{
  "scope": "1D scalar slit-pupil teaching calculation; not a process recommendation",
  "numpy_version": "2.5.4",
  "coordinate_unit": "lambda/NA",
  "pupil": "P(f)=1 for |f|<=1; zero otherwise",
  "mask": {
    "central_open_interval": [
      -0.4,
      0.4
    ],
    "remote_open_intervals": [
      [
        1.5,
        2.2
      ],
      [
        3.4,
        4.5
      ],
      [
        7.0,
        11.0
      ],
      [
        14.0,
        20.0
      ],
      [
        -2.6,
        -2.0
      ],
      [
        -6.0,
        -4.3
      ],
      [
        -18.0,
        -13.0
      ]
    ],
    "elsewhere": 0
  },
  "threshold": 0.25,
  "domain": [
    -32,
    32
  ],
  "core": [
    -0.95,
    0.95
  ],
  "method": "linear FFT convolution with zero padding; no kernel renormalization; source integration by Gauss-Legendre",
  "cases": [
    {
      "kind": "coherent",
      "dx": 0.0078125,
      "source_points": 1,
      "radii": [
        0.5,
        0.75,
        1.0,
        1.5,
        2.0,
        2.5,
        3.0,
        4.0,
        5.0,
        6.0,
        8.0,
        10.0,
        12.0,
        16.0,
        20.0,
        24.0,
        28.0,
        32.0
      ],
      "edge_positions": [
        [
          -0.44494188686789454,
          0.4449418868678944
        ],
        [
          -0.4059867959060818,
          0.40598679590608155
        ],
        [
          -0.3965646059909533,
          0.3965646059909532
        ],
        [
          -0.3965646059909533,
          0.42918657175119934
        ],
        [
          -0.37296949614200386,
          0.4122724248490803
        ],
        [
          -0.3985772051268359,
          0.4137177170155723
        ],
        [
          -0.3971914930586033,
          0.39627513210242327
        ],
        [
          -0.39269814854340146,
          0.3982119758484087
        ],
        [
          -0.3954880350269775,
          0.3928098267304953
        ],
        [
          -0.40223955049902826,
          0.3936114102202957
        ],
        [
          -0.3976723911015178,
          0.3945944920123535
        ],
        [
          -0.3981488023356548,
          0.3951935697885309
        ],
        [
          -0.40150029072813564,
          0.3994346874823835
        ],
        [
          -0.396722378585712,
          0.393596362684431
        ],
        [
          -0.399048441851531,
          0.39858446158556354
        ],
        [
          -0.40081249989693024,
          0.3985844615855636
        ],
        [
          -0.40081249989693024,
          0.3985844615855636
        ],
        [
          -0.4008124998969303,
          0.39858446158556354
        ]
      ],
      "reference_edges": [
        -0.4008124998969303,
        0.39858446158556354
      ],
      "max_edge_error": [
        0.04635742528233083,
        0.0074023343205180114,
        0.004247893905977018,
        0.0306021101656358,
        0.027843003754926432,
        0.015133255430008763,
        0.003621006838327001,
        0.008114351353528837,
        0.005774634855068239,
        0.004973051365267822,
        0.003989969573210017,
        0.003390891797032669,
        0.0008502258968199339,
        0.004988098901132554,
        0.0017640580453993082,
        5.551115123125783e-17,
        5.551115123125783e-17,
        0.0
      ],
      "sampled_tail_envelope": [
        0.04635742528233083,
        0.0306021101656358,
        0.0306021101656358,
        0.0306021101656358,
        0.027843003754926432,
        0.015133255430008763,
        0.008114351353528837,
        0.008114351353528837,
        0.005774634855068239,
        0.004988098901132554,
        0.004988098901132554,
        0.004988098901132554,
        0.004988098901132554,
        0.004988098901132554,
        0.0017640580453993082,
        5.551115123125783e-17,
        5.551115123125783e-17,
        0.0
      ],
      "core_max_intensity_error": [
        0.11407235975525709,
        0.06346505444241823,
        0.06346505444241823,
        0.11210046032021492,
        0.15885873274175466,
        0.052423316070530745,
        0.01966113162349465,
        0.05118003469838417,
        0.01804454385494214,
        0.013110083440503573,
        0.010850120359075954,
        0.008701398726734366,
        0.004877079789483707,
        0.01211109198928062,
        0.005054540857426182,
        8.881784197001252e-16,
        6.661338147750939e-16,
        0.0
      ]
    },
    {
      "kind": "broad",
      "dx": 0.0078125,
      "source_points": 81,
      "radii": [
        0.5,
        0.75,
        1.0,
        1.5,
        2.0,
        2.5,
        3.0,
        4.0,
        5.0,
        6.0,
        8.0,
        10.0,
        12.0,
        16.0,
        20.0,
        24.0,
        28.0,
        32.0
      ],
      "edge_positions": [
        [
          -0.43558812714446704,
          0.43558812714446693
        ],
        [
          -0.4196353990135479,
          0.4196353990135478
        ],
        [
          -0.41903349728214495,
          0.4190334972821449
        ],
        [
          -0.41903349728214495,
          0.4210008518326541
        ],
        [
          -0.41730205737976767,
          0.41773265494240486
        ],
        [
          -0.41811642068941146,
          0.41762641064242684
        ],
        [
          -0.4182542988586521,
          0.42005093304395585
        ],
        [
          -0.41850829782865057,
          0.4223732851570563
        ],
        [
          -0.41812444018980094,
          0.4220386174543567
        ],
        [
          -0.41763100097512196,
          0.42216529742242453
        ],
        [
          -0.41752326349107827,
          0.42304531301737636
        ],
        [
          -0.41754656155038844,
          0.4227015420100125
        ],
        [
          -0.41744952399238866,
          0.4228231320011069
        ],
        [
          -0.417440497496387,
          0.4227390017452893
        ],
        [
          -0.41756480625476217,
          0.42275515892128546
        ],
        [
          -0.41757940931294085,
          0.4227551589212855
        ],
        [
          -0.41757940931294085,
          0.4227551589212855
        ],
        [
          -0.4175794093129408,
          0.4227551589212855
        ]
      ],
      "reference_edges": [
        -0.4175794093129408,
        0.4227551589212855
      ],
      "max_edge_error": [
        0.018008717831526244,
        0.003119759907737718,
        0.0037216616391406165,
        0.0017543070886313905,
        0.005022503978880655,
        0.005128748278858675,
        0.002704225877329658,
        0.0009288885157097693,
        0.0007165414669287884,
        0.0005898614988609774,
        0.0002901540960908444,
        5.3616911273035583e-05,
        0.00012988532055213664,
        0.00013891181655378837,
        1.4603058178630501e-05,
        5.551115123125783e-17,
        5.551115123125783e-17,
        0.0
      ],
      "sampled_tail_envelope": [
        0.018008717831526244,
        0.005128748278858675,
        0.005128748278858675,
        0.005128748278858675,
        0.005128748278858675,
        0.005128748278858675,
        0.002704225877329658,
        0.0009288885157097693,
        0.0007165414669287884,
        0.0005898614988609774,
        0.0002901540960908444,
        0.00013891181655378837,
        0.00013891181655378837,
        0.00013891181655378837,
        1.4603058178630501e-05,
        5.551115123125783e-17,
        5.551115123125783e-17,
        0.0
      ],
      "core_max_intensity_error": [
        0.03890171646766527,
        0.01937578038257203,
        0.011202692207770482,
        0.01120269220777037,
        0.00923671951965907,
        0.009452915989570765,
        0.004964852789691554,
        0.0028335353484029158,
        0.0014642945619574022,
        0.0010585889530332349,
        0.0005519574056579435,
        0.000411279464076042,
        0.00023921866236101264,
        0.0003308055922950359,
        2.721176250042312e-05,
        4.440892098500626e-16,
        4.440892098500626e-16,
        0.0
      ]
    },
    {
      "kind": "two_poles",
      "dx": 0.0078125,
      "source_points": 162,
      "radii": [
        0.5,
        0.75,
        1.0,
        1.5,
        2.0,
        2.5,
        3.0,
        4.0,
        5.0,
        6.0,
        8.0,
        10.0,
        12.0,
        16.0,
        20.0,
        24.0,
        28.0,
        32.0
      ],
      "edge_positions": [
        [
          -0.41682125030998074,
          0.4168212503099807
        ],
        [
          -0.4347770676673654,
          0.43477706766736535
        ],
        [
          -0.4532369105899248,
          0.4532369105899247
        ],
        [
          -0.45323691058992477,
          0.491647184443156
        ],
        [
          -0.45225705962312884,
          0.48671810737601306
        ],
        [
          -0.43164767862330117,
          0.4866778961829834
        ],
        [
          -0.43535048602533954,
          0.49447592911439936
        ],
        [
          -0.4383779066706972,
          0.503344294833654
        ],
        [
          -0.4343080100494483,
          0.5020242067764383
        ],
        [
          -0.43229386471950426,
          0.5033568700043782
        ],
        [
          -0.43409712664835104,
          0.5033494582936942
        ],
        [
          -0.43075009109005974,
          0.5031441608900351
        ],
        [
          -0.4328937113981289,
          0.5030193889929292
        ],
        [
          -0.43369141851313364,
          0.5034711098197873
        ],
        [
          -0.4326673995002982,
          0.5030716406026398
        ],
        [
          -0.43242348891252297,
          0.5030716406026398
        ],
        [
          -0.43242348891252297,
          0.5030716406026398
        ],
        [
          -0.43242348891252297,
          0.5030716406026398
        ]
      ],
      "reference_edges": [
        -0.43242348891252297,
        0.5030716406026398
      ],
      "max_edge_error": [
        0.08625039029265907,
        0.06829457293527441,
        0.049834730012715045,
        0.0208134216774018,
        0.019833570710605875,
        0.016393744419656353,
        0.008595711488240398,
        0.005954417758174235,
        0.0018845211369253323,
        0.0002852294017384738,
        0.0016736377358280707,
        0.0016733978224632295,
        0.00047022248560590896,
        0.0012679296006106733,
        0.00024391058777523122,
        0.0,
        0.0,
        0.0
      ],
      "sampled_tail_envelope": [
        0.08625039029265907,
        0.06829457293527441,
        0.049834730012715045,
        0.0208134216774018,
        0.019833570710605875,
        0.016393744419656353,
        0.008595711488240398,
        0.005954417758174235,
        0.0018845211369253323,
        0.0016736377358280707,
        0.0016736377358280707,
        0.0016733978224632295,
        0.0012679296006106733,
        0.0012679296006106733,
        0.00024391058777523122,
        0.0,
        0.0,
        0.0
      ],
      "core_max_intensity_error": [
        0.133246665170734,
        0.11194733873197349,
        0.11194733873197349,
        0.1119473387319736,
        0.07445094357259174,
        0.030133169025013395,
        0.019438747202730755,
        0.008694817535302657,
        0.0026708610866365,
        0.0040091931761055966,
        0.0020446474234521173,
        0.00430349958745968,
        0.0008014932922317808,
        0.0018619416606279748,
        0.00030311048038389465,
        2.220446049250313e-16,
        2.220446049250313e-16,
        0.0
      ]
    }
  ],
  "refinement_checks": {
    "coherent": {
      "fine_reference_edges": [
        -0.4007847906354879,
        0.39858158020433526
      ],
      "base_to_refined_max_edge_change": 2.770926144241015e-05,
      "radius_32_to_40_change": 5.551115123125783e-17
    },
    "broad": {
      "fine_reference_edges": [
        -0.41755090884821633,
        0.4227473078490457
      ],
      "base_to_refined_max_edge_change": 2.850046472446799e-05,
      "radius_32_to_40_change": 5.551115123125783e-17
    },
    "two_poles": {
      "fine_reference_edges": [
        -0.4324371939094671,
        0.5030692797422855
      ],
      "base_to_refined_max_edge_change": 1.3704996944141623e-05,
      "radius_32_to_40_change": 0.0
    }
  },
  "gradient_demo": {
    "kernel_radius_pixels": 8,
    "tile_pixels": 128,
    "iterations": 80,
    "gradient_error_R": 0.020278442502099536,
    "gradient_error_2R": 0.0,
    "final_mask_error_synchronized": 0.0,
    "final_mask_error_frozen": 0.09074707654541925,
    "finite_difference_gradient_error": 9.14306963473166e-10
  }
}