illumination and uniformity for different beam angles. As shown in Table 4, the uniformity had its maximum value of 0.83 for a beam angle of 120 • . The average illumination was 1139 lux for a beam angle of 90 • ; this was higher than the values for beam angles of 100-120 • . The illumination value is greater than 500 lux to comply with the regulations for a desk lamp for a study desk.  Figure 3 shows the luminous intensity profile for beam angles of 70-120 • . The luminous intensity field for a beam angle of 70 • was the narrowest; with an increase in the beam angle, the luminous intensity field widened. In the determination of the UGR, a narrow beam angle outperformed a wide beam angle. By contrast, in the determination of the illumination uniformity, a wide beam angle was superior to a narrow beam angle. Tables 3 and 4 show the homogenized UGR and uniformity values, respectively.  Figure 3 shows the luminous intensity profile for beam angles of 70-120°.   Figure 4 shows the relationship between UGR and uniformity at various beam angles. For a beam angle of 90 • , the UGR is less than the threshold value of 19, and the uniformity is higher than that for beam angles of 70 • and 80 • ; this is similar to the uniformity for beam angles of 100 • and 110 • . Therefore, considering the UGR and the uniformity values simultaneously, the best beam angle is 90 • .
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 13 The luminous intensity field for a beam angle of 70° was the narrowest; with an increase in the beam angle, the luminous intensity field widened. In the determination of the UGR, a narrow beam angle outperformed a wide beam angle. By contrast, in the determination of the illumination uniformity, a wide beam angle was superior to a narrow beam angle. Tables 3 and 4 show the homogenized UGR and uniformity values, respectively. Figure 4 shows the relationship between UGR and uniformity at various beam angles. For a beam angle of 90°, the UGR is less than the threshold value of 19, and the uniformity is higher than that for beam angles of 70° and 80°; this is similar to the uniformity for beam angles of 100° and 110°. Therefore, considering the UGR and the uniformity values simultaneously, the best beam angle is 90°.  Table 5 shows the variation in the UGR with the desk lamp height for a beam angle of 90°. We can modulate desk lamp height without changing the beam angle of the desk lamp to compare UGR.   Table 5 shows the variation in the UGR with the desk lamp height for a beam angle of 90 • . We can modulate desk lamp height without changing the beam angle of the desk lamp to compare UGR. Figure 5 shows the isoline and color illumination map (lux) of uniformity for different desk lamp heights with a beam angle of 90 • .    Figure 5g shows the lux isolines simulated using a 45 cm high desk lamp; the 1000-1400 lux isoline is distributed in most of the space and the >1000 lux isoline is at the four corners, as indicated by the orange and yellow regions, respectively.

UGR and Uniformity at Beam Angle of 90 • for Different Desk Lamp Heights
The simulation results were used to calculate the illumination uniformity for different desk lamp heights. To comply with the regulations for a study desk, a desk lamp height of 50 cm resulted in the   Figure 5g shows the lux isolines simulated using a 45 cm high desk lamp; the 1000-1400 lux isoline is distributed in most of the space and the >1000 lux isoline is at the four corners, as indicated by the orange and yellow regions, respectively.
The simulation results were used to calculate the illumination uniformity for different desk lamp heights. To comply with the regulations for a study desk, a desk lamp height of 50 cm resulted in the highest uniformity, and a height of 35 cm resulted in the highest average flux.
Tables 5 and 6 present the homogenized UGR and uniformity values, respectively. Figure 6 shows the variation in the UGR and the uniformity with the desk lamp height. For a beam angle of 90 • and desk lamp height of 45 cm, the UGR is less than the threshold value of 19, and the uniformity is higher than that for heights of 35, 40, 41, 42, 43, and 44 cm. Tables 5 and 6 present the homogenized UGR and uniformity values, respectively. Figure 6 shows the variation in the UGR and the uniformity with the desk lamp height. For a beam angle of 90° and desk lamp height of 45 cm, the UGR is less than the threshold value of 19, and the uniformity is higher than that for heights of 35, 40, 41, 42, 43, and 44 cm.  Table 7 shows the UGR for a beam angle of 90° and desk lamp height of 45 cm with different rotation angles. We can modulate the desk lamp rotation angle without changing the beam angle and height of the desk lamp on the study desk to compare UGR.  Figure 7 shows the isoline and color illumination map (lux) of the uniformity for a beam angle  Table 7 shows the UGR for a beam angle of 90 • and desk lamp height of 45 cm with different rotation angles. We can modulate the desk lamp rotation angle without changing the beam angle and height of the desk lamp on the study desk to compare UGR. Figure 7 shows the isoline and color illumination map (lux) of the uniformity for a beam angle of 90 • and desk lamp height of 45 cm with different rotation angles.    Figure 7f shows the lux isolines simulated using a desk lamp rotation angle of 0°; the 1000-1400 lux isoline and the >1000 lux isoline are at the four corners, similar to the situation resulting from a rotation angle of 1°, as indicated by the orange and yellow regions, respectively.   Figure 7f shows the lux isolines simulated using a desk lamp rotation angle of 0 • ; the 1000-1400 lux isoline and the >1000 lux isoline are at the four corners, similar to the situation resulting from a rotation angle of 1 • , as indicated by the orange and yellow regions, respectively.
