Light Intensity Ontology

# Light Intensity Ontology — Flow Algebra

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

FLOW LightIntensityOntology {

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

  PURPOSE:
    Represent light intensity with explicit semantic separation between photometric luminous intensity, radiometric radiant intensity, irradiance, illuminance, radiance, luminance and informal uses of "intensity", including directional emission, solid angle, spectral weighting, inverse-square propagation, measurement geometry, detector response, units, calibration and uncertainty.

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

    DEFINITION:
      luminous_intensity := luminous_flux_per_unit_solid_angle_in_specified_direction

    FORM:
      I_v = dPhi_v/dOmega

    PROPERTIES:
      is_directional
      is_photometric
      is_spectrally_weighted
      depends_on_direction
      may_have_uncertainty
  }

  ENTITY RadiantIntensity {
    TYPE: RadiometricDirectionalQuantity
    SYMBOL: I_e
    SI_UNIT: watt_per_steradian
    SI_SYMBOL: W/sr

    DEFINITION:
      radiant_intensity := radiant_flux_per_unit_solid_angle_in_specified_direction

    FORM:
      I_e = dPhi_e/dOmega
  }

  RELATED_QUANTITIES {
    LuminousFlux {
      symbol: Phi_v
      unit: lumen
      relation: dPhi_v = I_v*dOmega
    }

    RadiantFlux {
      alias: OpticalPower
      symbol: Phi_e
      unit: watt
      relation: dPhi_e = I_e*dOmega
    }

    Illuminance {
      symbol: E_v
      unit: lux
      definition: incident_luminous_flux_per_unit_area
    }

    Irradiance {
      symbol: E_e
      unit: W/m^2
      definition: incident_radiant_flux_per_unit_area
    }

    Luminance {
      symbol: L_v
      unit: cd/m^2
    }

    Radiance {
      symbol: L_e
      unit: W/(m^2*sr)
    }
  }

  UNIT_SYSTEM {
    luminous_intensity:
      canonical_unit: candela
      symbol: cd

    radiant_intensity:
      canonical_unit: watt_per_steradian
      symbol: W/sr

    relations:
      1 lm = 1 cd*sr
      1 lx = 1 lm/m^2

    RULE:
      quantity_type MUST identify photometric_or_radiometric_domain
  }

  TERMINOLOGY_MODEL {
    phrase:
      "light intensity"

    possible_meanings:
      luminous_intensity
      radiant_intensity
      irradiance
      illuminance
      radiance
      luminance
      optical_power
      electromagnetic_energy_flux
      informal_brightness

    RULE:
      resolve_using_unit_geometry_spectrum_detector_and_context
      before_quantitative_reasoning
  }

  SOLID_ANGLE_MODEL {
    symbol: Omega
    SI_unit: steradian
    SI_symbol: sr

    full_sphere:
      Omega = 4*pi

    hemisphere:
      Omega = 2*pi

    RULE:
      intensity_is_flux_per_solid_angle
      not_flux_per_surface_area
  }

  LUMINOUS_INTENSITY_MODEL {
    general:
      I_v(theta, phi) = dPhi_v/dOmega

    uniform_over_solid_angle:
      Phi_v = I_v*Omega

    isotropic_source:
      Phi_v = 4*pi*I_v

    RULE:
      luminous_intensity != illuminance
  }

  RADIANT_INTENSITY_MODEL {
    general:
      I_e(theta, phi) = dPhi_e/dOmega

    isotropic_source:
      Phi_e = 4*pi*I_e

    spectral_form:
      I_e_lambda = dI_e/dlambda
  }

  INVERSE_SQUARE_MODEL {
    photometric_point_source:
      E_v = I_v*cos(theta)/r^2

    radiometric_point_source:
      E_e = I_e*cos(theta)/r^2

    aligned_receiver:
      cos(theta) = 1

    CONDITIONS:
      point_source_approximation
      negligible_propagation_loss
      distance > 0
      receiver_orientation_known

    RULE:
      inverse_square_model MUST_NOT be applied_to_extended_or_collimated_sources_without_validation
  }

  PHOTOMETRIC_WEIGHTING_MODEL {
    photopic_luminous_intensity:
      I_v = K_m*integral(V_lambda*I_e_lambda d_lambda)

    REQUIRE:
      spectral_radiant_intensity
      photopic_luminous_efficiency_function

    RULE:
      candela_and_W_per_sr MUST_NOT be converted_without_spectral_distribution
  }

  SPECTRAL_MODEL {
    wavelength_basis:
      I_e_lambda = dI_e/dlambda

    frequency_basis:
      I_e_nu = dI_e/dnu

    RULE:
      per_wavelength_and_per_frequency_values require_Jacobian_conversion
  }

  LAMBERTIAN_MODEL {
    ideal_planar_emitter:
      I(theta) = I(0)*cos(theta)

    PROPERTY:
      radiance_or_luminance_constant_with_viewing_direction
      for_ideal_Lambertian_surface

    RULE:
      source_cosine_distribution MUST be distinguished_from_receiver_cosine_projection
  }

  EXTENDED_SOURCE_MODEL {
    REQUIRE:
      source_area
      radiance_or_luminance
      viewing_geometry
      solid_angle

    RULE:
      near_field_extended_source SHOULD NOT be reduced_to_point_source_intensity_without_validation
  }

  POLARISATION_MODEL {
    Malus_law:
      I = I_0*cos^2(theta)

    CONDITIONS:
      linearly_polarised_input
      ideal_linear_analyser

    RULE:
      polarisation_context MUST be preserved_when_optics_or_detector_are_polarisation_sensitive
  }

  RELATIONSHIPS {
    LuminousIntensity -> LUMINOUS_FLUX_PER -> SolidAngle
    RadiantIntensity -> RADIANT_FLUX_PER -> SolidAngle
    LuminousIntensity -> MEASURED_IN -> Candela
    RadiantIntensity -> MEASURED_IN -> WattPerSteradian
    LuminousIntensity -> CONTRIBUTES_TO -> Illuminance
    RadiantIntensity -> CONTRIBUTES_TO -> Irradiance
    Luminance -> RELATES -> LuminousIntensityPerProjectedArea
    Radiance -> RELATES -> RadiantIntensityPerProjectedArea
    SpectralRadiantIntensity -> VISUALLY_WEIGHTED_TO -> LuminousIntensity
  }

  SEMANTIC_EQUIVALENCE {
    "luminous intensity" ~= candela_quantity
    "radiant intensity" ~= radiant_flux_per_steradian
    "cd" ~= candela
    "W/sr" ~= watt_per_steradian

    luminous_intensity != illuminance
    radiant_intensity != irradiance
    luminous_intensity != luminous_flux
    radiant_intensity != radiant_flux
    luminous_intensity != luminance
    radiant_intensity != radiance
    photometric_intensity != radiometric_intensity
  }

  CONSTRAINTS {
    luminous_intensity_is_directional = true
    radiant_intensity_is_directional = true
    solid_angle_context_is_required = true
    photometric_and_radiometric_intensities_are_not_semantically_equivalent = true
    intensity_and_surface_flux_density_are_not_semantically_equivalent = true
    inverse_square_model_requires_point_source_geometry = true
    spectral_conversion_requires_spectral_distribution = true
    detector_response_must_be_considered = true
  }

  MEASUREMENT_MODEL {
    methods:
      goniophotometry
      gonioradiometry
      calibrated_photometry
      calibrated_radiometry
      far_field_surface_measurement_inference

    instruments:
      goniophotometer
      photometer
      radiometer
      spectroradiometer
      calibrated_photodiode

    RECORD:
      quantity_type
      numerical_value
      unit
      photometric_or_radiometric
      source_geometry
      measurement_direction
      solid_angle
      distance
      detector_area
      detector_orientation
      wavelength_or_spectrum
      spectral_bandwidth
      polarisation
      timestamp
      instrument
      detector_response
      calibration_state
      reference_standard
      uncertainty

    UNCERTAINTY:
      measured_or_inferred_intensity = best_estimate +/- uncertainty
  }

  DETECTOR_MODEL {
    signal_dependencies:
      incident_optical_quantity
      detector_area
      spectral_response
      angular_response
      polarisation_response
      integration_time

    errors:
      dark_signal
      saturation
      nonlinearity
      stray_light
      spectral_mismatch
      angular_mismatch

    RULE:
      detector_reading MUST be calibrated_to_requested_intensity_quantity
  }

  REASONING_RULES {
    IF luminous_flux_known AND uniform_solid_angle_known AND solid_angle != 0
      THEN luminous_intensity = luminous_flux/solid_angle

    IF radiant_flux_known AND uniform_solid_angle_known AND solid_angle != 0
      THEN radiant_intensity = radiant_flux/solid_angle

    IF isotropic_luminous_source
      THEN luminous_flux = 4*pi*luminous_intensity

    IF isotropic_radiant_source
      THEN radiant_flux = 4*pi*radiant_intensity

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

    IF point_source_radiant_intensity_known AND distance > 0
      AND receiver_normal_aligned
      THEN irradiance = radiant_intensity/distance^2

