{
  "title": "Ideal imaging scales and sampling ambiguity",
  "status": "Analytical illustration with hypothetical detector and motion inputs; no measured image or device",
  "rows": {
    "camera": 27,
    "exposure": 1001,
    "alias": 21
  },
  "parameters": {
    "wavelength_m": 5.5e-07,
    "pixel_pitch_m": 5e-06,
    "horizontal_pixels": 1920,
    "aperture_m": [
      0.01,
      0.025,
      0.05
    ],
    "range_m": [
      1,
      10,
      100
    ],
    "focal_length_m": [
      0.025,
      0.05,
      0.1
    ],
    "signal_electrons_per_s": 1000,
    "background_electrons_per_s": 200,
    "read_noise_electrons_rms": 3,
    "transverse_speed_m_s": 0.1,
    "sample_rate_Hz": 20,
    "alias_frequencies_Hz": [
      3,
      17
    ]
  },
  "formulas": {
    "Rayleigh": "theta=1.22*lambda/D; linear scale=range*theta (small-angle)",
    "projected_pitch": "range*pixel_pitch/focal_length",
    "FOV": "2*atan(N*pixel_pitch/(2*focal_length))",
    "SNR": "signal/sqrt(signal+background+read_noise\u00b2)",
    "blur": "transverse_speed*exposure",
    "alias": "cos(2*pi*f*k/fs)=cos(2*pi*(fs-f)*k/fs), integer k"
  },
  "checks": {
    "all_pass": true,
    "alias_max_absolute_difference": 5.45029723684231e-15,
    "FOV_width_identity_max_error_m": 0.0,
    "Rayleigh_scaling": true,
    "SNR_variance_identity": true,
    "zero_time": true,
    "SNR_monotone": true
  },
  "limitations": [
    "Rayleigh criterion is for ideal unobstructed circular diffraction-limited aperture and incoherent point sources; not a universal feature-resolution threshold.",
    "Sampling pitch is not resolved detail. No pixel response, aberration, defocus, contrast transfer, atmosphere or reconstruction algorithm is modeled.",
    "Projection and field of view use ideal rectilinear pinhole geometry at fixed range; no finite-conjugate lens correction.",
    "SNR assumes independent Poisson signal/background counts and independent read noise for one measurement. Background mean is known without additional estimation noise; dark current, saturation, quantization and fixed-pattern noise are excluded.",
    "Motion blur is transverse displacement at constant range and speed, not a full image convolution or recoverability metric.",
    "Alias example contains two deterministic cosines, not a fabricated image. No clinical, identification or surveillance performance claim."
  ]
}