FDTD analysis of the light extraction efficiency of OLEDs with a random scattering layer

Selective Enhancement of Viewing Angle Characteristics and Light Extraction Efficiency of Blue Thermally Activated Delayed Fluorescence Organic Light-Emitting Diodes through an Easily Tailorable Si3N4 Nanofiber Structure

We selectively improved the viewing angle characteristics and light extraction efficiency of blue thermally activated delayed fluorescence (TADF) organic light-emitting diodes (OLEDs) by tailoring a nanofiber-shaped Si3N4 layer, which was used as an internal scattering layer. The diameter of the polymer nanofibers changed according to the mass ratio of polyacrylonitrile (PAN) and poly(methyl methacrylate) (PMMA) in the polymer solution for electrospinning. The Si3N4 nanofiber (SNF) structure was fabricated by etching an Si3N4 film using the PAN/PMMA nanofiber as a mask, making it easier to adjust parameters, such as the diameter, open ratio, and height, even though the SNF structure was randomly shaped. The SNF structures exhibited lower transmittance and higher haze with increasing diameter, showing little correlation with their height. However, all the structures demonstrated a total transmittance of over 80%. Finally, by applying the SNF structures to the blue TADF OLEDs, the external quantum efficiency was increased by 15.6%. In addition, the current and power efficiencies were enhanced by 23.0% and 25.6%, respectively. The internal light-extracting SNF structure also exhibited a synergistic effect with the external light-extracting structure. Furthermore, when the viewing angle changed from 0° to 60°, the peak wavelength and CIE coordinate shift decreased from 20 to 6 nm and from 0.0561 to 0.0243, respectively. These trends were explained by the application of Snell's law to the light path and were ultimately validated through finite-difference time-domain simulations.

Top-Emitting Quantum Dot Light-Emitting Diodes: Theory, Optimization, and Application

The superior optical properties of colloidal quantum dots (QDs) have garnered significant broad interest from academia and industry owing to their successful application in self-emitting QD-based light-emitting diodes (QLEDs). In particular, active research is being conducted on QLEDs with top-emission device architectures (TQLEDs) owing to their advantages such as easy integration with conventional backplanes, high color purity, and excellent light extraction. However, due to the complicated optical phenomena and their highly sensitive optoelectrical properties to experimental variations, TQLEDs cannot be optimized easily for practical use. This review summarizes previous studies that have investigated top-emitting device structures and discusses ways to advance the performance of TQLEDs. First, theories relevant to the optoelectrical properties of TQLEDs are introduced. Second, advancements in device optimization are presented, where the underlying theories for each are considered. Finally, multilateral strategies for TQLEDs to enable their wider application to advanced industries are discussed. This work believes that this review can provide valuable insights for realizing commercial TQLEDs applicable to a broad range of applications.

Resonant absorption of light by a two-dimensional imperfect lattice of spherical particles

The light absorption and scattering by an infinite two-dimensional array with an imperfect lattice of identical spherical particles is considered based on the statistical approach to a description of electromagnetic wave interaction with particulate media. Absorption resonances due to the coherent component of scattered light (zeroth order of diffraction) and resonances arising from the excitation of a flux of incoherently scattered light (higher diffraction orders) propagating at grazing angles to the array plane are studied. The dependence of absorption on the degree of positional ordering of particles is considered. It is shown that with an increase in ordering, the spatial coherence of the light flux along the array plane increases and the absorption resonance becomes more pronounced. Data are presented for silver wavelength-sized particles for s- and p-polarized incident waves. It is shown that at small angles of incidence, the first diffraction order can arise at the wavelength of zeroth-order resonance. In this case, the contributions to absorption created by the coherent and incoherent components of scattered light are summed up. The value of the absorption coefficient can be close to 0.95. A comparison with data for a partially ordered array is carried out.

Luminance enhancement of top-emitting blue organic light emitting diodes encapsulated with silicon nitride thin films by a double-layer nano-structure

Even though it is in high demand to introduce a nano-structure (NS) light extraction technology on a silicon nitride to be used as a thin film encapsulation material for an organic light-emitting diode (OLED), only an industry-incompatible wet method has been reported. This work demonstrates a double-layer NS fabrication on the silicon nitride using a two-step organic vapor phase deposition (OVPD) of an industry-compatible dry process. The NS showed a wrinkle-like shape caused by coalescence of the nano-lenses. The NS integrated top-emitting OLED revealed 40 percent enhancement of current efficiency and improvement of the luminance distribution and color change according to viewing angle.

