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Wavelength Calibration from Reference Lines

Source: R/wavelength_calibration.R
wavelength_calibration.Rd

Measures the positions of known emission lines in spectra and fits a correction of the wavelength axis, so that the lines fall at their reference wavelengths (for example, from the NIST Atomic Spectra Database). apply_calibration() then relabels the wavelengths of the spectra, without changing their intensities.

Usage

wavelength_calibration(
  spectra,
  lines,
  degree = 1,
  search = 0.3,
  min_snr = 20,
  segments = TRUE,
  reject = TRUE
)

Arguments

spectra

The spectra: a numeric vector named by wavelength, or a matrix or data frame with one spectrum per row and the wavelengths as column names (other columns are ignored). The lines are located in their mean.

lines

The reference lines: a numeric vector of wavelengths (nm), preferably named, or a data frame with a wavelength column (and optionally a species column), such as returned by nist_lines(). Choose isolated, strong but not saturated lines, spread over the range.

degree

The degree of the correction polynomial: 0 (shift), 1 (default) or 2.

The half-width of the window in which each line is searched, in nm. Default is 0.3.

min_snr

The minimum height of a line, in units of the noise of the spectrum. Default is 20.

segments

A logical: fit each detector segment separately (TRUE, default).

reject

A logical: remove the outlying lines after the fit (TRUE, default).

Value

An object of class specproc_wavelength_calibration, a list with

  • lines: a tibble with, for each reference line, its line label, reference and measured wavelengths, the offset (reference minus measured), its segment, snr, whether it was used (otherwise the reason), the correction of the fit at the line and the residual;

  • segments: a tibble with, for each segment, its wavelength range (from, to), the degree fitted, the number of lines n_lines and the root mean square residual rmse (nm);

  • wavelength: the wavelengths of the calibrated axis, in column order.

Use apply_calibration() to correct spectra, predict() to correct any wavelength, and plot_wavelength_calibration() to draw the fit.

Details

The lines are located in the mean of the spectra. For each reference line, the peak is the channel of highest intensity within search nm of the reference wavelength, and its position is refined to a fraction of a channel by the vertex of the parabola through the logarithms of the peak channel and its two neighbors, above the lowest channel of the window (Gaussian interpolation, exact for Gaussian lines; Caruana et al., 1986). A line is not used when

  • "edge": the highest channel is at the border of the search window (the peak is not in the window, or a stronger line is nearby);

  • "weak": its height above the lowest channel of the window is less than min_snr times the noise of the spectrum;

  • "flat": three channels or more are within 1% of its maximum, or its curvature is not that of a peak, as for saturated or strongly self-absorbed lines;

  • "outlier": its residual after the fit exceeds 3 robust standard deviations of the residuals (for example, a blend, or a line identified wrongly), when reject = TRUE.

The correction is a polynomial of degree degree of the measured wavelength, \(\lambda_{true} = \lambda + \sum_{j=0}^{d} c_j (\lambda - \lambda_0)^j\), where \(\lambda_0\) is the mean position of the lines: a constant shift for degree = 0, linear for degree = 1 (default). It needs at least degree + 1 usable lines, and more to estimate its residual error. Beyond the range of the lines, the polynomial is extrapolated: spread the reference lines over the spectral range, and prefer low degrees.

Instruments made of several spectrometers have one wavelength calibration per detector. With segments = TRUE (default), the axis is split where the wavelengths step back (overlapping detectors) or jump (gaps of more than 5 times the median channel spacing), and each segment gets its own correction. A segment with fewer usable lines than degree + 1 gets a constant shift if it has one line, and no correction otherwise, with a warning.

References

  • Caruana, R.A., Searle, R.B., Heller, T., Shupack, S.I. (1986). Fast algorithm for the resolution of spectra. Analytical Chemistry, 58(6):1162-1167.

See also

apply_calibration(), plot_wavelength_calibration(), nist_lines(), line_intensities(), line_finder()

Author

Christian L. Goueguel

Examples

# the first detector (199 to 766 nm) of the forage spectra
data(forageLIBS)
spectra <- forageLIBS[-(1:14)]
wl <- as.numeric(names(spectra))
first_detector <- spectra[seq_len(which(diff(wl) < 0)[1])]
reference <- c(`C I` = 247.856, `Mg I` = 285.213, `Ca II` = 317.933, `Ca II` = 370.603,
               `Ca II` = 373.690, `K I` = 404.414, `Ca I` = 430.253, `Ca I` = 445.478,
               `Mg I` = 516.732, `Mg I` = 517.268, `Mg I` = 518.360, `Na I` = 588.995,
               `Na I` = 589.592, `Ca I` = 616.217, `Ca I` = 643.907)
cal <- wavelength_calibration(first_detector, reference)
cal
#> Wavelength calibration (degree 1): 15 of 15 reference lines used
#> 
#>  segment     from       to degree n_lines   rmse
#>        1 199.3772 766.1501      1      15 0.0136
plot_wavelength_calibration(cal)


corrected <- apply_calibration(first_detector, cal)
head(names(corrected))
#> [1] "199.4025" "199.4897" "199.5770" "199.6643" "199.7515" "199.8388"