Fluorescent effects in a tristimulus render.

(a) We introduce a method to render fluorescent materials in a non-spectral rendererer, exhibiting typical increased luminance and hue-shifting effects when the same materials are placed under a different lighting.
(b) Our method (left insets) is based on a new reduction technique that accurately matches the spectral reference (center insets), significantly improving on previous work Hullin10 (right insets) where a naive formulation of the fluorescence reradiation matrix reduction was used.

We propose a method to accurately handle fluorescence in a non-spectral (, tristimulus) rendering engine, showcasing color-shifting and increased luminance effects.
Core to our method is a principled reduction technique that encodes the re-radiation into a low-dimensional matrix working in the space of the renderer's Color Matching Functions (CMFs).
Our process is independent of a specific CMF set and allows for the addition of a non-visible ultraviolet band during light transport.
Our representation visually matches full spectral light transport for measured fluorescent materials even for challenging illuminants.

<concept_desc>Computing methodologies Reflectance modeling</concept_desc>

[500]Computing methodologies Reflectance modeling

§ NAIVE RERADIATION MATRIX REDUCTION

In an RGB renderer, we track a triplet of outgoing and incoming radiance $\mathbf{c}_o$ and $\mathbf{c}_i$ in place of the spectral quantity $L_o$ and $L_i$:

\begin{align}
\label{eq:co}
\mathbf{c}_o(\wo) = \int L_o(\wo, \lo) \, \mathbf{s}(\lo) \dd{\lo},
\end{align}

where $\mathbf{s}$ is a vector of sensitivity functions, one per color channel.
The definition for $\mathbf{c}_i$ is similar.
In the case of a non-fluorescent Lambertian material with an albedo vector $\pmb{\rho}_d$, the rendering equation is approximated using the component-wise product $\odot$:

\begin{align}
\mathbf{c}_o(\wo) \approx \frac{1}{\pi} \int \pmb{\rho}_d \odot \mathbf{c}_i(\wi) \langle\wi,\wn\rangle\; \dd{\wi}.
\end{align}

By analogy, one can approximate the fluorescent counterpart (Equation <ref>) using vector-matrix multiplications:

\begin{align}
\label{eq:solution-hullin}
\mathbf{c}_o(\wo) \approx \frac{1}{\pi} \int \reduxh \times \mathbf{c}_i(\wi) \langle\wi,\wn\rangle\; \dd{\wi},
\end{align}

where $\reduxh$ is a reduced $3 \times 3$ reradiation matrix that accounts for reradiation from one color channel to the other. To render their BRRDF measurements, Hullin et al. <cit.> suggested to construct such a reduced matrix by integrating the reradiation:

\begin{align}
\reduxh_{k,l} = \iint \bar{s}_k(\li) \bar{s}_l(\lo) \rerad(\li, \lo) \dd{\li}\dd{\lo},
\end{align}

where the $\bar{s}_{k}(\lambda) = {s_{k}(\lambda) \over || s_k ||}$, $k \in \{r,g,b\}$ are normalized RGB Color Matching Functions (CMFs).
In matrix form, this yields:

\begin{align}
\reduxh = \bar{S}^\top \times \rerad \times \bar{S}
\label{eq:redux_hullin}
\end{align}

where $\bar{S}=[\bar{s}_r,\bar{s}_g,\bar{s}_b]$ is the $N \times 3$ matrix of normalized RGB sensitivity functions (with $N=431$ wavelength bins in their case).

*Limits of Naive Reduction.
As shown by Hullin , this naive reduction technique does not faithfully reproduce fluorescent materials (see Figure <ref>), from which they conclude that dense Donaldson matrices and spectral rendering are required.

We do not share their conclusion and show that a different formulation can more correctly reproduce fluorescence.
Indeed, with this naive approach, an identity Donaldson matrix does not yield an identity reduced matrix, and introduces unwanted energy (see the first row of Figure <ref>).
In the next section, we show that the correct construction of the reduced matrix is devoid of this issue, and hence produces much more faithful renderings.

= 6;
= (- ) / 2;

[inner sep=0, anchor=west] (matrix_3_hullin) at (0, 0) ;
(matrix_3_hullin.south west) rectangle (matrix_3_hullin.north east);
[below=3pt] at (matrix_3_hullin.south) (a) Naive Reduction;

[inner sep=0, anchor=east] (spectral) at (, 0) ;
(spectral.south west) rectangle (spectral.north east);
[below=3pt] at (spectral.south) (b) Spectral Reference;

Naive reduction. Using (a) the reduction method of Equation <ref> does not correctly capture the color of the fluorescent material compared to (b) the spectral reference. We use the HERPIOYE material lit by a D65 spectrum.

