A Frequency Domain Model for the Spatial Fixed-pattern Noise in Infrared Focal Plane Arrays Osvaldo J. Medina, Jorge E. Pezoa, and Sergio N. Torres Center for Optics and Photonics and Departamento de Ingenier´ ıa El´ ectrica Universidad de Concepci´on, Concepci´on, Chile ABSTRACT The multiplicative and additive components of the fixed-pattern noise (FPN) in infrared (IR) focal plane arrays (FPAs) are typically modeled as time-stationary, spatially unstructured random processes. Even though the latter assumption is convenient, it is also inaccurate due to FPN is indeed observed as a spatial pattern, with random intensity values, superimposed over the true images. In this paper, the spatial structure in both the multiplicative and the additive components of the FPN has been modeled in the frequency domain. The key observation in the proposed models is that regular spatial patterns manifest themselves as narrowband components in the magnitude spectrum of an image. Thus, the spatial structure of FPN can be abstracted in a straightforward manner by approximating the spectral response of the FPN. Moreover, the random intensity of the FPN has been also modeled by matching the empirically estimated distributions of the intensity values of both multiplicative and additive components of the FPN. Experimental characterization of FPN has been conducted using black-body radiator sources, and the theoretical as well as practical applicability of the proposed models has been illustrated by both synthesizing FPN from three different IR cameras and by proposing a simple yet effective metric to assess the amount of FPN in FPA-based cameras. Keywords: Infrared focal plane arrays, fixed pattern noise, spatial noise, spatially correlated noise 1. INTRODUCTION A focal plane array (FPA) is an ensemble of photodetectors constructed and packed so that they should respond, at least theoretically, in the very same manner to the incident infrared (IR) radiance. In particular, if a flat object is placed in front of the array, the ideal response of all the photosensors should render a flat image. In practice, however, the photodetectors in a FPA do not respond equally to an IR input, thereby producing a particular type of noise termed as fixed-pattern noise (FPN). In the technical literature, the FPN is attributed to different sources, being some of them manufacturing mismatches in the responsivity of the photodetectors forming the FPA, dark current variations across the FPA, and dark current generation at different electronic sources. 1, 2, 3 In a more practical matter, the FPN introduces major problems to the imaging systems because the quality of the acquired images is highly degraded and the temperature resolution of the entire system may be compromised. Moreover, the FPN is particularly problematic in staring arrays because it becomes larger than the temporal noise. 1 The FPN is a quasy-stationary, spatially structured kind of noise, which is observed in raw images either as a grid-like pattern or as a striping pattern laid on top of the true scene. Researchers have traditionally modeled the FPN as spatially unstructured and time-stationary. The assumption about the stationary behavior of the FPN is not restrictive at all, and more important, it is widely accepted in the literature because it is known that the FPN may change only after several minutes of continuous operation of the camera. However, we claim that spatially unstructured models for FPN are not appropriate because spatial patterns, such as grids and stripes, are indeed observed in the raw scenes acquired by FPA-based IR cameras. Moreover, since the FPN must be filtered out from the raw images before they can be used in final applications, it becomes mandatory to develop accurate FPN models capable of accurately compensate for the spatial noise. Furthermore, this work is motivated by the our conjecture that by properly modeling the spatial structure of the FPN, novel representations for IR-FPAs, Mail address: Casilla 160-C, Concepci´ on, Chile E-mail: osvaldomedina,jpezoa,sertorre@udec.cl, Telephone: +56-41-220 3333