The simulation results were used to calculate the illumination and uniformity for different desk lamp rotation angles, as shown in Table 8. For a desk lamp rotation angle of 0 • , the uniformity achieved the maximum value of 0.8. Table 8. Illumination and uniformity for different desk lamp heights of 35-50 cm.
Rotation Angle (θ) For the determination of the illumination and uniformity, a rotation angle of 0 • was better than other rotation angles. Tables 7 and 8 show the homogenized UGR and uniformity values, respectively. Figure 8 shows the variation in the UGR and the uniformity with the rotation angle. For a rotation angle of 0 • , the UGR was less than the threshold value of 19, and the uniformity was higher than that for the other rotation angles.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 13 For the determination of the illumination and uniformity, a rotation angle of 0° was better than other rotation angles. Tables 7 and 8 show the homogenized UGR and uniformity values, respectively. Figure 8 shows the variation in the UGR and the uniformity with the rotation angle. For a rotation angle of 0°, the UGR was less than the threshold value of 19, and the uniformity was higher than that for the other rotation angles. The simulation results indicate that the rotation of the desk lamp has a great effect on the glare value, and the glare value exceeds the threshold of 19 for a rotation angle of −1° to −5°. Figure 9 shows a side view of the structure of the desk lamp module. It contains a microstructure diffuser, a brightness enhancement film (BEF), a light guide, a reflective sheet at the bottom, and two LED strips on opposite sides of the light guide. The desk lamp has a width of 42.5 mm, height of 12 mm, and length of 100 mm. The LED model used was Lextar PC35H11, the color temperature of 4000 K and a color-rendering index of 80 was used.  The simulation results indicate that the rotation of the desk lamp has a great effect on the glare value, and the glare value exceeds the threshold of 19 for a rotation angle of −1 • to −5 • . Figure 9 shows a side view of the structure of the desk lamp module. It contains a microstructure diffuser, a brightness enhancement film (BEF), a light guide, a reflective sheet at the bottom, and two LED strips on opposite sides of the light guide. The desk lamp has a width of 42.5 mm, height of 12 mm, and length of 100 mm. The LED model used was Lextar PC35H11, the color temperature of 4000 K and a color-rendering index of 80 was used. Figure 9 shows a side view of the structure of the desk lamp module. It contains a microstructure diffuser, a brightness enhancement film (BEF), a light guide, a reflective sheet at the bottom, and two LED strips on opposite sides of the light guide. The desk lamp has a width of 42.5 mm, height of 12 mm, and length of 100 mm. The LED model used was Lextar PC35H11, the color temperature of 4000 K and a color-rendering index of 80 was used.     Figure 11 shows that the illumination values at heights of 0.27, 0.36, and 0.45 m were 3491, 2128, and 1414 lux, respectively, for a beam angle of 90°. The horizontal coordinate axis represents the illuminance and the vertical coordinate axis represents the distance from the light source. Figure 11. Illumination values at different heights for a beam angle of 90°. Table 9 shows a comparison between the simulated and the measured illumination values. The result indicates good agreement between the two sets of values.  Table 10 shows a comparison between the simulated and the measured illumination values at   Figure 11 shows that the illumination values at heights of 0.27, 0.36, and 0.45 m were 3491, 2128, and 1414 lux, respectively, for a beam angle of 90°. The horizontal coordinate axis represents the illuminance and the vertical coordinate axis represents the distance from the light source. Figure 11. Illumination values at different heights for a beam angle of 90°. Table 9 shows a comparison between the simulated and the measured illumination values. The result indicates good agreement between the two sets of values.  Table 10 shows a comparison between the simulated and the measured illumination values at  Table 9 shows a comparison between the simulated and the measured illumination values. The result indicates good agreement between the two sets of values. Table 10 shows a comparison between the simulated and the measured illumination values at the corners of the object area. The result indicates good agreement between the two sets of values.

Conclusions
Taking account of human factors, this study proposed modulation of the light-emitting field of a desk lamp without using a second optical element, louver structure, or second lens on the luminaire to reduce glare-related effects and maintain illumination uniformity in a reading range. The simulation results demonstrate that the light module in the desk lamp should ideally have a beam angle of 90 • ; the corresponding UGR is less than 19 and illumination uniformity is more than 0.8. The experimental results obtained using the prototype achieved good agreement with the simulation results. This light model can be used to design a desk lamp lighting plan with a UGR of 18.1 and uniformity of 0.8 and to obtain an average illumination value of 1394 lux at a height of 45 cm. Overall, this study proposes a model of a light module with an optimized luminous intensity field for realizing an antiglare light-emitting diode (LED) desk lamp without a second optical element complying with CNS 16048:2018 C4585 regulations.