Non-destructive and non-contact centering error measurement of optical surfaces in fully mounted optical systems can provide valuable insights into the optical and underlying mechanical properties of lens systems. Commercially available solutions measure this centration by detecting the angle at which incoming light is reflected from each optical surface. Advanced algorithms are then used to calculate the tilt and lateral offset of all optical elements with arcsecond and submicron accuracy. These centering error measuring systems generally use an axis of rotation as reference for each measurement. While this enables cost-efficient systems, it limits the principle to vertical designs and requires both linear and rotational movements for each surface, resulting in long overall process times. In our article, we introduce a new measuring system that uses a high-precision linear axis for the centering error measurement. The omission of the axis of rotation leads to a significant reduction of the measuring time. With our approach, the centering error measurement of a single optical surface can be performed on a single image. As the measuring head focus is shifted, the linear stage itself becomes the reference axis. Using special calibration techniques, we can ensure that the precision of the measurement results is similar to that of a conventional rotation axis system. The measuring method is ideal for optical assemblies whose position and orientation may not be changed during measurement, such as samples whose optical axis must always be aligned horizontally (e.g., those with floating lens elements), or workpieces that run through the production in large numbers in mass production on a tray together. This approach is also well-suited for samples that are tightly integrated into large and inflexible systems. In addition to the presentation of the principle of measurement, results of measurements of a complex objective are presented in direct comparison to the conventional measuring technique.