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phase scales in
Figure 11, a higher phase corresponds to a later signal.
The magnitude and phase spectra were calculated using Equations
(14) and (21)
from the same pair (in-phase and quadrature) of interferograms.
The PMMA magnitude spectrum in the bottom panel of the figure (dotted
line), shows no interferences larger than the small (about 1 unit tall) CO2
doublet at 2360 and 2335 cm-1 and no water-vapor structure.
Its companion phase spectrum in the top panel, on the other hand, has a
prominent (about 10°) CO2 doublet and smaller (about 2°) water-vapor structure between 1500 and 1850
cm-1. The PMMA itself
absorbs sufficiently strongly at most mid-infrared wavelengths that the phase
effects from the background or surface-film signal are modest.
The largest interference from the background signal is the broad, 9°-tall
feature between 3100 and 3550 cm-1.
This is a common phase-spectrum interference probably caused by water or
other hydroxyl species adhering to surfaces.
This broad feature demonstrates the apparent phase-band reversal that can
result from background-signal interference.
PMMA has a small absorption peak at 3440 cm-1, which shows up
in the phase spectrum as a gap in the interfering hydroxyl feature, so it looks
as if the 3440 cm-1 band were pointing toward higher phase instead of
lower phase like the other PMMA bands. This
is the characteristic appearance of phase interference from the background
signal – a broad region of faster than expected phase in which small
absorption bands of the sample appear to be partly or fully reversed in
direction.
Figure 11 also
shows a phase spectrum and companion magnitude spectrum (solid line) for
polyethylene. Polyethylene has a
generally lower absorption away from its main peaks than PMMA does.
As a result, its phase spectrum is much more susceptible to
background-signal interference. At
first glance, the polyethylene phase spectrum appears noisy because there are so
many features that apparently have little or no corresponding structure in the
magnitude spectrum, but many of the features are real, not random noise.
The water interference band between 3100 and 3550 cm-1 is
again present, and the dip in phase centered at 1690 cm-1 is also
probably from superficial water. Many
small absorption bands appear reversed in the phase spectrum because of the
background interference. The
upward-pointing features in the phase spectrum at 2350, 2150, 2020, 1900, 1815,
1360, 1300 and 910 cm-1 all correspond to small absorption peaks in
the magnitude spectrum. Phase
spectra contain much useful information complementary to magnitude spectra, but
the background interferences can make phase spectra more difficult to interpret
in weakly absorbing spectral regions, especially at high modulation frequencies.