This erratum corrects a mistake in Opt. Express32, 9042 (2024)10.1364/OE.510888.

The design of optical metasurfaces for CMOS imagers is challenging due to the influence numerous physical parameters such as pattern size, density, and layer thicknesses. In this work, an original inverse design methodology based on multi-objective and high-dimensional global optimization is proposed and applied to the design of an RGB-IR color router, achieving significant performance enhancements compared to conventional refractive microlens pixels. This approach provides insights into the design process and establishes a framework for future advances in CMOS imager technology.

Optical characterization and appearance prediction of translucent materials are required in many fields of engineering such as computer graphics, dental restorations or 3D printing technologies. In the case of strongly scattering materials, flux transfer models like the Kubelka-Munk model (2-flux) or the Maheu’s 4-flux model have been successfully used to this aim for decades. However, they lead to inaccurate prediction of the color variations of translucent objects of different thicknesses. Indeed, as they rely on the assumption of lambertian fluxes at any depth within the material, they fail to model the internal reflectance at the interfaces, penalizing the accuracy of the optical parameter extraction. The aim of this paper is to investigate the impact of translucency on light angular distribution and corresponding internal reflectances by the mean of the radiative transfer equation, which describes more rigorously the impact of scattering on light propagation. It turns out that the light angular distribution at the bordering interfaces is often far from being lambertian, and that the internal reflectance may vary significantly according to the layer’s thickness, refractive index, scattering and absorption coefficients and scattering anisotropy. This work enables to better understand the impact of scattering within a translucent layer and also invites to revisit the well-known Saunderson correction used in 2- or 4-flux models.

Objective: To assess the prediction accuracy of recent optical and numerical models for the spectral reflectance and color of monolithic samples of dental materials with different thicknesses. Methods: Samples of dental resin composites of Aura Easy Flow (Ae1, Ae3 and Ae4 shades) and Estelite Universal Flow Super Low (A1, A2, A3, A3.5, A4 and A5 shades) with thicknesses between 0.3 and 1.8 mm, as well as Estelite Universal Flow Medium (A2, A3, OA2 and OA3 shades) with thicknesses between 0.4 and 2.0 mm, were used. Spectral reflectance and transmittance factors of all samples were measured using a X-Rite Color i7 spectrophotometer. Four analytical optical models (2 two-flux models and 2 four-flux models) and two numerical models (PCA-based and L*a*b*-based) were implemented to predict spectral reflectance of all samples and then convert them into CIE-L*a*b* color coordinates (D65 illuminant, 2°Observer). The CIEDE2000 total color difference formula (ΔE00) between predicted and measured colors, and the corresponding 50:50% acceptability and perceptibility thresholds (AT00 and PT00) were used for performance assessment. Results: The best performing optical model was the four-flux model RTE-4F-RT, with an average ΔE00 = 0.72 over all samples, 94.87% of the differences below AT00 and 65.38% below PT00. The best performing numerical model was L*a*b*-PCHIP (interpolation mode), with an average ΔE00 = 0.48, and 100% and 79.69% of the differences below AT00 and PT00, respectively. Significance: Both optical and numerical models offer comparable color prediction accuracy, offering flexibility in model choice. These results help guide decision-making on prediction methods by clarifying their strengths and limitations.

The fluorescence property of human teeth under UV light has long been studied in dentistry and is now used in the diagnosis of anomalies, such as dental decays.Its role in the appearance of teeth and dental restorations has also been demonstrated, and fluorescence, even under daylight, may sensibly modify the appearance of dental restorations.As such, dental resin composites used in aesthetic restorative dentistry include fluorescent agents which aim to imitate the natural fluorescence of teeth.While several studies have measured the fluorescence properties of dental biomaterials and a few other studies have focused on predicting the color of samples, the influence of fluorescence on color prediction models remains to be assessed.In this paper, we propose a prediction model for the spectral emission of slices of a dental biomaterial as a function of their thickness, in reflection and in transmission modes, with the aim of improving color prediction models for these materials.

Objective: To evaluate the prediction accuracy of the Kubelka-Munk Reflectance Theory and other more innovative two-flux and four-flux models for predicting the reflectance and transmittance factors of two flowable dental resin composites of various thicknesses within clinically acceptable color difference.Methods: Cylindrical samples of Aura Easy Flow resin composite (Ae1, Ae2, Ae3, Ae4 shades) and Estelite Universal Flow SuperLow resin composite (A1, A2, A3, A3.5, A4, A5 shades) were prepared with thicknesses ranging from 0.3 mm to 1.8 mm. Their reflectance and transmittance factors were measured with a spectrophotometer based on an integrating sphere, and were also predicted by 3 different two-flux models and 2 different four-flux models. The accuracy of reflectance and transmittance factor predictions was assessed using the CIEDE2000 color distance metric and 50:50% acceptability and perceptibility threshold criteria. Results: Eymard's four-flux model is found to be the most accurate for predicting the spectral reflectance and transmittance factors, with 85% (resp. 100%) of all color deviations below the acceptability threshold, and below the perceptibility threshold for 40% (resp. 57%) of the samples with thickness ranging from 0.3 to 1.8 mm in reflectance (resp. transmittance) mode. The Kubelka-Munk Reflectance Theory is found to be the least accurate model for predicting the spectral reflectance and transmittance factors of dental resin of thickness ranging from 0.3 to 1.8 mm. Significance: Eymard's four-flux model enables to predict the color of slices of dental materials within acceptable color differences. Eymard's four-flux model's optical parameters thus describe light-matter interactions in dental materials more accurately than state of the art Kubelka-Munk Reflectance Theory.

Light-emitting diodes (LEDs) are of interest for implementation in radiation environments, such as part of illumination systems of radiation-tolerant cameras able to provide images at high doses (>MGy). It is then mandatory to characterize the radiation effects on all of the LED key properties exploited for such applications. To this aim, the evolution of the optical properties of commercial LEDs after they have been exposed to γ-rays, up to total ionizing dose (TID) levels of 2 MGy(air) at room temperature, is discussed. The devices under test include four LEDs of different colors (red, green, blue and white) in the same package. This allows a direct comparison between the responses of the different structures and technologies, as the proximity between the diodes ensures the uniformity of their irradiation conditions. The radiation effect on the electron–photon conversion mechanisms inside these LEDs is investigated through the evolution of their external quantum efficiency (EQE) vs. current characteristics. The spectral emission pattern of LEDs after irradiation at different dose levels is then characterized to estimate the TID effects on the lens which surrounds the LED package. The presented results show a monotone radiation-induced EQE decrease as a function of the TID, especially in the red LEDs. For the tested red LEDs, the EQE decreased up to 78% after a TID of 1 MGy when they were OFF during irradiation, and up to 8% when they were ON during irradiation. A visual inspection of the devices after irradiation shows a mechanical degradation of the lens shared among the four diodes. However, the emission pattern analysis does not show any significant radiation-induced changes in the optical properties of the lens. Based on these results, it appears possible to design LED-based illumination systems able to survive to MGy dose levels that can be integrated as subsystems of radiation-hardened cameras.

Electrical doping of metal halide perovskites (MPHs) is a key step towards the use of this efficient and cost-effective semiconductor class in modern electronics. In this work, we demonstrate n-type doping of methylammonium lead iodide (CH3NH3PbI3) by the post-fabrication introduction of Sm2+. The ionic radius of the latter is similar to that of Pb2+ and can replace it without altering the perovskite crystal lattice. It is demonstrated that once incorporated, Sm2+ can act as a dopant by undergoing oxidation to Sm3+. This results in the release of a negative charge that n-dopes the material, resulting in an increase of conductivity of almost 3 orders of magnitude. Unlike substitution doping with heterovalent ions, furtive dopants do not require counterions to maintain charge neutrality with respect to the ions they replace and are thus more likely to be incorporated into the crystalline structure. The incorporation of the dopant throughout the material is evidenced by XPS and ToF-SIMS, while the XRD pattern shows no phase separation at low and medium doping concentrations. A shift of the Fermi level towards a conduction energy of 0.52 eV confirms the doping to be n-type with a charge carrier density, calculated using the Mott-Schottky method, estimated to be nearly 10(17) cm(-3) for the most conductive samples. Variable-temperature conductivity experiments show that the dopant is only partially ionized at room temperature due to dopant freeze-out.

