In a previous work [Appl. Opt.44, 5688 (2005)] we found the optimum sensors for a planned multispectral system for measuring skylight in the presence of noise by adapting a linear spectral recovery algorithm proposed by Maloney and Wandell [J. Opt. Soc. Am. A3, 29 (1986)]. Here we continue along these lines by simulating the responses of three to five Gaussian sensors and recovering spectral information from noise-affected sensor data by trying out four different estimation algorithms, three different sizes for the training set of spectra, and various linear bases. We attempt to find the optimum combination of sensors, recovery method, linear basis, and matrix size to recover the best skylight spectral power distributions from colorimetric and spectral (in the visible range) points of view. We show how all these parameters play an important role in the practical design of a real multispectral system and how to obtain several relevant conclusions from simulating the behavior of sensors in the presence of noise.

In earlier work [J. Opt. Soc. Am. A 21, 13-23 (2004)], we showed that a combination of linear models and optimum Gaussian sensors obtained by an exhaustive search can recover daylight spectra reliably from broadband sensor data. Thus our algorithm and sensors could be used to design an accurate, relatively inexpensive system for spectral imaging of daylight. Here we improve our simulation of the multispectral system by (1) considering the different kinds of noise inherent in electronic devices such as change-coupled devices (CCDs) or complementary metal-oxide semiconductors (CMOS) and (2) extending our research to a different kind of natural illumination, skylight. Because exhaustive searches are expensive computationally, here we switch to a simulated annealing algorithm to define the optimum sensors for recovering skylight spectra. The annealing algorithm requires us to minimize a single cost function, and so we develop one that calculates both the spectral and colorimetric similarity of any pair of skylight spectra. We show that the simulated annealing algorithm yields results similar to the exhaustive search but with much less computational effort. Our technique lets us study the properties of optimum sensors in the presence of noise, one side effect of which is that adding more sensors may not improve the spectral recovery.

In a previous work [J. Opt. Soc. Am. A 24, 942-956 (2007)] we showed how to design an optimum multispectral system aimed at spectral recovery of skylight. Since high-resolution multispectral images of skylight could be interesting for many scientific disciplines, here we also propose a nonoptimum but much cheaper and faster approach to achieve this goal by using a trichromatic RGB charge-coupled device (CCD) digital camera. The camera is attached to a fish-eye lens, hence permitting us to obtain a spectrum of every point of the skydome corresponding to each pixel of the image. In this work we show how to apply multispectral techniques to the sensors' responses of a common trichromatic camera in order to obtain skylight spectra from them. This spectral information is accurate enough to estimate experimental values of some climate parameters or to be used in algorithms for automatic cloud detection, among many other possible scientific applications.

A new method is presented for retrieval of the aerosol and cloud optical depth using a CCD camera equipped with a fish-eye lens (all-sky imager system). In a first step, the proposed method retrieves the spectral radiance from sky images acquired by the all-sky imager system using a linear pseudoinverse algorithm. Then, the aerosol or cloud optical depth at 500 nm is obtained as that which minimizes the residuals between the zenith spectral radiance retrieved from the sky images and that estimated by the radiative transfer code. The method is tested under extreme situations including the presence of nonspherical aerosol particles. The comparison of optical depths derived from the all-sky imager with those retrieved with a sunphotometer operated side by side shows differences similar to the nominal error claimed in the aerosol optical depth retrievals from sunphotometer networks.

In a previous work [J. Opt. Soc. Am. A24, 942 (2007)JOAOD60740-323210.1364/JOSAA.24.000942] we made a complete theoretical and computational study of the influence of several parameters on the behavior of a planned multispectral system for imaging skylight, including the number of sensors and the spectral estimation algorithm. Here we follow up this study by using all the information obtained in the computational simulations to implement a real multispectral imaging system based on a monochrome CCD camera and a liquid-crystal tunable filter (LCTF). We were able to construct the optimum Gaussian sensors found in the simulations by adjusting the exposure times of some of the transmittance modes of the LCTF, hence obtaining really accurate spectral estimations of skylight with only a few optimum sensors.