Design and optical characterization of an efficient polarized organic light emitting diode based on refractive index modulation in the emitting layer

Luminescent liquid Crystal (LC) material is regarded as the most promising material for polarized organic light emission due to their intrinsic characteristics including orderly alignment and luminescence. Nevertheless, the optical extraction efficiency of LC based organic light emitting diodes (OLEDs) devices still requires significant effort and innovation towards real-world applications. In this paper, we propose the design of a highly linearly polarized light-emission from OLEDs with integrated refractive index nanograting in the emissive layer (EML) based on photo aligned luminescent liquid crystal material. The simulation results indicate that the geometrically optimized polarized device yields an external quantum efficiency (EQE) up to 47% with a polarized ratio up to 28 dB at a 550 nm emission wavelength. This conceptual design offers a new opportunity to achieve efficient polarized organic luminescence, and it is (to the best of our knowledge) the first approach that enhances the light extraction of OLEDs based on luminescent liquid crystal via index grating in the EML.

Enhancing extraction efficiency of quantum dot light-emitting diodes introducing a highly wrinkled ZnO electron transport layer

Light extraction efficiency is crucial for achieving highly efficient and bright quantum dot light-emitting diodes (QLEDs), and current efforts toward introducing light outcoupling nanostructures always require complicated procedures. An extremely simple and efficient method to introduce light outcoupling nanostructures in the ZnO electron transport layer (ETL) is demonstrated by adopting a certain heating rate during the annealing process. The ultimate device exhibits a current efficiency of 9.1 cd/A, giving a 50% efficiency improvement compared to the control device with a flat ZnO ETL. This arises from the increased light extraction efficiency induced by random nanostructures formed on a wrinkled ZnO ETL, which could also be modulated by adjusting the heating rate during the annealing process. This study not only provides a simple and efficient method to introduce light outcoupling nanostructures, but also shows ample room for further performance enhancement of QLEDs with the guideline of light extraction.

Enhanced optical efficiency and color purity for organic light-emitting diodes by finely optimizing parameters of nanoscale low-refractive index grid

To extract the confined waveguided light in organic light-emitting diodes (OLEDs), inserting a low refractive index (RI) periodic structure between the anode and organic layer has been widely investigated as a promising technology. However, the periodic-structure-based light extraction applied inside devices has been shown to severely distort spectrum and affect EL characteristics. In this study, a simple light extraction technology using periodic low-RI nanodot array (NDA) as internal light extraction layer has been demonstrated. The NDA was fabricated simply via laser interference lithography (LIL). The structural parameters of periodic pattern, distance, and height were easily controlled by the LIL process. From computational analysis using finite-difference time-domain (FDTD) method, the NDA with 300 nm pitch and 0.3 coverage ratio per unit cell with 60 nm height showed the highest enhancement with spectral-distortion-minimized characteristics. Through both computational and experimental systematic analysis on the structural parameters of low-RI NDA-embedded OLEDs, highly efficient OLEDs have been fabricated. Finally, as representative indicators, hexagonal and rectangular positioned NDA-embedded OLEDs showed highly improved external quantum efficiencies of 2.44 (+29.55%) and 2.77 (+57.38%), respectively. Furthermore, the disadvantage originating from the nanoscale surface roughness on the transparent conductive oxide was minimized.

Inside or outside: Evaluation of the efficiency enhancement of OLEDs with applied external scattering layers

Improving the efficiency of organic light-emitting diodes (OLEDs) by enhancing light outcoupling is common practise and remains relevant as not all optical losses can be avoided. Especially, externally attached scattering layers combine several advantages. They can significantly increase the performance and neither compromise the electric operation nor add high costs during fabrication. Efficiency evaluations of external scattering layers are often done with lab scale OLEDs. In this work we therefore study different characterization techniques of red, green and blue lab scale OLEDs with attached light scattering foils comprising TiO₂ particles. Although we observe an increased external quantum efficiency (EQE) with scattering foils, our analysis indicates that areas outside the active area have a significant contribution. This demonstrates that caution is required when efficiency conclusions are transferred to large area applications, for which effects that scale with the edges become less significant. We propose to investigate brightness profiles additionally to a standard EQE characterizations as latter only work if the lateral scattering length is much smaller than the width of the active area of the OLED. Our results are important to achieve more reliable predictions as well as a higher degree of comparability between different research groups in future.

2D to 3D Manipulation and Assembly of Microstructures Using Optothermally Generated Surface Bubble Microrobots

Hydrogel microstructures that encapsulate cells can be assembled into tissues and have broad applications in biology and medicine. However, 3D posture control for a single arbitrary microstructure remains a challenge. A novel 3D manipulation and assembly technique based on optothermally generated bubble robots is proposed. The generation, rate of growth, and motion of a microbubble robot can be controlled by modulating the power of a laser focused on the interface between the substrate and a fluid. In addition to 2D operations, bubble robots are able to perform 3D manipulations. The 3D properties of hydrogel microstructures are adjusted arbitrarily, and convex and concave structures with different heights are designed. Furthermore, annular micromodules are assembled into 3D constructs, including tubular and concentric constructs. A variety of hydrogel microstructures of different sizes and shapes are operated and assembled in both 2D and 3D conformations by bubble robots. The manipulation and assembly methods are simple, rapid, versatile, and can be used for fabricating tissue constructs.

Simulation method for study on outcoupling characteristics of stratified anisotropic OLEDs

We derive explicit power dissipation functions for stratified anisotropic OLEDs based on a radiation model of dipole antennas inside anisotropic microcavity. The dipole field expressed by vector potential is expanded into plane waves whose coefficients are determined by scattering matrix method, and then an explicit expression is derived to calculate the energy flux through arbitrary interfaces. Taking advantage of the formulation, we can easily perform quantitative analysis on outcoupling characteristics of stratified anisotropic OLEDs, including outcoupling efficiency, normalized decay rate and angular emission profile. Simulations are carried out on a prototypic stratified OLED structure to verify the validity and capability of the proposed model. The dependencies of the outcoupling characteristics on various emission feature parameters, including dipole position, dipole orientation, and the intrinsic radiative quantum efficiency, are comprehensively evaluated and discussed. Results demonstrate that the optical anisotropy in different organic layers has nonnegligible influences on the far-field angular emission profile as well as outcoupling efficiency, and thereby highlight the necessity of our method. The proposed model can be expected to guide the optimal design of stratified anisotropic OLED devices, and help to solve the inverse outcoupling problem for determining the emission feature parameters.

Theoretical comparison of the excitation efficiency of waveguide and surface plasmon modes between quantum-mechanical and electromagnetic optical models of organic light-emitting diodes

We theoretically compare the excitation efficiency of waveguide and surface plasmon modes between quantum-mechanical and classical electromagnetic optical models of organic light-emitting diodes (OLEDs). A sophisticated optical model combining the two approaches is required to obtain an accurate calculation result and a comprehensive understanding of the micro-cavity effect in OLEDs. In the quantum-mechanical approach based on the Fermi's golden rule, the mode expansion method is used to calculate the excitation efficiency. In the classical electromagnetic approach, the spectral power density calculated by the point dipole model is fitted by the summation of the Lorentzian line shape functions, which provide the excitation probability of each waveguide and surface plasmon modes. The mode coupling efficiencies on the basis of the two approaches are calculated in a bottom-emitting OLED when the position of a dipole emitter is varied. By comparing the calculation results, we confirm the equivalence of two approaches and obtain the better optical interpretation to the calculated excitation efficiency of waveguide and surface plasmon modes. The ratio of mode excitation efficiencies calculated by two approaches agrees well with each other except the contribution of the near-field absorption component.

Optical modeling of the emission zone profile and optimal emitter position based on the internal field profile of the air mode in organic light-emitting diodes

We propose a theoretical formulation to calculate the internal profile of the air mode in the organic light-emitting diode (OLED) on the combination of the transfer matrix method and source-term method. The spatial distributions of the air mode are calculated in a top-emitting OLED with respect to the light polarization, extraction angle, dipole orientation, and dipole position. Air modes are also calculated on the basis of the previously used external source model, where the input optical wave is injected from the air into the OLED multilayer. Comparison of the calculated air modes between two models checks the validity of the external source model. In addition, we propose an improved formula to determine the optimal emitter positions that maximize the two-beam interference of the micro-cavity effect. In the improved formula, a non-ideal reflection phase shift at a reflective metal anode is treated as the skin depth of the air mode. Finally, the effect of the dipole orientation on the air mode is investigated. Compared with the air mode emitted by the horizontally oriented dipole, the air mode generated by the vertically oriented dipole has relatively small intensity and shows the opposite dependence of the emitter position variation. The calculation results of the internal profile of the air mode within the emission layer are matched with the profile of the emission zone obtained by output radiant flux on the basis of the currently used point dipole model.

Light Extraction Enhancement in Flexible Organic Light-Emitting Diodes by a Light-Scattering Layer of Dewetted Ag Nanoparticles at Low Temperatures

We demonstrated light extraction improvement by applying a scattering layer of Ag nanoparticles physically synthesized through a low-temperature annealing process to flexible organic light-emitting diodes (OLEDs). In general, increasing the size of Ag nanoparticles is preferred to increase light scattering, but a high-temperature annealing process (∼400 °C) is required to produce them. However, flexible substrates generally cannot withstand high-temperature processes. In this study, we formed Ag nanoparticles at a low temperature of ∼200 °C by inserting a poly(3,4-ethylenedioxythiophene) polystyrene sulfonate buffer layer, thus promoting Ag dewetting. As a result, the scattering layer of enlarged Ag nanoparticles formed at low temperatures increased the external quantum efficiency by 24% in a flexible OLED compared to a reference device.

Overcoming the efficiency limit of organic light-emitting diodes using ultra-thin and transparent graphene electrodes

We propose an effective way to enhance the out-coupling efficiencies of organic light-emitting diodes (OLEDs) using graphene as a transparent electrode. In this study, we investigated the detrimental adsorption and internal optics occurring in OLEDs with graphene anodes. The optical out-coupling efficiencies of previous OLEDs with transparent graphene electrodes barely exceeded those of OLEDs with conventional transparent electrodes because of the weak microcavity effect. To overcome this issue, we introduced an internal random scattering layer for light extraction and reduced the optical absorption of the graphene by reducing the number of layers in the multilayered graphene film. The efficiencies of the graphene-OLEDs increased significantly with decreasing the number of graphene layers, strongly indicating absorption reduction. The maximum light extraction efficiency was obtained by using a single-layer graphene electrode together with a scattering layer. As a result, a widened angular luminance distribution with a remarkable external quantum efficiency and a luminous efficacy enhancement of 52.8% and 48.5%, respectively, was achieved. Our approach provides a demonstration of graphene-OLED having a performance comparable to that of conventional OLEDs.

Continuous Preparation of Hollow Polymeric Nanocapsules Using Self-Assembly and a Photo-Crosslinking Process of an Amphiphilic Block Copolymer

This paper presents a fabrication method of hollow polymeric nanocapsules (HPNCs). The HPNCs were examined to reduce light trapping in an organic light emitting diodes (OLED) device by increasing the refractive index contrast. They were continuously fabricated by the sequential process of self-assembly and photo-crosslinking of an amphiphilic block copolymer of SBR-b-PEGMA, poly(styrene-r-butadiene)-b-poly(poly(ethylene glycol) methyl ether methacrylate) in a flow-focusing microfluidic device. After the photo-crosslinking process, the produced HPNCs have a higher resistance to water and organic solvents, which is applicable to the fabrication process of optical devices. The morphology and hollow structure of the produced nanocapsules were determined by transmission electron microscopy (TEM), scanning electron microscopy (SEM), and atomic force microscopy (AFM). Also, their size control was examined by varying the ratio of inlet flow rates and the morphological difference was studied by changing the polymer concentration. The size was measured by dynamic light scattering (DLS). The refractive index of the layer with and without the HPNCs was measured, and a lower refractive index was obtained in the HPNCs-dispersed layer. In future work, the light extraction efficiency of the HPNCs-dispersed OLED will be examined.

Crystallization-assisted nano-lens array fabrication for highly efficient and color stable organic light emitting diodes

To date, all deposition equipment has been developed to produce planar films. Thus lens arrays with a lens diameter of <1 mm have been manufactured by combining deposition with other technologies, such as masks, surface treatment, molding etc. Furthermore, a nano-lens array (NLA) with a sufficiently small lens diameter (<1 μm) is necessary to avoid image quality degradation in high resolution displays. In this study, an organic NLA made using a conventional deposition technique - without combining with other techniques - is reported. Very interestingly, grazing-incidence small-angle X-ray scattering (GI-SAXS) experiments indicate that the NLA is formed by the crystallization of organic molecules and the resulting increase in surface tension. The lens diameter can be tuned for use with any kind of light by controlling the process parameters. As an example of their potential applications, we use NLAs as a light extraction film for organic light emitting diodes (OLEDs). The NLA is integrated by directly depositing it on the top electrode of a collection of OLEDs. This is a dry process, meaning that it is fully compatible with the current OLED production process. Devices with NLAs exhibited a light extraction efficiency 1.5 times higher than devices without, which corresponds well with simulation results. The simulations show that this high efficiency is due to the reduction of the guided modes by scattering at the NLA. The NLAs also reduce image blurring, indicating that they increase color stability.

Color uniformity enhancement for COB WLEDs using a remote phosphor film with two freeform surfaces

The color uniformity (CU) of chip-on-board (COB) white light emitting diodes (WLEDs) has been improved by using remote phosphor films with two freeform surfaces (TFS-RPFs). The finite-difference time-domain (FDTD), Monte Carlo ray-tracing, and color-thickness feedback (CTFB) methods were used to design the TFS-RPFs: the blue light distribution of COB WLEDs is greatly affected by the angular thickness distribution of TFS-RPFs, and a high CU can be achieved iteratively. The directional inconsistency of incident and emergent blue light, scattering effect of TFS-RPFs, and illumination characteristics of the COB source were also investigated. COB WLEDs containing optimized TFS-RPFs achieved high CU with a decrease of 26.2% in maximum CCT deviation; thus, TFS-RPFs can improve the CU of COB WLEDs.

Tailoring Directive Gain for High-Contrast, Wide-Viewing-Angle Organic Light-Emitting Diodes Using Speckle Image Holograpy Metasurfaces

Holography metasurfaces have been used to control the propagation of light to an unprecedented level, exhibiting the immense potential for light steering in organic light-emitting diodes (OLEDs). Here, a new approach to tailoring directive gain for high contrast, wide-viewing-angle OLEDs is proposed by implementing a spcekle image holography (SIH) metasurface. The experimental and theoretical results provide the direct proofs that the SIH metasurface can play very important roles not only in releasing the trapped energy flow insides the devices but also in tailoring the wavefronts to the preferred patterns due to its "regional orientation" k-vectors patterns. The resulting power efficiency and external quantum efficiency of the OLEDs using a SIH metasurface are 1.97 and 1.95 times that of the reference device with a standard architecture. Furthermore, the wavefronts of emitted light are delicately modulated in a polarization-independent manner, yielding 2.5 times higher contrast ratio compared to the reference device. This unique engineered directive gain property is also well-retained for the viewing angles varing from normal to titled ±60° without spectral distortion. These results enrich the understanding of light wavefronts control in OLEDs and highlight its potential application in display as well as light steering for other optoelectronics.

A Light Scattering Layer for Internal Light Extraction of Organic Light-Emitting Diodes Based on Silver Nanowires

We propose and fabricate a random light scattering layer for light extraction in organic light-emitting diodes (OLEDs) with silver nanodots, which were obtained by melting silver nanowires. The OLED with the light scattering layer as an internal light extraction structure was enhanced by 49.1% for the integrated external quantum efficiency (EQE). When a wrinkle structure is simultaneously used for an external light extraction structure, the total enhancement of the integrated EQE was 65.3%. The EQE is maximized to 65.3% at a current level of 2.0 mA/cm(2). By applying an internal light scattering layer and wrinkle structure to an OLED, the variance in the emission spectra was negligible over a broad viewing angle. Power mode analyses with finite difference time domain (FDTD) simulations revealed that the use of a scattering layer effectively reduced the waveguiding mode while introducing non-negligible absorption. Our method offers an effective yet simple approach to achieve both efficiency enhancement and spectral stability for a wide range of OLED applications.

