Abstract

Additive color mixing modulated by digital pulses enables universal applications in lights and displays. Conventional methods map binarized signals to ordinary red–green–blue color spaces, loosely connected with the color perception of human eyes, causing the complexity of gamut mapping and inaccuracy of chromatic manipulations. Here we developed a complete theory that encodes and decodes digital signals directly to a perceptually nonuniform color space of the commission internationale de l’éclairage, featuring a strict bijection between the duty cycles of each binary pulse and color components of the mixed light and an analytic nonlinear gamut volume. Exemplary applications in biophotonic lighting, active full-color displaying, and metaphotonic sensing confirmed our theory. The method applies to the fields with accurate manipulations of chromaticity and luminosity of a light, opening an avenue toward the next generation of perceptual displays, cameras, and sensors.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Additive color mixing is described as the creation of a color by mixing multiple primary colors or light sources [1]. It could be dated back to the first use of Newton’s color wheel in the 1660s [2]. Up to now such coloring scheme has been widespread to every corner of routine lives, including color televisions, stage lights, light-emitting diode (LED) panels, color screens for the computers, smartphones and tablets, data projectors, digital cameras, and virtual/augmented reality devices, to name just a few [35]. One proper approach to realize additive color mixing in a digital device is to employ pulse duration modulation, which controls the emission of each primary light with a constant but discretely chopped amplitude of power [6]. The potential chromaticity shift of individual light could be better suppressed with the digital driving, in comparison with the analog counterpart, due to a relative stable excited carrier density in the “on” phase and a prompt release of accumulated thermal energy in the “off” phase [69]. Also, the intrinsic nature of binary on and off states is ideal to communicate with and control over the digital lights, e.g., LEDs and lasers. Recent developments on such digital lights via exploring novel materials such as low dimensional materials [1012], organic materials [1315], plasmonic nanostructures [16,17], and perovskite solar cells [1820], and emerged manufacturing technologies involving laser-interfering lithography [21], photolithography [22], electron-beam lithography [23], and three-dimensional (3D) printing [24,25], endue future lights and displays with unique features of thin profile, large freeform factor, and small dimensions.

Present methods of additive mixed color modulated by digital pulses predominantly explore red–green–blue (RGB) color spaces, as illustrated in Fig. 1(a). The coordinates in RGB color spaces reflect the relative ratios of three primaries of a physical device, weakly linked to the color perception of human eyes [26]. This brings considerable gamut mismatches during the cross-media color reproduction, due to the chromaticity deviations of three primaries [27]. For instance, the same RGB-based digital image can show distinct color appearances in two liquid crystal displays, as shown in Fig. 1(a). To circumvent this problem, regular color characterizations and calibrations become essential, in which the coordinates in RGB color spaces are converted into standard perceptual color spaces. Similar complicate conversions are also indispensable in gamut boundary determination, in order to achieve a high dynamic range and wide gamut imaging for color displays and sensors [28,29]. Thus, a method that directly manipulates the source colors in a perceptual color space for the digital devices is clearly needed.

 figure: Fig. 1.

Fig. 1. Principle of the nonlinear CIE 1931 $xy{\rm Y}$ color space coded by digital pulses. (a) Gamut mismatch induced by conventional mapping methods that convert digital pulses to RGB color spaces. The same digital image with different color appearances is shown in two liquid crystal displays (screens 1 and 2) and the displayed images are taken via a digital camera in the same condition. (b) Proposing method that encodes and decodes digital pulses to the CIE 1931 $xy{\rm Y}$ color space. (c) Analytic nonlinear gamut boundaries in the 3D CIE 1931 $xy{\rm Y}$ color space for triprimary color mixing. The triangular prism represents the theoretical space. The surface colored in “jet” map denotes the upper gamut surface and ${\rm L}_{{b^ -}}^i$ ($i = {1}$, 2, 3) represents its $i$th primary component. (d) Analytic nonlinear gamut boundaries in the 2D CIE 1931 $xy{\rm Y}\;{c}$ olor space for biprimary color mixing [light “1” and “2” in (b)]. The rectangle and the gray regions represent the theoretical and accessible spaces, respectively. ${\rm L}_{{b^ -}}^i$ ($i = {1}$, 2) represents the $i$th primary component of upper gamut boundary. ${x_0}$ is the chromaticity $x$ of mixed light when two primary lights are equally mixed.

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2. THEORY

Here we develop a theory that bridges the digital space and a standard CIE 1931 $xy{\rm Y}$ color space, featuring a strict bijection between the digital signals and color components of the mixed light and analytic nonlinear gamut boundaries. The CIE 1931 $xy{\rm Y}$ color space is a color language corresponding to the nonuniform perception of human vision [3033], as shown in Fig. 1(b). The gamut mapping processed in such a color space shows privileges of semi-device-independence and simplicity [33]. The methodology includes both the encoding and decoding algorithms, as illustrated in Fig. 1(b). For the encoding process, digital pulses driving each primary light are converted to a unique coordinate (${x_m}$, ${y_m}$, ${{L}_m}$) of the CIE 1931 $xy{\rm Y}$ color space through additive color mixing. Here, (${x_m}$, ${y_m}$) denote the chromaticity coordinates and ${{\rm L}_m}$ is the luminosity, e.g.,  luminous flux, luminance, or luminous intensity, of the mixed light. The digital pulses are characterized with a pulse width vector ${\boldsymbol D} =({D_1},\;{{ D}_2},\ldots,\;{{D}_i},\ldots,\;{{D}_n})$, where ${{D}_i}$ is the duty cycle of the $i$th primary light and $n$ indicates the number of involved primary lights. The luminosity is represented by using a vector ${\boldsymbol L} = \;({L_1},\;{{L}_2},\ldots,\;{{L}_i},\;\ldots,\;{{L}_n})$, where ${{L}_i}$ is the luminosity of the $i$th primary light when ${{D}_i} = {100}\%$. In accordance with Hermann Grassmann’s law, the mixed coordinates can be calculated as (see Supplement 1) [6]

$${x_m} = \frac{{{{\boldsymbol R}_x} \cdot {\boldsymbol D}}}{{{\boldsymbol R} \cdot {\boldsymbol D}}},$$
$${y_m} = \frac{{{{\boldsymbol R}_y} \cdot {\boldsymbol D}}}{{{\boldsymbol R} \cdot {\boldsymbol D}}},$$
$${{L}_m} = {\boldsymbol L} \cdot {\boldsymbol D}.$$

In the above equations, ${\boldsymbol R}$ is a vector, defined as (${{R}_1},\;{{R}_2},\ldots,\;{{R}_i},\ldots,\;{{R}_n}$), where ${{R}_i} = {{L}_i}/{y_i}$ and ${y_i}$ is the chromaticity coordinate $y$ of the $i$th primary light. Similarly, ${{\boldsymbol R}_x}$ and ${{\boldsymbol R}_y}$ are defined as (${{ R}_1}\;{x_1},\;{{R}_2}\;{x_2},\;{\ldots},\;{{R}_i}\;{x_i},\;{\ldots},\;{{R}_n}\;{x_n}$) and (${{R}_1}\;{y_1},\;{{ R}_2}\;{y_2},\;{\ldots},\;{{R}_i}\;{y_i},\;{\ldots},\;{{R}_n}\;{y_n}$), respectively, where ${x_i}$ is the chromaticity coordinate $x$ of the $i$th primary light.

