Optical Measurements

# Optical Measurements Ontology — Flow Algebra

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

FLOW OpticalMeasurementsOntology {

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

  PURPOSE:
    Represent optical measurement quantities, units, radiometric and photometric quantities, wavelength, frequency, photon energy, optical power, irradiance, radiance, spectral measurements, refractive properties, transmission, reflection, polarisation, detector response, calibration and uncertainty for consistent AI interpretation and reasoning.

  CORE_QUANTITIES {
    Wavelength {
      symbol: lambda
      dimension: L
      SI_unit: metre
      common_units: nanometre, micrometre
    }

    Frequency {
      symbol: nu
      dimension: T^-1
      SI_unit: hertz
      relation: c = lambda*nu IN vacuum
    }

    PhotonEnergy {
      symbol: E_photon
      SI_unit: joule
      relation: E_photon = h*nu
      relation_vacuum: E_photon = h*c/lambda
    }

    RadiantEnergy {
      symbol: Q_e
      SI_unit: joule
    }

    RadiantFlux {
      alias: OpticalPower
      symbol: Phi_e
      SI_unit: watt
      relation: Phi_e = dQ_e/dt
    }

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

    RadiantIntensity {
      symbol: I_e
      SI_unit: W/sr
      definition: radiant_flux_per_unit_solid_angle
    }

    Radiance {
      symbol: L_e
      SI_unit: W/(m^2*sr)
      definition: directional_radiant_flux_per_projected_area_per_solid_angle
    }
  }

  PHOTOMETRIC_QUANTITIES {
    LuminousFlux {
      symbol: Phi_v
      SI_unit: lumen
      SI_symbol: lm
    }

    LuminousIntensity {
      symbol: I_v
      SI_unit: candela
      SI_symbol: cd
    }

    Illuminance {
      symbol: E_v
      SI_unit: lux
      SI_symbol: lx
      equivalence: 1 lx = 1 lm/m^2
    }

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

  UNIT_SYSTEM {
    canonical_system: SI

    RULE:
      quantity_type, spectral_basis, geometry_and_detector_context
      MUST be preserved

    PREFIXES:
      nano
      micro
      milli
      kilo
      mega
      tera
  }

  WAVE_FREQUENCY_MODEL {
    VACUUM:
      c = lambda_0*nu

    MEDIUM:
      v_phase = lambda_medium*nu

    REFRACTIVE_INDEX:
      n = c/v_phase

    RULE:
      wavelength MUST identify_vacuum_or_medium_context_when_material
  }

  PHOTON_MODEL {
    E = h*nu

    VACUUM:
      E = h*c/lambda_0

    PHOTON_RATE:
      N_dot = optical_power/E
      WHEN effective_photon_energy_defined

    RULE:
      optical_power != photon_flux_without_spectral_context
  }

  IRRADIANCE_MODEL {
    UNIFORM_NORMAL:
      E_e = Phi_e/A

    POINT_SOURCE:
      E_e = Phi_e/(4*pi*r^2)
      UNDER isotropic_free_space_point_source_conditions

    RULE:
      area_orientation_distance_and_source_geometry MUST be preserved
  }

  RADIANCE_MODEL {
    differential_definition:
      L_e = d^2(Phi_e)/(dA_projected*dOmega)

    projected_area:
      dA_projected = dA*cos(theta)

    RULE:
      radiance != irradiance
      radiance != radiant_intensity
  }

  SPECTRAL_MODEL {
    spectral_radiant_flux:
      Phi_e_lambda = dPhi_e/dlambda

    spectral_irradiance:
      E_e_lambda = dE_e/dlambda

    spectral_radiance:
      L_e_lambda = dL_e/dlambda

    RULE:
      per_wavelength_and_per_frequency_spectral_densities
      require_Jacobian_conversion_and_are_not_numerically_interchangeable
  }

  PHOTOMETRIC_RADIOMETRIC_MODEL {
    photopic_luminous_flux:
      Phi_v = K_m*integral(V_lambda*Phi_e_lambda d_lambda)

    RULE:
      watts_and_lumens MUST_NOT be converted
      without_spectral_distribution_and_visual_weighting
  }

  REFRACTIVE_INDEX_MODEL {
    n = c/v_phase

    DISPERSION:
      n = n(lambda, temperature, pressure, composition)

    SNELL:
      n_1*sin(theta_1) = n_2*sin(theta_2)

    RULE:
      refractive_index SHOULD preserve wavelength_and_environmental_conditions
  }

  TRANSMISSION_REFLECTION_MODEL {
    transmittance:
      T = transmitted_flux/incident_flux

    reflectance:
      R = reflected_flux/incident_flux

    absorptance:
      A = absorbed_flux/incident_flux

    passive_balance:
      R + T + A = 1
      UNDER complete_accounting

    RULE:
      spectral_directional_and_geometric_conditions MUST be preserved
  }

  BEER_LAMBERT_MODEL {
    transmittance:
      T = I/I_0

    absorbance:
      A_abs = -log10(T)

    solution_form:
      A_abs = epsilon_molar*c*l
      UNDER applicable_conditions

    RULE:
      absorbance != absorptance
  }

  POLARISATION_MODEL {
    states:
      linear
      circular
      elliptical
      unpolarised
      partially_polarised

    representations:
      Jones_vector
      Stokes_parameters
      Mueller_matrix

    Malus_law:
      I = I_0*cos^2(theta)
      FOR ideal_linear_polarisation_context

    RULE:
      polarisation_basis_and_coherence_context MUST be preserved
  }

  INTERFERENCE_MODEL {
    optical_path_length:
      OPL = integral(n ds)

    phase_difference:
      delta_phi = 2*pi*delta_OPL/lambda_0

    RULE:
      coherence_phase_stability_and_wavelength MUST be preserved
  }

  DIFFRACTION_MODEL {
    single_slit_minima:
      a*sin(theta) = m*lambda

    circular_aperture:
      theta approximately_equals 1.22*lambda/D
      UNDER diffraction_limited_small_angle_context
  }

  DETECTOR_MODEL {
    detector_types:
      photodiode
      photomultiplier
      CCD
      CMOS
      bolometer
      thermopile

    responsivity:
      R_detector = electrical_output/incident_optical_power

    quantum_efficiency:
      eta = detected_charge_carriers/incident_photons

    effects:
      dark_current
      read_noise
      shot_noise
      saturation
      nonlinearity
      spectral_response

    RULE:
      detector_signal MUST NOT be treated_as_calibrated_optical_quantity_without_response_model
  }

  RELATIONSHIPS {
    Wavelength -> INVERSELY_RELATES_TO -> Frequency
    Frequency -> DETERMINES -> PhotonEnergy
    RadiantEnergy -> RATE_OF_CHANGE_TO -> RadiantFlux
    RadiantFlux -> DISTRIBUTED_OVER_AREA_AS -> Irradiance
    RadiantFlux -> DISTRIBUTED_OVER_SOLID_ANGLE_AS -> RadiantIntensity
    Radiance -> DESCRIBES -> DirectionalSurfaceRadiation
    SpectralDistribution -> QUALIFIES -> RadiometricQuantity
    PhotometricQuantity -> VISUALLY_WEIGHTS -> RadiometricQuantity
    RefractiveIndex -> RELATES -> LightSpeedInMedium
    DetectorResponsivity -> MAPS -> OpticalInputToElectricalOutput
  }

  SEMANTIC_EQUIVALENCE {
    "optical power" ~= radiant_flux
    "radiant flux" ~= optical_power
    "lux" ~= lumen_per_square_metre

    optical_power != irradiance
    irradiance != radiance
    radiance != radiant_intensity
    luminous_flux != radiant_flux
    illuminance != irradiance
    luminance != radiance
    absorbance != absorptance
  }

  CONSTRAINTS {
    wavelength_medium_context_should_be_identified = true
    radiometric_and_photometric_quantities_must_be_distinguished = true
    spectral_basis_must_be_identified = true
    detector_geometry_and_area_must_be_preserved = true
    radiance_requires_area_solid_angle_and_directional_semantics = true
    photometric_conversion_requires_spectral_weighting = true
    polarisation_state_and_basis_must_be_preserved = true
    detector_response_and_calibration_must_be_preserved = true
  }

  MEASUREMENT_MODEL {
    INSTRUMENTS:
      optical_power_meter
      photodiode_meter
      spectrometer
      spectroradiometer
      lux_meter
      luminance_meter
      integrating_sphere
      interferometer
      refractometer
      polarimeter
      ellipsometer

    RECORD:
      quantity_type
      numerical_value
      unit
      wavelength_or_spectrum
      spectral_bandwidth
      spectral_basis
      detector_area
      geometry
      distance
      solid_angle
      polarisation
      material_or_medium
      temperature
      pressure
      timestamp
      instrument
      detector_type
      responsivity
      calibration_state
      reference_standard
      integration_time
      uncertainty

    UNCERTAINTY:
      optical_measurement = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF vacuum_wavelength_known AND wavelength != 0
      THEN frequency = c/wavelength

    IF frequency_known
      THEN photon_energy = h*frequency

    IF monochromatic_power_and_photon_energy_known AND photon_energy != 0
      THEN photon_rate = optical_power/photon_energy

