pixelshift op• Data kinds: none → table (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.pixel_shift_resolution_budget(pitch_um, f_number, wavelength_um=0.55, fill_factor=1.0, step_px=0.5) (to call the implementation directly, import pixelshift; pixelshift.pixel_shift_resolution_budget(pitch_um, f_number, wavelength_um=0.55, fill_factor=1.0, step_px=0.5); from the registry, opsoptics.get("pixel_shift_resolution_budget"))
Closed-form budget of whether pixel shift raises resolution (lens-limited or pixel-limited).
> The detailed description below is the original text — the summary and the headings are translated.
周波数 f は cyc/px(センサ画素あたり)。
• 画素の開口の MTF: |sinc(f · fill)|(箱の幅 fill 画素)。fill = 1 なら f = 1 で 0。
• 回折の MTF(円形の瞳、収差なし): (2/π)(acos x − x√(1 − x²))、x = f · Q、Q = λN/p(Fiete 1999)。レンズの遮断は f = 1/Q。
• ナイキスト: 1 枚 = 0.5、標本の間隔 *step_px* のシフト = 0.5 / step_px。1 枚で f > 0.5 の成分は f_alias = |f − round(f)| に折り返る(モアレ)。
• 律速の境目は Q = 2: レンズの遮断 1/Q が 1 枚のナイキスト 0.5 より上(Q < 2)なら、1 枚では折り返しが出てシフトで帯域が伸びる(画素律速)。Q ≥ 2 なら 0.5 より上に信号が無く、シフトしても増えない(レンズ律速)。★ただし Q = 2 は「折り返しが出るか」の境目で、gain(系の MTF ≥ 0.1 の帯域の比)はもっと手前で 1.0 に
なる: sinc(0.5)·MTF_diff(0.5 Q) = 0.1 の Q ≈ 1.47(fill = 1)。その間(例 Q = 1.75)は regime が
"pixel_limited" でも gain は 1.0 —— 折り返しは消えるが、見える細かさは増えない。
返り値の辞書: Q、lens_cutoff_cyc_px、nyquist_single、nyquist_shifted、aperture_zero_cyc_px、mtf_at_nyquist_single(開口・レンズ・系の 3 つ)、mtf_at_nyquist_shifted(同)、mtf50_cyc_px / mtf10_cyc_px(系の MTF が 0.5 / 0.1 を切る周波数、数値の二分法)、usable_band_single / usable_band_shifted(折り返しを起こさず、系の MTF が 0.1 以上の上限)、gain(後者 / 前者)、regime("pixel_limited" / "lens_limited")、lp_per_mm_per_cyc_px(1 cyc/px = 1000/p lp/mm)。
Raises ValueError: pitch_um・f_number・wavelength_um が正の有限でない / fill_factor が (0, 1] でない / step_px が {1/4, 1/3, 1/2, 1} でない。
Every optics op validates its input before computing (nothing slips through silently):
• Units are baked into the argument name — _mm / _um / _deg / _mrad. Confusing mm with µm does not crash; it yields a plausible-looking wrong answer, so the name prevents it. Nothing here guesses the unit from the magnitude.
• Strings raise ValueError — float('50') succeeds, so an unparsed configuration value would slip through as a length (measured: thin_lens('50', '200') returned a plausible 66.667 mm). bool is refused too, as the implicit promotion True == 1.
• complex / masked arrays raise ValueError (real-valued slots only; silently dropping the imaginary part or peeling off the mask is refused). NaN/Inf raises ValueError on every input.
• Division by zero and its relatives are refused by name: focal length 0, radius of curvature 0, refractive index <= 0, a fully opaque aperture (all zeros, so the normalisation is 0/0), a PSF whose sum is <= 0, a Stokes vector with S0 = 0, and an object sitting at the front focal point (the image is at infinity).
• Only two ops return a non-finite value, and both state it as a contract: depth_of_field returns far_mm = inf beyond the hyperfocal distance (that is what the hyperfocal distance means), and gaussian_beam returns wavefront_radius_mm = inf at the waist (the radius of curvature of a plane wavefront). Both also return a finite companion (far_is_infinite / curvature_per_mm). Any other silent NaN/Inf is detected internally and raises ValueError — "float64 overflowed" and "the answer is infinite" are different claims, so the first is never returned wearing the face of the second.
• Size caps: generated grids are capped by optics.MAX_GRID (4096); supplied fields/PSFs/apertures by optics.MAX_FIELD_ELEMENTS (2^24); ABCD element chains by optics.MAX_SYSTEM_ELEMENTS (1024); Zernike by MAX_ZERNIKE_TERMS (512) / MAX_ZERNIKE_ORDER (40) / MAX_ZERNIKE_BASIS (2^25). This closes, fail-closed, the paths where a small argument triggers a huge internal allocation (measured: n_max=40 × 4096² needs 108 GB).
• Physically impossible states are refused too: a Stokes vector with degree of polarisation > 1, negative transmittance, negative intensity, and invalid Zernike indices such as n-|m| odd.
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• poc_pixel_shift — py -3.11 examples/poc_pixel_shift.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
pixelshift)pixel_shift_pattern · pixel_shift_capture · pixel_shift_merge · pixel_shift_motion_mask · false_color_metric
*Provenance: pixelshift.py — OPTICS operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.