{
  "title": "Synthetic spectral bands and areal mixtures",
  "status": "Analytical hypothetical spectra; no real material or classification result",
  "rows": {
    "spectra": 601,
    "bands": 315,
    "width_sensitivity": 96
  },
  "equations": {
    "A": ".55-.12*exp(-.5*((lambda_nm-700)/70)^2)",
    "B": "A-.20*exp(-.5*((lambda_nm-850)/8)^2)",
    "mixture": "alpha*A+(1-alpha)*B",
    "illumination": "scale*(1+tilt*(lambda_nm-700)/300)",
    "band": "integral(E*R*d_lambda)/integral(E*d_lambda), top-hat response"
  },
  "parameters": {
    "wavelength_nm": [
      400,
      1000
    ],
    "bands_nm": [
      [
        400,
        500
      ],
      [
        500,
        600
      ],
      [
        600,
        750
      ],
      [
        750,
        900
      ],
      [
        900,
        1000
      ]
    ],
    "A_fractions": [
      0.0,
      0.05,
      0.1,
      0.15,
      0.2,
      0.25,
      0.3,
      0.35,
      0.4,
      0.45,
      0.5,
      0.55,
      0.6,
      0.65,
      0.7,
      0.75,
      0.8,
      0.85,
      0.9,
      0.95,
      1.0
    ],
    "tilts": [
      -0.8,
      0,
      0.8
    ],
    "integration_step_nm": 0.1
  },
  "checks": {
    "all_pass": true,
    "mix_linearity_max_abs_error": 2.220446049250313e-16,
    "half_step_max_abs_difference": 8.097676029716894e-09,
    "closed_form_flat_band_max_abs_error": 1.0175055076278028e-08,
    "bounds": true,
    "illumination_scale_cancellation": true,
    "dark_denominator_null": true,
    "width_dilution_monotone": true,
    "width_sensitivity_closed_form_max_abs_error": 2.1421436251500836e-06
  },
  "limitations": [
    "Normalized band response presumes a same-illumination reference. It is not raw detector counts or a direct uncalibrated reflectance observation.",
    "Zero illumination produces no recoverable normalized reflectance, represented by null, not a zero-reflectance material.",
    "Linear areal mixing assumes unresolved adjacent patches under common viewing and lighting; it excludes intimate mixture scattering, shadows and nonlinear interactions.",
    "No atmospheric absorption, emissivity, thermal emission, spatial misregistration, detector noise or calibration error is modeled.",
    "No named mineral, classifier accuracy, abundance estimate or confidence probability follows."
  ]
}