IMPACT OF PERSPECTIVE DISTORTION OF A BAR-CODE LEVELING STAFF FIELD ON THE ACCURACY OF DIGITAL LEVEL READINGS

Abstract

B a c k g r o u n d . This article presents the results of theoretical analysis and numerical modelling of the influence of perspective distortion in the image of a bar-code leveling staff on the accuracy of readings obtained by a digital level. The study examines the displacement of the peak in the correlation function caused by the rotation of the staff around its vertical axis. It is analytically demonstrated that the reading error exhibits a quadratic dependence on the rotation angle of the staff.

M e t h o d s . A systems analysis approach was used to comprehensively study the "level-staff" system. Projective geometry methods were applied to determine the dimensional changes in the bar elements due to perspective and their effect on the reading algorithm. Geometric analysis was employed to mathematically describe changes in the geometry of bar-code symbols during staff rotation. Correlation analysis was conducted to assess the relationship between the rotation angle of the staff, the distance to the staff, and the root-mean-square measurement error.

R e s u l t s . Numerical modelling performed at a sighting distance of 30 metres showed that for rotation angles up to 5°, the resulting error remains within 0.2 mm, which is negligible for most practical measurements. However, at rotation angles exceeding 10°, the systematic error surpasses 0.8 mm, which is critical for high-precision levelling requirements. The study demonstrates that perspective distortion reduces the apparent size of the bar elements proportionally to the cosine of the rotation angle.

C o n c l u s i o n s . The results of numerical modelling are consistent with analytical estimations, confirming the validity of the proposed model. The study concludes that controlling the position of the staff during measurement is essential to minimise systematic errors. The findings can be used to improve digital levelling technologies, develop methods for automatic staff positioning control, and enhance the overall accuracy of geodetic measurements.