The determination of the optical properties of encapsulant for photovoltaic modules is essential for cell-to module (CTM) performance analysis, UV-durability studies and as input parameters of modelling tools. Some innovative polymer encapsulants used in heterojunction module manufacturing, such as polyolefin elastomer or thermoplastic polyolefin, show a non-negligible optical scattering behaviour in addition to refraction and absorption mechanisms, making challenging the extraction of optical properties in general, and optical indices in particular. In this work, a 4-flux optical model was applied on total and diffuse transmittance and reflectance measurements of a Thermoplastic PolyOlefin (TPO) encapsulant layer to extract values of refractive index, absorption, scattering coefficient and anisotropy coefficient of scattered light. This model was found mandatory to obtain a satisfactory fitting and plausible value of the optical parameters, in opposition to simpler models based on collimated light, or only diffuse light, or isotropic 4-flux model. The model was applied on two diffusive TPO: a low and a high UV cut-off. The absorption was found respectively to be 1.7% and 3.8%. Therefore, a new Cell To-Module source of loss was identified, induced by the backscattered light in the encapsulant bulk, whose value is near 0.8% of the incoming light in both samples.

Optical characterization and appearance prediction of translucent materials is needed in several fields of engineering such as computer graphics, dental restorations or 3D printing technologies.In the case of strongly diffusing materials, flux transfer models like the Kubelka-Munk model (2-flux) or 4-flux model have been successfully used to this aim for decades.However, they lead to inaccurate prediction of the color variations of translucent objects of different thicknesses.Indeed, as they assume Lambertian fluxes at any depth within the material and in particular at the bordering interfaces, they fail to model the internal reflectance at the interfaces, penalizing the accuracy of the optical parameter extraction.The aim of the paper is to investigate the impact of translucency on light angular distribution and corresponding internal reflectances, by the mean of the radiative transfer equation, which describes more rigorously the impact of the scattering on the light propagation.It turns out that the light angular distribution at the bordering interfaces, assumed to be flat, is far from being Lambertian, and the internal reflectance may vary a lot according to the layer's thickness, refractive index, scattering and absorption coefficients.This work not only enables to better understand the impact of scattering within a translucent layer but also invites to revisit the well-known Saunderson correction used in 2-or 4-flux models.

McIntyre's local and non-local equations are used to calculate the avalanche triggering probability, useful in the modeling of Dark Count Rates and Probability Detection Efficiency of Single Photon Avalanche Detectors (SPAD). Although non-linear, the local equations have a closed-form solution, while the more rigorous non-local history-dependent equations can be solved only by an iterative approach. However, the convergence of the latest approach is fairly slow, making the modeling of SPAD properties relatively time consuming. An alternative and numerically efficient method is proposed to solve the local equations, avoiding the use of the closed-form solution and its time-consuming root finding step. Several approaches are then discussed to improve the convergence of the non-local history-dependent equations.

Two-flux models are practical tools for predicting the appearance of strongly scattering materials, but may fail to predict the spectral reflectance factor of translucent (i.e

Doped hole (respectively electron) transport layers [HTLs (respectively ETLs)] are commonly used in evaporated organic devices to achieve high work function hole contact (respectively low work function electron contact) in organic LEDs to inject large current, in solar cells to increase the open circuit voltage, and in photodetectors to minimize the dark current. However, optimization of the HTL thickness results from a delicate trade-off. Indeed, on the one hand, to minimize the impact of HTLs on light propagation and series resistance effects, it is commonly admitted that HTLs must be kept as thin as possible. In this work, a model, validated by drift and diffusion simulations, has shown that, depending of the doping level, a minimum thickness between 10 and 20 nm was needed to prevent the transport layer work function from degradation due to field effects. Experiments have been performed on template p-only devices featuring a single HTL of various thicknesses and doping, confirming the validity of the model. Finally, simulations have been performed on a p-i-n device featuring both HTL and ETL. These results constitute precious indications for the design of efficient evaporated organic LEDs, solar cells, or photodetectors.

Single photon avalanche diodes (SPADs) are widely used to monitor fast and weak optical signals. The modeling of two main figures of merit of SPAD, namely the dark count rate (DCR) and the photon detection probability, requires one to calculate the avalanche triggering probability (ATP), usually obtained by numerically solving two transcendental equations (the McIntyre model) as post processing of technology computer-aided design simulations. This paper proposes an analytical alternative to this approach, exploiting an approximation of the impact ionization rates, in principle valid only under high field conditions, but extended to all fields by a simple fitting procedure. The proposed approximated/analytical ATP calculation can be efficient and relevant for SPAD compact modeling that is compatible with a spice-like simulator. As an illustration, a full analytical calculation for DCR based on both ATP and generation terms for a P + N abrupt diode junction is presented.

The determination of the optical properties of encapsulant for photovoltaic modules is essential for cell-to-module (CTM) performance analysis, UV-durability studies and as input parameters of modelling tools. Some innovative polymer encapsulants used in heterojunction module manufacturing, such as polyolefin elastomer or thermoplastic polyolefin, show a non-negligible optical scattering behaviour in addition to refraction and absorption mechanisms, making challenging the extraction of optical properties in general, and optical indices in particular.In this work, a four-flux optical model was applied on total and diffuse transmittance and reflectance measurements of an encapsulant layer to extract values of refractive index, absorption and scattering coefficients and anisotropy coefficient of scattered light. This model was found mandatory to obtain a satisfactory fitting and plausible value of the optical parameters, in opposition to simpler models based on collimated light, or only diffuse light, or isotropic four-flux model. The model was applied on two diffusive TPO: a low and a high UV cut-off. The absorption was found respectively to be 1.7 % and 3.8 %. Therefore, a new Cell-To-Module source of loss was identified, induced by the backscattered light in the encapsulant bulk, whose value is near 0.8% of the incoming light in both samples.

Most existing methods using hyperspectral imaging (HSI) to estimate skin chromophore concentrations fail to give an account of scattering properties crucial to many medical applications. To address this limitation, we propose to combine HSI with spatial frequency domain imaging (SFDI). Total acquisition time is around five seconds, making the process suitable for in vivo application. Skin absorption and scattering analysis is performed from these images by successive optimizations on the absorption and scattering properties. The problem of shadows occurring on complex shapes such as the face is addressed by an original approach that make results robust to irradiance drift.

In many commercial instruments for measuring reflectance, the area illuminated on the measured object is identical to the area from which light is collected. This configuration is suitable for strongly scattering materials such as paper, but issues arise with translucent materials, because a portion of the incident light spreads around the illuminated area by subsurface transport and escapes the detection system. This phenomenon, referred to as edge loss, yields erroneous, underestimated reflectance measurements. In the case of colored and opalescent materials, the impact of edge loss on the measured reflectance varies with the wavelength, which is a significant issue for spectrophotometer and colorimeter users. In the present study, we investigate the edge-loss phenomenon with an emphasis on human skin measurement. In particular, we use a mathematical model to estimate the PSF of translucent materials, relying on the diffusion approximation of the radiative transfer theory, to predict edge-loss measurement error. We use this model to discuss the suitability of several commercial spectrophotometers to accurately measure the translucent materials of various optical properties and show that not all devices can adapt to all translucent materials.

Halved and shingled solar cells are a powerful technology to reduce cell-to-module losses and ultimately increase the output power of a photovoltaic module. The combination of this approach with high-efficiency silicon solar cells architectures, like heterojunction or passivated contacts solar cells, is a promising option, but comes also with new challenges. In particular, the low level of carrier recombination in these cells makes them highly sensitive to any additional defects, as it is the case for the unpassivated edge created when splitting in half a solar cell. In order to optimize the cutting processes, an accurate method to characterize edge losses, adapted to high-efficiency solar cells, is required. In this work, two approaches are proposed and compared. In the first one, edge losses are modelled with a parallel diode, and the associated recombination current (J02edge) is fitted with current-voltage measurements, as usually done in previous studies. The conditions of application of this method are widely discussed and precisely redefined for an accurate extraction of parameters in the case of high-efficiency solar cells. The second method proposed consists in simply calculating relative losses out of the main current-voltage parameters. We demonstrate that simple estimation of open-circuit voltage (Voc) losses is perfectly adapted to our characterization needs, provided that adapted measurement methodology is applied. Results obtained with both methods are then compared on heterojunction cells and discussed. If these two characterization techniques both provide accurate results for the laser scribing processes tested, the method based on open-circuit voltage loss comparison shows slightly less dispersion. Moreover, this last method does not rely on curve fitting, making it faster and insensitive to modeling issues. The Voc approach appears thus more adapted for a fine optimization of different cutting processes and eventual characterization step implemented in an industrial environment. However, the alternative J02edge method based on curve fitting remains of high interest, for example to compare cell losses obtained with usual values reported in the literature, provided that extraction of this parameter is done with the conditions assessed in this work.

Flowable direct resin composite materials used in the dental domain are among materials that scatter light rather weakly, giving to millimeter-thick samples a certain translucent aspect. In order to predict the spectral reflectance and the color of such samples, the two-flux theory, i.e., Kubelka-Munk model (with Saunderson correction), remains the standard approach used in the dental domain, in spite of its known limitations when scattering is too weak. The present study, however, shows that a careful analysis of the light signal effectively measured on weakly scattering samples with instruments based, as usually recommended, on the d:8° measurement geometry, and a subsequent reevaluation of the parameters used in the Saunderson correction formulas with respect to the effective measurement geometry, can considerably improve the prediction accuracy of the model in both reflectance and transmittance modes, as confirmed by experiments carried out with samples of dental flowable resin composite material of different thicknesses. This broadens the applicability domain of the model, and might satisfy users preferring the simplicity of the two-flux model and the affordable equipment it needs to more relevant but more complex light scattering theories.

Several experimental groups have reported recently an intriguing high level of gain (Photomultiplication) in vertical organic photoresistance (as well as in other technologies, such as perovskite for instance). This mechanism is sometimes named as “Trap-Assisted Photomultiplication.” This paper investigates the origin of this mechanism by means of drift diffusion simulations, analytical theory, and experiments, considering the particular case of PCDTBT:PC60BM photoresistors, although some conclusions are likely to apply in other technologies. It turns out that an excess of charges (induced by electron–hole carrier generation) may trigger additional carrier injection, leading to photomultiplication, under specific circumstances. We call this mechanism “gain by injection enhancement.” Electron (respectively, hole) trapping for P only (respectively, N only) devices can play this role efficiently. As these additional carriers came from contacts, significant dark current injection is thus needed to achieve a large value of gain, explaining why this mechanism can occur only in P (or N) only photoresistors (and not photodiodes or intrinsic photoresistors, i.e., with midgap contacts). In such devices, however, the detectivity remains intrinsically limited by the high level of dark injection currents required to get gain, and consequently, this type of device may be interesting, in particular, in technologies where it is not possible to achieve low dark currents using photodiodes. However, penalized by the slow trap dynamics, the cut-off frequency of these devices remains extremely low (<100 Hz). Also, this gain takes a high value only at low irradiance, making photoresistor responsivity light dependent. All these results bring new light in analyzing and optimizing photoresistors, opening a large field of investigation to take advantage of gain by injection enhancement.