Theory of bokeh image structure in camera lenses with an aspheric surface
Bibliographic record
Abstract
We present theoretical, numerical, and experimental analysis of the cause of internal structure in out-of-focus images of point light sources seen in shots taken with camera lenses that incorporate aspheric surfaces. This “bokeh” structure is found to be due to diffraction on the phase grating at the lens exit pupil induced by small-scale undulations (ripples) of aspheric surfaces. We develop a phase-to-intensity transfer function approach which leads to a simple formula for estimating the intensity modulation ratio in the resulting bokeh based on the out-of-focus distance, amplitude, and frequency of surface undulations. Numerical simulations of bokeh image formation are carried out for a parabolic mirror imager and a double Gauss objective. We find that modulation depth in the bokeh structure calculated by light propagation based simulation agrees with theory when the modulation depth is <30%. Bokeh images are shown to be more sensitive to manufacturing artifacts of an aspheric surface than corresponding degradation in the lens modulation transfer function for a sharp focused image. We apply the transfer function approach to the calculation of the bokeh produced by a measured aspheric surface in a built camera lens and find reasonable agreement between the calculated and measured bokeh structure.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".