film op• Data kinds: pairs → table
• Call: import fullseye as fs; fs.ledger.film_thickness_fft(spectrum, film='SIO2', window='hann', pad_factor=16) (to call the implementation directly, import filmoptics; filmoptics.film_thickness_fft(spectrum, film='SIO2', window='hann', pad_factor=16); from the registry, opsoptics.get("film_thickness_fft"))
Film thickness from the period of the interference fringes in a reflectance spectrum (FFT method), with dispersion corrected from the material table's n(λ).
> The detailed description below is the original text — the summary and the headings are translated.
spectrum: pairs(λ [nm], R)。等間隔でなくてよい。
film: 膜の材料(鍵・数値)。縞の位相は 4π n(λ) d / λ = 2π d x、x = 2 n(λ)/λ [1/nm] なので、x の等間隔格子に
取り直してから FFT すると、ピークの周波数がそのまま膜厚 d [nm] になる(分散の補正込み)。
window: "hann"(既定、漏れが小さい)/ "rect"(主ローブが細い)。
pad_factor: ゼロ詰めの倍率(ピークの位置を細かく読む。分解能は増えない)。
返り値 dict: thickness_nm / peak_amplitude / span_x(x の幅 Δx [1/nm])/ n_fringes(= d·Δx、帯域に入る縞の本数)/
resolution_nm(= 1/Δx、2 つの膜厚を見分ける幅)/ min_thickness_nm(この窓の主ローブの半幅 = 測れる下限の閉形式:
hann 2/Δx、rect 1/Δx)/ reliable(d ≥ min_thickness_nm)/ frequency_nm と magnitude(FFT の振幅スペクトル)。
★下限は閉形式で先に分かる: 帯域 λ₁〜λ₂ の縞の本数は 2 n̄ d (1/λ₁ − 1/λ₂)。窓の主ローブ(DC の山)よりピークが外に出ないと、FFT 法は DC に引きずられて系統的に外れる(薄い膜ではモデルあてはめを使う)。
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_thin_film_reflectometry — py -3.11 examples/poc_thin_film_reflectometry.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
film)multilayer_reflectance · film_color · film_thickness_fit · film_thickness_map
*Provenance: filmoptics.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.