Bayesian deconvolution method applied to experimental bidirectional transmittance distribution functions

Abstract

Optical simulations are a common tool in the development of luminaires for lighting applications. The reliability of the virtual prototype is strongly dependent on the accuracy of the input data such as the emission characteristics of the light source and the scattering properties of the optical components (reflectors, filters and diffusers). These scattering properties are characterized by the bidirectional scatter distribution function (BSDF). Experimental determination of the BSDF of the materials is however very sensitive to the characteristics of the measuring instrument, i.e. the dimensions of the illumination spot, the detector aperture, etc. These instrumental characteristics are reflected in the instrument function. In order to eliminate the influence of the instrument function the use of a Bayesian deconvolution technique is proposed. A suitable stopping rule for the iterative deconvolution algorithm is presented. The deconvolution method is validated using Monte Carlo ray tracing software by simulating a BSDF measurement instrument and a virtual sample with a known bidirectional transmittance distribution function (BTDF). The Bayesian deconvolution technique is applied to experimental BTDF data of holographic diffusers, which exhibit a symmetrical angular broadening under normal incident irradiation. In addition, the effect of applying deconvolved experimental BTDF data on simulations of luminance maps is illustrated.

A new approach to bandpass correction in spectrometer measurements using the Richardson-Lucy method

“…This premature stopping then acts as a kind of regularization. Several approaches have been proposed to determine an automatic stopping criterion, see, e.g., [16][17]. From our investigations, the following criterion, which is similar to the so-called L-curve method in classical regularization, proved to work well in our applications.…”

“…Another approach is to carry out a fixed number of iterations and determine the optimal solution based on 14005-p.2 some criterion. In [16] the authors propose the weighted error of the estimated measurement as the criterion for the estimation quality. As in [5] we propose the application of the change in the estimated spectrum during one iteration as a criterion.…”

Theoretical evaluation of the impact of finite intervals in the measurement of the bidirectional reflectance distribution function

“…However, if a high error is expected in the measurement, as for low aspecular angles in highly glossy specimens, some deconvolution algorithm needs to be applied to estimate b and h 0 from the deconvolved BRDF. 14,15 In these cases, equation 18is recommended to be used to characterize the limitations of the instrument to measure BRDFs with high angular dependence, and to redesign it if required.…”

Automatic measurement of spectral bidirectional transmittance distribution function on translucent optical materials

“…In 2009 to 2011, Finck, Lequime and Zerra designed a serial of light scattering measurement facilities for a comprehensive research of optical coatings, which reveal perfect measurement abilities, only the operation is a bit complicated [16][17][18]. In 2013, Jan Audenaert applied the Bayesian deconvolution technique to experimental BTDF data of holographic diffusers, which exhibit a symmetrical angular broadening under normal incident irradiation, but this study was limited to symmetrical BTDF and normal incident light [19]. In 2014, Leloup designed an alternative goniometric measurement system for measuring the photometric BSDF in full 3D space, while the measurement error was not given [20].…”