Now we turn our attentions to the decoding process. As depicted in Fig. 1(b), the pulse width of each primary light is expected to be extracted from the CIE 1931 $xy{\rm Y}$ color space of a mixed light. Obviously, a bijection can be established between the duty cycles of each primary light and each component of the coordinate in the CIE 1931 $xy{\rm Y}$ color space when $n$ equals 3 in Eqs. (1)–(3), corresponding to the case of triprimary color mixing. The unique solution can be obtained as (see Supplement 1)

$${{D}_i} = \frac{{({x_j} - {x_k})({y_m} - {y_k}) - ({y_j} - {y_k})({x_m} - {x_k})}}{{({x_j} - {x_k})({y_i} - {y_k}) - ({y_j} - {y_k})({x_i} - {x_k})}}\frac{{{{R}_m}}}{{{{R}_i}}},$$
where ${{R}_m} = {{L}_m}/{y_m}$; $i,\;j,\;k = {1}$, 2, 3, denoting three primary lights for the color mixing.

A special case is that the chromaticity of a mixed light (${x_m},\;{y_m}$) locates on a line bounded by the chromaticity coordinates of two primary lights, e.g.,  “1” and “2,” corresponding to the case of biprimary color mixing. Similarly, a bijection between the duty cycles and each component of the CIE 1931 $xy{\rm Y}$ coordinates can still be established, by combining Eqs. (1) and (3) or (2) and (3), considering chromaticity ${x_m}$ and ${y_m}$ are linearly dependent. The decoding equations for biprimary color mixing can be written as

$${{{D}}_{i}}=\frac{({{x}_{m}}-{{x}_{j}})}{({{x}_{i}}-{{x}_{j}})}\frac{{{{\boldsymbol R}}_{m}}}{{{{\boldsymbol R}}_{i}}}=\frac{({{y}_{m}}-{{y}_{j}})}{({{y}_{i}}-{{y}_{j}})}\frac{{{{\boldsymbol R}}_{m}}}{{{{\boldsymbol R}}_{i}}},$$
where $i,\;j = {1}$, 2, representing two primary lights for the color mixing. Equations (1)–(5) are the core algorithms for mapping a multi-dimensional digital space to a standard CIE color space.

It is also worthy to determine the physical gamut boundaries of devices in the color mixing, which specify the maximum achievable color volume in a perceptual color space. A common example of breaking the physical gamut boundaries is that one might suffer from the exceptions of ${{D}_i}\; \gt \;{100}\%$ by directly applying the above decoding algorithms, implying the impossibility of realizing certain regions in the standard CIE color space. To better analyze the gamut boundaries, the following mathematic constraints should be taken into account during the additive color mixing:

$$\left({{x_m},{y_m}} \right) \in \mathop \bigcup \limits_{i = 1}^n \left({{x_i},{y_i}} \right),$$
$${{L}_m} \in \left[{0,\;\;\mathop \sum \limits_{i = 1}^n {{L}_i}} \right],$$
$${{ D}_i} \in \left[{0,1} \right].$$

Equation (6), namely chromaticity constraint, implies that the chromaticity of a mixed light should locate in the interior of the 2D gamut geometry (including the borders) enclosed by the chromaticity coordinates of each primary light in the CIE 1931 $xy$ chromaticity diagram. For instance, the gamut geometry is a line segment for the case of biprimary color mixing, while it becomes a triangle for the triprimary case. Equation (7), namely luminosity constraint, holds true due to the conservation of energy. Equation (8), namely digital constraint, is always valid from its definition. The color volume limited by the chromaticity and luminosity constraints, hereafter what we called theoretical space, is a triangular prism for the case of triprimary color mixing, as shown in Fig. 1(c). The physical gamut boundaries are mainly determined by the digital constraint, which, however, is routinely ignored. The upper and lower physical gamut boundaries of the mixed color can be gained by substituting Eq. (4) into the digital constraint Eq. (8) for the triprimary case (see Supplement 1). Let ${{D}_i} = {0}$, from which the lower physical gamut boundary is obtained, maintaining the same as the lower triangular base of theoretical space, as shown in Fig. 1(c). Let ${{D}_i} = {1}$, from which the upper physical gamut boundary can be calculated as

$${L}_b^i\left({{x_m},{y_m}} \right) = \frac{{({x_j} - {x_k})({y_i} - {y_k}) - ({y_j} - {y_k})({x_i} - {x_k})}}{{({x_j} - {x_k})({y_m} - {y_k}) - ({y_j} - {y_k})({x_m} - {x_k})}}{y_m}{{R}_i},$$
where ${L}_b^i$ ($i = {1}$, 2, 3) represents the upper physical gamut boundary of $i$th primary light. Obviously, the luminosity behaves in a nonlinear manner of corresponding chromaticity. The upper gamut surface of the mixed light can thus be obtained as (see Supplement 1)
$${{L}_b}\left({{x_m},{y_m}} \right) = \min \left({{ L}_b^1,\;{L}_b^2,{L}_b^3} \right) = \mathop \bigcup \limits_{i = 1}^3 {L}_{{b^ -}}^i\left({{x_m},{y_m}} \right),$$
where the “min” denotes the function that returns the lowest value of the expression, and “$\bigcup $” represents the union operator. ${L}_{{b^ -}}^i({x_m},\;{y_m})\;(i = {1},\;{2},\;{3})$ represents the $i$th primary component of the upper gamut surface, which is the lowest one among three upper gamut boundaries at the given chromaticity coordinates (${x_m},\;{y_m}$). As shown in Fig. 1(c), the upper gamut surface of the mixed light expressed in Eq. (10) is plotted with a “jet” colormap. The space between the upper and lower gamut surface (the lower triangular base) in the triangular prism is called the accessible space, which denotes the whole codable color volume with digital pulses. Notably, maximum intensities are mixed at the white point. The chromaticity of the mixed light can be tuned in the whole 2D gamut geometry in the $x {-} y$ plane, which is the triangular base in Fig. 1(c), as long as its luminosity is lower than the smallest one of three primary lights, which is $L_{3}$ in Fig. 1(c). The ratio between the accessible space and the theoretical space, defined as the codable ratio, can be used to characterize the realizable nonlinear gamut volume:
$$\delta = \frac{\displaystyle{\int_0^{{{L}_b}} {\rm d}{{L}_m}\mathop{\displaystyle{\int\!\!\!\!\int\!\!\!\!\!\!\!\bigcirc}} {\rm d}s}}{{S \times \mathop \sum \nolimits_{i = 1}^3 {{L}_i}}},$$
where $S$ represents the area of the triangular base and ${\rm d}s$ is its derivative. Notably, the codable ratio shows independence on the duty cycles, reflecting the configuration quality of constituting primary lights (see Supplement 1).

The physical gamut boundaries for the biprimary color mixing could be correspondingly obtained by projecting the 3D gamut surface to one of three rectangular sides of the triangular prism. Figure 1(d) shows the nonlinear gamut boundaries (${L}_{{b^ -}}^1$ and ${L}_{{b^ -}}^2$) and the accessible space (gray area) for the case of biprimary color mixing [lights “1” and “2” in Fig. 1(c)]. ${ L}_{{b^ -}}^i$ ($i = {1}$, 2) represents the $i$th primary component of upper physical gamut boundary, which is the lower one between two primary lights at given a chromaticity ${x_m}$. The chromaticity ${x_0}$ denotes the case that two primary lights are equally mixed, in which the luminosity of the mixed light can be achieved a maximum tunable range [0, ${{ L}_1} + {{L}_2}$].

