Illuminance Ontology

# Illuminance Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/optical-measurements/illuminance-ontology.html

FLOW IlluminanceOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Optical Measurements
    -> Illuminance Ontology

  PURPOSE:
    Represent illuminance as a measurable photometric surface quantity describing incident luminous flux per unit area, including lux, luminous intensity relationships, inverse-square and cosine laws, spatial distribution, spectral visual weighting, measurement geometry, photometer response, calibration, uncertainty, and distinctions from luminous intensity, luminance, irradiance and luminous flux.

  ENTITY Illuminance {
    TYPE: DerivedPhotometricSurfaceQuantity
    SYMBOL: E_v
    DIMENSION: J_luminous * L^-2
    SI_UNIT: lux
    SI_SYMBOL: lx

    DEFINITION:
      illuminance := incident_luminous_flux_per_unit_surface_area

    DIFFERENTIAL_FORM:
      E_v = dPhi_v/dA

    UNIFORM_FORM:
      E_v = Phi_v/A
      WHEN luminous_flux_uniformly_distributed_over_area

    PROPERTIES:
      is_scalar_surface_quantity
      is_photometric
      has_value
      has_unit
      depends_on_surface_orientation
      depends_on_source_geometry
      may_vary_with_position
      may_vary_with_time
      may_have_uncertainty
  }

  ENTITY LuminousFlux {
    TYPE: PhotometricFluxQuantity
    SYMBOL: Phi_v
    SI_UNIT: lumen
    SI_SYMBOL: lm

    RELATION:
      Illuminance = incident_luminous_flux_per_area
  }

  ENTITY LuminousIntensity {
    TYPE: DirectionalPhotometricQuantity
    SYMBOL: I_v
    SI_UNIT: candela
    SI_SYMBOL: cd

    RELATION:
      point_source_illuminance =
        luminous_intensity*cos(theta)/distance^2
  }

  ENTITY Irradiance {
    TYPE: RadiometricSurfaceQuantity
    SYMBOL: E_e
    SI_UNIT: watt_per_square_metre
    SI_SYMBOL: W/m^2

    RULE:
      irradiance_is_radiometric_not_photometric
  }

  ENTITY Luminance {
    TYPE: DirectionalPhotometricSurfaceQuantity
    SYMBOL: L_v
    SI_UNIT: candela_per_square_metre
    SI_SYMBOL: cd/m^2
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: lux
      symbol: lx

      equivalence:
        1 lx = 1 lm/m^2
    }

    COMMON_ALTERNATIVES:
      kilolux
      millilux
      foot_candle

    COMMON_CONVERSION:
      1 foot_candle approximately_equals 10.7639 lux

    CONVERSION_RULE:
      illuminance_value(target_unit)
        = illuminance_value(source_unit)
        * conversion_factor(source_unit, target_unit)
  }

  CLASSIFICATION {
    by source:
      direct_illuminance
      diffuse_illuminance
      reflected_illuminance
      total_illuminance

    by geometry:
      normal_illuminance
      horizontal_illuminance
      vertical_illuminance
      cylindrical_illuminance
      hemispherical_illuminance

    by time:
      instantaneous_illuminance
      average_illuminance
      time_integrated_exposure
  }

  LUMINOUS_FLUX_AREA_MODEL {
    GENERAL:
      E_v = dPhi_v/dA

    UNIFORM:
      E_v = Phi_v/A

    CONDITIONS:
      flux_incident_on_defined_surface
      area > 0

    RULE:
      luminous_flux_and_illuminance
      MUST_NOT be treated_as_semantically_equivalent
  }

  POINT_SOURCE_MODEL {
    GENERAL:
      E_v = I_v*cos(theta)/r^2

    NORMAL_INCIDENCE:
      E_v = I_v/r^2

    PARAMETERS:
      I_v = luminous_intensity_in_source_to_receiver_direction
      r = source_to_surface_distance
      theta = angle_between_incident_ray_and_surface_normal

    CONDITIONS:
      point_source_approximation
      r > 0
      negligible_attenuation
      surface_orientation_defined

    RULE:
      inverse_square_and_cosine_terms MUST both_be_preserved_when_receiver_is_tilted
  }

  INVERSE_SQUARE_MODEL {
    aligned_point_source:
      E_2/E_1 = (r_1/r_2)^2

    CONDITIONS:
      same_source_intensity
      same_directional_emission
      same_receiver_orientation
      point_source_geometry

    RULE:
      inverse_square_law MUST_NOT be assumed_for_extended_near_field_or_collimated_sources
  }

  COSINE_LAW_MODEL {
    RECEIVER_PROJECTION:
      E_v(theta) = E_v_normal*cos(theta)

    NAME:
      Lambert_cosine_law_for_incidence

    CONDITIONS:
      same incident beam
      planar receiving surface

    RULE:
      receiver_cosine_law MUST be distinguished_from_Lambertian_source_emission_law
  }

  EXTENDED_SOURCE_MODEL {
    GENERAL:
      illuminance =
        integral_over_visible_source(
          luminance
          * geometric_projection_terms
          * solid_angle_terms
        )

    REQUIRE:
      source_area
      source_luminance_distribution
      receiver_location
      receiver_orientation
      occlusion_or_visibility

    RULE:
      extended_source_near_field_illuminance
      SHOULD NOT be reduced_to_single_point_intensity_without_validation
  }

  PHOTOMETRIC_WEIGHTING_MODEL {
    photometric_origin:
      illuminance derives_from_spectral_irradiance
      weighted_by_human_photopic_visual_response

    FORM:
      E_v =
        K_m * integral(V_lambda * E_e_lambda d_lambda)

    REQUIRE:
      spectral_irradiance
      luminous_efficiency_function

    RULE:
      lux_and_W_per_m2
      MUST_NOT be converted_without_spectral_distribution
  }

  SPECTRAL_ILLUMINANCE_MODEL {
    spectral_illuminance:
      E_v_lambda = dE_v/dlambda

    broadband:
      E_v = integral(E_v_lambda d_lambda)

    RULE:
      spectral_basis_and_wavelength_interval MUST be identified
  }

  SPATIAL_FIELD_MODEL {
    illuminance_field:
      E_v = E_v(x, y, z, surface_normal, t)

    mapping:
      grid_measurements
      point_measurements
      spatial_average
      minimum
      maximum
      uniformity_ratio

    RULE:
      spatial_statistics MUST preserve_sampling_grid_and_surface_definition
  }

  AVERAGING_MODEL {
    arithmetic_average:
      E_avg = sum(E_i)/N

    area_weighted_average:
      E_avg =
        integral_A(E_v dA)/A

    uniformity_examples:
      E_min/E_avg
      E_min/E_max

    RULE:
      averaging_method_and_sampling_geometry MUST be preserved
  }

  DAYLIGHT_MODEL {
    possible_components:
      direct_sunlight
      diffuse_sky_light
      reflected_daylight

    dependencies:
      time
      solar_position
      sky_condition
      glazing
      orientation
      shading

    RULE:
      daylight_illuminance_is_dynamic_and_context_dependent
  }

  ARTIFICIAL_LIGHTING_MODEL {
    possible_sources:
      LED
      fluorescent
      incandescent
      discharge_lamp
      laser_based_source

    dependencies:
      luminous_intensity_distribution
      mounting_height
      aiming
      optical_distribution
      dimming
      ageing
      surface_reflectance

    RULE:
      luminaire_luminous_flux_alone
      does_not_determine_task_plane_illuminance_without_geometry_and_distribution
  }

  RELATIONSHIPS {
    Illuminance -> LUMINOUS_FLUX_PER -> Area
    Illuminance -> MEASURED_IN -> Lux
    Illuminance -> DEPENDS_ON -> LuminousIntensity
    Illuminance -> DEPENDS_ON -> Distance
    Illuminance -> DEPENDS_ON -> SurfaceOrientation
    Illuminance -> MAY_DEPEND_ON -> SourceSpectralDistribution
    Illuminance -> MAY_VARY_OVER -> Position
    Illuminance -> MAY_VARY_OVER -> Time
    SpectralIrradiance -> VISUALLY_WEIGHTED_TO -> Illuminance
    LuminanceDistribution -> CONTRIBUTES_TO -> ExtendedSourceIlluminance
  }

  SEMANTIC_EQUIVALENCE {
    "illuminance" ~= incident_luminous_flux_density
    "lux" ~= "lx"
    "lumen per square metre" ~= "lm/m^2"

    illuminance != luminous_intensity
    illuminance != luminous_flux
    illuminance != luminance
    illuminance != irradiance
    lux != candela
    lux != lumen
  }

  CONSTRAINTS {
    illuminance_is_photometric_surface_quantity = true
    SI_unit = lux
    area_must_be_nonzero_for_flux_area_ratio = true
    receiver_surface_and_orientation_must_be_defined_for_directional_incidence = true
    illuminance_and_luminous_intensity_are_not_semantically_equivalent = true
    illuminance_and_luminance_are_not_semantically_equivalent = true
    illuminance_and_irradiance_are_not_semantically_equivalent = true
    point_source_inverse_square_model_requires_valid_geometry = true
    photometric_radiometric_conversion_requires_spectral_information = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE:
      Illuminance

    COMMON_INSTRUMENTS:
      lux_meter
      photometer
      calibrated_photodiode_with_photopic_filter
      imaging_photometer

    SENSOR_REQUIREMENTS:
      photopic_spectral_response
      cosine_angular_response
      linearity
      dynamic_range

    RECORD:
      numerical_value
      unit
      measurement_position
      surface_orientation
      detector_normal
      source_or_scene
      distance_when_relevant
      spectral_distribution_when_available
      source_state
      timestamp
      integration_time
      instrument
      detector_type
      photopic_mismatch
      cosine_response_error
      calibration_state
      reference_standard
      uncertainty

    UNCERTAINTY:
      measured_illuminance = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF incident_luminous_flux_known AND area_known AND area != 0
      AND uniform_distribution
      THEN illuminance = luminous_flux/area

    IF point_source_luminous_intensity_known AND distance > 0
      AND receiver_angle_known
      THEN illuminance =
        luminous_intensity*cos(receiver_angle)/distance^2

    IF point_source_luminous_intensity_known AND distance > 0
      AND normal_incidence
      THEN illuminance = luminous_intensity/distance^2

    IF illuminance_at_distance_1_known
      AND distances_known
      AND valid_inverse_square_conditions
      THEN illuminance_2 =
        illuminance_1*(distance_1/distance_2)^2

    IF spectral_irradiance_known
      THEN illuminance =
        integrate_with_photopic_visual_weighting

    IF spatial_illuminance_samples_known
      THEN compute_average_minimum_maximum_and_uniformity
      USING declared_sampling_method
  }

  DETECTOR_MODEL {
    ideal_lux_detector:
      spectral_response proportional_to photopic_V_lambda
      angular_response proportional_to cosine_of_incidence_angle

    practical_errors:
      spectral_mismatch
      cosine_error
      nonlinearity
      temperature_dependence
      dark_signal
      saturation
      stray_light

    RULE:
      detector_response MUST be considered_for_high_accuracy_illuminance_measurement
  }

  GEOMETRY_MODEL {
    REQUIRE:
      measurement_point
      receiving_surface
      surface_normal
      source_position_or_distribution

    point_source_context:
      distance
      source_direction
      receiver_angle

    extended_source_context:
      visible_solid_angle
      luminance_distribution

    RULE:
      illuminance_measurement_without_surface_orientation
      MAY be semantically_incomplete
  }

  UNCERTAINTY_MODEL {
    sources:
      calibration
      photopic_spectral_mismatch
      cosine_response
      detector_linearity
      source_stability
      distance
      alignment
      spatial_sampling
      stray_light
      temperature
      instrument_resolution
      reference_standard

    PROPAGATION:
      derived_illuminance_uncertainty
      <- detector_geometry_source_and_calibration_uncertainties
  }

  CONFIDENCE {
    definition_confidence: 1.00
    SI_unit_confidence: 1.00
    point_source_relationship_confidence: 1.00
    photometric_weighting_confidence: 0.99
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when surface orientation, source geometry,
      spectrum, detector response, sampling method,
      calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK quantity_is_illuminance
    CHECK unit_consistency
    CHECK surface_area_when_flux_ratio_used
    CHECK measurement_surface_and_orientation
    CHECK point_vs_extended_source
    CHECK distance_for_inverse_square_model
    CHECK receiver_angle_for_cosine_model
    CHECK illuminance_vs_luminous_intensity
    CHECK illuminance_vs_luminance
    CHECK illuminance_vs_irradiance
    CHECK photopic_spectral_response
    CHECK detector_cosine_response
    CHECK spatial_sampling_when_average_or_uniformity_reported
    CHECK calibration_state
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_measurement_position
      identify_receiving_surface
      identify_surface_orientation
      identify_source_or_scene
      attach_distance_when_relevant
      attach_spectral_information_when_available
      attach_timestamp
      identify_detector_and_response
      normalize_to_lux
      preserve_original_value_and_unit
      attach_uncertainty
      update_illuminance_state

    ON source_change:
      update_luminous_flux_or_intensity_distribution
      update_spectrum
      recompute_illuminance_when_geometry_known
      preserve_previous_source_state

    ON geometry_change:
      update_distance
      update_surface_orientation
      update_source_position
      recompute_point_or_extended_source_illuminance
      preserve_previous_geometry

    ON spatial_sampling_update:
      update_measurement_grid
      recompute_average_minimum_maximum_and_uniformity
      preserve_sampling_provenance

    ON calibration_revision:
      preserve_previous_calibration
      recompute_affected_measurements
      update_uncertainty
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: Illuminance
    canonical_symbol: E_v
    canonical_SI_unit: lux

    interpretation_order:
      identify_quantity
      identify_value
      identify_unit
      identify_measurement_surface
      identify_position_and_orientation
      identify_source_geometry
      identify_point_or_extended_source
      identify_luminous_intensity_or_flux_context
      identify_distance
      identify_spectral_distribution
      identify_detector_photopic_and_cosine_response
      identify_spatial_or_temporal_averaging
      identify_measurement_method
      identify_uncertainty
      normalize_units
      validate_geometry
      infer_photometric_relationships

    ambiguity_controls:
      distinguish_illuminance_from_luminous_intensity
      distinguish_illuminance_from_luminous_flux
      distinguish_illuminance_from_luminance
      distinguish_illuminance_from_irradiance
      distinguish_lux_from_candela_and_lumen
      distinguish_point_source_from_extended_source
      distinguish_receiver_cosine_law_from_Lambertian_emission
      preserve_surface_orientation_spectrum_detector_and_sampling_context
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_optical_illuminance_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Optical Measurements
      -> Illuminance Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      units
      relationships
      constraints
      luminous_flux_area_model
      point_source_model
      inverse_square_model
      cosine_law_model
      extended_source_model
      photometric_weighting_model
      spectral_illuminance_model
      spatial_field_model
      averaging_model
      daylight_model
      artificial_lighting_model
      detector_model
      geometry_model
      uncertainty_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      photometric_model_changes
      source_geometry_model_changes
      spectral_weighting_model_changes
      detector_model_changes
      spatial_sampling_model_changes
      measurement_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW