## 2 Materials and Methods
### The Method--MIIM  
This research is based on deploying the MIIM method developed by [PERSON] et al. [34] in a fully automated manner to measure the machine tool's thermal drift across the entire volumetric workspace. The proposed method integrates a tracking interferometer attached to the machine tool spindle, enabling an integrated multilateration measurement scheme as detailed in [30; 33]. Thus, a predefined volumetric point grid is established for measurement, consisting of specific locations to which the machine tool directs the tracking interferometer for data acquisition. This sequential movement enables the interferometer to perform accurate distance measurements for four reflectors fixed to the machine tool table, which serve as reference benchmarks for the multilateration measurement scheme. These reflectors are strategically positioned on the machine tool table to ensure accurate and comprehensive spatial data acquisition. As a result, the measurement approach operates continuously, reducing the measurement time to a single pass over the MT working volume and generating a volumetric error map of the machine every 40-50 min (depending on the size of the MT and the number of measurement points). This measurement frequency is sufficiently rapid to monitor and evaluate thermal errors induced by environmental temperature fluctuations over extended periods. Figure 1 illustrates the measurement setup for the Zayer ZERO(tm) machine tool under shop floor conditions. Thus, a LEICA AT960(tm) laser tracker is mounted on the tool holder using a specially designed support with a standard interface (HSK 100). For this specific test, four wide-angle retro-reflectors are positioned at the corners of the machine tool table. Figure 1: Wide-angle reflectors’ disposition for the ZEROTM Zayer machine tool. Table 1 summarises the key specifications of the laser tracker and retro-reflectors used during the MIIM tests. A LEICA AT960(tm) laser tracker was employed, which is based on an absolute distance meter (ADM) system [37]. The total number of points in the point cloud can be configured for each experiment, with the traversal path being customised to align with the specific objectives of the assessment. When the temperature fluctuates rapidly, a smaller number of points is selected to expedite measurements and minimise the overall duration of each measurement cycle. Conversely, when temperature changes are more gradual and a higher spatial resolution is required, a larger number of points is included in each sequence. Figure 2 presents the spatial configuration of the point cloud along with the TCP positions, which are uniformly distributed across the XY, XZ, and YZ planes and strategically located within the mid-range of each axis. This arrangement of points is designed to enhance the efficiency of the inverse kinematics (IK) procedure, enabling the determination of MT kinematic parameters critical for potential volumetric adjustments. Starting from point P1, the machine sequentially progresses through each subsequent point until reaching the final point, thereby completing a full measurement cycle. Subsequently, the machine returns to point P1 to initiate a new measurement sequence. For full automation of the measurement acquisition sequence, as explained in [30], it is essential to determine the spatial relationship between the reflectors positioned on the machine tool table and the laser tracker integrated into the machine tool spindle, and to do so all within the machine tool's coordinate system. This relationship is established by performing two sequential best-fit transformations at four corner points within the machine tool's working volume. The first best-fit transformation aligns the laser tracker reference system with the reflectors fixed on the machine tool table. This is accomplished by sequentially moving the