Comparison of linear and nonlinear calibration methods for phase-measuring profilometry
Bibliographic record
Abstract
In phase-shifting-based fringe-projection surface-geometry measurement, phase unwrapping techniques produce a continuous phase distribution that contains the height information of the 3-D object surface. Mapping of the phase distribution to the height of the object has often involved complex derivations of the nonlinear relationship. In this paper, the phase-to-height mapping is formulated using both linear and nonlinear equations, the latter through a simple geometrical derivation. Furthermore, the measurement accuracies of the linear and nonlinear calibrations are compared using measurement simulations where noise is included at the calibration stage only, and where noise is introduced at both the calibration and measurement stages. Measurement accuracies for the linear and nonlinear calibration methods are also compared, based on real-system measurements. From the real-system measurements, the accuracy of the linear calibration was similar to the nonlinear calibration method at the lower range of depth. At the higher range of depth, however, the nonlinear calibration method had considerably higher accuracy. It seems that as the object approaches the projector and camera for the higher range of depth, the assumption of linearity based on small divergence of light from the projector becomes less valid.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".