spectrometer 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.czerny_turner_design(groove_density_per_mm=1200.0, wavelength_min_nm=500.0, wavelength_max_nm=750.0, incidence_deg=9.0, collimator_f_mm=52.083, detector_length_mm=28.672, collimator_offaxis_deg=6.5, order=1, camera_f_mm=None, n_curve=41) (to call the implementation directly, import gratingspec; gratingspec.czerny_turner_design(groove_density_per_mm=1200.0, wavelength_min_nm=500.0, wavelength_max_nm=750.0, incidence_deg=9.0, collimator_f_mm=52.083, detector_length_mm=28.672, collimator_offaxis_deg=6.5, order=1, camera_f_mm=None, n_curve=41); from the registry, opsoptics.get("czerny_turner_design"))
First-order design of a Czerny–Turner spectrometer (plane grating + two concave mirrors): camera focal length, coma-free mirror angle and the wavelength mapping.
> The detailed description below is the original text — the summary and the headings are translated.
groove_density_per_mm / order / incidence_deg: 格子と入射角 α(中心波長でも端でも同じ α)。wavelength_min_nm / wavelength_max_nm: 検出器に並べる帯域。中心 λ_c はその中点で、検出器の中央に来る。
collimator_f_mm: コリメータ鏡の焦点距離(曲率半径の半分)。detector_length_mm: 検出器の長さ L(分散方向)。帯域の両端が検出器の両端に乗るようにカメラの f を決める。collimator_offaxis_deg: コリメータ鏡の軸外し角 θ₁(入射と反射のなす角の半分)。
camera_f_mm: カメラ鏡の焦点距離を与える(None なら帯域が L にちょうど乗る値を厳密に解く)。
n_curve: 波長 → 位置の写像の標本数。
返り値(table、kind = "czerny_turner"。下流の op がそのまま受ける):
• center_wavelength_nm / beta_center_deg / deviation_deg(α − β_c)。
• camera_f_mm(使った値)/ camera_f_linear_mm(線形近似 f = L d cos β_c / (m Δλ)、Feng 2021 の式 (16))/ camera_f_exact_mm(像の写像 x = f tan(β − β_c) で両端が L に乗る値)。
• mirror_radii_mm —— (2 f_col, 2 f_cam)。
• shafer_offaxis_deg —— Shafer の条件でコマを消すカメラ鏡の軸外し角 θ₂。
• dispersion_curve —— pairs(λ [nm], 検出器の位置 x [mm])。nonlinearity_mm は直線からの最大のずれ。
• reciprocal_dispersion_nm_per_mm —— (端, 中心, 端) の P。
• detector_coverage_mm —— 帯域の両端の位置。second_order_band_nm —— 帯域へ 2 次で重なる波長の範囲(λ_min/2 〜 λ_max/2)。order_overlap_from_nm —— 帯域の中の光自身が 2 次で重なり始める波長(2 λ_min が帯域内なら。無ければ None)。
Raises ValueError: 帯域が逆・帯域の一部が伝わらない、検出器に乗らない、Shafer の解が無い、非正の長さ、|α| ≥ 90°。
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_spectrometer_illumination — py -3.11 examples/poc_spectrometer_illumination.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
spectrometer)grating_dispersion · spectrometer_bandpass · spectrometer_slit_image · spectrometer_spectrum
*Provenance: gratingspec.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.