3. EXPERIMENTS

In order to validate the method, we first use LEDs to conduct the biprimary and triprimary color mixing, demonstrating their practical applications in biophotonic lighting and full-color displaying, respectively. As it is known, a precise control of the chromaticity, especially correlated color temperature (CCT), and luminosity at the mean time is the key to alter the specific hormone secretions, e.g.,  melatonin, and therefore adjust the circadian rhythms in mammals [34,35]. Here we show such an example of dynamically varying the color of a light following a designed function of time, e.g.,  a sinusoid. As illustrated in Fig. 2(a), an office luminaire made of “cold” and “warm” white LEDs is driven by two independent digital current pulses (see Supplement 1). The experimental CCT (cyan dots with error bars) and luminous flux (solid orange squares with error bars) are in agreement with the theoretical ones (cyan and orange curves, respectively), as seen in Fig. 2(b). The corresponding chromaticity coordinates (see Supplement 1) and luminous flux are also mapped to a 2D CIE 1931 $xy{\rm Y}$ color space, shown in Fig. 2(c). As it can be seen, the theoretical (red crosses) and experimental (green dots) data are all located in the accessible space (gray area) and agree with each other, indicating the feasibility and validity of digital pulse modulation.

 figure: Fig. 2.

Fig. 2. (a)–(c) Biophotonic lighting and (d)–(h) CIE-based full-color displaying using biprimary and triprimary color mixing of LEDs, respectively. (a) Sketch of biprimary color mixing, using a luminaire made of “cold” and “warm” white LEDs. (b) Biprimary color mixing by precisely controlling the CCT (cyan curve and dots) and luminous flux (orange curve and squares) as sinusoidal functions of time. The experimental (cyan dots and orange squares with the error bars) and theoretical (cyan and orange curves) data are compared. The error bars indicate the averages and tolerances of four times’ measurements. (c) Comparisons between the experimental (green dots) and theoretical (red crosses) chromaticity $x$ and luminosity coordinates in the 2D CIE 1931 $xy{\rm Y}$ color space realized by biprimary color mixing. The rectangle and gray regions denote the theoretical and accessible spaces, respectively. (d) Sketch of triprimary color mixing, using a luminaire made of red, green, and blue LEDs. (e) Comparisons between the experimental (green circles with error bars) and theoretical (magenta crosses and dashed black curves) chromaticity and luminosity coordinates in the 3D CIE 1931 $xy{\rm Y}$ color space realized by triprimary color mixing. The blue dashed curve represents the outline of the CIE 1931 chromaticity diagram. The triangle represents the theoretical gamut geometry in the $x - y$ plane, and the color contrast represents the upper gamut surfaces. The inset shows the ${\rm Y}$ components of 16 data points. The error bars indicate the averages and tolerances of four times’ measurements. (f)–(h) Reconstruction of a digital color frame by using triprimary color mixing of LEDs. One original frame in an RGB color space (f) is first transformed to the CIE 1931 $xy{\rm Y}$ color space (g), and then reproduced (h) by the decoding process.

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In addition, a luminaire made of red, green, and blue LEDs is demonstrated for a CIE-based full-color display. Figure 2(e) shows 16 sets of chromaticity coordinates in the CIE 1931 $xy{\rm Y}$ color space realized by a home-built luminaire (see Supplement 1). The triangle is the theoretical gamut geometry, enclosed by the chromaticity coordinates of the used triprimary lights. The color contrast indicates the upper gamut surface of the accessible space. The chromaticity coordinates of mixed light are designed to follow the elliptical traces (black dashed curves) and the luminosity is expected to keep a constant luminous flux of 280 lm. A good agreement between the experiment (green circles with error bars) and the theory (magenta crosses) can be clearly seen. The luminous fluxes have an average of 274 lm and almost keep constant with a root-mean-square deviation of 8.6 lm, as shown in the inset of Fig. 2(e). In order to further demonstrate the practice application in displays, the same luminaire is used to reproduce a color frame of an animation, in which the color of a single pixel is extracted from one emission spectrum of the mixed light. Figures 2(f)–2(h) show the reconstruction processes of a digital frame. One original frame in an RGB color space Fig. 2(f) is first transformed into the CIE 1931 $xy{\rm Y}$ color space Fig. 2(g). The reproduced frame Fig. 2(h) is then realized by the decoding process (see Supplement 1). Notably, the brightness of the digital image can be easily tuned by altering the ${\rm Y}$ component of the CIE 1931 $xy{\rm Y}$ color space regardless of the chromaticity shift, showing the superiority over the ordinary RGB color space mapping.

 figure: Fig. 3.

Fig. 3. Full-color optical imaging with precise chromaticity and luminosity realized by color mixing of three primary lasers via a home-built laser beam scanning projector. (a) Sketch of the laser beam scanning projector, where D1–D3 are laser diodes, BS1–BS3 are beam splitters, and GM1–GM2 are galvo scanning mirrors. (b) Optical scanning images of a crab sketch projected to a screen using seven different colors. The chromaticity coordinate of each color is plotted in the CIE 1931 $xy$ diagram and labeled with corresponding numbers.

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In addition to LEDs, the methodology works perfectly for lasers as well. Owing to their unique properties such as coherence and monochromaticity, lasers with precise chromaticity and luminosity provide new perspectives to real-color displays, remote wireless communications, and spectral sensors in the processes of light–matter interactions. Hereafter two prototypes of a laser beam scanning projector and a plasmonic-metasurface sensor are demonstrated, respectively. As shown in Fig. 3(a), three laser diodes with central wavelengths of 450 nm, 515 nm, and 637 nm are driven by coded digital pulses and combined as a single beam using three beam splitters. The mixed light passes through a couple of galvo scanning mirrors, which then project the programmed image to a target screen (see Supplement 1). Thanks to our encoding and decoding algorithms, a crab-shape image with seven different colors, which correspond to a cancer-horoscopic-like chromatic pattern labeled in the CIE 1931 $xy$ diagram, are obtained, as shown in Fig. 3(b). The chromatic deviation can be well controlled with a tolerance of 0.001. The laser projector with precise manipulation of the color as well as the brightness could serve as an ideal display engine for the next-generation virtual reality and augmented reality devices [36].

Ancient arts such as the Roman Lycurgus cup and stained glass in churches give vibrant colors by doping plasmonic nanoparticles that strongly depend on the size, shape, and material. Vice versa, the size of nanoparticles, for instance, could be distinguished by directly comparing the colors of scattered light. Here we demonstrate a prototype that senses the dimension of plasmonic metasurfaces without employing complex optical spectroscopy technologies. As shown in Fig. 4(a), an RGB laser beam (red dashed lines) passes through a sample including five patterns of nanodiscs fabricated by electron-beam lithography (see Supplement 1). In order to visualize metasurfaces and focus the beam on specific nanostructure patterns, the sample is sandwiched between two confocal objectives (O1 and O2, NA 0.65) and a Köhler illumination is implemented with a visible LED on one side (green dashed lines), and a CCD camera allows the sample to be imaged on the other side (blue dashed lines). The transmitted light is collected with an integration sphere and further analyzed using a spectrocolorimeter. The laser beam that travels through plasmonic metasurfaces as well as the reference (blank region of the sample) changes its chromaticity coordinates sequentially along a circular path [central coordinates (0.2764, 0.3203), radius 0.1], which is precisely controlled by using programmed digital signals. The diameter of the nanostructure varies from 60 nm to 135 nm, the scanning electron microscope (SEM) images of which are shown on the top of Fig. 4(b). When the beam is focused on the reference, the chromaticity coordinates reproduce a circular pattern, as shown by the boundary of the black region in Fig. 4(b), matching the theoretical expectations. When the beam is switched to the plasmonic metasurfaces, the circular chromaticity experiences an apparent blueshift and elongates in the $y$ axis as the dimension increases, as shown in Fig. 4(b). The trend agrees with the theoretical predictions in Fig. 4(c), wherein theoretical chromaticity coordinates of the transmittance are calculated for the nanostructures with the diameter ranging from 60 nm to 140 nm in a step of 10 nm (see Supplement 1). The blueshift and elongation in the $y$ axis of the chromaticity circle can be well explained by the redshift of plasmonic resonance as the diameter of the nanostructure increases [37]. Notably, the sensing process can be further simplified by tracing the changes of a single chromaticity of an excitation laser. For instance, a laser beam with the chromaticity coordinates (0.3764, 0.3203) is served as the light source. The chromatic shifting path of the beam across the plasmonic metasurfaces is plotted with a dashed green line in Fig. 4(c). The $x$ component of chromaticity shift (colored dots) versus the diameter of the nanodiscs is well fitted with an inversed sigmoid function (green curve) in the detecting range, as shown in the inset of Fig. 4(c). Therefore, the dimension of the nanodisc could be fast predicted by solely comparing the offset of chromaticity $x$. The sensor can be further integrated on a single chip, as both the light source and the chromatic detector are able to be downsized to microscales and even nanoscales [17,38].

 figure: Fig. 4.

Fig. 4. Integrable chromatic sensor for detecting the nanoscale dimension of lithographically defined plasmonic metasurfaces. (a) Schematic optical path of a home-built chromatic sensor, where L1–L3 are lenses, BS1–BS2 are beam splitters, O1–O2 are objectives, GF is gray filter, BF is bandpass filter, SMP is the sample, IS is integration sphere, SCM is the spectrocolorimeter, and CCD represents charged-coupled device. The polygons enclosed by the red, green, and blue dashed lines imply the programmed RGB laser, illumination, and imaging parts of the optical system. (b) Experimental chromaticity shifts of transmission light passing through the plasmonic metasurfaces with different diameters of nanostructures (colored curves) as well as the reference (black area) by using circular chromatic laser beams. The diameter of the nanodisc varies from 60 nm, 70 nm, 90 nm, 110 nm to 135 nm. The SEM images for each dimension are provided on the top. The scale bar in the SEM images represents 200 nm. (c) Theoretical chromaticity shifts of transmission light passing through the plasmonic metasurfaces with different diameters of nanostructures (colored curves) as well as the reference (black area) by using circular chromatic laser beams. The diameter of the nanodisc ranges from 60 nm to 140 nm in a step of 10 nm. The green dashed line represents the chromaticity shifting path of transmission light by using the excitation laser with a constant chromaticity (0.3764, 0.3203). The inset shows the $x$ component of chromaticity shift as a function of the diameter of the nanodisc. The experimental data (colored dots) are fitted with an inversed sigmoid function (green curve) for guiding eyes.

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4. CONCLUSION

We introduced a theory that encodes and decodes digital signals to the CIE 1931 $xy{\rm Y}$ color space with nonlinear gamut boundaries. Demonstrations with standard LEDs and lasers validated our theory. The related methodologies could be further transplanted to other CIE-based color spaces, e.g.,  perceptually uniform color spaces [39,40]. The digital pulse coded CIE color spaces show the versatility in both lighting, displaying, and sensing fields, owning the superiority of perceptual color volume, analytic gamut boundaries, and accurate chromatic control over ordinary RGB color spaces. The method can be readily applied in current commercialized displays to maximize the dynamic range and gamut volume. It also provides perspectives to cutting-edge applications in virtual/augmented reality devices [36], microdisplays [4143], artificial visions [4446], and fundamental sciences involving multiplex laser pulses [47,48]. Given the substantial advantages of chromatic accuracy, the digital devices with eye-perceptual characters are expected to become the leading technology for the next generation of videos, images, and sensors.

Funding

National Key Research and Development Program of China (2017YFA0205700); National Natural Science Foundation of China (51806199, 61905200, 61927820).

Acknowledgment

The authors gratefully acknowledge fruitful discussions with Prof. Tong Qiao from the School of Cyberspace, Hangzhou Dianzi University; Dr. Ding Zhao from the School of Engineering, Westlake University; and Dr. Yu Hong from College of Optical Science and Engineering, Zhejiang University.

J. W. conceived the concept and developed the theory and M. Q. supervised the research. N. T, J. Z., and J. Y. constructed the luminaires and experimental instruments. J. W., J. Z., and J. Y. performed the LED-based experiments. N. T., L. Z., B. C., and J. W. performed the laser beam scanning projection experiment; L. Z. and B. C. prepared the sample of plasmonic metasurfaces; and N. T., L. Z., B. C., Y. P., X. T., and J. W. performed the chromatic sensing experiment and related theoretical calculations. J. W., W. Y., and M. Q. discussed the results and corrected the paper. All authors contributed to editing and preparing the paper.

Disclosures

The authors declare no competing financial interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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14. M. A. Baldo, D. F. O’Brien, Y. You, A. Shoustikov, S. Sibley, M. E. Thompson, and S. R. Forrest, “Highly efficient phosphorescent emission from organic electroluminescent devices,” Nature 395, 151–154 (1998). [CrossRef]  

15. H. Zhang, Q. Su, and S. Chen, “Quantum-dot and organic hybrid tandem light-emitting diodes with multi-functionality of full-color-tunability and white-light-emission,” Nat. Commun. 11, 2826 (2020). [CrossRef]  

16. S. I. Azzam, A. V. Kildishev, R. M. Ma, C. Z. Ning, R. Oulton, V. M. Shalaev, M. I. Stockman, J. L. Xu, and X. Zhang, “Ten years of spasers and plasmonic nanolasers,” Light Sci. Appl. 9, 90 (2020). [CrossRef]  

17. Y. Liang, C. Li, Y. Z. Huang, and Q. Zhang, “Plasmonic nanolasers in on-chip light sources: prospects and challenges,” ACS Nano 14, 14375–14390 (2020). [CrossRef]  

18. H. Cho, S. H. Jeong, M. H. Park, Y. H. Kim, C. Wolf, C. L. Lee, J. H. Heo, A. Sadhanala, N. Myoung, S. Yoo, S. H. Im, R. H. Friend, and T. W. Lee, “Overcoming the electroluminescence efficiency limitations of perovskite light-emitting diodes,” Science 350, 1222–1225 (2015). [CrossRef]  

19. J. Luo, X. Wang, S. Li, J. Liu, Y. Guo, G. Niu, L. Yao, Y. Fu, L. Gao, Q. Dong, C. Zhao, M. Leng, F. Ma, W. Liang, L. Wang, S. Jin, J. Han, L. Zhang, J. Etheridge, J. Wang, Y. Yan, E. H. Sargent, and J. Tang, “Efficient and stable emission of warm-white light from lead-free halide double perovskites,” Nature 563, 541–545 (2018). [CrossRef]  

20. Y. Miao, L. Cheng, L. Gu, J. Zhang, Q. Peng, M. Xu, Y. He, S. Zhang, Y. Cao, R. Li, N. Wang, W. Huang, and J. Wang, “Microcavity top-emission perovskite light-emitting diodes,” Light Sci. Appl. 9, 89 (2020). [CrossRef]  

21. Y. C. Kim and Y. R. Do, “Nanohole-templated organic light-emitting diodes fabricated using laser-interfering lithography: moth-eye lighting,” Opt. Express 13, 1598–1603 (2005). [CrossRef]  

22. W. Mei, Z. Zhang, A. Zhang, D. Li, X. Zhang, H. Wang, Z. Chen, Y. Li, X. Li, and X. Xu, “High-resolution, full-color quantum dot light-emitting diode display fabricated via photolithography approach,” Nano Res. 13, 2485–2491 (2020). [CrossRef]  

23. E. Bodenstein, M. Schober, M. Hoffmann, C. Metzner, and U. Vogel, “Realization of RGB colors from top-emitting white OLED by electron beam patterning,” J. Soc. Inf. Disp. 26, 555–560 (2018). [CrossRef]  

24. Y. L. Kong, I. A. Tamargo, H. Kim, B. N. Johnson, M. K. Gupta, T. W. Koh, H. A. Chin, D. A. Steingart, B. P. Rand, and M. C. McAlpine, “3D printed quantum dots light-emitting diodes,” Nano Lett. 14, 7017–7023 (2014). [CrossRef]  

25. J. Bae, S. Lee, J. Ahn, J. H. Kim, M. Wajahat, W. S. Chang, S. Y. Yoon, J. T. Kim, S. K. Seol, and J. Pyo, “3D-printed quantum dot nanopixels,” ACS Nano 14, 10993–11001 (2020). [CrossRef]  

26. N. A. Ibraheem, M. M. Hasan, R. Z. Khan, and P. K. Mishra, “Understanding color models: a review,” ARPN J. Sci. Technol. 2, 265–275 (2012).

27. M. O. Yang and S. W. Huang, “Determination of gamut boundary description for multi-primary color displays,” Opt. Express 15, 13388–13403 (2007). [CrossRef]  

28. T. J. Cholewo and S. Love, “Gamut boundary determination using alpha-shapes,” in IS&T and SID’s 7th Color Imaging Conference: Color Science, Systems and Applications (1999), pp. 200–204.

29. A. M. Bakke, I. Farup, and J. Y. Hardeberg, “Evaluation of algorithms for the determination of color gamut boundaries,” J. Imaging Sci. Technol. 54, 050502 (2010). [CrossRef]  

30. G. Sharma and H. J. Trussell, “Digital color imaging,” IEEE Trans. Image Process. 6, 901–932 (1997). [CrossRef]  

31. P. E. Morse, A. M. Reading, and T. Stål, “Well-posed geoscientific visualization through interactive color mapping,” Front. Earth Sci. 7, 274 (2019). [CrossRef]  

32. G. Sharma and H. J. Trussell, “Figures of merit for color scanners,” IEEE Trans. Image Process. 6, 990–1001 (1997). [CrossRef]  

33. E. L. van den Broek and E. M. van Rikxoort, “Evaluation of color representation for texture analysis,” 16th Belgium-Netherlands Artificial Intelligence Conference, Groningen, The Netherlands, 2004, pp. 35–42.

34. D. M. Berson, F. A. Dunn, and M. Takao, “Phototransduction by retinal ganglion cells that set the circadian clock,” Science 295, 1070–1073 (2002). [CrossRef]  

35. S. Wahl, M. Engelhardt, P. Schaupp, C. Lappe, and I. V. Ivanov, “The inner clock—blue light sets the human rhythm,” J. Biophoton. 12, e201900102 (2019). [CrossRef]  

36. B. C. Kress and I. Chatterjee, “Waveguide combiners for mixed reality headsets: a nanophotonics design perspective,” Nanophotonics 10, 41–74 (2020). [CrossRef]  

37. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

38. Z. Yang, T. A. Owen, H. Cui, J. A. Webber, F. Gu, X. Wang, T. C. Wu, M. Zhuge, C. Williams, P. Wang, A. V. Zayats, W. Cai, L. Dai, S. Hofmann, M. Overend, L. Tong, Q. Yang, Z. Sun, and T. Hasan, “Single-nanowire spectrometers,” Science 365, 1017–1020 (2019). [CrossRef]  

39. M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006). [CrossRef]  

40. M. Safdar, G. H. Cui, Y. J. Kim, and M. R. Luo, “Perceptually uniform color space for image signals including high dynamic range and wide gamut,” Opt. Express 25, 15131–15151 (2017). [CrossRef]  

41. Z. Liu, C. H. Lin, B. R. Hyun, C. W. Sher, Z. Lv, B. Luo, F. Jiang, T. Wu, C. H. Ho, H. C. Kuo, and J. H. He, “Micro-light-emitting diodes with quantum dots in display technology,” Light Sci. Appl. 9, 83 (2020). [CrossRef]  

42. S. H. Kim, Y. K. Yeon, J. M. Lee, J. R. Chao, Y. J. Lee, Y. B. Seo, M. T. Sultan, O. J. Lee, J. S. Lee, S. Yoon, I. Hong, G. Khang, S. J. Lee, J. J. Yoo, and C. H. Park, “Precisely printable and biocompatible silk fibroin bioink for digital light processing 3D printing,” Nat. Commun. 9, 1620 (2018). [CrossRef]  

43. J. Zhao, Y. Yan, Z. Gao, Y. Du, H. Dong, J. Yao, and Y. S. Zhao, “Full-color laser displays based on organic printed microlaser arrays,” Nat. Commun. 10, 870 (2019). [CrossRef]  

44. K. Servick, “Next-generation artificial vision comes into view,” Science 366, 671–672 (2020). [CrossRef]  

45. L. Mennel, J. Symonowicz, S. Wachter, D. K. Polyushkin, A. J. Molina-Mendoza, and T. Mueller, “Ultrafast machine vision with 2D material neural network image sensors,” Nature 579, 62–66 (2020). [CrossRef]  

46. L. Gu, S. Poddar, Y. Lin, Z. Long, D. Zhang, Q. Zhang, L. Shu, X. Qiu, M. Kam, A. Javey, and Z. Fan, “A biomimetic eye with a hemispherical perovskite nanowire array retina,” Nature 581, 278–282 (2020). [CrossRef]  

47. J. Wang, A. Coillet, O. Demichel, Z. Wang, D. Rego, A. Bouhelier, P. Grelu, and B. Cluzel, “Saturable plasmonic metasurfaces for laser mode locking,” Light Sci. Appl. 9, 50 (2020). [CrossRef]  

48. J. Lu, Q. Li, C. W. Qiu, Y. Hong, P. Ghosh, and M. Qiu, “Nanoscale lamb wave–driven motors in nonliquid environments,” Sci. Adv. 5, eaau8271 (2019). [CrossRef]  

References

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    [Crossref]
  15. H. Zhang, Q. Su, and S. Chen, “Quantum-dot and organic hybrid tandem light-emitting diodes with multi-functionality of full-color-tunability and white-light-emission,” Nat. Commun. 11, 2826 (2020).
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  16. S. I. Azzam, A. V. Kildishev, R. M. Ma, C. Z. Ning, R. Oulton, V. M. Shalaev, M. I. Stockman, J. L. Xu, and X. Zhang, “Ten years of spasers and plasmonic nanolasers,” Light Sci. Appl. 9, 90 (2020).
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    [Crossref]
  18. H. Cho, S. H. Jeong, M. H. Park, Y. H. Kim, C. Wolf, C. L. Lee, J. H. Heo, A. Sadhanala, N. Myoung, S. Yoo, S. H. Im, R. H. Friend, and T. W. Lee, “Overcoming the electroluminescence efficiency limitations of perovskite light-emitting diodes,” Science 350, 1222–1225 (2015).
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    [Crossref]
  20. Y. Miao, L. Cheng, L. Gu, J. Zhang, Q. Peng, M. Xu, Y. He, S. Zhang, Y. Cao, R. Li, N. Wang, W. Huang, and J. Wang, “Microcavity top-emission perovskite light-emitting diodes,” Light Sci. Appl. 9, 89 (2020).
    [Crossref]
  21. Y. C. Kim and Y. R. Do, “Nanohole-templated organic light-emitting diodes fabricated using laser-interfering lithography: moth-eye lighting,” Opt. Express 13, 1598–1603 (2005).
    [Crossref]
  22. W. Mei, Z. Zhang, A. Zhang, D. Li, X. Zhang, H. Wang, Z. Chen, Y. Li, X. Li, and X. Xu, “High-resolution, full-color quantum dot light-emitting diode display fabricated via photolithography approach,” Nano Res. 13, 2485–2491 (2020).
    [Crossref]
  23. E. Bodenstein, M. Schober, M. Hoffmann, C. Metzner, and U. Vogel, “Realization of RGB colors from top-emitting white OLED by electron beam patterning,” J. Soc. Inf. Disp. 26, 555–560 (2018).
    [Crossref]
  24. Y. L. Kong, I. A. Tamargo, H. Kim, B. N. Johnson, M. K. Gupta, T. W. Koh, H. A. Chin, D. A. Steingart, B. P. Rand, and M. C. McAlpine, “3D printed quantum dots light-emitting diodes,” Nano Lett. 14, 7017–7023 (2014).
    [Crossref]
  25. J. Bae, S. Lee, J. Ahn, J. H. Kim, M. Wajahat, W. S. Chang, S. Y. Yoon, J. T. Kim, S. K. Seol, and J. Pyo, “3D-printed quantum dot nanopixels,” ACS Nano 14, 10993–11001 (2020).
    [Crossref]
  26. N. A. Ibraheem, M. M. Hasan, R. Z. Khan, and P. K. Mishra, “Understanding color models: a review,” ARPN J. Sci. Technol. 2, 265–275 (2012).
  27. M. O. Yang and S. W. Huang, “Determination of gamut boundary description for multi-primary color displays,” Opt. Express 15, 13388–13403 (2007).
    [Crossref]
  28. T. J. Cholewo and S. Love, “Gamut boundary determination using alpha-shapes,” in IS&T and SID’s 7th Color Imaging Conference: Color Science, Systems and Applications (1999), pp. 200–204.
  29. A. M. Bakke, I. Farup, and J. Y. Hardeberg, “Evaluation of algorithms for the determination of color gamut boundaries,” J. Imaging Sci. Technol. 54, 050502 (2010).
    [Crossref]
  30. G. Sharma and H. J. Trussell, “Digital color imaging,” IEEE Trans. Image Process. 6, 901–932 (1997).
    [Crossref]
  31. P. E. Morse, A. M. Reading, and T. Stål, “Well-posed geoscientific visualization through interactive color mapping,” Front. Earth Sci. 7, 274 (2019).
    [Crossref]
  32. G. Sharma and H. J. Trussell, “Figures of merit for color scanners,” IEEE Trans. Image Process. 6, 990–1001 (1997).
    [Crossref]
  33. E. L. van den Broek and E. M. van Rikxoort, “Evaluation of color representation for texture analysis,” 16th Belgium-Netherlands Artificial Intelligence Conference, Groningen, The Netherlands, 2004, pp. 35–42.
  34. D. M. Berson, F. A. Dunn, and M. Takao, “Phototransduction by retinal ganglion cells that set the circadian clock,” Science 295, 1070–1073 (2002).
    [Crossref]
  35. S. Wahl, M. Engelhardt, P. Schaupp, C. Lappe, and I. V. Ivanov, “The inner clock—blue light sets the human rhythm,” J. Biophoton. 12, e201900102 (2019).
    [Crossref]
  36. B. C. Kress and I. Chatterjee, “Waveguide combiners for mixed reality headsets: a nanophotonics design perspective,” Nanophotonics 10, 41–74 (2020).
    [Crossref]
  37. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  38. Z. Yang, T. A. Owen, H. Cui, J. A. Webber, F. Gu, X. Wang, T. C. Wu, M. Zhuge, C. Williams, P. Wang, A. V. Zayats, W. Cai, L. Dai, S. Hofmann, M. Overend, L. Tong, Q. Yang, Z. Sun, and T. Hasan, “Single-nanowire spectrometers,” Science 365, 1017–1020 (2019).
    [Crossref]
  39. M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
    [Crossref]
  40. M. Safdar, G. H. Cui, Y. J. Kim, and M. R. Luo, “Perceptually uniform color space for image signals including high dynamic range and wide gamut,” Opt. Express 25, 15131–15151 (2017).
    [Crossref]
  41. Z. Liu, C. H. Lin, B. R. Hyun, C. W. Sher, Z. Lv, B. Luo, F. Jiang, T. Wu, C. H. Ho, H. C. Kuo, and J. H. He, “Micro-light-emitting diodes with quantum dots in display technology,” Light Sci. Appl. 9, 83 (2020).
    [Crossref]
  42. S. H. Kim, Y. K. Yeon, J. M. Lee, J. R. Chao, Y. J. Lee, Y. B. Seo, M. T. Sultan, O. J. Lee, J. S. Lee, S. Yoon, I. Hong, G. Khang, S. J. Lee, J. J. Yoo, and C. H. Park, “Precisely printable and biocompatible silk fibroin bioink for digital light processing 3D printing,” Nat. Commun. 9, 1620 (2018).
    [Crossref]
  43. J. Zhao, Y. Yan, Z. Gao, Y. Du, H. Dong, J. Yao, and Y. S. Zhao, “Full-color laser displays based on organic printed microlaser arrays,” Nat. Commun. 10, 870 (2019).
    [Crossref]
  44. K. Servick, “Next-generation artificial vision comes into view,” Science 366, 671–672 (2020).
    [Crossref]
  45. L. Mennel, J. Symonowicz, S. Wachter, D. K. Polyushkin, A. J. Molina-Mendoza, and T. Mueller, “Ultrafast machine vision with 2D material neural network image sensors,” Nature 579, 62–66 (2020).
    [Crossref]
  46. L. Gu, S. Poddar, Y. Lin, Z. Long, D. Zhang, Q. Zhang, L. Shu, X. Qiu, M. Kam, A. Javey, and Z. Fan, “A biomimetic eye with a hemispherical perovskite nanowire array retina,” Nature 581, 278–282 (2020).
    [Crossref]
  47. J. Wang, A. Coillet, O. Demichel, Z. Wang, D. Rego, A. Bouhelier, P. Grelu, and B. Cluzel, “Saturable plasmonic metasurfaces for laser mode locking,” Light Sci. Appl. 9, 50 (2020).
    [Crossref]
  48. J. Lu, Q. Li, C. W. Qiu, Y. Hong, P. Ghosh, and M. Qiu, “Nanoscale lamb wave–driven motors in nonliquid environments,” Sci. Adv. 5, eaau8271 (2019).
    [Crossref]

