DOI: https://doi.org/10.20535/1810-0546.2018.6.149681

### Modulation Transfer Function of the Remote Sensing System when the Line of Sight Deviates From the Nadir

#### Abstract

**Background.** Today, one of the main requirements, which relates to space optical-electronic viewing systems (OEVS) is shooting by a spacecraft (SC) of a requisite area at different angles of sighting. When the line of sight deviates from the nadir, the image quality gets worse. Primarily, the deformation of the projection of pixels on the Earth's surface (ES) and changing of the velocity and direction of vector of movement of the sub-satellite point of SC affect the image quality. Generally, the resulting image quality is estimated by the modulation transfer function (MTF) of OEVS. The evaluation of the MTF of OEVS by only two components, such as the MTF of a lens and detector is insufficient, since there is a high probability that the image will have significantly lower quality compared to theoretically calculated one. Therefore, it is necessary to take into account in the resulting MTF the effect of additional factors such as vibration, movement velocity of the sub-satellite point, detector reading frequency, height instability and position of the line of sight, the atmosphere, to name a few.

**Objective.** The aim of the paper is to develop physico-mathematical model for determining MTF of space OEVS, that takes into account the deformation of the projection of pixels, the variation of velocity and movement vector direction of the SC sub-satellite point and the influence of additional factors at the different angles of sighting.

**Methods.** In the basis of physico-mathematical model is proposed to use a Sun-synchronous orbit trajectory and to calculate the resulting MTF of OEVS in the direction and transverse to the direction of flight.

**Results.** Practical results of the calculations confirm that the deformation of the projection of the pixels and the mentioned additional factors significantly affect the resulting MTF of space OEVS and also depending on the angles of sighting the MTF in the direction and transverse to the direction of flight differ.

**Conclusions.**The analysis of the proposed physico-mathematical model for MTF calculation of the OEVS showed that when a scanner with a large number of pixels is deviated at the significant angles of sighting, heterogeneity appears on sensitive matrix of detector. Attention is drawn to the fact that when scanner deviates at the angles of sighting, the affect of the reading frequency of detector should also be reduced by negotiating it with the image movement velocity in the focal plane. In the process of the research, it was discovered that when use the slight additional turn of yaw angle it is possible to improve the MTF and reduce the difference between the MTF of in the direction and transverse to the direction of flight affecting the image perception efficiency.

#### Keywords

#### Full Text:

PDF (Українська)#### References

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

V.M. Tiagur, “The resolution of the optical systems of space multispectral images of remote sensing of the Earth”, Ph.D. dissertation, Deptertment of Optical and Optoelectronic Devices, NTUU KPI, Kyiv, Ukraine, 2008.

R.J. Schott, *Remote Sensing: The Image Chain Approach*, 2nd ed. Oxford, UK: Oxford University Press, 2007, 701 p.

I. Dowman *et al*., *High Resolution Optical Satellite Imagery*. Dunbeath, Scotland: Whittles Publishing, 2012, 230 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

Qin Deng *et al*., “Study on MTF of remote sensing imaging under arbitrary known vibration”, *Proc. SPIE*, vol. 8420, pp. 84200W-1–84200W-6, 2012. doi: 10.1117/12.966412

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

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

B.Yu. Pinchuk *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

B.Yu. Pinchuk *et al*., “Influence of angles of shighting and the earth's surface curvature on the spatial resolution of the space electro-optical viewing system”, *Naukovi Visti NTUU KPI*, no. 5, pp. 63–75, 2018. doi: 10.20535/1810-0546.2018.5.140106

M. Capderou, *Satellites Orbits and Missions*. Springer-Verlag France, 2005, 558 p.

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

R.H. Vollmerhausen *et al*., *Analysis and Evaluation of Sampled Imaging Systems*. SPIE Press, 2010, 304 p.

V.L. Panteleev, *Theory of Figure of the Earth*. Moscow, Russia: Lomonosov Moscow State University, 2000, 98 p.

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

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

R.G. Driggers *et al*., *Introduction to Infrared and Electro-Optical Systems*, 2nd ed. Artech House, 2012, 583 p.

R.D. Fiete, *Modeling the Imaging Chain of Digital Cameras*. SPIE Press, 2010, 225 p.

G.D. Boreman, *Modulation Transfer Function in Optical and Electro-Optical Systems*. SPIE Press, 2001, 111 p.

V.G. Kolobrodov, “Parameters optimization of the imager’s lens and microbolometer matrix”, *Naukovi Visti NTUU KPI*, no. 1, pp 91–95, 2015.

#### GOST Style Citations

Copyright (c) 2018 Igor Sikorsky Kyiv Polytechnic Institute

This work is licensed under a Creative Commons Attribution 4.0 International License.