§ CORRECT RERADIATION MATRIX REDUCTION

Here, we show that the correct way to model the reduced matrix is through spectral upsampling & downsampling with non-orthogonal bases.
We start by describing our approach using XYZ triplets, as the corresponding sensitivity functions are non-negative.

§.§ Reduction through upsampling & downsampling

In the following, we approximate the bi-spectral rendering equation by a series of spectral downsampling and upsampling (see Figure <ref>). While our approach is applicable to the general form (Equation <ref>), we demonstrate it on the diffuse case of Equation <ref> for simplicity.

We start by describing our spectral upsampling and downsampling operators, using the CMFs as spectral bases. The $k$-th color channel after spectral downsampling is then defined as:

\begin{align}
\down[f]_k =  \int f(\lo) \; s_k(\lo) \dd{\lo}.
\label{eq:downsampling}
\end{align}

We can discretize downsampling with $S=[s_x, s_y, s_z]$ the $N \times 3$ matrix of sensitivity functions, and $\mathbf{f}$ the $N$-D vector of the spectrum:

\begin{align}
\down[\mathbf{f}] =  S^T \times \mathbf{f},
\label{eq:downsampling_vec}
\end{align}

Since the $s_k$ ($k \in \{x,y,z\}$) form a non-orthogonal basis, we must use its dual basis $\tilde{s}_l$ ($l \in \{x,y,z\}$) to define upsampling from a color vector $\mathbf{c} = \left[ \dots,  c_i, \dots \right]$:

\begin{align}
\up[\mathbf{c}](\li) = \sum c_l \; \tilde{s}_l(\li).
\label{eq:upsampling}
\end{align}

The dual basis also has an associated $N \times 3$ matrix $\tilde{S} = ({S} {S}^{\top})^{-1} {S}$ (i.e., verifying $S^{\top}\tilde{S} = \mathrm{I}_3$, the $3 \times 3$ identity matrix[
Since we have $S^T \times \tilde{S} = I_3 \iff ({S} {S}^{\top})\times \tilde{S} = S \iff \tilde{S} = ({S} {S}^{\top})^{-1} {S}$.]) to obtain the vector formulation for upsampling:

\begin{align}
\up[\mathbf{c}] = \tilde{S} \times \mathbf{c}.
\label{eq:upsampling_vec}
\end{align}

In a tristimulus renderer, instead of transporting spectral radiance, we transport tristimulus radiance
$\mathbf{c} = \down\left[ L(\omega, \cdot) \right]$,

as illustrated in Figure <ref>.
Using a downsampled incoming radiance $\mathbf{c}_i = \down\left[ L_i(\wi, \cdot) \right]$ as input, we approximate Equation <ref>  by upsampling $\mathbf{c}_i$ and multiplying the resulting spectrum by the reradiation matrix:

\begin{align}
L_o(\wo, \lo) \approx \int {\rerad(\li, \lo) \over \pi} \int   \, \up\left[ \mathbf{c}_i \right](\li) \, \langle\wi,\wn\rangle\, \dd{\wi} \, \dd{\li},
\end{align}

with the final pixel color given by $\mathbf{c}_o = \down\left[ L_o(\wo, \cdot) \right]$, which is equivalent to Equation <ref>.

Since all operators are linear, we re-write $\mathbf{c}_o$ in matrix form by swapping the order of integrals:

\begin{align}
\label{eq:solution-ours}
\mathbf{c}_o \approx {1 \over \pi} \int \left( \reduxo \times \mathbf{c}_i \right)\, \langle\wi,\wn\rangle\, \dd{\wi},
\end{align}

with the matrix-vector product given by:

\begin{align}
\reduxo \times \mathbf{c}_i = \down \left[ \int \rerad(\li, \cdot) \; \up[\mathbf{c}_i](\li) \; \dd{\li} \right].
\label{eq:least_square}
\end{align}

Our reduced matrix is obtained by using the discretized forms provided in Equations <ref> and <ref> into Equation <ref>, yielding:

\begin{align}
\reduxo = S^{\top} \times \rerad \times \tilde{S},
\label{eq:solution}
\end{align}

= 6;
= (- ) / 2;

[inner sep=0, anchor=west] (ours) at (0, 0) ;
(ours.south west) rectangle (ours.north east);
[below=3pt] at (ours.south) (a) Our Reduction;

[inner sep=0, anchor=east] (ref) at (, 0) ;
(ref.south west) rectangle (ref.north east);
[below=3pt] at (ref.south) (b) Spectral Reference;

Optimized reduction. Using (a) our formulation, we obtain a new reduced re-radiation matrix that is better conditioned for rendering fluorescent materials compared to (b) the spectral reference, using the same material and illumination as in Figure <ref>.

