Bidirectional reflectance measurements over a micrometric surface area using a goniospectrophotometer

The increasing use of a spatially varying bidirectional reflectance distribution function (svBRDF) to describe the appearance of an object raises the important question of how BRDF values change when measured on a small scale. For this reason, we present a new goniospectrophotometer with the ability to measure the BRDF at the micrometer scale (μBRDF). The instrument produces BRDF measurements with a measurement surface diameter of 31 µm. This device is designed to aid in the extension of the BRDF metrological scale from centimeter to micrometer size. We support the credibility of our μBRDF measurements using a specially made test sample with uniform diffuse white dots on a uniform black background, measuring its bidirectional reflectance in one geometrical configuration at many spatial locations. This sample can easily be modeled using a few unknown parameters. The agreement between our measurements and the model demonstrates the credibility of the measurement technique.

Empirical BRDF model for goniochromatic materials and soft proofing with reflective inks

The commonly used analytic bidirectional reflectance distribution functions (BRDFs) do not model goniochromatism, that is, angle-dependent material color. The material color is usually defined by a diffuse reflectance spectrum or RGB vector and a specular part based on a spectral complex index of refraction. Extension of the commonly used BRDFs based on wave theory can help model goniochromatism, but this comes at the cost of significant added model complexity. We measured the goniochromatism of structual color pigments used for additive color printing and found that we can fit the observed spectral angular dependence of the bidirectional reflectance using a simple modification of the standard microfacet BRDF model. All we need to describe the goniochromatism is an empirically-based spectral parameter, which we use in our model together with a specular reflectance spectrum instead of the spectral complex index of refraction. We demonstrate the ability of our model to fit the measured reflectance of red, green, and blue commercial structural color pigments. Our BRDF model enables straightforward implementation of a shader for interactive preview of 3D objects with printed spatially and angularly varying texture.

Surface Roughness and Grain Size Variation When 3D Printing Polyamide 11 Parts Using Selective Laser Sintering

Selective laser sintering (SLS) is a well-established technology that is used for additive manufacturing. Significant efforts have been made to improve SLS by optimizing the powder deposition, laser beam parameters, and temperature settings. The purpose is to ensure homogeneous sintering and prevent geometric and appearance inaccuracies in the manufactured objects. We evaluated the differences in the surface roughness and grain size of curved objects manufactured by using upcoming SLS technology that features two CO laser sources. Our analysis was carried out on polyamide 11 (PA11), which is a sustainable biobased polymer that has been gaining popularity due to its high-performance properties: its low melting point, high viscosity, and excellent mechanical properties. By using a Taguchi experimental design and analysis of variance (ANOVA), we examined the influence on the surface roughness and grain size of the build setup, the presence of thin walls, and the position of the sample on the powder bed. We found significant differences in some surface roughness and grain size measurements when these parameters were changed.

Surface Reconstruction from Structured Light Images Using Differentiable Rendering

When 3D scanning objects, the objective is usually to obtain a continuous surface. However, most surface scanning methods, such as structured light scanning, yield a point cloud. Obtaining a continuous surface from a point cloud requires a subsequent surface reconstruction step, which is directly affected by any error from the computation of the point cloud. In this work, we propose a one-step approach in which we compute the surface directly from structured light images. Our method minimizes the least-squares error between photographs and renderings of a triangle mesh, where the vertex positions of the mesh are the parameters of the minimization problem. To ensure fast iterations during optimization, we use differentiable rendering, which computes images and gradients in a single pass. We present simulation experiments demonstrating that our method for computing a triangle mesh has several advantages over approaches that rely on an intermediate point cloud. Our method can produce accurate reconstructions when initializing the optimization from a sphere. We also show that our method is good at reconstructing sharp edges and that it is robust with respect to image noise. In addition, our method can improve the output from other reconstruction algorithms if we use these for initialization.

Fundamental scattering quantities for the determination of reflectance and transmittance

The bidirectional reflectance distribution function (BRDF) and the bidirectional scattering - surface reflectance distribution function (BSSRDF), which relate radiance at the surface to irradiance and radiant flux, respectively, are regarded as the most fundamental scattering quantities used to determine the reflectance of objects. However, for materials where the optical radiation is transmitted under the surface, this radiance depends not only on irradiance and radiant flux, but also on the size of the irradiated area of the surface. This article provides insight into such dependence under the special condition in which the radiance is evaluated within the irradiated area and, consequently, is produced by both the insurface reflection and the subsurface scattering, in contrast to the situation in which the radiance is evaluated at non-irradiated areas and only subsurface scattering contributes. By explicitly considering both contributions, two other scattering quantities are defined: one that accounts exclusively for the insurface reflection and the other that accounts for subsurface scattering. In this regard, these quantities might be considered more fundamental than the BRDF and the BSSRDF, although they are coincident with these two functions apart from the above-mentioned special condition and for materials with negligible subsurface scattering. In this work, the relevance of the proposed scattering quantities is supported by experimental data, practical considerations are given for measuring them, and their relation to the bidirectional transmittance distribution function (BTDF) is discussed.

Alignment of rendered images with photographs for testing appearance models

We propose a method for direct comparison of rendered images with a corresponding photograph in order to analyze the optical properties of physical objects and test the appropriateness of appearance models. To this end, we provide a practical method for aligning a known object and a point-like light source with the configuration observed in a photograph. Our method is based on projective transformation of object edges and silhouette matching in the image plane. To improve the similarity between rendered and photographed objects, we introduce models for spatially varying roughness and a model where the distribution of light transmitted by a rough surface influences direction-dependent subsurface scattering. Our goal is to support development toward progressive refinement of appearance models through quantitative validation.

Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave

In absorbing media, electromagnetic plane waves are most often inhomogeneous. Existing solutions for the scattering of an inhomogeneous plane wave by a spherical particle provide no explicit expressions for the scattering components. In addition, current analytical solutions require evaluation of the complex hypergeometric function F₁2 for every term of a series expansion. In this work, I develop a simpler solution based on associated Legendre functions with argument zero. It is similar to the solution for homogeneous plane waves but with new explicit expressions for the angular dependency of the far-field scattering components, that is, the phase function. I include recurrence formulas for practical evaluation and provide numerical examples to evaluate how well the new expressions match previous work in some limiting cases. The predicted difference in the scattering phase function due to inhomogeneity is not negligible for light entering an absorbing medium at an oblique angle. The presented theory could thus be useful for predicting scattering behavior in dye-based random lasing and in solar cell absorption enhancement.

Scene reassembly after multimodal digitization and pipeline evaluation using photorealistic rendering

Transparent objects require acquisition modalities that are very different from the ones used for objects with more diffuse reflectance properties. Digitizing a scene where objects must be acquired with different modalities requires scene reassembly after reconstruction of the object surfaces. This reassembly of a scene that was picked apart for scanning seems unexplored. We contribute with a multimodal digitization pipeline for scenes that require this step of reassembly. Our pipeline includes measurement of bidirectional reflectance distribution functions and high dynamic range imaging of the lighting environment. This enables pixelwise comparison of photographs of the real scene with renderings of the digital version of the scene. Such quantitative evaluation is useful for verifying acquired material appearance and reconstructed surface geometry, which is an important aspect of digital content creation. It is also useful for identifying and improving issues in the different steps of the pipeline. In this work, we use it to improve reconstruction, apply analysis by synthesis to estimate optical properties, and to develop our method for scene reassembly.

Noninvasive particle sizing using camera-based diffuse reflectance spectroscopy

Diffuse reflectance measurements are useful for noninvasive inspection of optical properties such as reduced scattering and absorption coefficients. Spectroscopic analysis of these optical properties can be used for particle sizing. Systems based on optical fiber probes are commonly employed, but their low spatial resolution limits their validity ranges for the coefficients. To cover a wider range of coefficients, we use camera-based spectroscopic oblique incidence reflectometry. We develop a noninvasive technique for acquisition of apparent particle size distributions based on this approach. Our technique is validated using stable oil-in-water emulsions with a wide range of known particle size distributions. We also measure the apparent particle size distributions of complex dairy products. These results show that our tool, in contrast to those based on fiber probes, can deal with a range of optical properties wide enough to track apparent particle size distributions in a typical industrial process.

Importance sampling the Rayleigh phase function

Rayleigh scattering is used frequently in Monte Carlo simulation of multiple scattering. The Rayleigh phase function is quite simple, and one might expect that it should be simple to importance sample it efficiently. However, there seems to be no one good way of sampling it in the literature. This paper provides the details of several different techniques for importance sampling the Rayleigh phase function, and it includes a comparison of their performance as well as hints toward efficient implementation.

Empirical formula for the refractive index of freezing brine

The refractive index of freezing brine is important in order to, for example, estimate oceanic scattering as sea ice develops. Previously, no simple continuous expression was available for estimating the refractive index of brine at subzero temperatures. I show that extrapolation of the empirical formula for the refractive index of seawater by Quan and Fry [Appl. Opt.34, 3477 (1995)APOPAI0003-693510.1364/AO.34.003477] provides a good fit to the refractive index of freezing brine for temperatures above -24 degrees C and salinities below 180 per thousand.