## 1 Introduction  
Space debris has become an important global problem because the exponential growth of its population poses a significant threat to not only human space activities but also operational satellites. Improving the orbital prediction accuracy of space debris is required to mitigate or eliminate the threat through avoidance of catastrophic collisions, which is attainable by using various measurements from the optical, radar and laser tracking systems. Even though these tracking systems provide accurate measurements, the dynamic model has to take into consideration the space debris characteristics such as size, shape and orientation information in order to improve the orbital prediction accuracy. Unlike the gravitational perturbations, non-gravitational perturbations such as the atmospheric drag and solar radiation pressure are dominated by these characteristics [1]. Thus the orientation determination including rotation rates and axis of space debris became a topic of interest in the space situational awareness communities. There are several methods to achieve orientation information of space debris in terms of the ground-based observations: photometry, adaptive optics (AO) and satellite laser ranging (SLR). Photometry is literally the measurement of light intensity or brightness and provides light curves which are commonly used in the astronomical communities to extract physical information of asteroids. Recently light curves have been recognized as a promising tool to determine shapes, spin axis orientation and spin rate of space debris by analyzing amplitude variation as well as periodic difference, thus are widely used by many researchers [2; 3; 4; 5; 6; 7]. The AO is a technology to improve the image quality nearly to diffraction limited resolution by compensating the incoming wavefronts distorted by the atmospheric turbulence. So the high-resolution optical images obtained from the AO system provide a means of characterizing size, shape and orientation of space debris and its identification [8; 9; 10]. As opposed to the passive technologies (i.e., photometry and AO) which receive sunlight reflected by space debris and so work only at night (in particular, twilight for space debris in low earth orbit), the SLR technology actively fires laser pulses into space objects and then measures the distance between the ground station and space objects equipped with corner cube reflectors (CCRs). The spinning array of the CCRs causes a millimeter-scale distance variation from which information of spin axis orientation and spin rate is achievable [11] for not only geodetic satellites with CCRs on the outer surface [12; 13; 14] but also defunct satellites equipped with CCRs [15; 16; 17]. Moreover, the SLR technology combined with photometry has been applied to space debris without CCRs, called uncooperative targets [18; 19; 20]. Debris laser ranging (DLR) is similar to SLR but applicable to uncooperative targets by employing a higher power laser rather than the SLR (normally 2 or 3 orders of power). It generates ranging data even under the low signal-to-noise ratio resulting from a small laser cross-section of uncooperative targets. For DLR, a Geiger-mode avalanche photodiode, called a photon-counting detector, is applied to respond to the presence of return signals and then records accurate timing of the first arrived photon [21; 22; 23; 24]. In spite of benefits from the photon-counting detector with higher detection sensitivity and lower dark noise, it does not provide an echo laser pulse waveform (ELPW) which records the scattering signals as a function of time. The ELPWs are achievable for uncooperative targets by employing a linear-mode avalanche photodiode (LmAPD) and a much higher power laser on the DLR system because the LmAPD output current is linearly proportional to photocurrent and thus can provide intensity information as well as ranging measurements.