# A Single Motor-Driven Focusing Mechanism with Flexure Hinges for Small Satellite Optical Systems
## 1 Introduction  
Although a small satellite has limited dimensions, it has shown promising potential to observe the earth [1; 2; 3] with many advantages, i.e., lower launching expenses [4], less energy consumption [5; 6], and shorter lead-times [7], etc. Recently, small satellites have been able to accommodate an expandingrange of functions due to the rapid development of device miniaturization, including advances in chipsets. Hence, despite its limited volume, the small satellite can perform various missions in space [8; 9; 10]. For these reasons, small satellites have been emerging as a new and energy-efficient technology, enabling them to replace bulkier, more expensive and less efficient conventional satellites. For small satellites, an optical system is crucial to perform observations towards the earth or space, providing both high image resolution and minimum geometric distortion. However, the optimization of these optical systems is still a challenge due to their limited dimensions and the extreme environmental conditions, i.e., vibrations [11], shock loading during launch [12; 13], a dramatic temperature change [14], or high vacuum pressure in space [15], etc. Also, these harsh environments could cause mechanical damage, i.e., material failures of the system [16; 17]. For instance, high vacuum pressure in space causes outgassing between the mounted (assembled) surfaces [18; 19]. The extremely high temperature causes the evaporation of atomic oxygen distributed on the surface of the secondary mirror, which possibly leads to distortion and mis-alignment of the optical system [20]. Consequently, such mis-alignment causes degradation of the image quality and/or resolution [21]. In light of these constraints, optical systems should have features that ensure consistent performance in harsh environments, and rigorous design is needed to successfully integrate the specified type of optics. In particular, the performance of the optical system should be evaluated in terms of image resolution (i.e., pixel, MTF, etc.). Among the evaluation parameters, MTF (Modulation Transfer Function) has been commonly used to quantify optical alignments [22; 23; 24]. By forecasting and anticipating these quantified mis-alignments, high-resolution pictures can be obtained by means of mechanical or systemic compensation solutions [25; 26; 27]. In the case of the former, by investigating the novel mechanisms or identifying the optimal structures, the performance of the optical system can be improved. Indeed, many structural designs for small satellites have been studied [28; 29; 30]. Among them, [PERSON] et al. approximated the deflection of the primary mirror due to its own weight and presented an optical system based on an evaluation of optical tolerance [31]. The error (0.0015\({}^{\circ}\) in deflection) that occurred between the primary mirror and supporting shaft was well-defined, yet these measurements and the resulting bulky structure of the optical system cannot be accommodated or adapted for small satellites. On the other hand, [PERSON] et al. proposed a refocusing mechanism that can be controlled by means of thermal expansion [32]. The degradations of Tilt and De-center were only 0.5 arcsec and \(\pm\)10 \(\upmu\)m, respectively. The main advantage of this design was to implement the accurate actuation of the inner and outer cylinders, and its mechanical characteristics are independent of the environmental conditions. Despite these efforts, both cooling and heating actions could consume lots of energy to operate. To decrease working temperatures of the thermally-driven refocusing mechanisms, [PERSON] et al. presented a novel mechanism that produces 30 \(\upmu\)m of De-space, with respect to 10 \({}^{\circ}\)C variation in temperature [33]. Here, they reduced energy consumption, but the stroke was relatively small, compared to the size of the secondary mirror (Diameter: 144 mm). In summary, such thermally driven refocusing mechanisms need to be further developed in order to achieve low energy consumption and adequate performance.