    IF spectral_radiant_intensity_known
      THEN luminous_intensity = integrate_with_photopic_visual_weighting

    IF linearly_polarised_intensity_known AND analyser_angle_known
      THEN transmitted_intensity = incident_intensity*cos^2(analyser_angle)
      UNDER Malus_law_conditions
  }

  GEOMETRY_MODEL {
    REQUIRE:
      source_position
      measurement_position
      distance
      source_direction
      detector_normal
      source_extent
      angular_distribution

    far_field:
      directional_intensity_distribution_can_often_be_used

    near_field:
      extended_source_geometry_may_require_radiance_or_luminance_model
  }

  UNCERTAINTY_MODEL {
    sources:
      calibration
      detector_spectral_response
      distance
      angular_alignment
      solid_angle
      source_stability
      detector_area
      stray_light
      polarisation
      spectral_distribution
      instrument_resolution
      reference_standard

    PROPAGATION:
      derived_intensity_uncertainty
      <- optical_geometry_detector_and_calibration_uncertainties
  }

  CONFIDENCE {
    definition_confidence: 1.00
    luminous_intensity_unit_confidence: 1.00
    radiant_intensity_unit_confidence: 1.00
    inverse_square_relationship_confidence: 0.99
    photometric_weighting_confidence: 0.99
    measurement_context_confidence: 0.97

    RULE:
      confidence decreases when intensity meaning, unit,
      spectral distribution, geometry, direction,
      detector response, calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK requested_meaning_of_light_intensity
    CHECK photometric_vs_radiometric_domain
    CHECK unit_consistency
    CHECK solid_angle
    CHECK measurement_direction
    CHECK source_geometry
    CHECK point_vs_extended_source
    CHECK intensity_vs_illuminance_or_irradiance
    CHECK intensity_vs_luminance_or_radiance
    CHECK spectral_distribution_for_photometric_conversion
    CHECK detector_response
    CHECK polarisation_when_relevant
    CHECK calibration_state
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      resolve_light_intensity_semantics
      identify_photometric_or_radiometric_quantity
      validate_unit
      attach_source_and_geometry
      attach_direction_and_solid_angle
      attach_distance_and_detector_orientation
      attach_wavelength_or_spectrum
      attach_polarisation_when_relevant
      identify_detector_and_response
      normalize_to_canonical_unit
      preserve_original_value_and_unit
      attach_timestamp
      attach_uncertainty
      update_intensity_state

    ON spectral_change:
      update_spectral_radiant_intensity
      recompute_photometric_weighting
      update_detector_response

    ON geometry_change:
      update_distance
      update_direction
      update_solid_angle
      update_source_extent
      recompute_surface_received_quantity_when_valid

    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_primary_entity: LuminousIntensity
    canonical_primary_symbol: I_v
    canonical_primary_SI_unit: cd

    alternate_radiometric_entity: RadiantIntensity
    alternate_radiometric_symbol: I_e
    alternate_radiometric_SI_unit: W/sr

    interpretation_order:
      resolve_phrase_light_intensity
      identify_photometric_or_radiometric_domain
      identify_value
      identify_unit
      identify_flux_solid_angle_or_surface_quantity
      identify_direction
      identify_source_geometry
      identify_distance_and_detector_orientation
      identify_wavelength_or_spectrum
      identify_polarisation
      identify_detector_response
      identify_measurement_method
      identify_uncertainty
      normalize_units
      validate_geometry
      infer_optical_relationships

    ambiguity_controls:
      distinguish_luminous_intensity_from_radiant_intensity
      distinguish_luminous_intensity_from_illuminance
      distinguish_radiant_intensity_from_irradiance
      distinguish_intensity_from_flux
      distinguish_intensity_from_luminance_or_radiance
      distinguish_photometric_from_radiometric_quantities
      distinguish_point_source_from_extended_source
      distinguish_optical_intensity_from_electric_field_amplitude
      preserve_spectrum_direction_geometry_detector_and_polarisation_context
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_optical_intensity_semantics

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

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_primary_entity
      ontology_path
      terminology_model
      solid_angle_model
      luminous_intensity_model
      radiant_intensity_model
      inverse_square_model
      photometric_weighting_model
      spectral_model
      Lambertian_model
      extended_source_model
      polarisation_model
      relationships
      constraints
      measurement_model
      detector_model
      geometry_model
      uncertainty_model
      reasoning_rules
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      intensity_semantic_model_changes
      photometric_or_radiometric_model_changes
      spectral_model_changes
      geometry_model_changes
      detector_model_changes
      measurement_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW