Wavelength Measurement Ontology

# Wavelength Measurement Ontology — Flow Algebra

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

FLOW WavelengthMeasurementOntology {

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

  PURPOSE:
    Represent wavelength measurement as the quantitative determination of the spatial period of an optical or electromagnetic wave, including vacuum and medium wavelength, frequency relationships, refractive index, spectral wavelength, monochromatic and broadband sources, interferometric and spectrometric measurement methods, calibration, resolution, uncertainty, and distinctions from frequency, wavenumber and spectral bandwidth.

  ENTITY Wavelength {
    TYPE: OpticalSpatialQuantity
    SYMBOL: lambda
    DIMENSION: L
    SI_UNIT: metre
    SI_SYMBOL: m

    DEFINITION:
      wavelength := spatial_period_of_wave_phase

    VACUUM_RELATION:
      lambda_0 = c/nu

    MEDIUM_RELATION:
      lambda_medium = v_phase/nu

    PROPERTIES:
      is_scalar_magnitude
      has_value
      has_unit
      has_dimension
      depends_on_phase_velocity
      depends_on_medium
      frequency_is_invariant_across_stationary_interface
      may_have_uncertainty
  }

  ENTITY VacuumWavelength {
    TYPE: Wavelength
    SYMBOL: lambda_0

    RELATION:
      lambda_0 = c/nu
  }

  ENTITY MediumWavelength {
    TYPE: Wavelength
    SYMBOL: lambda_m

    RELATION:
      lambda_m = lambda_0/n
      UNDER refractive_index_context
  }

  ENTITY Frequency {
    TYPE: TemporalFrequencyQuantity
    SYMBOL: nu
    DIMENSION: T^-1
    SI_UNIT: hertz
    SI_SYMBOL: Hz

    RELATION:
      nu = c/lambda_0
  }

  ENTITY Wavenumber {
    TYPE: ReciprocalLengthQuantity
    SYMBOL: k_or_sigma

    ANGULAR_WAVENUMBER:
      k = 2*pi/lambda

    SPECTROSCOPIC_WAVENUMBER:
      sigma = 1/lambda

    RULE:
      angular_wavenumber_and_spectroscopic_wavenumber
      MUST_NOT be treated_as_identical
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: metre
      symbol: m
    }

    COMMON_OPTICAL_UNITS:
      nanometre
      micrometre
      picometre
      angstrom

    CONVERSIONS:
      1 nm = 1e-9 m
      1 micrometre = 1e-6 m
      1 pm = 1e-12 m
      1 angstrom = 1e-10 m

    RULE:
      preserve_original_unit_and_normalized_SI_value
  }

  CLASSIFICATION {
    by propagation:
      vacuum_wavelength
      medium_wavelength

    by source:
      monochromatic_wavelength
      central_wavelength
      peak_wavelength
      effective_wavelength

    by spectral representation:
      wavelength_domain
      frequency_domain
      wavenumber_domain

    by measurement:
      absolute_wavelength
      relative_wavelength
      wavelength_shift
      spectral_bandwidth
  }

  WAVE_RELATION_MODEL {
    GENERAL:
      v_phase = nu*lambda

    VACUUM:
      c = nu*lambda_0

    MEDIUM:
      v_phase = c/n_phase
      lambda_medium = lambda_0/n_phase

    RULE:
      phase_refractive_index MUST be used_for_phase_wavelength_relation
  }

  FREQUENCY_WAVELENGTH_MODEL {
    VACUUM:
      nu = c/lambda_0

    INVERSE:
      lambda_0 = c/nu

    REQUIRE:
      lambda_0 > 0
      nu > 0

    RULE:
      frequency_and_wavelength_are_related_but_not_semantically_equivalent
  }

  REFRACTIVE_INDEX_MODEL {
    phase_refractive_index:
      n = c/v_phase

    wavelength_relation:
      lambda_medium = lambda_0/n

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

    RULE:
      wavelength_in_medium SHOULD preserve refractive_index_and_environmental_conditions
  }

