Calculations ============ .. _uuid-c9755e34-9135-4415-b7c0-c39e287a70d8: Calculation C1 - Observed Complete-Frame Rate --------------------------------------------- UUID: :ref:`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``. .. _uuid-22f91c7c-d310-486a-ac24-bdc8be1b11ac: Calculation C2 - Wavelength Error --------------------------------- UUID: :ref:`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``. .. _uuid-60b5dbf0-f84f-4fef-8768-ca31ad5d905b: Calculation C3 - Full Width At Half Maximum ------------------------------------------- UUID: :ref:`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``. .. _uuid-cc509fbf-a260-4193-a556-5a97d39d7953: Calculation C4 - Signal-To-Noise Ratio -------------------------------------- UUID: :ref:`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``. .. _uuid-501567a5-fa56-4264-91ce-91edb0486cb1: Calculation C5 - Linearity Residual ----------------------------------- UUID: :ref:`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``. .. _uuid-ed22b205-1bb5-4ea3-9ac2-05890bb529b1: Calculation C6 - Repeatability Statistic ---------------------------------------- UUID: :ref:`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``. .. _uuid-22971c51-a176-427e-9509-c552d1b1c6c3: Calculation C7 - Dark Or Baseline Improvement --------------------------------------------- UUID: :ref:`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``. .. _trace-cf2f2048: .. _uuid-f767c5db-2f93-4e8d-97e3-eeef9f1bc530: Calculation C8 - Uncertainty Reporting -------------------------------------- UUID: :ref:`F767C5DB-2F93-4E8D-97E3-EEEF9F1BC530 ` **Local Traceability ID:** :ref:`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``.