Design methodology for micro-discrete planar optics with minimum illumination loss for an extended source

Jongmyeong Shim; Changsu Park; Jinhyung Lee; Shinill Kang

doi:10.1364/OE.24.018607

1. Introduction

Recently, the demand for optical systems based on light-emitting diode (LED) sources has been increasing due to their advantages of high efficiency, longevity, and light weight [1,2]. The emission from LED light sources is based on a Lambertian distribution, which leads to limited applications. Therefore, studies have examined ways to design optical systems that obtain the desired light distribution in the target area [3–5]. General optics design is a simple, intuitive design method that involves repeated design and revision based on Snell’s law. However, this method is time consuming, and it is difficult to control the light distribution in the target area effectively. The energy mapping technique was developed to overcome these limits. In this approach, the optical system is designed by dividing the energy distributions of the LED source and target area and matching each domain, which enables efficient design and easy control of the optical distribution in the target area. Therefore, it has been developed in various studies of LED optical systems [6–8]. These studies assume that the LED source is a point source, which is valid if the distance between the light source and optical system is sufficiently long when compared with the emitting area of the LED. With the miniaturization of optical systems and expansion of the emitting area with the application of high-power LEDs, the accuracy of the conventional design technique using the point source approximation reached its limit. To overcome this, a design method that compensates for the energy distribution of the extended source after initial design using a point source was proposed [9]. However, this method is time consuming as it involves multiple iterations and it has limited accuracy. Therefore, a new design method that considers an extended light source from the initial design stage is needed.

With the increasing demand for small, lightweight optical systems, discrete planar optics have been sought to miniaturize optical systems. Discrete planar optics is advantageous because of its small thickness, low material consumption, and low optical absorption by the optical system. Unfortunately, optical loss due to the loss of light from the groove facets is inevitable in discrete planar optics. A modified Fresnel lens (MFL) that reduces light loss by changing the groove angle for desired light path was proposed to overcome such limitations, as shown in Fig. 1(a) [9,10]. Nevertheless, optical loss still occurs when applied with an actual extended source because the groove angle of a conventional MFL is based on a point source, as shown in Fig. 1(b). Therefore, an optical design method that minimizes the optical loss by optimizing the groove angle for an extended source is needed.

Fig. 1 (a) Optical path of the light emitted from a point source. (b) Optical loss of the light emitted from an extended source due to the discrete groove facets.

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This study proposes a design method for discrete planar optics with an extended source that controls the light distribution in the target area via energy mapping, and verifies the proposed design method experimentally. The flow chart in Fig. 2 shows the micro-discrete planar optics design process applied with an extended source. First, a light source reflecting the emission characteristics and area of the extended source was modeled, and the energy distribution illuminating the lens plane from the modeled light source was defined. Then, the desired target illuminance distribution was defined in the target area, and the previously established energy distributions on the lens plane and target area were mapped. Finally, the geometrical lens profile was designed so that the energy from each area of the lens illuminates the target area of the target plane. Here, a design method for discrete planar optics that minimizes optical loss was also proposed by defining the groove angle optimized for an extended source. To verify the proposed design method, discrete planar optics for applications in illumination for LED flash was designed with the desired illuminance distributions. Discrete planar optics was also designed for a uniform illuminance distribution using the conventional method and our method. The discrete planar optics designed using the proposed method was fabricated using an imprinting process to characterize the optical properties. We demonstrated that the design described here was optimal by plotting the optical losses as a function of the groove angle. The simulated and measured optical properties show that efficient discrete planar optics could be achieved for an extended source using the proposed design method.

Fig. 2 Flow chart of the design process for discrete planar optics with an extended source.

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2. Design methodology for micro-discrete planar optics with minimal optical loss for an extended source

First, the extended source was modeled to design micro-discrete planar optics with an extended source. The shape of the emitting area was defined as a rectangular LED with an area of a × b mm², and the light source was divided into M × N identical unit light source areas, as shown in Fig. 3(a). Because each emitting region in the divided area is nearly equivalent to a point source, the luminous intensity of an arbitrary emitting point P(x_ij, y_ij, 0) can be expressed identically for each area, as in Eq. (1) [11–14].

I (θ) = I_{0} \cos^{m} (θ)

where θ represents the emitting angle relative to the axis normal to the emitting plane, and I₀ is the luminous intensity of the divided unit light source normal to the direction of the emitting plane. Equation (2) defines m using θ_1/2_, where the luminous intensity is one half of I₀_.

Fig. 3 Schematic diagram of (a) energy modeling between the extended source and lens plane, and (b) energy mapping for designing the discrete planar optics.

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m = \frac{- \ln 2}{\ln (\cos θ_{1 / 2})}

Equation (3) gives the illuminance E(x, y, z) at the coordinate (x, y, z) from the light source at (x_i, y_j, 0) with area A and luminance L [15–20].

E (x, y, z) = \frac{z^{m} L A}{{[{(x - x_{i})}^{2} + {(y - y_{j})}^{2} + z^{2}]}^{(m + 2) / 2}}

Therefore, as shown in Fig. 3(a), the illuminance E_u(x, y, s) at coordinate Q(x, y, s), which is located at distance s from the unit light source at P(x_ij, y_ij, 0), with an area of ab/MN when the extended source is divided by M × N, can be defined as in Eq. (4).

E_{u} (x, y, s) = \frac{z^{m} L_{u} a b / M N}{{[{(x - x_{i j})}^{2} + {(y - y_{i j})}^{2} + s^{2}]}^{(m + 2) / 2}}

Here, L_u is the luminance of the unit light source at the coordinate (x_ij, y_ij, 0). Therefore, the total illuminance E_total(x, y, s) at the coordinate Q(x, y, s) from the extended source with area ab is equal to the sum of the illuminance from every unit light source, as shown in Eq. (5). Equation (5) also gives the total optical energy from the extended source illuminating each point in the lens plane.

E_{t o t a l} (x, y, s) = \sum_{j = 1}^{N} \sum_{i = 1}^{M} \frac{z^{m} L_{u} a b / M N}{{[{(x - x_{i j})}^{2} + {(y - y_{i j})}^{2} + s^{2}]}^{(m + 2) / 2}}

Then, the desired target illuminance distribution in the target area was defined. The target area was divided into n equal areas, and the amount of energy illuminating the k^th area on the target plane was defined as E_t_,_k. Therefore, the energy illuminating each area was defined from E_t,1 to E_t_,_n. In addition, the energy between the lens plane and target area was mapped by dividing the total energy of the lens plane derived from Eq. (5), so that the energy E_s_,_k, the k^th energy on the lens plane, equals E_t_,_k, as in Eq. (6).

E_{s, k} = E_{t, k}

Therefore, as shown in Eq. (7), the sum of the energy E_s_,_k of the divided lens plane is equal to the total energy E_total that is emitted from the light source, which is also equal to the sum of the target illuminance E_t_,_k of each domain in the target area.

E_{t o t a l} = \sum_{k = 1}^{n} E_{s, k} = \sum_{k = 1}^{n} E_{t, k}

Using the amounts of energy mapped between the lens plane and target area, a geometrical profile of a micro-discrete planar optics that maps the divided energy from the lens plane entering each mapped area on the target plane was generated, as in Fig. 3(b). First, A_s_,_k was defined as the k^th area of the lens plane with energy E_s_,_k, and A_t_,_k as the k^th area of the target area with energy E_t_,_k. The y coordinate of the k^th area A_s_,_k of the lens plane ranges from y_s_,_k-1 to y_s_,_k based on Eq. (8), and the y coordinate of the k^th area A_t_,_k of the target area ranges from y_t_,_k-1 to y_t_,_k by Eq. (9).

A_{s, k} = π (y_{s, k}^{2} - y_{s, k - 1}^{2})

A_{t, k} = π (y_{t, k}^{2} - y_{t, k - 1}^{2})

The light entering (0, y_s_,_k, t) on the discrete planar optics from the light source must enter (0, y_t_,_k, h) on the target area after passing the designed discrete planar surfaces, as shown in Fig. 3(b). To obtain the incidence angle of the light that enters each domain of the lens plane, the incidence angle of light entering the lens plane from the source must be defined first. For a point source, the light emitted from a single point enters all lens planes, whereas in the case of an extended source, light reaches the lens plane from various angles due to the large area of the emitting plane. Therefore, if the extended source emits light onto a micro-discrete planar optics with multiple grooves, the effect of the optical loss at each groove facet is large due to the various angles of incidence. To minimize the optical loss at the groove facet, an optimized groove angle is required. The minimum optical loss can be achieved when the incident light with the highest intensity reaching each groove facet is controlled by its groove angle. We define the dominant angle as the incidence angle of the light with the highest intensity entering each groove of the lens.

The optical intensity of the light entering each groove of the lens must be defined to obtain the dominant angle of each groove; in this study, the x coordinate was fixed as 0 because the discrete planar optics was designed axis-symmetrically for ease of fabrication. Angle ϕ from an arbitrary point S(0, y_l, 0) on the y-axis of the light source to the point (0, y, s) on the bottom surface of the lens can be expressed as in Eq. (10).

ϕ = \tan^{- 1} (\frac{y - y_{l}}{s}),_{}_{} (- \frac{b}{2} \leq y_{l} \leq \frac{b}{2})

Therefore, the intensity I_i of the light entering the point (0, y, s) on the bottom surface of the lens from each point on the y-axis of the extended source is expressed as in Eq. (11).

I_{i} = I_{0} \cos^{m} ϕ = I_{0} \cos^{m} [\tan^{- 1} (\frac{y - y_{l}}{s})],_{}_{} (- \frac{b}{2} \leq y_{l} \leq \frac{b}{2})

The dominant angle ϕ_dom is the incidence angle for which the intensity I_i entering (0, y, s) on the lens plane is maximal. The light entering at dominant angle ϕ_dom is refracted on the bottom surface of the lens at angle ϕ_dom'; the relationship between the two angles is given by Eq. (12), where n_a and n_l are the refractive indices of air and the lens, respectively.

n_{a} \sin ϕ_{d o m} = n_{l} \sin ϕ_{d o m}^{'}

The final geometric profile of the micro-discrete planar optics is generated from the point data mapped onto the lens plane and target area and the dominant angle defined above. The groove profile of the discrete planar optics is generated by defining the slope at each y coordinate of the lens plane. First, for precise implementation of the mapping features in each groove of a discrete planar optics with n grooves, each groove was divided into 10 sections, and its i^th division point was defined as y_s_,_k_,_i, as shown in Fig. 3(b). The target area was divided in the same manner, such that the i^th division point was y_t_,_k_,_i, and the geometric profile was designed so that the light propagates to each mapped point. Equation (13) defines the slope of the groove such that the light entering coordinate (0, y_s_,_k_,_i, t) at angle ϕ_dom_,_k_,_i' enters coordinate (0, y_t_,_k_,_i, h) of the target area [9,21].

θ_{k, i} = \tan^{- 1} {\frac{n \sin ϕ_{d o m, k, i}^{'} - \sin [\tan^{- 1} (\frac{y_{t, k, i} - y_{s, k, i}}{h - t})]}{n \cos ϕ_{d o m, k, i}^{'} - \cos [\tan^{- 1} (\frac{y_{t, k, i} - y_{s, k, i}}{h - t})]}}

The profile of the entire micro discrete planar optics can be acquired by determining the slope of each groove and connecting these values using Eq. (13). The design methodology for micro-discrete planar optics applied with an extended source that minimizes the optical loss was defined using the above steps. The resulting algorithm enables the design of an efficient optical system for an extended source.

3. Verification of the design methodology for an extended source

We designed discrete planar optics for applications in illumination for LED flash. As shown in Fig. 4, the 800 × 800 mm² target area was defined to have a viewing angle of 75°, located 1000 mm from the LED. The viewing angle was 120°. The discrete planar optics had 65% illuminance at 0.7 F and 35% illuminance at 1.0 F (relative to the illuminance at the central region of the target area at 0.0 F). Figure 5 shows the simulated illuminance distributions (a) from a bare LED, and using the discrete planar optics designed with the (b) conventional and (c) proposed methods, where the light energy is collected within the target region. Figure 5(d) shows profiles of the relative illuminance from a bare LED, and those using discrete planar optics designed with the conventional and proposed methods. Compared with the illuminance from a bare LED, that from the LED with the discrete planar optics shows significant enhancement due to the improved collection efficiency. Compared with the illuminance at 0.0 F, 65% and 35% was obtained at 0.7 F and 1.0 F, respectively, using the discrete planar optics designed with both the conventional and proposed methods, which satisfied the desired target illuminance distribution. The simulation results show that the total flux at the detector was 252.87 lm using the proposed method, compared with 233.31 lm using the conventional method, an increase of about 8.4%. These results verify the effectiveness of the proposed method in reducing optical loss at the groove facets by optimizing the groove angle of the discrete planar optics. These results also demonstrate that we were able to design discrete planar optics with the desired illuminance distribution.

