DOI: https://doi.org/10.20535/1810-0546.2018.5.140106

### Influence of Angles of Shighting and the Earth's Surface Curvature on the Spatial Resolution of the Space Electro-Optical Viewing System

#### Abstract

**Background.** One of the key differences between the aeronautical and space optical-electronic viewing systems (OEVS) of remote sensing of the Earth is the height from which the Earth's surface picture is taken. The difference between the heights of aircraft and spacecraft devises can reach several orders of magnitude, so if for aeronautical OEVS you can calculate spatial division on a plane, then for space OEVS this is critical and it is necessary to additionally consider the Earth's surface curvature, especially for angles of sighting other than zero.

**Objective. **The aim of the paper is to develop physico-mathematical model for determining the resolution of the OEVS, which considers the Earth's surface curvature, the orbital height and location of the spacecraft position for different angles of shighting.

**Methods.** In the basis of physical and mathematical model is proposed to use a biaxial ellipsoid as an approximation of the Earth shape to determine its surface curvature and Sun-synchronous orbit trajectory.

**Results. **Practical results of the calculations prove that the Earth's surface curvature for space OEVS significantly influence the spatial resolution and differs from the results obtained by physical and mathematical model in which the spatial resolution is determined on a flat surface. The results of the design show, that when deflected at the angles of shighting, it is necessary to consider the additional deflection in calculations, which it increases, when distance increases for the nadir. At maximum angles of sight, pitch and roll to ±35º, i.e. when the OEVS is deflected at 44.7º from the nadir, the additional deflection is 6.3º, which significantly influences the determination of spatial resolution.

**Conclusions.**The analysis of the proposed the physico-mathematical model of the OEVS showed that the Earth's surface curvature orbit trajectory and the location of the spacecraft, unlike the height, influence the pixels’ projection shape deformation. In this case, the values of the projection tilt angles of the rows and columns of the matrix detector relative to the flight direction change nonlinearly, which adversely influence the system modulation transfer function and require the calibration for some parameters during the flight depending on the angles of shighting and location coordinates.

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R. Sandau,* **Digital** **Airborne** **Camera** **Introduction** **and** **Technology*. Springer, 2010, 343 p. doi: 10.1007/978-1-4020-8878-0

M.A. Gomarasca, *Basics of Geomatics*. Springer, 2009, 656 p. doi: 10.1007/978-1-4020-9014-1

V.V. Belous *et al.*, *Remote Sensing and the Photogrammetry Basics*. Kyiv, Ukraine: Publishing Center “Kyiv University”, 2011, 368 p.

C. Pohl and J.L. van Genderen, *Remote Sensing Image Fusion: A Practical Guide*. CRC Press, 2016, 288 p.

G. Moser and J. Zerubia, *Mathematical Models for Remote Sensing Image Processing**.** Models and Methods for the Analysis of 2D Satellite and Aerial Images*. Springer, 2018, 441 p. doi: 10.1007/978-3-319-66330-2

M.S. Molodensky,* The Gravitational Field. The Figure and the Internal Structure of the Earth*. Moscow, Russia: Nauka, 2001, 569 p.

*Table of Integrals, Series, and Products*, 8rd ed., D. Zwillinger,* *Ed. Academic Press, 2014, 1184 p. doi: 10.1016/C2010-0-64839-5

*CRC Standard Mathematical Tables and Formulas*, 33rd ed., D. Zwillinger,* *Ed. New York: CRC Press, 2017, 858 p.

V.G. Kolobrodov *et al.*, “Spatial resolution of the remote sensing system when changing the angle of sighting”, *Naukovi Visti NTUU KPI*, no. 1, pp 54–64, 2018. doi: 10.20535/1810-0546.2018.1.111880

V.G. Kolobrodov and М.І. Lykholyt, *Design of Thermal Imaging and Television Observation Systems*. Kyiv, Ukraine: NTUU KPI, 2007, 364 p.

V.G. Kolobrodov and N. Shuster, *Thermal Imaging Systems (Physical Bases, Methods of Design and Control, Application)*. Kyiv, Ukraine: Tyrazh, 1999, 340 p.

M.P. Danilevsky *et al.*, *Fundamentals of Spherical Geometry and Trigonometry*. Kharkiv, Ukraine: KNAME, 2011, 92 p.

V.G. Kolobrodov *et al.*, “Spaceborne linear array imager's spatial resolution for arbitrary viewing angles”, *Proc. SPIE*, vol. 10445, pp. 104450J-1–104450J-9, 2017. doi: 10.1117/12.2280909

M. Capderou, *Satellites Orbits and Missions*. Switzerland: Springer International Publishing, 2014, 922 p. doi: 10.1007/978-3-319-03416-4

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