Lambertian Source Research Articles

Investigative photometry experiments on planar extended-light sources

The inverse-square decay law of the illuminance of a point light source with distance is a common notion of basic optics theory, which is readily demonstrated to be a direct consequence of the propagation of spherical wave fronts with the centre at the light source. It is far less common to address the experimental verification of this law and, even less, to study the illuminance decay with the distance of extended light sources, which somehow represent an unknown topic. We propose a scientific experiment where the light sensor of a smartphone is used to collect illuminance data as a function of the source-to-sensor distance and orientation. Through this procedure, students can realize the limit of validity of the inverse-square law and determine the luminance flux of the chosen point-like light source (e.g. the white LED flashlight of a smartphone). More interestingly, when dealing with extended sources (e.g. the LCD of a laptop displaying a white image) subtle characteristics of the decay trend emerge, particularly for distances lower that the source size. A detailed analysis of these characteristics is presented though a process allowing student engagement in a real scientific investigation, envisaging steps of data acquisition through experimental measurements, model construction on the basis of the observed patterns, and finally model testing. We provide a guided formulation for the general modelling of planar emitters, starting from the theoretical treatment of Lambertian sources. In this way, students are able to quantify the luminous emission also for extended sources and their deviation from a Lambertian behaviour.

Wide angle mini-LEDs combined with multifocal micro reflector cavity for thin portable device flashlight

LEDs employed in portable device flashes are Lambertian light sources, additional optical components such as Fresnel lenses and reflector cups must be incorporated to adjust the light distribution. This results in a need for a certain module thickness or high alignment precision. This paper introduces a modification in the packaging structure of mini-LEDs by employing a first optical design to create wide-angle mini-LEDs (WA mini-LEDs) with a light emission angle of 180°. A multi-focal micro-reflector cavity (MF-MRC) is included in the packaging process, thus enabling the achievement of a slim flash module. For the prototype design, measurements were conducted using WA mini-LEDs combined with a 2 mm height MF-MRC. The full width at half maximum can be reduced to 56° while maintaining a uniformity of up to 60% across all measurement points. Additionally, the center illuminance is 3.24 times higher compared to Lambertian mini-LED light sources.

Optimizing freeform lenses for extended sources with algorithmic differentiable ray tracing and truncated hierarchical B-splines.

We propose a method for optimizing the geometry of a freeform lens to redirect the light emitted from an extended source into a desired irradiance distribution. We utilize a gradient-based optimization approach with MITSUBA 3, an algorithmic differentiable non-sequential ray tracer that allows us to obtain the gradients of the freeform surface parameters with respect to the produced irradiance distribution. To prevent the optimizer from getting trapped in local minima, we gradually increase the number of degrees of freedom of the surface by using Truncated Hierarchical B-splines (THB-splines) during optimization. The refinement locations are determined by analyzing the gradients of the surface vertices. We first design a freeform using a collimated beam (zero-etendue source) for a complex target distribution to demonstrate the method's effectiveness. Then, we demonstrate the ability of this approach to create a freeform that can project the light of an extended Lambertian source into a prescribed target distribution.

Full-angle chip scale package of mini LEDs with a V-shape packaging structure.

The light distribution of light-emitting diodes (LEDs) generally resembles that of a Lambertian light source. When used as large-area light sources, the light distribution angle of LEDs must be modified through secondary optics design to achieve uniformity and minimize the number of light sources. However, secondary optical components pose several challenges such as demanding alignment accuracy, material aging, detachment, and lower reliability. Therefore, this paper proposes a primary optical design approach to achieve full-angle emission in LEDs without the need for lenses. The design employs a flip-chip as the light source and incorporates a V-shaped packaged structure, including a white wall layer, optical structure layers, and a V-shaped diffuse structure. With this design, the LEDs achieve full-angle emission without relying on lenses. Our experimental results demonstrated a peak intensity angle of 77.7°, a 20.3% decrease in the intensity of the central point ratio, and a full width at half maximum (FWHM) of the light distribution of 175.5°. This design is particularly suitable for thin, large-area, and flexible backlight light sources. Moreover, the absence of secondary optical components allows for a thinner light source module.

Boosting the Performances of Semitransparent Organic Photovoltaics via Synergetic Near-Infrared Light Management.

