Estimation of Reactive Torque Effect on Image Blur

Introduction. When the optical system of a spacecraft rotates, the motion of its internal components initiates the emergence of a reactive torque. This torque causes unintended angular displacement of the spacecraft body, leading to a deviation of the line of sight and the formation of images with geometric distortions, commonly referred to as spatial blur. Such distortions limit the quality of remote sensing and astrophotography data. Despite the extensive study of stabilization problems, the influence of internal reactive torque arising from the motion of internal optical elements on the spatial accuracy of line-of-sight stabilization remains insufficiently investigated.

Aim. To evaluate the effect of the reactive torque of an opt_оmechanical system on the spatial blur of the resultant image and to determine whether the blur level complies with the acceptable requirements for data quality.

Materials and methods. An analysis of angular oscillations of an actual spacecraft during the operation of its optomechanical system was conducted based on the data of gyroscopic measurements. To estimate the amount of image blur, time series of angular velocities were processed at intervals corresponding to the camera exposure time. On this basis, the shift of the line-of-sight axis and the linear shift of the image in the focal plane were calculated. Additionally, a mathematical model based on the methods of theoretical mechanics was used to describe the relationship between the reactive torque of the rotating optical system and the dynamic response of the spacecraft body. This model made it possible to compare the actual data obtained with the calculated effect of the reactive torque.

Results. The analysis established the presence of low-frequency angular oscillations, creating a spatial blur of several micrometers. In this case, the modulation transfer function remains above 0.99, indicating minimal impact on image quality. The developed model confirmed the dependence of the angular deflection amplitude on the magnitude of the reactive torque.

Conclusion. The reactive torque of an optomechanical system with a value of less than 0.05 N·m cause image blur; however, its magnitude is insignificant. Thus, the MTF of 0.99 corresponds to maintaining the required clarity.

1. Hiraoka T., Nishihara O., Kumamoto H. Steering Reactive Torque Presentation Method for a Steer-ByWire Vehicle. Review of Automotive Engineering. 2008, vol. 29, no. 2, pp. 287–294.

2. Yoon J., Doh J. Optimal PID Control for Hovering Stabilization of Quadcopter Using Long Short Term Memory. Advanced Engineering Informatics. 2022, vol. 53, art. no. 101679. doi: 10.1016/j.aei.2022.101679

3. Kumar S., Dewan L. Quadcopter Stabilization Using Hybrid Controller Under Mass Variation and Disturbances. J. of Vibration and Control. 2022, p. 107754632211256. https://doi.org/10.1177/10775463221125628

4. Lui C. Stabilization Control of Quadrotor Helicopter through Matching Solution by Controlled Lagrangian Method. Asian J. of Control. 2022, vol. 24, no. 4, pp. 1885–1894. doi: 10.1002/asjc.2622

5. Krodkiewski J. M., Faragher J. S. Stabilization of Motion of Helicopter Rotor Blades Using Delayed Feedback–Modelling, Computer Simulation and Experimental Verification. J. of Sound and Vibration. 2000, vol. 234, no. 4, pp. 591–610. doi: 10.1006/jsvi.1999.2878

6. Wahballah W. A., Bazan T. M., Ibrahim M. Smear Effect on High-Resolution Remote Sensing Satellite Image Quality. IEEE Aerospace Conf., Big Sky, USA, 03–10 March 2018. IEEE, 2018, pp. 1–14. doi: 10.1109/AERO.2018.8396589

7. Haghshenas J. Maximum Allowable Low-Frequency Platform Vibrations In High Resolution Satellite Missions: Challenges and Look-Up Figures. Proc. of Optical Systems Design 2015: Optical Design and Engineering VI. Vol. 9626. SPIE, 2015, pp. 740–749. doi: 10.1117/12.2191109

8. Gecha V. Ya., Zhilenev M. Yu., Novoselov S. A. Obzor sredstv otsenki sostavlyayushchikh kachestva izobrazheniya na vykhode sputnikovoi optiko-elektronnoi apparatury distantsionnogo zondirovaniya zemli v tselyakh obespecheniya bortovoi obrabotki snimkov na bortu kosmicheskogo apparata [Overview of Facilities for Assesing Components of Image Quality at Output of Satellite Opto-Electronic Equipment for Earth Remote Sensing in Order to Provide on-Board Image Processing on Spacecraft Board]. Questions of Electromechanics. 2021, vol. 185, no. 6, pp. 38–48. (In Russ.)

9. Smith S. L., Mooney J. A., Fiete R. D. Understanding Image Quality Losses Due to Smear in HighResolution Remote Sensing Imaging Systems. Optical Engineering. 1999, vol. 38, no. 5, pp. 821–826. doi: 10.1109/AERO.2018.8396589

10. Wahballah W. A., Bazan T. M., El-Tohamy F., Fathy M. Analysis of smear in high-resolution remote sensing satellites. Sensors, Systems, and Next-Generation Satellites XX. SPIE. 2016, vol. 10000, pp. 375–385. doi: 10.1117/12.2241634

11. Holst G. C. CCD Arrays, Cameras, and Displays. 2nd ed. Winter Park, FL, JCD Publishing, 1998, 378 p.

12. Zhong W., Deng H., Sun Zh., Wu X. Computation Model of Image Motion Velocity for Space Optical Remote Cameras. Intern. Conf. on Mechatronics and Automation, Changchun, 09–12 Aug. 2009. IEEE, 2009, pp. 588–592. doi: 10.1109/ICMA.2009.5245072

13. Xu P., Hao Q., Huang Ch., Wang Y. Degradation of Modulation Transfer Function in Push-Broom Camera Caused by Mechanical Vibration. Optics & laser technology. 2003, vol. 35, no. 7, pp. 547–552. doi: 10.1016/S0030-3992(03)00084-7

14. Joseph G. Building Earth Observation Cameras. Boca Raton, CRC Press, 2015, 368 p.

15. Schowengerdt R. A. Remote Sensing: Models and Methods for Image Processing. Amsterdam, Elsevier, 2006, 560 p.