Equation <ref> has the same form as Equation <ref>, but is derived from a principled approach that highlights the importance of using the dual basis.
Note that there is no need to normalize sensitivity functions with our approach.
More importantly, our solution in Equation <ref> yields an identity reduced matrix when given an identity reradiation matrix.
Indeed, when $\rerad = \mathrm{I}_N$, $\reduxo = S^{\top} \tilde{S} = \mathrm{I}_3$.

We show in Figure <ref> that our solution produces a closer match to the spectral reference.
In particular, it does not introduce unwanted energy.
As with the naive method, our approach may be applied iteratively to build paths starting from the light source and ending at the camera.
However, our solution is justified thanks to our formulation based on downsampling and upsampling operators, as illustrated in Figure <ref>.
As shown in the top row, even though the upsampled spectra (in purple) do not initially match the exact spectra (in orange), they do closely reproduce them after a single multiplication by $\rerad$.
The main advantage of our method is that this accurate approximation is done implicitly through $\reduxo$ (blue boxes), as shown in the bottom row.
Note that $\reduxo$ will likely be entirely filled due to the wide basis support, even though $\rerad$ is close to upper triangular (although not exactly due to measurement errors).

The final step of the rendering process (green boxes in Figure <ref>) is to integrate spectra over XYZ CMFs.
For reduced light transport, this is done through a mere multiplication by a matrix $T$, which is the identity in the case of XYZ transport.
It might differ with a different choice of basis, as discussed in the next section where we consider the extension of the XYZ basis functions to account for the reradiation from the UV-range.

§.§ Extending Reduction to Incorporate Non-Visible Spectra

We can use Equations <ref> to <ref> with an arbitrary set of non-orthogonal functions.
We experimented the use of a fourth sensitivity function to capture the UV-range.
To do so, we added the first element of a non-uniform B-spline Partition of Unity of $5$ elements and degree $2$ as detailed in Appendix <ref> (the pink curve in Figure <ref> (b), top row).
During rendering, we need to transport an additional float with our XYZ triplet, which we denote by the term XYZU rendering.
Figure <ref> shows the impact of this additional basis function to handle fluorescence from UV lighting.

However, when using an alternative basis, a final projection by a transfer matrix $T$ is required to project the n-uple in the rendering basis to the triplet of the CMF.
In the case of XYZU rendering:

\begin{bmatrix}
x \\ y \\ z
\end{bmatrix}
T \times \mathbf{c}_o,
\quad \mbox{with}\;
T =
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
\end{bmatrix}.

= 6;
= (- 2*) / 3;
1 = 0;
2 = 1 + + ;
3 = 2 + + ;
= .5 * ;

[inner sep=0, anchor=west] (matrix_3) at (1 pt, 0) ;
(matrix_3.south west) rectangle (matrix_3.north east);
[col sep=comma]figures/scene/cmf/ciexyz06_2deg.csv
scale only axis,
[thick,color=tab_red  ,forget plot,] table[x index = 0, y index = 1];
[thick,color=tab_green,forget plot,] table[x index = 0, y index = 2];
[thick,color=tab_blue ,forget plot,] table[x index = 0, y index = 3];

[below=3pt] at (matrix_3.south) (a) XYZ basis);

[inner sep=0, anchor=west] (matrix_4) at (2 pt, 0) ;
(matrix_4.south west) rectangle (matrix_4.north east);
[col sep=comma]figures/scene/cmf/xyzu.csv
scale only axis,
[thick,color=tab_red  ,forget plot,] table[x index = 0, y index = 1];
[thick,color=tab_green,forget plot,] table[x index = 0, y index = 2];
[thick,color=tab_blue ,forget plot,] table[x index = 0, y index = 3];
[thick,color=tab_pink ,forget plot,] table[x index = 0, y index = 4];

[below=3pt] at (matrix_4.south) (b) XYZU basis;

[inner sep=0, anchor=west] (reference) at (3 pt, 0) ;
(reference.south west) rectangle (reference.north east);
[below=3pt] at (reference.south) (c) Spectral Reference;

Adding a UV channel. Adding a fourth channel in the ultra-violet range, shown by the (b) pink curve, permits a more faithful reproduction of the (c) spectral reference when lit with UV lights. We used the HERPIOYE material lit by a Gaussian spectrum centred at $350\:\mathrm{nm}$ with a standard deviation of $50\:\mathrm{nm}$.

Missing 'biblatex' package
The bibliography requires the 'biblatex' package.

journaltitleIEEE Transactions on Image Processing
titleSimultaneous Surface Reflectance and Fluorescence Spectra Estimation
Estimation;Photonics;Cameras;Optimization;Light sources;Fluorescence;Reflectance and fluorescence spectra recovery;multispectral and hyperspectral imaging;image color analysis;inverse problems

booktitle2008 IEEE Symposium on Interactive Ray Tracing
titleSimulation of fluorescent concentrators
Fluorescence;Absorption;Data models;Reflection;Probes;Monte Carlo methods;Computational modeling;I.3.3 [Computing Methodologies]: Computer Graphics—Picture/Image Generation;G.3 [Mathematics of Computing]: Probability and Statistics—Monte Carlo;J.2 [Computer Applications]: Physical Sciences and Engineering—Physics

The Eurographics Association

booktitleEurographics Symposium on Rendering
titleA Microfacet Model for Specular Fluorescent Surfaces and Fluorescent Volume Rendering using Quantum Dots

booktitleACM SIGGRAPH Courses
titlePhysically-Based Shading at Disney

IOP Publishing

abstractA method is described for measuring the spectral reflexion of fluorescent pigments for incident monochromatic light covering the ultra-violet and visible regions of the spectrum. The results are recorded in the form of a square table from which quantum efficiencies and spectral reflexion curves for sunlight or any illuminant of known energy distribution are calculated. Data are given for a red pigment and an optical bleach. Three curves only, showing the variation of tristimulus values with incident wavelength, are sufficient for the calculation of colour. The curves of tristimulus values may be derived from the reflexion curves or measured directly by a template colorimeter.
journaltitleBritish Journal of Applied Physics
titleSpectrophotometry of fluorescent pigments

Budmerice, Slovakia

Association for Computing Machinery

abstractReal-time rendering of participating media in nature presents a difficult problem. The reason is that realistic reproduction of such media requires a proper physical simulation in all cases. In our work we focus on real-time rendering of planetary atmospheres and large areas of water. We first formulate a physically-based model for simulation of light transport in these environments. This model accounts for all necessary light contributions — direct illumination, indirect illumination caused by the scattered light and interreflections between the planetary surface and the atmospheric volume, as well as reflections from the seabed. We adopt the precomputation scheme presented in the previous works to precompute the colours of the arbitrarily dense atmosphere and large-scale water surfaces into a set of lookup tables. All these computations are fully spectral, which increases the realism. Finally we utilize these tables in a GPU-based algorithm that is capable of rendering a whole planet with its atmosphere from all viewpoints above the planetary surface. This approach is capable to achieve hundreds of frames per second on today's graphics hardware.
booktitleProceedings of the 26th Spring Conference on Computer Graphics
seriesSCCG '10
titleReal-time spectral scattering in large-scale natural participating media
atmospheric and aquatic light scattering,natural phenomena,participating media

booktitleProceedings of Color Imaging Conference
titleEvaluation of Bispectral Spectrophotometry for Accurate Colorimetry of Printing Materials

Berlin, Heidelberg

Springer Berlin Heidelberg

booktitlePhotorealistic Rendering Techniques
titleA Model for Fluorescence and Phosphorescence

journaltitleACM Trans. Graph. (Proc. SIGGRAPH 2010)
titleAcquisition and analysis of bispectral bidirectional reflectance and reradiation distribution functions

Optica Publishing Group

abstractWe present an accurate and low-cost method for measuring fluorescence in materials. Our method outputs an estimate of the material’s Donaldson matrix, which is a commonly used two-dimensional spectral characterization of its fluorescence and reflectance properties. To find the estimate, only a few measurements of the material’s reflectance under a few illuminants are needed, which we demonstrate using low-cost optical components. Internally, our algorithm is based on representing each Donaldson matrix with a multivariate Gaussian mixture model and its diagonal with a bounded MESE (maximum entropy spectral estimate). It parametrizes and constrains the estimate in a robust and simple way, allowing the use of gradient-descent optimization. We evaluate our algorithm on a combination of real and synthetic data, and four examples of distinct optical components. We reach significantly lower errors than the current state of the art on the exact same inputs, our estimates do not suffer from artifacts such as oscillations of the spectra, and they are stable and robust.
journaltitleOpt. Express
titleAffordable method for measuring fluorescence using Gaussian distributions and bounded MESE
Fluorescence; Illuminants; Inverse design; Light sources; Optical components; Remote sensing

Wiley Online Library

booktitleComputer Graphics Forum
titleBidirectional rendering of vector light transport

Wiley Online Library

booktitleComputer Graphics Forum
titleSpectral mollification for bidirectional fluorescence

booktitleProceedings of the Eurographics 2018 Workshop on Material Appearance Modeling
titleA simple diffuse fluorescent BBRRDF model

abstractAbstract Physically based spectral rendering has become increasingly important in recent years. However, asset textures in such systems are usually still drawn or acquired as RGB tristimulus values. While a number of RGB to spectrum upsampling techniques are available, none of them support upsampling of all colours in the full spectral locus, as it is intrinsically bigger than the gamut of physically valid reflectance spectra. But with display technology moving to increasingly wider gamuts, the ability to achieve highly saturated colours becomes an increasingly important feature. Real materials usually exhibit smooth reflectance spectra, while computationally generated spectra become more blocky as they represent increasingly bright and saturated colours. In print media, plastic or textile design, fluorescent dyes are added to extend the boundaries of the gamut of reflectance spectra. We follow the same approach for rendering: we provide a method which, given an input RGB tristimulus value, automatically provides a mixture of a regular, smooth reflectance spectrum plus a fluorescent part. For highly saturated input colours, the combination yields an improved reconstruction compared to what would be possible relying on a reflectance spectrum alone. At the core of our technique is a simple parametric spectral model for reflectance, excitation, and emission that allows for compact storage and is compatible with texture mapping. The model can then be used as a fluorescent diffuse component in an existing more complex BRDF model. We also provide importance sampling routines for practical application in a path tracer.
journaltitleComputer Graphics Forum
titleWide Gamut Spectral Upsampling with Fluorescence

Virtual Event, USA

Association for Computing Machinery

abstractWe present a visual effects production workflow for using spectral sensitivity data of DSLR and digital cinema cameras to reconstruct the spectral energy distribution of a given live-action scene and perform rendering in physical units. We can then create images that respect the real-world settings of the cinema camera, properly accounting for white balance, exposure, and the characteristics of the sensor.
booktitleACM SIGGRAPH 2020 Talks
seriesSIGGRAPH '20
titlePhysLight: An End-to-End Pipeline for Scene-Referred Lighting
HDRI,image based lighting,lighting,path tracing,rendering,spectral rendering

abstractAbstract We present two separate improvements to the handling of fluorescence effects in modern uni-directional spectral rendering systems. The first is the formulation of a new distance tracking scheme for fluorescent volume materials which exhibit a pronounced wavelength asymmetry. Such volumetric materials are an important and not uncommon corner case of wavelength-shifting media behaviour, and have not been addressed so far in rendering literature. The second one is that we introduce an extension of Hero wavelength sampling which can handle fluorescence events, both on surfaces, and in volumes. Both improvements are useful by themselves, and can be used separately: when used together, they enable the robust inclusion of arbitrary fluorescence effects in modern uni-directional spectral MIS path tracers. Our extension of Hero wavelength sampling is generally useful, while our proposed technique for distance tracking in strongly asymmetric media is admittedly not very efficient. However, it makes the most of a rather difficult situation, and at least allows the inclusion of such media in uni-directional path tracers, albeit at comparatively high cost. Which is still an improvement since up to now, their inclusion was not really possible at all, due to the inability of conventional tracking schemes to generate sampling points in such volume materials.
journaltitleComputer Graphics Forum
titleHandling Fluorescence in a Uni-directional Spectral Path Tracer
CCS Concepts,•Computing methodologies → Rendering,Ray tracing

titleThe Advanced Rendering Toolkit

journaltitleJournal of the Optical Society of America (JOSA)
titleTheory for Off-Specular Reflection from Roughened Surfaces