Semitransparent organic photovoltaics (ST-OPVs) offer promising prospects for application in building-integrated photovoltaic systems and greenhouses, but further improvement of their performance faces a delicate trade-off between the two competing indexes of power conversion efficiency (PCE) and average visible transmittance (AVT). Herein, the authors take advantage of coupling plasmonics with the optical design of ST-OPVs to enhance near-infrared absorption and hence simultaneously improve efficiency and visible transparency to the maximum extent. By integrating core-bishell PdCu@Au@SiO2 nanotripods that act as optically isotropic Lambertian sources with near-infrared-customized localized surface plasmon resonance in an optimal ternary PM6:BTP-eC9:L8-BO-based ST-OPV, it is shown that their interplay with a multilayer optical coupling layer, consisting of ZnS(130nm)/Na3AlF6(60nm)/WO3(100nm)/LaF3(50nm) identified from high-throughput optical screening, leads to a record-high PCE of 16.14% (certified as 15.90%) along with an excellent AVT of 33.02%. The strong enhancement of the light utilization efficiency by ≈50% as compared to the counterpart device without optical engineering provides an encouraging and universal pathway for promoting breakthroughs in ST-OPVs from meticulous optical design.

Off-axis limiting photometric distance of Lambertians and narrow beams

The near-field - far-field disparity of light sources leads to discussion within the lighting community. In the far-field, light sources are approximated by a point source with a luminous intensity distribution from which other photometric quantities can be computed. In the near-field, light sources must be considered as extended sources and no closed-loop analytical solutions can be found for the illuminance in off-axis directions. The illuminance allows to compute the apparent intensity used for the assessment of the limiting photometric distance (LPD), that is, the threshold between near- and far-field regions. Numerically, the illuminance can be determined through a discretisation of the luminous surface. This approach is verified for on- and off-axis directions through direct comparison with ray tracing simulations based on near-field goniophotometric measurements. A good match is observed for Lambertian and narrow beam light sources. Using the numerical approach, the LPD in all directions is assessed. For light sources of which the luminous intensity strictly decreases while moving away from the optical axis, the LPD decreases as well until a minimal value is reached. After this, the LPD increases again, in certain scenarios up to values resulting in the invalidity of the inverse square law.

P‐12.5: Optical film microstructure design for ultra‐thin MiniLED backlight modules

The backlight module is a key component for providing a light source for a Liquid Crystal Display (LCD), and its thickness has a direct impact on the thickness of the display. In order to reduce the thickness of the display product, it can be realized by reducing the thickness of the backlight module. In order to solve this problem, this paper proposes a design method for the microstructure of the optical film applied to the mini LED backlight module. The microstructured optical film designed in this paper can effectively improve the uniformity of brightness and realize the ultra‐thinning of the backlight module. Based on the principle of total reflection, the optical film microstructure is designed for the miniLED Lambertian light source. Under the assumption that the point light source is established, the extended light source is discretized into point light sources, and then the light energy that can be used for circulation is calculated for each point light source, and all point light sources The cyclic energy of is accumulated as the cyclic energy corresponding to the extended light source, and when its value is the largest, the best shape of the microstructure is obtained. The simulation results show that after adding the microstructured optical film, the illumination uniformity of the backlight module reaches 91.2%, which meets the uniformity requirements of the backlight module. The method of designing microstructured optical film proposed in this paper can effectively realize the ultra‐thinness of the backlight module and has strong practicability.

Visible Light Positioning With Lens Compensation for Non-Lambertian Emission

With greater demands for cost-effective, reliable, and highly accurate positioning, indoor wireless localisation using Visible Light Positioning (VLP) is a promising solution for future networks. One can expect VLP solutions to appear in all environments, from homes to industry; however, the existing literature primarily considers Visible Light Communication (VLC) sources with purely Lambertian emission patterns. To facilitate greater versatility within VLP solutions, this paper considers non-Lambertian sources. It evaluates practical Received Signal Strength Indicator (RSSI) data obtained during the Internet of Radio Light (IoRL) 5G Measurement Campaign conducted in a home environment using non-Lambertian Total Internal Reflection (TIR) lenses, which produce a halo lighting effect. The initial analysis explores the calibration of Lambertian source parameters against datasheet values leading to reductions in the average Positioning Error (PE) of 17% and 3% for averaged and individual RSSI measurement sets, respectively. While this highlights improvements from correct calibration, the Lambertian model proved to be unsuitable for non-Lambertian sources. In the absence of any existing non-Lambertian models, the authors proposed the Halo Lens Compensation (HLC) method to calibrate the considered non-Lambertian TIR sources correctly. The HLC further reduced PE in the calibrated results by 50% and 39%, with mean PE of 3.1 cm and 4.6 cm for averaged and individual RSSI measurement sets, respectively. In conclusion, for VLP using non-Lambertian sources, the existing Lambertian model is unsuitable. However, the proposed HLC is highly effective and achieves positioning accuracy comparable to existing literature using Lambertian sources.

