Performance Modeling of Earth Resources Remote Sensors

A technique i s presented for constructing a mathematical model of an Earth resources remote sensor. The technique combines established models of electronic and optical components with formulated models of scan and vibration effects, and it includes a model of the radiation effects of the Earth’s atmosphere. The resulting composite model is useful for predicting in-flight sensor performance, and a descriptive set of performance parameters is derived in terms of the model. A method is outlined for validating the model for each sensor of interest. The validation for one airborne infrared scanning system is accomplished in part by a satisfactory comparison of predicted response with laboratory data for that sensor. Introduction Multispectral scanning systems are used to gather remotely sensed radiometric data for a wide variety of applications, e.g., pollution monitoring, geological and urban surveying, and crop classification [ 1 31. The measure of performance of such a system can be expressed in terms of its image-resolving capability and its radiometric accuracy. The former measures the system’s capability to discern a scene from imposed noise, and the latter expresses the accuracy to which the system measures the radiant power from the scene. These performance parameters are critical in assessing the usefulness of a particular system for a particular remote sensing program, and they are instrumental in determining the design requirements of an advanced sensor system. The desired performance parameters are generally not measured directly, and they must be inferred by mathematical analysis from more direct laboratory measurements and manufacturer’s specifications. Such a performance evaluation of existing systems or the development of design requirements for an advanced system can be carried out in a systematic way by constructing a mathematical model of the sensor system, component by component, where each component model is parametrized by performance values obtainable from laboratory measurements or design specifications. The purpose of this paper is to develop a linear systems approach to mathematically model a typical remote sensor configuration and to predict system Performance characteristics. This approach, which treats the remote sensor as a communication system, has been used extensively to model electronic systems, as described by Papoulis [4]. The theory has been extended to optical imaging systems by Goodman [ 5 ] . Thus, this paper applies the combined optical and electronic systems theories to provide an end-to-end model of the sensor system. In addition to the sensor component characteristics, atmospheric effects are considered. The discussion is opened with a description of the sensor configuration to be modeled. Next, the mathematical models of the atmosphere and individual system components are developed, and these models are combined to provide the total system model. The components are assumed to be linear, invariant systems, and their models are expressed in terms of transfer functions. The prediction of overall system capability is derived in terms of the transfer functions and system noise characteristics. Finally, the procedure for validating the model with test data is outlined and applied to available laboratory tests for an infrared sensor used in the NASA Earth resources aircraft program. Typical sensor system The sensor system considered measures, in a number of spectral bands, the solar radiation reflected from or the thermal radiation emitted by the ground. The general spectral characteristics of the received radiation are illustrated in Fig. l for an orbital sensor viewing 300-K ground with 20 percent reflectivity [6]. These characteristics are representative of airborne sensors as well. Typically, a number of narrow spectral bands are utilized in the 0.4 pm to 2 pm wavelength region (from ultraviolet, through visible, to near infrared, respectively), and one or two bands are defined for the thermal infrared region from 8 pm to 14 pm, as shown in Fig. 1 . 29 JANUARY 1976 REMOTE SENSOR MODELING