Effect of the finite pixel boundary on the angular emission characteristics of top-emitting organic light-emitting diodes

We numerically investigate the effect of the pixel boundary on the angular emission characteristics of top-emitting organic light-emitting diodes (OLEDs) using the finite element method. A three-dimensional OLED structure has the square pixel boundary, which is surrounded by the pixel definition layer. The angular emission characteristics based on the Poynting vectors are calculated in various positions of a Hertz dipole emitter within the pixel boundary. When the dipole emitter is located near the center of the square pixel, the angular emission characteristics have a symmetric forward-directed pattern, which is similar to the angular emission pattern calculated by the thin-film-based optical model. When the position of the dipole emitter is close to the pixel boundary, the angular emission pattern becomes asymmetric because the optical reflections from the pixel boundary in the horizontal direction affect the emission pattern of the dipole emitter. The total angular emission characteristics of the top-emitting OLED are obtained by summing the individual angular emission pattern of the whole dipole emitters, which are assumed to be uniformly distributed in the two-dimensional emission plane. The asymmetrical angular emission characteristics of the dipole emitters near the pixel boundary contribute to narrowing the total angular emission pattern.

Enhancing the outcoupling efficiency of quantum dot LEDs with internal nano-scattering pattern

We report an effective method to extract light from quantum-dot light emitting diodes (QLEDs) by embedding an internal nano-scattering pattern structure. We use finite-difference time-domain method to analyze the light extraction efficiency of red QLEDs with periodic, quasi-random, and random internal nano-scattering pattern structures. Our simulation results indicate that random internal nano-scattering pattern can greatly enhance the outcoupling efficiency while keeping wide viewing angle for the red QLED. Similar results are obtained by extending this approach to green and blue QLEDs. With the proposed red, green, and blue QLEDs combination, we achieve 105.1% Rec. 2020 color gamut in CIE 1976 color space. We demonstrate that internal nano-scattering pattern structures are attractive for display applications, especially for enhancing the outcoupling efficiency of blue QLEDs.

Novel composite layer based on electrospun polymer nanofibers for efficient light scattering

We fabricated a PAN (polyacrylonitrile) NF (nanofiber)-embedded composite layer to adjust the light-control layer in light-emitting-diode (LED) and organic-light-emitting-diode (OLED) lighting systems with unique optical characteristics, for effective light scattering. The newly designed light-control composite layers with a composition of PAN NF/SU-8 exhibited a change in the optical properties, which was identified by the diameter control of the NF using a simple process. The change in the optical properties was largely dependent on the embedded NF's features. Therefore, the NF can be applied in different types of lighting systems, depending on each lighting device's purpose.

Light diffusing effects of nano and micro-structures on OLED with microcavity

We examined the light diffusing effects of nano and micro-structures on microcavity designed OLEDs. The results of FDTD simulations and experiments showed that the pillar shaped nano-structure was more effective than the concave micro-structure for light diffusing of microcavity OLEDs. The sharp luminance distribution of the microcavity OLED was changed to near Lambertian luminance distribution by the nano-structure, and light diffusing effects increased with the height of the nano-structure. Furthermore, the nano-structure has advantages including light extraction of the substrate mode, reproducibility of manufacturing process, and minimizing pixel blur problems in an OLED display panel. The nano-structure is a promising candidate for a light diffuser, resolving the viewing angle problems in microcavity OLEDs.

Multi-periodic nanostructures for photon control

We propose multi-periodic nanostructures yielded by superposition of multiple binary gratings for wide control over photon emission in thin-film devices. We present wavelength- and angle-resolved photoluminescence measurements of multi-periodically nanostructured organic light-emitting layers. The spectral resonances are determined by the periodicities of the individual gratings. By varying component duty cycles we tune the relative intensity of the main resonance from 12% to 82%. Thus, we achieve simultaneous control over the spectral resonance positions and relative intensities.

Random nanostructure scattering layer for suppression of microcavity effect and light extraction in OLEDs

In this study, we investigated the effect of a random nanostructure scattering layer (RSL) on the microcavity and light extraction in organic light emitting diodes (OLEDs). In the case of the conventional OLED, the optical properties change with the thickness of the hole transporting layer (HTL) because of the presence of a microcavity. However, OLEDs equipped with the an RSL showed similar values of external quantum efficiency and luminous efficacy regardless of the HTL thickness. These phenomena can be understood by the scattering effect because of the RSL, which suppresses the microcavity effect and extracts the light confined in the device. Moreover, OLEDs with the RSL led to reduced spectrum and color changes with the viewing angle.