* Entry 'Torrance67' (main.bib): Invalid format '22-01-2008' of date field 'urldate' - ignoring

Springer Vienna

booktitleRendering Techniques 2001
titleCombined Rendering of Polarization and Fluorescence Effects

Missing 'biblatex' package
The bibliography requires the 'biblatex' package.

journaltitleIEEE Transactions on Image Processing
titleSimultaneous Surface Reflectance and Fluorescence Spectra Estimation
Estimation;Photonics;Cameras;Optimization;Light sources;Fluorescence;Reflectance and fluorescence spectra recovery;multispectral and hyperspectral imaging;image color analysis;inverse problems

booktitle2008 IEEE Symposium on Interactive Ray Tracing
titleSimulation of fluorescent concentrators
Fluorescence;Absorption;Data models;Reflection;Probes;Monte Carlo methods;Computational modeling;I.3.3 [Computing Methodologies]: Computer Graphics—Picture/Image Generation;G.3 [Mathematics of Computing]: Probability and Statistics—Monte Carlo;J.2 [Computer Applications]: Physical Sciences and Engineering—Physics

The Eurographics Association

booktitleEurographics Symposium on Rendering
titleA Microfacet Model for Specular Fluorescent Surfaces and Fluorescent Volume Rendering using Quantum Dots

booktitleACM SIGGRAPH Courses
titlePhysically-Based Shading at Disney

IOP Publishing

abstractA method is described for measuring the spectral reflexion of fluorescent pigments for incident monochromatic light covering the ultra-violet and visible regions of the spectrum. The results are recorded in the form of a square table from which quantum efficiencies and spectral reflexion curves for sunlight or any illuminant of known energy distribution are calculated. Data are given for a red pigment and an optical bleach. Three curves only, showing the variation of tristimulus values with incident wavelength, are sufficient for the calculation of colour. The curves of tristimulus values may be derived from the reflexion curves or measured directly by a template colorimeter.
journaltitleBritish Journal of Applied Physics
titleSpectrophotometry of fluorescent pigments

Budmerice, Slovakia

Association for Computing Machinery

abstractReal-time rendering of participating media in nature presents a difficult problem. The reason is that realistic reproduction of such media requires a proper physical simulation in all cases. In our work we focus on real-time rendering of planetary atmospheres and large areas of water. We first formulate a physically-based model for simulation of light transport in these environments. This model accounts for all necessary light contributions — direct illumination, indirect illumination caused by the scattered light and interreflections between the planetary surface and the atmospheric volume, as well as reflections from the seabed. We adopt the precomputation scheme presented in the previous works to precompute the colours of the arbitrarily dense atmosphere and large-scale water surfaces into a set of lookup tables. All these computations are fully spectral, which increases the realism. Finally we utilize these tables in a GPU-based algorithm that is capable of rendering a whole planet with its atmosphere from all viewpoints above the planetary surface. This approach is capable to achieve hundreds of frames per second on today's graphics hardware.
booktitleProceedings of the 26th Spring Conference on Computer Graphics
seriesSCCG '10
titleReal-time spectral scattering in large-scale natural participating media
atmospheric and aquatic light scattering,natural phenomena,participating media

booktitleProceedings of Color Imaging Conference
titleEvaluation of Bispectral Spectrophotometry for Accurate Colorimetry of Printing Materials

Berlin, Heidelberg

Springer Berlin Heidelberg

booktitlePhotorealistic Rendering Techniques
titleA Model for Fluorescence and Phosphorescence

journaltitleACM Trans. Graph. (Proc. SIGGRAPH 2010)
titleAcquisition and analysis of bispectral bidirectional reflectance and reradiation distribution functions

Optica Publishing Group

abstractWe present an accurate and low-cost method for measuring fluorescence in materials. Our method outputs an estimate of the material’s Donaldson matrix, which is a commonly used two-dimensional spectral characterization of its fluorescence and reflectance properties. To find the estimate, only a few measurements of the material’s reflectance under a few illuminants are needed, which we demonstrate using low-cost optical components. Internally, our algorithm is based on representing each Donaldson matrix with a multivariate Gaussian mixture model and its diagonal with a bounded MESE (maximum entropy spectral estimate). It parametrizes and constrains the estimate in a robust and simple way, allowing the use of gradient-descent optimization. We evaluate our algorithm on a combination of real and synthetic data, and four examples of distinct optical components. We reach significantly lower errors than the current state of the art on the exact same inputs, our estimates do not suffer from artifacts such as oscillations of the spectra, and they are stable and robust.
journaltitleOpt. Express
titleAffordable method for measuring fluorescence using Gaussian distributions and bounded MESE
Fluorescence; Illuminants; Inverse design; Light sources; Optical components; Remote sensing

Wiley Online Library

booktitleComputer Graphics Forum
titleBidirectional rendering of vector light transport

Wiley Online Library

booktitleComputer Graphics Forum
titleSpectral mollification for bidirectional fluorescence

booktitleProceedings of the Eurographics 2018 Workshop on Material Appearance Modeling
titleA simple diffuse fluorescent BBRRDF model

abstractAbstract Physically based spectral rendering has become increasingly important in recent years. However, asset textures in such systems are usually still drawn or acquired as RGB tristimulus values. While a number of RGB to spectrum upsampling techniques are available, none of them support upsampling of all colours in the full spectral locus, as it is intrinsically bigger than the gamut of physically valid reflectance spectra. But with display technology moving to increasingly wider gamuts, the ability to achieve highly saturated colours becomes an increasingly important feature. Real materials usually exhibit smooth reflectance spectra, while computationally generated spectra become more blocky as they represent increasingly bright and saturated colours. In print media, plastic or textile design, fluorescent dyes are added to extend the boundaries of the gamut of reflectance spectra. We follow the same approach for rendering: we provide a method which, given an input RGB tristimulus value, automatically provides a mixture of a regular, smooth reflectance spectrum plus a fluorescent part. For highly saturated input colours, the combination yields an improved reconstruction compared to what would be possible relying on a reflectance spectrum alone. At the core of our technique is a simple parametric spectral model for reflectance, excitation, and emission that allows for compact storage and is compatible with texture mapping. The model can then be used as a fluorescent diffuse component in an existing more complex BRDF model. We also provide importance sampling routines for practical application in a path tracer.
journaltitleComputer Graphics Forum
titleWide Gamut Spectral Upsampling with Fluorescence

Virtual Event, USA

Association for Computing Machinery

abstractWe present a visual effects production workflow for using spectral sensitivity data of DSLR and digital cinema cameras to reconstruct the spectral energy distribution of a given live-action scene and perform rendering in physical units. We can then create images that respect the real-world settings of the cinema camera, properly accounting for white balance, exposure, and the characteristics of the sensor.
booktitleACM SIGGRAPH 2020 Talks
seriesSIGGRAPH '20
titlePhysLight: An End-to-End Pipeline for Scene-Referred Lighting
HDRI,image based lighting,lighting,path tracing,rendering,spectral rendering

abstractAbstract We present two separate improvements to the handling of fluorescence effects in modern uni-directional spectral rendering systems. The first is the formulation of a new distance tracking scheme for fluorescent volume materials which exhibit a pronounced wavelength asymmetry. Such volumetric materials are an important and not uncommon corner case of wavelength-shifting media behaviour, and have not been addressed so far in rendering literature. The second one is that we introduce an extension of Hero wavelength sampling which can handle fluorescence events, both on surfaces, and in volumes. Both improvements are useful by themselves, and can be used separately: when used together, they enable the robust inclusion of arbitrary fluorescence effects in modern uni-directional spectral MIS path tracers. Our extension of Hero wavelength sampling is generally useful, while our proposed technique for distance tracking in strongly asymmetric media is admittedly not very efficient. However, it makes the most of a rather difficult situation, and at least allows the inclusion of such media in uni-directional path tracers, albeit at comparatively high cost. Which is still an improvement since up to now, their inclusion was not really possible at all, due to the inability of conventional tracking schemes to generate sampling points in such volume materials.
journaltitleComputer Graphics Forum
titleHandling Fluorescence in a Uni-directional Spectral Path Tracer
CCS Concepts,•Computing methodologies → Rendering,Ray tracing

titleThe Advanced Rendering Toolkit

journaltitleJournal of the Optical Society of America (JOSA)
titleTheory for Off-Specular Reflection from Roughened Surfaces

* Entry 'Torrance67' (main.bib): Invalid format '22-01-2008' of date field 'urldate' - ignoring

Springer Vienna

booktitleRendering Techniques 2001
titleCombined Rendering of Polarization and Fluorescence Effects