Study of linear phase shift algorithms and application to deflectometry
Bibliographic record
Abstract
For a number of optical methods, including deflectometry, information is encoded in fringe patterns. To extract the phase data from intensity values, a number of phase shift algorithms have been designed. In deflectometry, the nonlinearity of the fringe display implies that the displayed fringe pattern presents a harmonic content even if the input pattern is perfectly sinusoidal. The propagation of these harmonics through phase shift algorithms creates parasitic fringe patterns, reminiscent of the initial fringe pattern on the estimated phase. This phenomenon, known as print-through, has been identified as a serious performance limitation. In this paper, we revisit Surrel’s work on harmonic insensitive phase shift algorithms and demonstrate that the class of Discrete Fourier Transform (DFT) phase shift algorithms he defines is very appropriate for the field of deflectometry. We show how to choose the most suitable one depending on the application by performing a complete modeling of the harmonic print-through phenomenon for these DFT algorithms and studying the error propagation for shot noise and temporal perturbations. In a deflectometry context, we demonstrate by means of simulations that carefully chosen DFT algorithms can simultaneously be robust to print-through and perform better with respect to noise than the state of the art nonlinear phase shift algorithms. Lastly, by comparing experimental mirror shape measurements of the matrix of the secondary mirror of the European Extremely Large Telescope made on the one hand by DFT deflectometry and on the other hand by phase shift interferometry, we demonstrate that the use of DFT algorithms can substantially improve the high spatial frequency measurement capabilities of a deflectometry setup, without the need for a calibration of the display’s nonlinearities.
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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 | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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".