## 1 Introduction
[21] suggested using a color 2f alignment method for measuring the mirror shape error of a dish concentrator by utilizing a video camera and a color target affixed to a lightweight tower at a distance nearly twice the focal length (2f) from the vertex of the dish concentrator. The camera and target were centered on the optical axis of the concentrator. [PERSON] et al. [22] developed color-coded targets for measuring the slope error of a parabolic dish concentrator. The method used a flat target with colored stripes placed close to the focal plane of the concentrator and a digital camera located at an observation point on the optical axis at some arbitrary distance. [PERSON] et al. [11] proposed a method to implement certain alignments in manufacturing processes using the Fringe Analysis Slope technique, which was shown to reduce the time taken to align the mirror of each dish concentrator to approximately 2 h. Using the reflection imaging method, the target image could be displayed in \"real-time\" on the mirror surface of the concentrator so as to guide the mirror installation alignment however pre-calibration was required to set the spatial relationships between the devices, which reduce the flexibility and convenience of this method. Such as the color 2f alignment [20; 21] and color-coded target methods [22] both required alignment of the center-line of the camera and target with the focal axis of the dish concentrator. Furthermore, it was found that the adjustment value and adjustment order of each support bolt could not be determined when the mirror facet was aligned hence leading to the requirement for repeat adjustments of the support bolts. [PERSON] and [PERSON] [23; 24] adopted a photogrammetry method to measure the shape error of the SG3 400 m\({}^{2}\) solar dish concentrator. Similarly, [PERSON] et al. [25] used photogrammetry in the construction of a 500 m\({}^{2}\) dish concentrator to control the assembly of a convex paraboloidal jig for ensuring the installation accuracy of each mirror unit. [PERSON] et al. [26] measured the surface shape error of the dish concentrator with photogrammetry at different elevation angles. Finally, [PERSON] et al. [8] measured the spatial coordinates of ten randomly distributed positioning targets on each mirror unit in a dish concentrator. Again, the adjustment value and adjustment order of each support bolt could not be determined when the mirror facet was aligned. The photogrammetry method is flexible, simple and convenient and theoretically, could be used to measure the surface shape error of any geometrical concentrator in order to guide the mirror facet alignment for the dish concentrator and trough concentrator [27; 28; 29; 30]. However, a large number of markers on the reflective mirror of the concentrator are needed, and could cause the reflective mirror become optically polluted, therefore, a \"clean\" mirror facet installation measurement method should be developed. In the above literature, whilst measuring the surface error of the concentrator to guide the mirror installation or facet alignment, the adjustment value and order of each support bolt could not be determined before the alignment of the mirror facet. In this paper, we focus on the facet installation error measurement and facet alignment of the mirror unit (the surface quality of the mirror unit installed is considered to be satisfactory). A \"clean\" mirror facet installation measurement method is presented. The spatial coordinates of three feature points were measured by photogrammetry to reverse the facet alignment parameters of the mirror unit (i.e., the axis vector and vertex position vector of the mirror unit). The feature points were pasted on the reflective mirror and formed a triangular distribution (in Section 3).