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Looking at Error Propagation and Data Analysis
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This is Chemometrics in Spectroscopy Column Number 251. In Column Number 250, we left you with a puzzle. We had just shown that a little-known piece of two-hundred-year-old mathematics, Lagrange's method of undetermined multipliers, could force an MLR calibration to ignore one particular, carefully chosen direction of repack-induced spectral change. It worked, but it only handled one direction at a time, and we admitted we had no idea whether the trick could be extended to PCR or PLS. That bothered us. So in this installment we go looking for the more general version of the idea, and we find it sitting in some very good recent work by Neal Gallagher and Nathanial Watson on what they call clutter suppression (a framework built for a completely different problem, target detection in hyperspectral imaging, that turns out to fit ours almost perfectly). Put the two together and you get an algorithm that whitens the calibration spectra with a clutter covariance matrix estimated from repack replicates, then hands the whitened data to the same Lagrangian machine we built last time. The payoff: the correction now generalizes to several, non-proportional directions of diffuse-reflection variability at once, and, because it is just a preprocessing step, it works ahead of PLS and PCR as well as MLR, which finally answers the question we could not answer before. This approach may very well be an answer to repack variation in repeated solid or slurry sample measurements using diffuse reflection. In this column we change gears with our writing tone and format by taking a "chemometry" approach, rather than a strict tutorial one. In future columns we hope to "unpack" this information in our more typical extended and tutorial manner. Let's explore solving this repack variation problem together.

A study using fiber laser induced breakdown spectroscopy (FL-LIBS) to evaluate how pulse width and repetition rate affect the quantitative analysis of elements in aluminum alloys, reporting improved detection sensitivity and limit of detection at high repetition rate.

Spectroscopy Top 10 DOI Articles of the Month (July 2026)

Spectroscopy Top 10 Articles of the Month (July 2026)

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The following articles are the most accessed digital object identifier (DOI) manuscripts for Spectroscopy and LCGC International during the month of July 2026. Nine articles are ranked here by DOI page views; a tenth entry in the July report (135 views) was recorded against the bare journal-level DOI rather than an individual article and is therefore not attributable to a single manuscript.

Refraction of Light Through a Solid © Graphicazzy -chronicles-stock.adobe.com

For 170 years, spectroscopists have built quantitative analysis on only one number pulled from every spectrum they ever recorded, discarding its inseparable twin. New dispersion-theory and complex-valued chemometric methods recover that missing half, the refractive index, and in favorable systems cut calibration error by as much as an order of magnitude.

Traditional Blood Glucose Meter © pittawut -chronicles-stock.adobe.com

Nearly every diabetic on earth still stabs a finger to measure their blood sugar, but a small army of lasers, infrared beams, and machine-learning algorithms is quietly plotting to end that ritual for good. This review tracks the photons chasing glucose through skin, from near-infrared reflectance to Raman fingerprints, and asks why the “needle-free” promise keeps slipping just out of reach.

Linear Regression Trend Line Plot ©  Safeer -chronicles-stock.adobe.com

A technical white paper deriving the classical least squares (CLS) and weighted least squares (WLS) models and showing how generalized least squares (GLS) and extended least squares (ELS) extend CLS to provide clutter suppression for characterized interference signals in spectroscopic and hyperspectral measurements.

United States White House with Waving American Flag ©  Bijac -chronicles-stock.adobe.com

A rule proposed by the White House Office of Management and Budget (OMB) would give political appointees final authority over discretionary grant decisions ahead of peer reviewers, allow agencies to terminate active grants without a formal right of appeal, and restrict international collaboration and publication funding across federal science agencies. For the optical, molecular, vibrational, and atomic spectroscopy community, the proposal could affect the grants, journal support, and student and postdoctoral positions that sustain the field.

Spectroscopy’s “What’s Nu” newsletter in May highlights the development of lasers in spectroscopy, compensating for repack variation in near-infrared (NIR) spectroscopy, and validity by design.

Gold Anniversary Candles: Our 250th Article on Statistics, Chemometrics, and AI in over 40 years! ©  Valerii Evlakhov -chronicles-stock.adobe.com

In their milestone 250th column, Howard Mark and Jerome Workman, Jr. describe a mathematically rigorous algorithm that minimizes or eliminates sampling repack variation in near-infrared spectroscopy. The method separates systematic spectral changes caused by sample rearrangement from true compositional information, enabling more robust calibration models and significantly improving analytical repeatability for powdered and heterogeneous solid samples.

Two people wearing protective suits working at crime scene evaluating evidence © Seventyfour -chronicles-stock.adobe.com

Over the past two years, molecular spectroscopy has undergone a marked transformation from a predominantly laboratory-based analytical approach into a field-deployable, data-rich forensic toolkit. This evolution has been driven by three converging trends: (i) advances in vibrational spectroscopic instrumentation (Fourier transform infrared [FT-IR], Raman, and near-infrared [NIR], (ii) the integration of chemometrics and machine learning for extracting actionable information from complex spectra, and (iii) the emergence of portable and miniaturized devices suitable for in situ analysis. The ten papers reviewed here collectively demonstrate how spectroscopy is now addressing some of the most persistent challenges in forensic science—such as time since deposition (TSD), post-mortem interval (PMI), trace evidence discrimination, and rapid drug identification—while maintaining evidentiary integrity through non-destructive analysis. Importantly, these works also reflect a shift toward interpretability, validation, and legal defensibility, which are essential for courtroom acceptance.