Parallel ray tracing through freeform lenses with NURBS surfaces

We implement Monte Carlo-based parallel ray tracing to achieve quick irradiance evaluation for freeform lenses with non-uniform rational B-splines (NURBS) surfaces. We employ the inverse transform sampling method to sample rays uniformly from the Lambertian light source and adopt the analytical form of the B-spline basis function to achieve fast surface interpolation. When performing parallel calculations for the intersections between the rays and the NURBS surfaces, we propose a parameter transformation method to avoid the parameters escaping from the defined range in the iteration process. Simulation results of two complex picture-generating freeform lenses show that our method is fast and effective.

Optical Uplink, D2D and IoT Links Based on VCSEL Array: Analysis and Demonstration

In this paper, vertical cavity surface emitting laser (VCSEL) array is used to establish gigabits/second (Gbps) optical uplink, device-to-device (D2D), and Internet-of-thing (IoT) links, as a supplementary for visible light communication (VLC) and ultra-low latency near-field communication in a typical indoor scenario. The mathematical model based on a modified Monte-Carlo ray-tracing (MMCR) algorithm for VCSEL-based optical wireless communication (OWC) is presented, which takes into account both accuracy and time complexity for the calculation of the channel characteristics including power distribution, impulse response, error analysis, and signal-to-noise ratio (SNR). Simulation firstly takes a global approach to the optical uplink lens design method, compared between Lambertian and Gaussian sources, and then extended six typical line-of-sight (LOS) or non-line-of-sight (NLOS) VCSEL-based OWC models. For demonstration, we adopted a 940-nm VCSEL array and 850-nm single-pixel VCSEL to establish LOS and NLOS systems after measuring the optics-electronics and bandwidth characteristics, respectively. Furthermore, multiple multi-carrier schemes are adopted to improve the OWC performance system based on a 940-nm VCSEL array including uniform-loading orthogonal frequency division multiplexing (OFDM), channel-coded OFDM, bit-loading/ power-allocation OFDM, and OFDM access (OFDMA). Results show that OFDM can effectively decrease the inter-symbol interference (ISI) of the indoor channel and increase the data rate, and the bit/ power-loading method achieves the highest 7.2 Gbps transmission with the bit error rate (BER) within the forward error correction (FEC). All the theoretical and experimental results, for the first time, provide a comprehensive design and optimizing process of VCSEL-based indoor high-capacity OWC systems for future optical uplink, D2D, and IoT applications.

Implementation and uniformity calibration of LED array for photodynamic therapy

Irradiance uniformity is an important parameter for a Photodynamic Therapy (PDT) device. The calibration and verification of a LED array light source based on computer vision technology were implemented and carried out. First, the correlation coefficients between the pulse width modulate value and the irradiance were calibrated. Then, the correction of the actual light center and divergence angle were solved by image processing to reduce errors from each LED lens. Finally, uniformity was optimized according to the irradiance formula of the Lambertian source. The lowest coefficients of variation of irradiance were 4.87% in a [Formula: see text] area and 3.55% in a [Formula: see text] area within the depth range of 8–12[Formula: see text]cm when the expected irradiance was 100[Formula: see text]mW/cm2. This finding indicated that the light source can achieve a more uniform illumination and provide a better therapeutic effect for the PDT of port-wine stains.

High CRI RGB Laser Lighting With 11-Gb/s WDM Link Using Off-the-Shelf Phosphor Plate

In this letter, a practical structure enabling both high-speed visible light communication (VLC) and high-quality white-light is presented. The proposed structure directly mixes red-green-blue colors from semiconductor laser diodes (LD) without dichroic mirrors. The three colors are mixed by a thermally stable off-the-shelf phosphor plate. The broad yellow photoluminescence spectrum excited by a portion of blue LD light fills the vacant spectrum, leading to a high color rendering index (CRI). It is experimentally verified that the phosphor plate works as an excellent diffuser even for the green and red channels. Consequently, an incoherent Lambertian source suitable for indoor lighting is created. It is also found that the impact of the broad yellow spectrum on the green and red communication channels is insignificant. A proof-of-concept demonstration shows a 90 CRI (3503 K) white-light delivering 11 Gb/s of wavelength division multiplexing VLC link, using channel adaptive DC-biased optical orthogonal frequency division multiplexing.

