# A Range-Extension Method for an Indoor Standard Device for Large-Scale Length Measurement
## 1 Introduction  
A wide range of measurement methods and techniques have seen upgrades in the continuous development of industrial manufacturing. Large-scale metrology techniques refer to geometric measurement, with an effective range of tens of meters and an accuracy of micrometers. They are intertwined with modern manufacturing, with multiple applications, including assembling aircraft, reinstalling systems, developing large particle accelerators, and measuring antennas and automobile production lines. The large-size measuring instrument is the core of large-size measurement. To meet production needs, there is an increasing demand for large-size measuring instruments. The linear indication error of the large-size measuring instrument is traced back to the indoor large-scale standard device. Main large-size measuring instruments include long-range laser interferometers, laser trackers, laser radars, laser alignment instruments, laser rangefinders, indoor GPS, frequency-modulated laser rangefinders, etc. The measuring range of these instruments exceeds 50 m, and that of laser interferometers can be up to 80 m.  
Standard devices for large-scale length measurement can be classified into indoor and outdoor variants. Indoor standard devices for large-scale length measurement are known for their exceptional measurement accuracy and ease of controlling environmental factors, albeit with a limited measuring range. Conversely, their outdoor equivalents boast a longer range of measurement, but exhibit lower accuracy and difficulties in regulating the measurement environment. Globally, indoor standard devices for large-scale length measurement measure distances less than 100 m, with the figure for the National Metrology Institute of Japan at 96 m, the National Institute of Standards and Technology of the US at 60 m, the Korea Research Institute of Standards and Science and the Physikalisch-Technische Bundesanstalt of Germany at 50 m, and that for our institute at 56 m.  
Given the problems related to large-scale measurement, many studies have been conducted around the world. While [PERSON] formulated measurement standards for a range of 35 m [1], [PERSON] et al. introduced a variety of large-scale measuring instruments and the development trend of large-scale measurement [2]. [PERSON] et al. established an 80 m indoor large-scale standard device [3]. From the perspectives of the curved-surface evaluation and a united spatial measurement network, [PERSON] carried out in-depth research on large coordinate metrology techniques [4]. Based on folding optics, [PERSON] calibrated a total station using plane mirrors and an indoor fixed-length baseline [5]. With multiple rectangular prisms, [PERSON] researched how a geodimeter can be calibrated at a distance of 40 m within a structure [6]. [PERSON] et al. used a plane reflector to reproduce a standard length of 50 m on a 16-m-long indoor guide rail [7]. [PERSON] et al. proposed establishing a virtual length baseline field through successive rectangular prism reflections [8]. Moreover, [PERSON] and [PERSON] et al. raised a hypothesis about creating a virtual indoor baseline field through multiple reflections of two plane mirrors [9; 10]. [PERSON] et al. conducted a theoretical analysis of the straightness of a 26 m-long linear guide rail [11]. [PERSON] et al. investigated the measurement accuracy of a multi-beam laser tracking interferometer [12]. [PERSON] et al. explored how temperature can influence the accuracy of large-scale metrology instruments [13]. [PERSON] studied the calibration methods of laser frequency, counting system, and other parameters of displacement laser interferometer system [14]. Voluminous studies have been undertaken on large-size metrology, some of which focus on the indoor standard device for large-scale length measurement. This suggests that it is of significant scientific value to extend the measuring range of these indoor standard devices. We think that there are two problems when using a plane reflector as a reflecting medium.