fpm 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.fp_design(na_obj=0.1, wavelength_um=0.532, led_pitch_mm=4.0, led_distance_mm=70.0, n_side=13, magnification=4.0, camera_pixel_um=5.2, target_na=None, field_of_view_um=None, boundary_tolerance_na=0.005) (to call the implementation directly, import fourierptycho; fourierptycho.fp_design(na_obj=0.1, wavelength_um=0.532, led_pitch_mm=4.0, led_distance_mm=70.0, n_side=13, magnification=4.0, camera_pixel_um=5.2, target_na=None, field_of_view_um=None, boundary_tolerance_na=0.005); from the registry, opsoptics.get("fp_design"))
• GPU: none (CPU reference implementation only)
Fourier ptychography performance in closed form before measuring (table): synthetic NA, cut-off period, spectral overlap ratio, number of LEDs and pixel sampling.
A square grid of LEDs (n_side × n_side, pitch led_pitch_mm) placed led_distance_mm below the sample, with the centre LED aligned to the optical axis.
• Illumination NA: for the on-axis edge LED, NA_ill = e/√(e² + h²) (e = (n_side − 1)/2 · pitch); the value for the diagonal corner is also returned.
• Synthetic NA = NA_obj + NA_ill (axis). For a USAF chart whose bars run along the axes, the resolution is set by the axis value (diagonal LEDs do not bring x-only frequencies into the pupil). Coherent cutoff period λ/NA_syn (λ/NA_obj for the objective alone), half-period λ/(2 NA_syn).
• Overlap ratio: area of intersection of the pupil circles (radius NA_obj/λ, centre spacing = difference in sinθ/λ) of the centre LED and its neighbour / area of the circle = (2/π)[acos a − a√(1 − a²)], a = d/(2r). Smallest at the centre (the sinθ steps get narrower further out); the edge value is also returned. overlap_ok = centre value ≥ 0.35 (lower bound from Sun et al. 2016).
• Sampling: the object-side pixel Δx = camera_pixel_um / magnification must be ≤ λ/(2 NA_obj) (R_cam = λ·M/(2 NA_obj Δx_cam) ≥ 1). The Nyquist limit for the intensity band, λ/(4 NA_obj), is also returned (FP recovers the field, so λ/(2 NA_obj) suffices).
• Upsampling factor: the smallest integer for which the high-resolution pixel is ≤ λ/(2 NA_syn).
• Boundary LEDs: number of LEDs whose illumination NA is within boundary_tolerance_na of NA_obj (boundary_leds). Their images sit on the border between bright field and dark field, and whether the pupil edge clips the illumination's zero order flips with a 1-pixel rounding of k —— in measurements, a configuration with 39 % overlap failed to converge because of this single LED (with a 256-pixel field of view; shifting the LED distance from 70 → 76 mm made it converge. With a 384-pixel field of view it converged even with the LED left on the boundary —— it can happen, but not always). boundary_ok = 0 LEDs.
• target_na: the grid side length, total number of LEDs, and number of LEDs with sufficient illumination NA required for that synthetic NA.
• field_of_view_um: space-bandwidth product (field of view / half-period)².
Returns: dict(kind="fp_design", na_synthetic, na_illumination_max_axis, coherent_cutoff_period_um, overlap_ratio_centre, overlap_ratio_edge, overlap_ok, n_leds, n_brightfield, boundary_leds, boundary_ok, object_pixel_um, r_cam, pixel_sampling_ok, upsample_needed, …).
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. Exception, declared: the u_map of bottle_fit_from_pattern takes pixels that could not be measured as NaN (infinity is still refused).
• 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. Exception, declared: bottle_background_map returns NaN in u_mm for pixels whose ray is unusable (total internal reflection and the like), together with a valid mask and the counts.
• 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_fourier_ptychography — py -3.11 examples/poc_fourier_ptychography.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
fpm)fp_usaf_target · fp_capture · fp_stack_from_images · fp_reconstruct · fp_element_contrast
*Provenance: fourierptycho.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.