2020 (15)

Y. Huang, E. L. Hsiang, M. Y. Deng, and S. T. Wu, “Mini-LED, Micro-LED and OLED displays: present status and future perspectives,” Light Sci. Appl. 9, 105 (2020).
[Crossref]

T. Zhan, J. Xiang, J. Zou, and S. T. Wu, “Multifocal displays: review and prospect,” Photonix 1, 10 (2020).
[Crossref]

M. Yu, R. Huang, J. Guo, Z. Zhao, and B. Z. Tang, “Promising applications of aggregation-induced emission luminogens in organic optoelectronic devices,” Photonix 1, 11 (2020).
[Crossref]

H. Zhang, Q. Su, and S. Chen, “Quantum-dot and organic hybrid tandem light-emitting diodes with multi-functionality of full-color-tunability and white-light-emission,” Nat. Commun. 11, 2826 (2020).
[Crossref]

S. I. Azzam, A. V. Kildishev, R. M. Ma, C. Z. Ning, R. Oulton, V. M. Shalaev, M. I. Stockman, J. L. Xu, and X. Zhang, “Ten years of spasers and plasmonic nanolasers,” Light Sci. Appl. 9, 90 (2020).
[Crossref]

Y. Liang, C. Li, Y. Z. Huang, and Q. Zhang, “Plasmonic nanolasers in on-chip light sources: prospects and challenges,” ACS Nano 14, 14375–14390 (2020).
[Crossref]

Y. Miao, L. Cheng, L. Gu, J. Zhang, Q. Peng, M. Xu, Y. He, S. Zhang, Y. Cao, R. Li, N. Wang, W. Huang, and J. Wang, “Microcavity top-emission perovskite light-emitting diodes,” Light Sci. Appl. 9, 89 (2020).
[Crossref]

W. Mei, Z. Zhang, A. Zhang, D. Li, X. Zhang, H. Wang, Z. Chen, Y. Li, X. Li, and X. Xu, “High-resolution, full-color quantum dot light-emitting diode display fabricated via photolithography approach,” Nano Res. 13, 2485–2491 (2020).
[Crossref]

J. Bae, S. Lee, J. Ahn, J. H. Kim, M. Wajahat, W. S. Chang, S. Y. Yoon, J. T. Kim, S. K. Seol, and J. Pyo, “3D-printed quantum dot nanopixels,” ACS Nano 14, 10993–11001 (2020).
[Crossref]

B. C. Kress and I. Chatterjee, “Waveguide combiners for mixed reality headsets: a nanophotonics design perspective,” Nanophotonics 10, 41–74 (2020).
[Crossref]

Z. Liu, C. H. Lin, B. R. Hyun, C. W. Sher, Z. Lv, B. Luo, F. Jiang, T. Wu, C. H. Ho, H. C. Kuo, and J. H. He, “Micro-light-emitting diodes with quantum dots in display technology,” Light Sci. Appl. 9, 83 (2020).
[Crossref]

K. Servick, “Next-generation artificial vision comes into view,” Science 366, 671–672 (2020).
[Crossref]

L. Mennel, J. Symonowicz, S. Wachter, D. K. Polyushkin, A. J. Molina-Mendoza, and T. Mueller, “Ultrafast machine vision with 2D material neural network image sensors,” Nature 579, 62–66 (2020).
[Crossref]

L. Gu, S. Poddar, Y. Lin, Z. Long, D. Zhang, Q. Zhang, L. Shu, X. Qiu, M. Kam, A. Javey, and Z. Fan, “A biomimetic eye with a hemispherical perovskite nanowire array retina,” Nature 581, 278–282 (2020).
[Crossref]

J. Wang, A. Coillet, O. Demichel, Z. Wang, D. Rego, A. Bouhelier, P. Grelu, and B. Cluzel, “Saturable plasmonic metasurfaces for laser mode locking,” Light Sci. Appl. 9, 50 (2020).
[Crossref]

2019 (7)

J. Lu, Q. Li, C. W. Qiu, Y. Hong, P. Ghosh, and M. Qiu, “Nanoscale lamb wave–driven motors in nonliquid environments,” Sci. Adv. 5, eaau8271 (2019).
[Crossref]

J. Zhao, Y. Yan, Z. Gao, Y. Du, H. Dong, J. Yao, and Y. S. Zhao, “Full-color laser displays based on organic printed microlaser arrays,” Nat. Commun. 10, 870 (2019).
[Crossref]

Z. Yang, T. A. Owen, H. Cui, J. A. Webber, F. Gu, X. Wang, T. C. Wu, M. Zhuge, C. Williams, P. Wang, A. V. Zayats, W. Cai, L. Dai, S. Hofmann, M. Overend, L. Tong, Q. Yang, Z. Sun, and T. Hasan, “Single-nanowire spectrometers,” Science 365, 1017–1020 (2019).
[Crossref]

P. E. Morse, A. M. Reading, and T. Stål, “Well-posed geoscientific visualization through interactive color mapping,” Front. Earth Sci. 7, 274 (2019).
[Crossref]

S. Wahl, M. Engelhardt, P. Schaupp, C. Lappe, and I. V. Ivanov, “The inner clock—blue light sets the human rhythm,” J. Biophoton. 12, e201900102 (2019).
[Crossref]

M. Asad, R. Wang, Y. H. Ra, P. Gavirneni, Z. Mi, and W. S. Wong, “Optically invariant InGaN nanowire light-emitting diodes on flexible substrates under mechanical manipulation,” npj Flex. Electron. 3, 16 (2019).
[Crossref]

Y. H. Won, O. Cho, T. Kim, D. Y. Chung, T. Kim, H. Chung, H. Jang, J. Lee, D. Kim, and E. Jang, “Highly efficient and stable InP/ZnSe/ZnS quantum dot light-emitting diodes,” Nature 575, 634–638 (2019).
[Crossref]

2018 (4)

D. J. Lynn, M. C. Karmann, B. Georgiy, J. R. Kelley, L. Michel, Y. Robert, and J. Cortina, “Understanding chromaticity shifts in LED devices through analytical models,” Microelectron. Reliab. 84, 149–156 (2018).
[Crossref]

J. Luo, X. Wang, S. Li, J. Liu, Y. Guo, G. Niu, L. Yao, Y. Fu, L. Gao, Q. Dong, C. Zhao, M. Leng, F. Ma, W. Liang, L. Wang, S. Jin, J. Han, L. Zhang, J. Etheridge, J. Wang, Y. Yan, E. H. Sargent, and J. Tang, “Efficient and stable emission of warm-white light from lead-free halide double perovskites,” Nature 563, 541–545 (2018).
[Crossref]

S. H. Kim, Y. K. Yeon, J. M. Lee, J. R. Chao, Y. J. Lee, Y. B. Seo, M. T. Sultan, O. J. Lee, J. S. Lee, S. Yoon, I. Hong, G. Khang, S. J. Lee, J. J. Yoo, and C. H. Park, “Precisely printable and biocompatible silk fibroin bioink for digital light processing 3D printing,” Nat. Commun. 9, 1620 (2018).
[Crossref]

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2017 (1)

2016 (1)

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2015 (1)

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2014 (1)

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2012 (2)

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2010 (1)

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2007 (2)

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2006 (1)

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2002 (1)

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Supplementary Material (1)

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Supplement 1       Supplemental document

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (4)

Fig. 1.
Fig. 1. Principle of the nonlinear CIE 1931 $xy{\rm Y}$ color space coded by digital pulses. (a) Gamut mismatch induced by conventional mapping methods that convert digital pulses to RGB color spaces. The same digital image with different color appearances is shown in two liquid crystal displays (screens 1 and 2) and the displayed images are taken via a digital camera in the same condition. (b) Proposing method that encodes and decodes digital pulses to the CIE 1931 $xy{\rm Y}$ color space. (c) Analytic nonlinear gamut boundaries in the 3D CIE 1931 $xy{\rm Y}$ color space for triprimary color mixing. The triangular prism represents the theoretical space. The surface colored in “jet” map denotes the upper gamut surface and ${\rm L}_{{b^ -}}^i$ ($i = {1}$, 2, 3) represents its $i$th primary component. (d) Analytic nonlinear gamut boundaries in the 2D CIE 1931 $xy{\rm Y}\;{c}$ olor space for biprimary color mixing [light “1” and “2” in (b)]. The rectangle and the gray regions represent the theoretical and accessible spaces, respectively. ${\rm L}_{{b^ -}}^i$ ($i = {1}$, 2) represents the $i$th primary component of upper gamut boundary. ${x_0}$ is the chromaticity $x$ of mixed light when two primary lights are equally mixed.
Fig. 2.
Fig. 2. (a)–(c) Biophotonic lighting and (d)–(h) CIE-based full-color displaying using biprimary and triprimary color mixing of LEDs, respectively. (a) Sketch of biprimary color mixing, using a luminaire made of “cold” and “warm” white LEDs. (b) Biprimary color mixing by precisely controlling the CCT (cyan curve and dots) and luminous flux (orange curve and squares) as sinusoidal functions of time. The experimental (cyan dots and orange squares with the error bars) and theoretical (cyan and orange curves) data are compared. The error bars indicate the averages and tolerances of four times’ measurements. (c) Comparisons between the experimental (green dots) and theoretical (red crosses) chromaticity $x$ and luminosity coordinates in the 2D CIE 1931 $xy{\rm Y}$ color space realized by biprimary color mixing. The rectangle and gray regions denote the theoretical and accessible spaces, respectively. (d) Sketch of triprimary color mixing, using a luminaire made of red, green, and blue LEDs. (e) Comparisons between the experimental (green circles with error bars) and theoretical (magenta crosses and dashed black curves) chromaticity and luminosity coordinates in the 3D CIE 1931 $xy{\rm Y}$ color space realized by triprimary color mixing. The blue dashed curve represents the outline of the CIE 1931 chromaticity diagram. The triangle represents the theoretical gamut geometry in the $x - y$ plane, and the color contrast represents the upper gamut surfaces. The inset shows the ${\rm Y}$ components of 16 data points. The error bars indicate the averages and tolerances of four times’ measurements. (f)–(h) Reconstruction of a digital color frame by using triprimary color mixing of LEDs. One original frame in an RGB color space (f) is first transformed to the CIE 1931 $xy{\rm Y}$ color space (g), and then reproduced (h) by the decoding process.
Fig. 3.
Fig. 3. Full-color optical imaging with precise chromaticity and luminosity realized by color mixing of three primary lasers via a home-built laser beam scanning projector. (a) Sketch of the laser beam scanning projector, where D1–D3 are laser diodes, BS1–BS3 are beam splitters, and GM1–GM2 are galvo scanning mirrors. (b) Optical scanning images of a crab sketch projected to a screen using seven different colors. The chromaticity coordinate of each color is plotted in the CIE 1931 $xy$ diagram and labeled with corresponding numbers.
Fig. 4.
Fig. 4. Integrable chromatic sensor for detecting the nanoscale dimension of lithographically defined plasmonic metasurfaces. (a) Schematic optical path of a home-built chromatic sensor, where L1–L3 are lenses, BS1–BS2 are beam splitters, O1–O2 are objectives, GF is gray filter, BF is bandpass filter, SMP is the sample, IS is integration sphere, SCM is the spectrocolorimeter, and CCD represents charged-coupled device. The polygons enclosed by the red, green, and blue dashed lines imply the programmed RGB laser, illumination, and imaging parts of the optical system. (b) Experimental chromaticity shifts of transmission light passing through the plasmonic metasurfaces with different diameters of nanostructures (colored curves) as well as the reference (black area) by using circular chromatic laser beams. The diameter of the nanodisc varies from 60 nm, 70 nm, 90 nm, 110 nm to 135 nm. The SEM images for each dimension are provided on the top. The scale bar in the SEM images represents 200 nm. (c) Theoretical chromaticity shifts of transmission light passing through the plasmonic metasurfaces with different diameters of nanostructures (colored curves) as well as the reference (black area) by using circular chromatic laser beams. The diameter of the nanodisc ranges from 60 nm to 140 nm in a step of 10 nm. The green dashed line represents the chromaticity shifting path of transmission light by using the excitation laser with a constant chromaticity (0.3764, 0.3203). The inset shows the $x$ component of chromaticity shift as a function of the diameter of the nanodisc. The experimental data (colored dots) are fitted with an inversed sigmoid function (green curve) for guiding eyes.

Equations (11)

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x m = R x D R D ,
y m = R y D R D ,
L m = L D .
D i = ( x j x k ) ( y m y k ) ( y j y k ) ( x m x k ) ( x j x k ) ( y i y k ) ( y j y k ) ( x i x k ) R m R i ,
D i = ( x m x j ) ( x i x j ) R m R i = ( y m y j ) ( y i y j ) R m R i ,
( x m , y m ) i = 1 n ( x i , y i ) ,
L m [ 0 , i = 1 n L i ] ,
D i [ 0 , 1 ] .
L b i ( x m , y m ) = ( x j x k ) ( y i y k ) ( y j y k ) ( x i x k ) ( x j x k ) ( y m y k ) ( y j y k ) ( x m x k ) y m R i ,
L b ( x m , y m ) = min ( L b 1 , L b 2 , L b 3 ) = i = 1 3 L b i ( x m , y m ) ,
δ = 0 L b d L m d s S × i = 1 3 L i ,

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