This function implements normalization methods based on background, total area, internal standard, and the L1, L2 and maximum norms of each spectrum.
Arguments
- x
A numeric matrix or data frame containing the spectra.
- method
A character vector specifying the normalization method to apply. Available methods are: "area", "l1", "l2", "max", "background", and "internal". Spectra whose L1, L2 or maximum norm is zero are set to
NA, with a warning.- bkg
A numeric matrix or data frame of the same dimension as
x, specifying the intensity of the continuum radiation (background emission) used for normalizingx. Required for "background" method.- wlength
A character vector of the selected wavelength(s) (column names). Required for the "internal" method, where the intensities at these wavelengths are summed to give the internal standard. Optional for the "background" method, where only these wavelengths are normalized and returned.
- drop.na
A logical value indicating whether to remove spectra (rows) containing missing values before normalizing. Default is
TRUE.
Details
The normalization methods:
Normalization to the background: Spectra are divided by the intensity of the background emission. Note that it is recommended that the detector dark current be subtracted prior to the normalization.
Normalization to the total area: Each spectrum is divided by the total area of the spectrum over the whole spectral range. The detector dark current must be subtracted prior to this normalization. The total area is calculated as the sum of all intensity levels.
L1 normalization (
"l1"): each spectrum is divided by the sum of the absolute values of its intensities. It equals the total area for non-negative spectra, and also suits derivative spectra, whose values change sign.L2 (vector) normalization (
"l2"): each spectrum is divided by its Euclidean norm, so that its sum of squares is 1. Unlike SNV, the spectrum is not centered.Maximum normalization (
"max"): each spectrum is divided by its largest absolute intensity, so that its strongest feature is 1 (or -1).Normalization to an internal standard: The peak intensity (or area) of the emission line related to the analyte is divided by the peak intensity (or area) of a selected emission line related to the internal standard. The internal standard concentration is assumed constant or known.
References
De Giacomo, A., Dell’Aglio, M., De Pascale, O., Gaudiuso, R., Santagata, A., Teghil, R., (2008). Laser-induced breakdown spectroscopy methodology for the analysis of copper based alloys used in ancient artworks. Spectrochimica Acta Part B, 63(5):585-590
Body, D., Chadwick, B.L., (2001). Optimization of the spectral data processing in a LIBS simultaneous elemental analysis system. Spectrochimica Acta Part B, 56(6):725-736.
Rinnan, A., Van den Berg, F., Balling Engelsen, S., (2009). Review of the most common preprocessing techniques for near-infrared spectra, Trends in Analytical Chemistry, 28(10):1201-1222.
Examples
data(forageLIBS)
spectra <- forageLIBS[-(1:14)] # the spectral channels
normalize(spectra[1:3, ], method = "area")[, 1:4]
#> # A tibble: 3 × 4
#> `199.3771616` `199.4644141` `199.5516666` `199.6389192`
#> <dbl> <dbl> <dbl> <dbl>
#> 1 0.0000444 0.0000452 0.0000484 0.0000451
#> 2 0.0000449 0.0000464 0.0000484 0.0000445
#> 3 0.0000430 0.0000442 0.0000473 0.0000442
normalize(spectra[1:3, ], method = "l2")[, 1:4]
#> # A tibble: 3 × 4
#> `199.3771616` `199.4644141` `199.5516666` `199.6389192`
#> <dbl> <dbl> <dbl> <dbl>
#> 1 0.00185 0.00188 0.00201 0.00188
#> 2 0.00191 0.00197 0.00206 0.00189
#> 3 0.00183 0.00188 0.00201 0.00188
# internal standard: the C I 247.86 nm line of the organic matrix
carbon <- names(spectra)[which.min(abs(as.numeric(names(spectra)) - 247.856))]
normalize(spectra[1:3, ], method = "internal", wlength = carbon)[, 1:4]
#> # A tibble: 3 × 4
#> `199.3771616` `199.4644141` `199.5516666` `199.6389192`
#> <dbl> <dbl> <dbl> <dbl>
#> 1 0.0207 0.0211 0.0226 0.0210
#> 2 0.0225 0.0232 0.0242 0.0223
#> 3 0.0196 0.0202 0.0216 0.0202