    IF radiant_power_known AND area_known AND area != 0
      AND uniform_normal_context
      THEN irradiance = radiant_power/area

    IF isotropic_point_source_power_known AND distance > 0
      THEN irradiance = power/(4*pi*distance^2)
      UNDER inverse_square_conditions

    IF incident_and_transmitted_flux_known AND incident_flux != 0
      THEN transmittance = transmitted_flux/incident_flux

    IF transmittance_known AND transmittance > 0
      THEN absorbance = -log10(transmittance)

    IF spectral_radiant_flux_known
      THEN luminous_flux =
        integrate_with_visual_weighting
  }

  REFERENCE_MODEL {
    wavelength:
      identify_vacuum_or_medium

    geometry:
      identify_area_orientation_distance_solid_angle

    spectral:
      identify_bandwidth_resolution_and_basis

    photometry:
      identify_visual_observer_function

    detector:
      identify_calibration_responsivity_and_spectral_response

    RULE:
      missing_reference_or_geometry_context reduces_semantic_confidence
  }

  UNCERTAINTY_MODEL {
    sources:
      wavelength_calibration
      power_calibration
      detector_responsivity
      spectral_mismatch
      dark_signal
      shot_noise
      read_noise
      geometry
      alignment
      polarisation
      stray_light
      bandwidth
      integration_time
      temperature
      reference_standard
      model_assumptions

    PROPAGATION:
      derived_optical_quantity_uncertainty
      <- measurement_geometry_spectral_detector_and_model_uncertainties
  }

  CONFIDENCE {
    quantity_definition_confidence: 1.00
    SI_unit_confidence: 1.00
    radiometric_relationship_confidence: 1.00
    photometric_relationship_confidence: 0.99
    spectral_relationship_confidence: 0.99
    measurement_context_confidence: 0.97

    RULE:
      confidence decreases when wavelength, spectral basis,
      geometry, polarisation, detector response,
      calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK wavelength_frequency_context
    CHECK vacuum_vs_medium_wavelength
    CHECK radiometric_vs_photometric_quantity
    CHECK irradiance_vs_radiance_vs_intensity
    CHECK spectral_basis
    CHECK area_orientation_and_solid_angle
    CHECK absorbance_vs_absorptance
    CHECK polarisation_representation
    CHECK detector_linearity_and_saturation
    CHECK detector_calibration_and_spectral_response
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      identify_quantity_type
      validate_unit
      identify_wavelength_or_spectrum
      identify_spectral_basis
      attach_geometry
      identify_polarisation
      identify_material_or_medium
      identify_detector_and_responsivity
      normalize_to_canonical_SI
      preserve_original_value_and_unit
      attach_timestamp
      attach_uncertainty
      update_optical_state

    ON wavelength_or_spectrum_change:
      update_frequency
      update_photon_energy
      update_detector_response
      update_photometric_weighting_when_required

    ON geometry_change:
      update_area
      update_distance
      update_orientation
      update_solid_angle
      recompute_geometry_dependent_quantities

    ON detector_calibration_revision:
      preserve_previous_calibration
      update_responsivity
      recompute_affected_measurements
      update_uncertainty
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_domain: OpticalMeasurements

    interpretation_order:
      identify_quantity
      identify_radiometric_or_photometric_domain
      identify_value
      identify_unit
      identify_wavelength_frequency_or_spectrum
      identify_spectral_basis
      identify_geometry
      identify_polarisation
      identify_material_or_medium
      identify_detector_and_calibration
      identify_uncertainty
      normalize_units
      validate_dimensions
      infer_optical_relationships

    ambiguity_controls:
      distinguish_wavelength_from_frequency
      distinguish_optical_power_from_irradiance
      distinguish_irradiance_from_radiance
      distinguish_radiant_intensity_from_radiance
      distinguish_radiometric_from_photometric_quantities
      distinguish_absorbance_from_absorptance
      distinguish_detector_signal_from_calibrated_optical_quantity
      preserve_spectral_geometry_polarisation_and_detector_context
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_optical_quantity_semantics

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

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_domain
      ontology_path
      core_quantities
      photometric_quantities
      unit_system
      wave_frequency_model
      photon_model
      irradiance_model
      radiance_model
      spectral_model
      photometric_radiometric_model
      refractive_index_model
      transmission_reflection_model
      Beer_Lambert_model
      polarisation_model
      interference_model
      diffraction_model
      detector_model
      relationships
      constraints
      measurement_model
      reference_model
      uncertainty_model
      reasoning_rules
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      optical_quantity_model_changes
      spectral_model_changes
      radiometric_or_photometric_model_changes
      geometry_model_changes
      detector_model_changes
      measurement_model_changes
      reference_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW