Spectral Image Formation Process

Abstract

In this chapter, we describe the image formation process resulting from the transfer of light energy with different wavelengths from the source to the spectral imaging sensor. To commence the chapter, we provide preliminary concepts in radiometry and photogrammetry concerning foreshortening, solid angle, radiance, irradiance and the bidirectional reflectance distribution function (BRDF). These concepts are later employed to quantify the amount of energy transmitted, reflected, absorbed or refracted when light interacts with object surfaces. With these ingredients, we derive a general formula of the wavelength-dependent image irradiance arriving at the imaging sensor as a result of reflection and scattering from surfaces. The formula takes into account the light source radiance, the surface reflectance, the reflection geometry and the camera optics. Here, we note that the spectral irradiance of images is a physical quantity independent of any colour sensing device. We next derive a colour rendering equation of the image irradiance with the spectral sensitivity function of a colour sensor, and we demonstrate the visualisation and rendering of spectral images through a number of examples involving both synthetic and real-world data.