Infrared Focal Plane Arrays (FPA) are increasingly used to measure multi- or hyperspectral images. Therefore, it is crucial to control and modelize their spectral response. The purpose of this paper is to propose a modeling approach, adjustable by experimental data, and applicable to the main cooled detector technologies. A physical model is presented, taking into account various optogeometrical properties of the detector, such as disparities of the pixels cut-off wavelengths. It describes the optical absorption phenomenon inside the pixel, by considering it as a stack of optical bulk layers. Then, an analytical model is proposed, based on the interference phenomenon occurring into the structure. This model considers only the three major waves interfering. It represents a good approximation of the physical model and a complementary understanding of the optical process inside the structure. This approach is applied to classical cooled FPAs as well as to specific instruments such as Microspoc (MICRO SPectrometer On Chip), a concept of miniaturized infrared Fourier transform spectrometer, integrated on a classical Mercury-Cadmium-Telluride FPA, and cooled by a cryostat.