We describe several methods to extend security techniques based on optical processing to work under broadband illumination. The key question of our procedures is the design of dispersion-compensated optical processors by combining a small number of diffractive and refractive lenses. Our optical configurations provide, in a first-order approximation, the Fraunhofer diffraction pattern of the input signal in a single plane and with the same scale for all the wavelengths of the incident light. In this way, our achromatic hybrid systems allow us to reconstruct color holograms with white light. These achromatic hybrid (diffractive-refractive) systems are applied, in a second stage, for implementing color processing operations with white light, such as color pattern recognition. In this direction, we design also a technique to encrypt color input objects into computer generated color holograms, which are decrypted optically with an achromatic joint transform correlator architecture under white-light illumination. Finally, we describe a totally-incoherent optical processor that is able to perform color processing operations under natural illumination (both spatially and temporally incoherent). This system is applied to perform color pattern recognition and optical encryption operations under natural light. Numerical and experimental results are shown.