Lustre Reflectivity Ratio

Audit measured specular/total reflected signal with independently supplied background and angular exposure, retaining signed overcorrection; not absolute reflectance, Fresnel theory or validated lustre grading.

Description

Specular share compares specular signal with total reflected signal under matched angular exposure.

Specular share compares specular signal with total reflected signal under matched angular exposure. Background correction can produce a signed negative numerator without implying a physical negative reflectance.^[1]

When to use Lustre Reflectivity Ratio

Use this tool to audit measured specular/total reflected signal with independently supplied background and angular exposure, retaining signed overcorrection; not absolute reflectance, Fresnel theory or validated lustre grading.

Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.

How to use Lustre Reflectivity Ratio and understand its results

Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.
Enter measuredSpecularSignals, measuredTotalReflectedSignals, backgroundSignals, representedAngularWeights using the field table and calculation rules, then run the tool.
Read backgroundCorrectedSpecularShare, backgroundCorrectedTotalSignal. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
measuredSpecularSignals	Measured specular signals	list of number	Required
measuredTotalReflectedSignals	Measured total reflected signals	list of number	Required
backgroundSignals	Background signals	list of number	Required
representedAngularWeights	Represented angular weights	list of number	Required

Pair nonnegative specular, total and background signals with positive angular weights; require raw specular≤raw total and positive corrected total. Return signed corrected specular share and total, retaining overcorrection in the numerator.

Paired lists must be nonempty and have equal lengths.

share=Σweight(specular−background)/Σweight(total−background)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
backgroundCorrectedSpecularShare	Background corrected specular share	number
backgroundCorrectedTotalSignal	Background corrected total signal	number

json

{
  "input": {
    "measuredSpecularSignals": [
      5,
      10
    ],
    "measuredTotalReflectedSignals": [
      10,
      20
    ],
    "backgroundSignals": [
      1,
      2
    ],
    "representedAngularWeights": [
      1,
      2
    ]
  },
  "output": {
    "backgroundCorrectedSpecularShare": 0.4444444444444444,
    "backgroundCorrectedTotalSignal": 45
  }
}

Limitations and assumptions

This is not absolute reflectance or validated luster grading. Background calibration and angular coverage are supplied.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Pearl Luster Grade Rater: Measure unique specular highlight FWHM from observed calibrated profile and background, not total specular share or a universal pearl-luster grade; missing/multiple half-height crossings are not invented. For a complementary task, use Fresnel Reflection Loss: Compute lossless real-index oblique Fresnel s/p energy reflection and transmission with explicit TIR; not normal-only lustre proxy, absorbing media or integrated gemstone light return.

References

Lustre Reflectivity Ratio — tool.io

Similar or alternative tools

Pearl Luster Grade Rater
Measure unique specular highlight FWHM from observed calibrated profile and background, not total specular share or a universal pearl-luster grade; missing/multiple half-height crossings are not invented.
Fresnel Reflection Loss
Compute lossless real-index oblique Fresnel s/p energy reflection and transmission with explicit TIR; not normal-only lustre proxy, absorbing media or integrated gemstone light return.