Symmetrization and Amplification of Germicidal Radiation Flux Produced by a Mercury Amalgam UV Lamp in Cylindrical Cavity with Diffusely Reflective Walls

The study focused on increasing the efficiency of germicidal UV radiation by using highly diffuse reflective materials such as PTFE in irradiated cavities of UV air purifiers. In a conventional cylindrically symmetric cavity with a linear amalgam mercury lamp as UV-radiation source on the axis UV-radiation, flux directed from the lamp to the walls dropped from the axis to the periphery. To increase the UV irradiation, the walls are often made mirror-reflective, but the radiation flux distribution remained radially symmetric with a maximum on the source emitting surface in this case as well. When most of the emitted light is returned to the source after one reflection, the conditions of its operation are disturbed. If the walls are made of highly diffuse reflective materials, the radiation flux density inside the cavity increases on average, and its distribution becomes uniform and highly symmetric. Thus, the effect of amplification of the radiation flux due to the highly diffuse reflectivity of the walls increases with radius and reaches a maximum at the wall. Experiments were performed to demonstrate increasing amplification of germicidal UV radiation flux with a diffuse reflection coefficient in cylindrical cavities with walls of PTFE and ePTFE. The irradiation of the cavity wall was observed to increase up to 20 times at the resonant mercury line of 253.7 nm and up to 40 times at some non-resonant lines of the visible range due to highly diffuse reflectivity of the cavity walls. The flux amplification effect was limited by the diffuse reflectivity value of the walls and absorption coefficient of the radiation emitting surface. A formula for calculating the radiation flux amplification factor in a diffusely reflecting cylindrically symmetric cavity was derived for the case of Lambertian source and reflector, including wall reflectivity and source surface absorption coefficients. The effects of heating and cooling of the mercury lamp amalgam directly affected the amplification, and symmetrization of germicidal irradiation was observed and is discussed in the paper. Numerical calculations were performed by the ray tracing method. The calculated model was verified by comparing the numerical results with those of both the approximate theoretical consideration and experiments. The promising use of diffusely reflecting cylindrical cavities for UV air purifiers is discussed. Designs of air inlet and outlet ports that allow effective locking of germicidal radiation inside the UV air purifiers were considered. The results of this work may be of interest for further developments in the UV disinfection technique.

27‐4: Organic Light‐Emitting Diodes with Directional Polarized Light Emission

Organic light emitting diodes (OLEDs) with directional and polarized light emission have many photonic applications, and beam shaping of these devices is fundamentally challenging because they are Lambertian light sources. In this work, using OLEDs for demonstrations, by selectively diffracting the TE waveguide mode while suppressing other optical modes in a nanostructured substrate, we demonstrated highly directional light emission from a full‐area OLED with a small divergence angle less than 3°, and a TE to TM polarization extinction ratio of 13. The highly selective diffraction of only the TE waveguide mode is possible due to the planarization of the device stack by thermal evaporation and solution processing.

Haze‐Suppressed Transparent Electrodes Using IZO/Ag/IZO Nanomesh for Highly Flexible and Efficient Blue Organic Light‐Emitting Diodes

AbstractNano‐mesh (NM) structures have been employed as flexible and stretchable electrodes for organic light‐emitting diodes (OLEDs). However, high optical haze induced by NM structures should be diminished while enhancing the transparency and lowering the sheet resistance simultaneously for their practical use. Herein, a highly flexible transparent electrode is demonstrated using indium zinc oxide (IZO)/Ag/IZO NM structure to satisfy all these requirements without complex designs in NM structures. The proposed NM electrode shows remarkably low haze (<10%), high optical transparency (>90%), and low sheet resistance (≈9.4 Ω sq–1), together with superior flexibility. Moreover, the smart NM‐based blue OLED shows characteristics of a Lambertian light source, with high external quantum efficiency (≈18.8%) and unprecedentedly outstanding bending properties. The experimental and theoretical analyses ascribe these improvements to the enhanced charge injection via conductive IZO with high work function as well as reduced surface reflection and diffraction of emitted light via anti‐reflective NM structure.

Directional Polarized Light Emission from Thin-Film Light-Emitting Diodes.

Light-emitting diodes (LEDs) with directional and polarized light emission have many photonic applications, and beam shaping of these devices is fundamentally challenging because they are Lambertian light sources. In this work, using organic and perovskite LEDs (PeLEDs) for demonstrations, by selectively diffracting the transverse electric (TE) waveguide mode while suppressing other optical modes in a nanostructured LED, the authors first demonstrate highly directional light emission from a full-area organic LED with a small divergence angle less than 3° and a TE to transverse magnetic (TM) polarization extinction ratio of 13. The highly selective diffraction of only the TE waveguide mode is possible due to the planarization of the device stack by thermal evaporation and solution processing. Using this strategy, directional and polarized emission from a perovskite LED having a current efficiency 2.6 times compared to the reference planar device is further demonstrated. This large enhancement in efficiency in the PeLED is attributed to a larger contribution from the TE waveguide mode resulting from the high refractive index in perovskite materials.

Retraction: Revised instellation patterns for close-in exoplanets

The distribution of instellation at the top of a planet's atmosphere or surface is usually calculated using the inverse-square law of radiation. This is based on the assumption that the host star is far enough to be considered a point-sized Lambertian source. This assumption, which works well for the solar system planets and most exoplanets, must be revised for close-in exoplanets. The objective of this work is to derive accurate instellation patterns for close-in exoplanets, for which the effects of the spherical shape of the star must be taken into account. First an analytical formula of the insolation as a function of latitude was derived, taking the star and the planet as 3-D bodies, and incorporating the limb darkening effects of the star. Then numerical techniques were used to compute the distribution of the insolation on close-in planets as a function of latitude for a wide range of stellar and planetary properties.There are significant deviations in instellation values and their distribution on close-in exoplanets, due in similar proportions to the physical size of the star and stellar limb-darkening effects. The insolation at the susbtellar point is always higher -- by as much as 21% for known exoplanets -- than the standard calculation. The substellar longitude of the terminator can significantly extend on the nightside, from 90 degrees up to 110 degrees for known exoplanets.

Full Field Radiant Flux Distribution of Multiple Tilted Flat Lambertian Light Sources

The emergence of visible light communication (VLC) as a subset of optical wireless communication (OWC) in the early 2000s has turned any light-emitting diode (LED) source into a potential data transmitter. The design process for any VLC or OWC system typically involves a link budget analysis performed by studying the signal-to-noise ratio (SNR) at the receiver. Since this SNR strongly depends on the radiant flux collected by the receiver, an accurate model for this parameter is required. The point-source model has been widely used since 1979 and generally provides a good approximation of the received radiant flux. However, it might be less accurate for typical extended lighting sources like LED panels or large-area organic LEDs. In this paper, the radiant flux distribution of flat Lambertian rectangular or circular sources is derived from a vector analysis of their irradiance. It is then validated through actual measurements in the case of a circular source. The resulting extended-source models thus better capture the light beam pattern of such transmitters to enable a more accurate link budget. It provides at the same time almost identical results to the point-source model for small sources and can, therefore, be seen as a natural extension of this already widely used model. INDEX TERMS LED pattern, irradiance pattern, light power pattern, non-imaging optics, link budget, optical wireless communication, visible light communication.

Iterative freeform lens design for prescribed irradiance on curved target

Current freeform illumination optical designs are mostly focused on producing prescribed irradiance distributions on planar targets. Here, we aim to design freeform optics that could generate a desired illumination on a curved target from a point source, which is still a challenge. We reduce the difficulties that arise from the curved target by involving its varying z-coordinates in the iterative wavefront tailoring (IWT) procedure. The new IWT-based method is developed under the stereographic coordinate system with a special mesh transformation of the source domain, which is suitable for light sources with light emissions in semi space such as LED sources. The first example demonstrates that a rectangular flat-top illumination can be generated on an undulating surface by a spherical-freeform lens for a Lambertian source. The second example shows that our method is also applicable for producing a non-uniform irradiance distribution in a circular region of the undulating surface.

Enhancing brightness of Lambertian light sources with luminescent concentrators: the light extraction issue.

Luminescent concentrators (LC) enable breaking the limit of geometrical concentration imposed by the brightness theorem. They enable increasing the brightness of Lambertian light sources such as (organic) light-emitting diodes. However, for illumination applications, light emitted in the high-index material needs to be outcoupled to free space, raising important light extraction issues. Supported by an intuitive graphical representation, we propose a simple design for light extraction: a wedged output side facet, breaking the symmetry of the traditional rectangular slab design. Angular emission patterns as well as ray-tracing simulations are reported on Ce:YAG single crystal concentrators cut with different wedge angles, and are compared with devices having flat or roughened exit facets. The wedge output provides a simple and versatile way to simultaneously enhance the extracted power (up to a factor of 2) and the light directivity (radiant intensity increased by up to 2.2.).