Fig. 4 Schematic diagrams of the optical arrangement, showing the discrete planar optics, as well as the target illuminance distribution.

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Fig. 5 Images of the simulated illuminance distribution at the target plane (a) from a bare LED and using planar optics designed using the (b) conventional and (c) proposed methods. (d) Profiles of the simulated relative illuminance distributions.

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Also, we designed a discrete planar optics for a uniform distribution, as shown in Fig. 6. Three discrete planar optics were designed: two using the conventional design method with a point source and an extended source, and one using the proposed design method applied to an extended light source. Then, optical simulations were conducted applying real LED ray data to analyze the design accuracy of each method. The distance from the light source to the target plane was set to 25 mm, the target area was 32 × 32 mm², and the distance from the light source to the discrete planar optics was 1 mm. As the LED light source, a 5050 surface-mounted-device LED module was used. The simulation results show illuminance uniformity of 93.3% and 97.5% with discrete planar optics designed using the conventional method with a point source and extended source compared with 98.7% with discrete planar optics designed with the proposed method. This simulation confirmed that an efficient optical design with considerably reduced deviation using the proposed method is possible.

Fig. 6 Schematic diagram of the optical system for discrete planar optics, and the illuminance distribution of a bare LED and the target distribution after passing through the discrete planar optics.

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The designed discrete planar optics was fabricated to analyze its optical performance and verify the proposed design method experimentally. Figure 7(a) shows the fabrication process of the designed discrete planar optics. First, a mold with the reverse shape of the designed discrete planar optics was fabricated using an ultra-precision directing machining process with a diamond tool (Nanoform-200, Precitech, USA). Using the fabricated mold, an ultraviolet (UV) imprinting process was used to fabricate the final pattern of the designed discrete planar optics. The mold was coated with a self-assembled monolayer of dichlorodimethylsilane (DDMS) as an anti-adhesion layer to improve the release of the lens from the mold. The UV photopolymer was heated at 50 °C to enhance replication. During the imprinting process, the photopolymer was cured by irradiating it with UV light at a wavelength of 365 nm and intensity of 100 mW cm⁻². Figure 7(b) shows an image of the fabricated discrete planar optics designed using the proposed method with an extended source.

Fig. 7 (a) Fabrication process of the discrete planar optics and (b) an image of the fabricated discrete planar optics designed using the proposed method with an extended source.

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To analyze the optical performances of the fabricated discrete planar optics, an optical measuring system was constructed based on the design specifications. An LED was positioned at the bottom of the system, and the fabricated discrete planar optics was positioned 1 mm from the LED and aligned precisely using micro-stages. Then, the target plane was positioned 25 mm from the LED, and the image emitted from the LED illuminated on the target plane after passing the discrete planar optics was measured.

Figure 8(a) shows the simulated illuminance distribution at the target plane with the discrete planar optics designed using the conventional method with a point source, and Fig. 8(b) shows the simulated illuminance distribution at the target plane with an extended source. Figure 8(c) shows the simulated illuminance distribution of discrete planar optics designed using the proposed method with an extended source. Figures 8(d) and 8(e) show the respective measured illuminance distributions of discrete planar optics fabricated using designs by the conventional and proposed methods with an extended source. The measured illuminance uniformity at the target plane using the proposed method was 96.2%, which is close to the simulated uniformity of 98.7%. The uniformity was improved significantly compared with that using the conventional design method which was 95.2% with an extended source. Figure 8(f) shows the relative illuminance distribution profiles from Figs. 8(a)–8(e). These profiles confirm that the illuminance uniformity is theoretically improved by applying the proposed design method. Furthermore, the measured illuminance uniformity is very close to the simulated illuminance uniformity, verifying the effectiveness of the proposed design method with an extended source.