  PHOTON_ENERGY_MODEL {
    photon_energy:
      E = h*nu

    vacuum_wavelength_form:
      E = h*c/lambda_0

    RULE:
      photon_energy_from_wavelength requires_vacuum_wavelength_or_equivalent_frequency_context
  }

  SPECTRAL_MODEL {
    spectrum_in_wavelength_domain:
      S_lambda(lambda)

    central_wavelength:
      definition_depends_on_weighting_convention

    peak_wavelength:
      wavelength_at_spectral_maximum

    bandwidth:
      may_be_FWHM
      RMS_width
      equivalent_bandwidth
      specified_interval

    RULE:
      central_peak_and_nominal_wavelength MUST_NOT be assumed_identical
  }

  SPECTRAL_DOMAIN_TRANSFORMATION {
    frequency:
      nu = c/lambda_0

    differential:
      abs(dnu/dlambda) = c/lambda^2

    spectral_density:
      S_nu = S_lambda*lambda^2/c
      under_consistent_density_definition

    RULE:
      spectral_density_per_wavelength
      MUST NOT be numerically_relabelled_as_per_frequency_density
  }

  INTERFEROMETRY_MODEL {
    optical_path_difference:
      OPD = m*lambda
      FOR integer_fringe_order_under_simple_constructive_condition

    Michelson_displacement:
      fringe_count_relation =
        2*delta_x/lambda
      FOR mirror_displacement_delta_x

    INFERENCE:
      lambda = 2*delta_x/N
      WHEN N != 0

    REQUIRE:
      interference_order
      geometry
      medium
      refractive_index
      fringe_count

    RULE:
      optical_path_length_and_geometric_path_length
      MUST be distinguished
  }

  DIFFRACTION_GRATING_MODEL {
    grating_equation:
      m*lambda =
        d*(sin(theta_m) - sin(theta_i))
      under_defined_sign_convention

    normal_incidence_special_case:
      m*lambda = d*sin(theta_m)

    REQUIRE:
      grating_spacing
      diffraction_order
      incidence_angle
      diffraction_angle

    RULE:
      diffraction_order_and_angle_convention MUST be preserved
  }

  PRISM_SPECTROMETER_MODEL {
    principle:
      wavelength_inferred_from_angular_dispersion_and_calibration

    dependencies:
      refractive_index_dispersion
      prism_geometry
      incidence_geometry
      detector_angle

    RULE:
      wavelength_scale requires_calibration_against_known_spectral_lines_or_traceable_model
  }

  SPECTROMETER_MODEL {
    instrument_types:
      grating_spectrometer
      monochromator
      Fourier_transform_spectrometer
      wavemeter
      optical_spectrum_analyser

    characteristics:
      spectral_resolution
      resolving_power
      wavelength_accuracy
      repeatability
      instrument_line_shape
      free_spectral_range

    RULE:
      wavelength_resolution_and_wavelength_accuracy
      MUST_NOT be treated_as_synonyms
  }

  RESOLUTION_MODEL {
    wavelength_resolution:
      delta_lambda_min

    resolving_power:
      R = lambda/delta_lambda

    REQUIRE:
      wavelength
      resolution_definition

    RULE:
      resolution_may_depend_on_wavelength_slit_width_grating_order_and_instrument_configuration
  }

  DOPPLER_SHIFT_MODEL {
    nonrelativistic_radial_approximation:
      delta_lambda/lambda approximately_equals v_r/c
      FOR abs(v_r) much_less_than c
      with_sign_convention_defined

    RULE:
      wavelength_shift MUST preserve_reference_wavelength_and_velocity_sign_convention
  }

  RELATIONSHIPS {
    Wavelength -> HAS_DIMENSION -> Length
    Wavelength -> MEASURED_IN -> Metre
    Wavelength -> INVERSELY_RELATES_TO -> Frequency
    VacuumWavelength -> RELATES_TO -> SpeedOfLightAndFrequency
    MediumWavelength -> DEPENDS_ON -> RefractiveIndex
    Wavelength -> DETERMINES -> PhotonEnergy
    Wavelength -> RELATES_TO -> Wavenumber
    Wavelength -> MEASURED_BY -> SpectrometerOrInterferometer
    DiffractionAngle -> RELATES_TO -> WavelengthAndGratingSpacing
    WavelengthMeasurement -> QUALIFIED_BY -> ResolutionAndUncertainty
  }

  SEMANTIC_EQUIVALENCE {
    "wavelength" ~= spatial_wave_period
    "vacuum wavelength" ~= lambda_0
    "nanometre" ~= "nm"

    wavelength != frequency
    wavelength != wavenumber
    wavelength != spectral_bandwidth
    vacuum_wavelength != medium_wavelength
    central_wavelength != peak_wavelength
    wavelength_accuracy != wavelength_resolution
  }

  CONSTRAINTS {
    wavelength_dimension = L
    SI_unit = metre
    wavelength_value_should_be_positive_for_standard_optical_frequency = true
    vacuum_or_medium_context_should_be_identified = true
    refractive_index_context_required_for_medium_conversion = true
    wavelength_and_frequency_are_not_semantically_equivalent = true
    wavelength_and_wavenumber_are_not_semantically_equivalent = true
    spectral_bandwidth_and_wavelength_are_not_semantically_equivalent = true
    measurement_resolution_and_accuracy_must_be_distinguished = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE_OR_INFERRED:
      Wavelength

    COMMON_METHODS:
      diffraction_grating_spectrometry
      prism_spectrometry
      interferometry
      Fourier_transform_spectroscopy
      calibrated_wavemeter
      optical_spectrum_analysis

    RECORD:
      numerical_value
      unit
      vacuum_or_medium_wavelength
      medium
      refractive_index
      temperature
      pressure
      source
      monochromatic_or_spectral
      central_peak_or_nominal_definition
      diffraction_order_when_relevant
      instrument_configuration
      spectral_resolution
      resolving_power
      calibration_reference
      calibration_state
      timestamp
      uncertainty

    UNCERTAINTY:
      measured_wavelength = best_estimate +/- uncertainty
  }

  CALIBRATION_MODEL {
    references:
      known_atomic_or_molecular_spectral_lines
      stabilised_laser_reference
      frequency_comb
      traceable_wavelength_standard

    calibration_function:
      detector_coordinate_or_angle -> wavelength

    REQUIRE:
      calibration_points
      fit_model
      residuals
      valid_range
      traceability
      calibration_uncertainty

    RULE:
      extrapolation_beyond_calibrated_range SHOULD be_flagged
  }

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

    IF frequency_known AND frequency != 0
      THEN vacuum_wavelength = c/frequency

    IF vacuum_wavelength_known AND phase_refractive_index_known
      AND refractive_index != 0
      THEN medium_wavelength = vacuum_wavelength/refractive_index

    IF vacuum_wavelength_known
      THEN photon_energy = h*c/vacuum_wavelength

    IF wavelength_known AND wavelength != 0
      THEN spectroscopic_wavenumber = 1/wavelength
      AND angular_wavenumber = 2*pi/wavelength

    IF grating_spacing_order_and_angles_known
      AND diffraction_order != 0
      THEN wavelength =
        grating_spacing*(sin(diffraction_angle)-sin(incidence_angle))
        / diffraction_order

    IF Michelson_mirror_displacement_known AND fringe_count != 0
      THEN wavelength = 2*mirror_displacement/fringe_count
      UNDER simple_interferometer_conditions

    IF wavelength_and_resolution_known AND resolution != 0
      THEN resolving_power = wavelength/resolution
  }

  ENVIRONMENT_MODEL {
    air_wavelength:
      depends_on air_refractive_index

    air_refractive_index:
      may_depend_on
        temperature
        pressure
        humidity
        composition
        wavelength

    RULE:
      high_accuracy_air_wavelength_measurement
      SHOULD preserve_environmental_conditions
  }

  UNCERTAINTY_MODEL {
    sources:
      wavelength_reference
      calibration_fit
      angular_measurement
      grating_spacing
      fringe_count
      displacement_measurement
      refractive_index
      temperature
      pressure
      instrument_line_shape
      spectral_resolution
      detector_sampling
      source_stability

    PROPAGATION:
      derived_wavelength_uncertainty
      <- calibration_geometry_environment_and_model_uncertainties
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    vacuum_frequency_relationship_confidence: 1.00
    diffraction_relationship_confidence: 0.99
    interferometric_relationship_confidence: 0.99
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when vacuum_or_medium context,
      refractive index, instrument configuration,
      spectral definition, calibration state,
      resolution or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK wavelength_positive
    CHECK vacuum_vs_medium_context
    CHECK refractive_index_when_required
    CHECK wavelength_vs_frequency_distinction
    CHECK wavelength_vs_wavenumber_distinction
    CHECK central_vs_peak_wavelength
    CHECK spectral_bandwidth_definition
    CHECK diffraction_order_and_angle_convention
    CHECK interferometer_geometry
    CHECK spectral_resolution_vs_accuracy
    CHECK environmental_conditions_for_high_accuracy_air_measurement
    CHECK calibration_range
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_vacuum_or_medium_context
      identify_source
      identify_monochromatic_or_spectral_context
      identify_wavelength_definition
      attach_medium_and_refractive_index_when_relevant
      attach_temperature_and_pressure
      identify_measurement_method
      attach_instrument_configuration
      attach_resolution
      apply_valid_calibration
      normalize_to_metre
      preserve_original_value_and_unit
      attach_timestamp
      attach_uncertainty
      update_wavelength_state

    ON medium_or_environment_change:
      update_refractive_index
      update_temperature
      update_pressure
      recompute_medium_wavelength_when_valid
      preserve_vacuum_wavelength
      preserve_previous_environment

    ON calibration_revision:
      preserve_previous_calibration
      update_calibration_function
      recompute_affected_wavelengths
      update_uncertainty
      update_confidence

    ON spectral_definition_change:
      preserve_previous_definition
      update_central_peak_or_nominal_semantics
      recompute_reported_wavelength_when_required

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: Wavelength
    canonical_symbol: lambda
    canonical_dimension: L
    canonical_SI_unit: metre

    interpretation_order:
      identify_quantity
      identify_value
      identify_unit
      identify_vacuum_or_medium_wavelength
      identify_medium_and_refractive_index
      identify_monochromatic_or_spectral_context
      identify_central_peak_or_nominal_definition
      identify_frequency_or_wavenumber_context
      identify_measurement_method
      identify_instrument_resolution
      identify_environmental_conditions
      identify_calibration_and_traceability
      identify_uncertainty
      normalize_units
      validate_dimensions
      infer_wave_relationships

    ambiguity_controls:
      distinguish_wavelength_from_frequency
      distinguish_wavelength_from_wavenumber
      distinguish_vacuum_from_medium_wavelength
      distinguish_wavelength_from_spectral_bandwidth
      distinguish_central_from_peak_wavelength
      distinguish_measurement_accuracy_from_resolution
      distinguish_geometric_path_from_optical_path
      preserve_medium_environment_calibration_and_spectral_definition
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_optical_wavelength_semantics

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

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      units
      relationships
      constraints
      wave_relation_model
      frequency_wavelength_model
      refractive_index_model
      photon_energy_model
      spectral_model
      spectral_domain_transformation
      interferometry_model
      diffraction_grating_model
      prism_spectrometer_model
      spectrometer_model
      resolution_model
      Doppler_shift_model
      calibration_model
      environment_model
      uncertainty_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      vacuum_or_medium_model_changes
      refractive_index_model_changes
      spectral_definition_changes
      interferometry_or_diffraction_model_changes
      calibration_model_changes
      environment_model_changes
      measurement_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW