A framework for the Analysis and Evaluation of Optical Imaging Systems with Arbitrary Response Functions

Abstract

The scientific applications and engineering aspects of multispectral and hyperspectral imaging systems have been studied extensively. The traditional geometric spectral imaging system model is specifically developed aiming at spectral sensors with spectrally non-overlapping bands. Spectral imaging systems with overlapping bands also exist. For example, the quantum-dot infrared photodetectors (QDIPs) for midwave- and longwave-infrared (IR) imaging systems exhibit highly overlapping spectral responses tunable through the bias voltages applied. This makes it possible to build spectrally tunable imaging system in IR range based on single QDIP. Furthermore, the QDIP based system can be operated as being adaptive to scenes. Other optical imaging systems like the human eye and some polarimetric sensing systems also have overlapping bands. To analyze such sensors, a functional analysis-based framework is provided in this dissertation. The framework starts from the mathematical description of the interaction between sensor and the radiation from scene reaching it. A geometric model of the spectral imaging process is provided based on the framework. The spectral response functions and the scene spectra are considered as vectors inside an 1-dimensional spectral space. The spectral imaging process is abstracted to represent a projection of scene spectrum onto sensor. The projected spectrum, which is the least-square error reconstruction of the scene vectors, contains the useful information for image processing. Spectral sensors with arbitrary spectral response functions are can be analyzed with this model. The framework leads directly to an image pre-processing algorithm to remove the data correlation between bands. Further discussion shows that this model can also serve the purpose of sensor evaluation, and thus facilitates comparison between different sensors. The spectral shapes and the Signal-to-Noise Ratios (SNR) of different bands are seen to influence the sensor's imaging ability in different manners, which are discussed in detail. With the newly defined SNR in spectral space, we can quantitatively characterize the photodetector noise of a spectral sensor with overlapping bands. The idea of adaptive imaging with QDIP based sensor is proposed and illustrated.