Fig. 8 Images of the simulated illuminance distribution at the target plane of discrete planar optics designed using the conventional method with (a) a point source or (b) an extended source and (c) the proposed method with an extended source. The measured illuminance distribution from the fabricated discrete planar optics designed using the (d) conventional and (e) proposed methods with an extended source. (f) The simulated and measured relative illuminance distributions.

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The optical losses were simulated as a function of the groove angle of the discrete planar optics to show that the design was optimal. Consecutive numbering from 1 to 44 was used (starting from the nearest groove facet from the center). As the optimal groove angle for the discrete planar optics differed for each groove, the optical losses were investigated as a function of the difference between the groove angle of each of the two grooves and the optimized angle. The optical losses were calculated as follows:

O_{l o s s} = (\frac{E (θ_{o} + δ) - E (θ_{o})}{E (θ_{o})}) \times 100 (%)

where E(θ_o) is the illuminance from a groove facet with an optimized angle, and E(θ_o + δ) is the illuminance with a tilt of δ away from the optimal angle. We carried out simulations with δ in the range ± 4°, and with intervals of 2°. As shown in Fig. 9, the maximum optical loss was 1.87% with a tilt of ± 4°, compared with that for the optimal angle. These results show that the discrete planar optics had optimized groove angles for each groove.

Fig. 9 Optical losses as a function of the groove angles of the groove facets. (a) From the 1st to the 8th groove, (b) from the 9th to the 16th groove, (c) from the 17th to 24th groove, (d) from the 25th to the 32nd groove, (e) from the 33rd to the 40th groove, and (f) from the 41st to 44th groove.

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4. Conclusion

This study proposed a method for designing a discrete planar optics that effectively controls the light distribution by modeling the energy from an extended source and mapping the energy to the desired target distribution. A discrete planar optics for applications in illumination for LED flash was designed and analyzed. A discrete planar optics designed to achieve a uniform illuminance distribution was also designed and fabricated to verify the proposed design methodology. The optical losses were characterized as a function of the groove angle. First, the extended source was modeled by dividing it into dozens of unit areas, and the total illuminance from the light source to the lens plane was formulated. Next, the desired light distribution in the target area was defined, and the energy was mapped from the lens plane to the target area. Finally, the geometric profile of the micro-discrete planar optics was designed to illuminate the light on the target area. To verify the proposed design methodology, a discrete planar optics for applications in illumination for LED flash was designed, with the desired illuminance distribution. Compared with the illuminance distribution of a bare LED, the illuminance distribution of an LED with the discrete planar optics showed significant enhancement of the illuminance; 65% of the illuminance was achieved at 0.7 F, and 35% was achieved at 1.0 F (these figures are relative to the target illuminance at 0.0 F). A discrete planar optics was designed and fabricated to achieve a uniform illuminance distribution. The simulation result for the discrete planar optics designed with the proposed method showed an illuminance uniformity of 98.7%, whereas that using the conventional design method with a point source and an extended source gave an illuminance uniformity of 93.7% and 97.5%. For experimental verification, a mold was fabricated using ultra-precision direct machining and replicated via the imprinting process to fabricate the designed micro-discrete planar optics, and the illuminance uniformity was measured. The measurements indicate an illuminance uniformity of 96.2%, which is similar to the simulated results. The optical losses were analyzed as a function of the groove angle, and exhibited a difference of ≤1.87% compared with the optimized angle for tilt angles of up to ± 4°. These results proved that an efficient optical design considering an extended source is possible. Studies to design and construct optical systems in various fields using the proposed design methodology are in progress to minimize differences in the optical properties of the designed and constructed optical systems.

Funding

The National Research Foundation of Korea (NRF) (No.2015R1A5A1037668).

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Design methodology for micro-discrete planar optics with minimum illumination loss for an extended source

Abstract

1. Introduction

2. Design methodology for micro-discrete planar optics with minimal optical loss for an extended source

3. Verification of the design methodology for an extended source

4. Conclusion

Funding

References and links

Cited By

Figures (9)

Equations (14)

Optics Express