Trichromatic Reflectance Capture Using a Tunable Light Source: Setup, Characterization and Reflectance Estimation

A research project is underway to develop a gonio imager particularly dedicated to sample the Bidirectional Reflectance Distribution Function (BRDF) of materials and material compositions employed and created by multimaterial 3D printers. It comprises an almost colorimetric RGB camera and a spectrally tunable light source. In this paper, we investigate an important part of this system, particularly the approach to estimate reflectances from RGB values acquired under multiple illuminants. We first characterize the system by estimating the spectral sensitivities of the camera. Then, we use the sensitivities, a set of illuminants produced by the tunable light source and the corresponding sensor responses to estimate reflectances. For evaluating this approach, we measure the Neugebauer primary reflectances of a polyjet printer employing highly translucent photo polymer printing materials colored in cyan, magenta, yellow and white. Spectral and colorimetric deviations to spectroradiometric comparison measurements (average 0.67 CIEDE2000 units 0.0286 spectral RMS) are within the inter instrument variability of hand held spectrophotometers used in graphic arts for prints on paper.  Today's high resolution 3D printers particularly polyjetting printers can combine multiple colored materials on a droplet basis in a single object enabling the reproduction of various appearance attributes such as color, gloss or goniochromatic effects. This is possible by arranging printing materials in halftone patterns to create various color shades, printing varnish halftones to create multiple gloss shades or by printing microfacets on top of the surface to produce anisotrpopic reflectance. The presented work is motivated by the challenging task to spectrally modeling such printers particularly to accurately measure the reflectances of printed samples used to develop and to fit spectral printer models. Even if we consider the simple case of flat printed samples and are interested only in a 45/0 measurement geometry, measurements made by spectrophotometers from graphic arts are biased towards lower reflectances because of the high translucency of the used photo polymeric printing materials as explained in detail in  In this reference, a measurement methodology is presented to obtain CIELAB values employing an almost colorimetric camera, highly uniform broadband illumination simulating CIED50, flat fielding to account for inhomogeneous light intensities and a polynomial approach to map RGB values to CIEXYZ. As long as the number of printing materials is low, these measurements can be used in a full empirical printer model (regular sampling of the colorant space and interpolating intermediate colors) e.g. to create ICC profiles. Figure 1 shows a target to colorimetrically model a CMYW 3D printer with 512 patches. If the number of materials increases, full empirical models are impractical because the number of measurements increases exponentially with the number of materials. In this case, physical models, e.g. based on the radiative transfer theory, or partly empirical models are necessary requiring accurate bidirectional reflectance measurements of selected print samples. For this, a spectral acquisition system is required, which allows us to capture reflectance data for the whole printed target employing arbitrary bidirectional measurement geometries. Furthermore, the target must be illuminated very uniformly, because flat fielding cannot correct errors caused by subsurface light transport between the target's patches. We are in the process of developing a gonio imager to sample the Bidirectional Reflectance Distribution Function (BRDF) of printed samples. Instead of using a spectral camera, it contains a commercially available spectrally tunable light source and an almost colorimetric RGB camera. The light source employs 22 different LEDs (20 spectrally narrowband LEDs covering the whole visible wavelength range and two white light LEDs) and an internal spectroradiometer ensuring a stable spectral power distribution (SPD) Furthermore, the actual SPD of the light source during the capturing process is recorded and is available for reflectance estimation. Capturing a white reference for canceling out the illuminant is not required in this setup. Both the camera and the tunable light source can be controlled by an Application Programming Interface (API) allowing a fully automatic multichannel acquisition. In this way, both the intensity of the illuminant or the exposure time can be adjusted to capture High Dynamic Range (HDR) images, which is necessary to measure the specular lobe. Another interesting property is the combination of an almost colorimetric camera with a spectrally tunable light source: Accurate CIEXYZ data of samples for a particular illuminant can be captured in a single shot for each geometry by simply adjusting the tunable light source to the desired SPD. To reduce measurement time, a sparse spectral reflectance sampling and a dense CIEXYZ sampling can be performed. A dense spectral representation of the BRDF can then be computed from these data subject to a high colorimetric accuracy for the considered illuminant. A similar strategy was proposed in the scope of 2D spectral imaging [16, 17] In this work, we are investigating the spectral accuracy of this setup. This includes measuring the spectral sensitivities of the camera and estimating reflectance from multi illuminant RGB acquisitions. Since the mechanical setup is still under construc(c)2016 Society for Imaging Science and Technology IS&T International Symposium on Electronic Imaging 2016 Measuring, Modeling, and Reproducing Material Appearance 2016 MMRMA 355.1 tion, all measurements conducted in this work are restricted to the 0/45 geometry.  3D printed target used to characterize a printing system. Related Work For the sake of simplicity, we use a vector representation of spectra and sensitivities, i.e. each wavelength dependent quantity X(l is equidistantly sampled in the sensitivity range O of the camera resulting in x (X(l1) ,X(ln) where [l1,ln] O and i, j n li+1 li l j+1 l j. Assuming linearity, the m dimensional column vector of camera responses c is modeled as follows: