Calculations

Calculation C1 - Observed Complete-Frame Rate

UUID: C9755E34-9135-4415-B7C0-C39E287A70D8

Summary: Calculate the average complete-frame rate over a documented observation interval.

Variables: N_complete is the number of complete frames and delta_t is elapsed time.

Calculation: R_frame = N_complete / delta_t.

Equation Reasoning: Counting only complete frames keeps interface qualification separate from partial receive activity.

Implementation Note: Future evidence tooling and timestamp source are Not In Docs.

Acceptance Profile: Embedded minimum transfer acceptance is R_frame >= 10 frames/s at minimum integration time, counting only complete frames that each contain 3648 effective detector samples. This profile is distinct from the above-100-fps system design target and from display updates.

Open Requirement: Observation duration, warm-up interval, aggregation method, display update profile, and conditions for the above-100-fps system target are Not In Docs.

Calculation C2 - Wavelength Error

UUID: 22F91C7C-D310-486A-AC24-BDC8BE1B11AC

Summary: Calculate signed wavelength error for each suitable reference.

Variables: lambda_observed is the reported peak wavelength and lambda_reference is the reference value under recorded conditions.

Calculation: e_lambda = lambda_observed - lambda_reference.

Equation Reasoning: Signed error retains both magnitude and direction of the mapping difference.

Implementation Note: Peak extraction and reference matching are future verification activities.

Rationale: Wavelength accuracy is a required characterization metric.

Open Requirement: Peak window, interpolation, reference matching, aggregation, and tolerance are Not In Docs.

Calculation C3 - Full Width At Half Maximum

UUID: 60B5DBF0-F84F-4FEF-8768-CA31AD5D905B

Summary: Calculate the wavelength separation between the two half-maximum crossings of a suitable narrow spectral feature.

Variables: lambda_left and lambda_right are the wavelength locations of the left and right half-maximum crossings.

Calculation: FWHM = lambda_right - lambda_left.

Equation Reasoning: The crossing separation expresses spectral width in wavelength units for comparison with the approximately 5 nm target.

Implementation Note: Crossing extraction is not assigned to an implementation location in this first run.

Rationale: FWHM is the documented spectral-resolution measure.

Open Requirement: Baseline removal, peak selection, interpolation, source linewidth treatment, and aggregation are Not In Docs.

Calculation C4 - Signal-To-Noise Ratio

UUID: CC509FBF-A260-4193-A556-5A97D39D7953

Summary: Express a stable signal level relative to the selected noise statistic.

Variables: mu_signal is the mean selected signal and sigma_noise is the standard deviation of the selected noise samples.

Calculation: SNR = mu_signal / sigma_noise when sigma_noise is nonzero.

Equation Reasoning: The ratio provides a repeatable comparison only when the signal region, noise population, and preprocessing are fixed.

Implementation Note: Future analysis tooling and zero-noise handling are Not In Docs.

Rationale: SNR is a required characterization metric, especially where detector response is lower.

Open Requirement: Wavelength bands, sample population, dark treatment, statistic, units, and threshold are Not In Docs.

Calculation C5 - Linearity Residual

UUID: 501567A5-FA56-4264-91CE-91EDB0486CB1

Summary: Calculate the deviation of each observation from an approved linearity fit.

Variables: y_i is the observed response and y_fit_i is the response predicted by the approved fit at the same controlled input.

Calculation: r_i = y_i - y_fit_i.

Equation Reasoning: Residuals expose both the magnitude and pattern of departure from the selected model.

Implementation Note: The fit procedure and reporting tool are future work.

Rationale: Linearity shall be characterized versus controlled input at fixed integration time.

Open Requirement: Input levels, fit model, weighting, residual aggregation, and threshold are Not In Docs.

Calculation C6 - Repeatability Statistic

UUID: ED22B205-1BB5-4EA3-9AC2-05890BB529B1

Summary: Calculate sample standard deviation for repeated observations when that statistic is selected by the approved method.

Variables: x_i are repeated values, x_bar is their mean, and n is the number of observations.

Calculation: s = sqrt(sum((x_i - x_bar)^2) / (n - 1)) for n > 1.

Equation Reasoning: Sample standard deviation measures variation over a defined repeat sequence without claiming a tolerance.

Implementation Note: Future analysis location is not assigned.

Rationale: Repeatability is required over acquisitions made without realignment.

Open Requirement: Selected metric, sequence length, duration, environmental profile, aggregation, and threshold are Not In Docs.

Calculation C7 - Dark Or Baseline Improvement

UUID: 22971C51-A176-427E-9509-C552D1B1C6C3

Summary: Compare a documented baseline or noise statistic before and after the configured bias/dark operation.

Variables: m_before and m_after are the same selected statistic evaluated under matched conditions.

Calculation: Candidate reports are delta_m = m_before - m_after and, when m_after is nonzero, ratio_m = m_before / m_after.

Equation Reasoning: Reporting paired difference and ratio preserves useful comparison options until the project selects one normative measure.

Implementation Note: These candidate reports are non-normative.

Rationale: Bias and dark correction require a controlled comparative evaluation.

Open Requirement: Selected statistic, detector region, conditions, aggregation, normative measure, and threshold are Not In Docs.

Calculation C8 - Uncertainty Reporting

UUID: F767C5DB-2F93-4E8D-97E3-EEEF9F1BC530

Local Traceability ID: CF2F2048

Summary: Report measurement conditions, identified uncertainty contributions, and the selected combined or expanded uncertainty.

Variables: u_i are standard uncertainty contributions and u_c is combined standard uncertainty.

Calculation: When contributions are independent and expressed as standard uncertainties, u_c = sqrt(sum(u_i^2)).

Equation Reasoning: Root-sum-square combination is conditional on the independence assumption; correlated terms require a documented covariance treatment.

Implementation Note: No uncertainty-analysis implementation or evidence artifact is assigned in this first run.

Rationale: Reference comparisons and characterization metrics are not interpretable without conditions and uncertainty context.

Open Requirement: Uncertainty budget, probability model, correlations, coverage factor, confidence statement, significant figures, and reporting format are Not In Docs.