7. Possible Causes of Asymmetry in Laser Spectra

Spectra of the infrared laser made at Table Mountain (section 6.2) and Lauder (section 6.3) showed serious asymmetry that was not present in hydrogen bromide lines recorded simultaneously. This chapter shall consider possible causes of this aberration.

The asymmetry in the measured laser spectra could be caused by a number of factors:
• error in the phase correction for the spectrum;
• internal misalignment of the interferometer;
• misalignment of the infrared laser to the spectrometer;
• changes in the frequency of the spectrometer's internal reference laser during a measurement;
• changes in the frequency of the infrared laser during a measurement;
• non-uniform illumination of the field stop.

These will be considered in the following sections.

7.1 Improper Correction of Phase Error

As explained in section 3.4, each measurement will be subject to phase errors which must be corrected for if the retrieved spectrum is to be accurate. Should this phase correction be calculated incorrectly, artefacts will be introduced into the final phase spectrum (Mertz [1967], Park [1983]). This section shall only consider possible shortcomings in the phase correction resulting from the manner in which it is carried out in the Bruker IFS 120M, and not those errors resulting from the instrument being used in a manner outside its design remit.

Since the phase correction is unreliable at frequencies where there is very low signal (Mertz [1967]), it might be supposed that the laser line could be abnormally susceptible to phase errors, situated as it is in a broad methane feature, saturated across an interval of about one wavenumber (figure 7-1); it might also be supposed that the phase curve might contain localised errors due to the sharpness of the laser line (Mertz [1967], Keens (private communication)) but while both are possible in theory, neither will occur in practise due to the way the Bruker carries out the phase correction.

Figure 7-1. Window from combined atmospheric/laser measurement showing laser line in saturated methane feature. Lower plot shows detail of atmospheric spectrum and ringing of ILS (section 7.1).

Prior to recording the single sided interferogram that will be transformed to give the desired spectrum, a short, double-sided interferogram is recorded. It is the Fourier transform of this interferogram that is used for the phase correction. The calculated phase curve covers the spectral region 0 - 7880 cm^-1 but at an apparent resolution of approximately fifteen wavenumbers so that such 'fine detail' as the methane feature and the laser line will have no significant effect. In order to carry out the phase correction for the measurement scan (at resolutions up to 0.0028 cm^-1), the data processing software interpolates between the points of the low resolution phase curve; this will obviously not introduce any sharp changes or discontinuities.

Figure 7-2. Phase curves from Table Mountain. Upper plots show full phase curves for spectra used in figures 6-4 and 6-5; lower plots are details of the upper, showing 50 cm^-1 either side of laser line (+ indicates stored data point) (section 7.1).

Figure 7-2 shows the phase curves for scans 52 and 53 (figure 6-3) taken at Table Mountain on 3rd November 1996. The upper plots show the full phase curves while the lower plots show the region covering 2900 - 3000 cm^-1 in detail (+ indicating individual data points). We can see that below 1000 cm^-1 and above 6000 cm^-1, where the detector signal is very low, the phase correction fails, and the curve appears as random noise, while between these limits it is smooth. The detail plots (lower axes) confirm that over the region of the laser line and the hydrogen chloride feature used for vertical column retrieval, there are no sharp variations of the phase angle.

A discrepancy was subsequently found between the recorded phase curves, which show a point spacing of some fifteen wavenumbers, and the data parameters recorded by the instrument which claim two wavenumbers. It was established by consultation with the designer of the 120M that there is indeed an error in the OPUS operating software that, under certain conditions, causes the phase curve to be stored and displayed at one seventh its actual resolution (Keens (private communication)). Although this means that the spectrum used for the phase correction has seven times greater resolution than was originally supposed or shown in figure 7-2 the resolution is still too low to contain any errors local to the laser line, and no errors are visible in the baseline of the saturated methane feature in which the line sits (figure 7-1).

From this we can conclude that the excessive asymmetry in the laser line is not the result of an error in the phase correction local to the laser line.

7.2 Misalignment

Misalignment of the equipment could take two main forms: either internal misalignment of the interferometer, or misalignment of the infrared laser system to the spectrometer.

Although internal misalignment of the interferometer is a common cause of spectral asymmetry (Park [1983], Birch & Clarke [1995]), it is easily discounted in this case: since all the solar radiation entering the instrument must follow the same optical path (assuming that the solar and laser beams are coaxial), it follows that any misalignment causing asymmetry in one spectral line must cause similar asymmetry in other lines. It is clear from figure 6-3 that although there is significant asymmetry in the laser line, the hydrogen bromide lines lack this aberration. From this we may assume that the solar beam, at least, was correctly aligned to the instrument.

The other possibility is that the infrared laser system was incorrectly aligned to the interferometer, with the result that the laser and solar beams were not following precisely the same path through the instrument.

The situation may be considered as follows. The alignment and profile of the laser and solar beams are not, in themselves, important; the critical issue is that the laser beam has the same profile as the solar beam and is coaxial with it. The solar beam will propagate through the interferometer in some manner, giving rise to an interference pattern which is recorded and transformed; a phase correction will be calculated and applied. The laser radiation will, likewise propagate through the instrument, and its interference pattern will be recorded and processed as part of the solar interferogram, which is where problems may arise. The very narrow band width of the laser radiation and its position in a saturated region of the spectrum prevents it making any meaningful contribution to the phase correction; this will be based solely on the solar spectrum and thus, if the laser and solar beams are not precisely coaligned, there will be some uncorrected phase shift associated with the laser line resulting in asymmetric distortion and a shift in the position of the peak towards lower wavenumbers. A mathematical treatment of the effects of a misaligned source (qualitatively similar to the effects of a misaligned cube corner mirror in the interferometer (Kauppinen & Saarinen [1992]) is provided in Saarinen & Kauppinen [1992]. While a shift in the position of the line may not be obvious on inspection, the associated asymmetry is; the majority of laser measurements made at Lauder exhibit such asymmetry suggesting a shift to lower wavenumber.

Although the prescribed method of aligning the laser system to the spectrometer was believed to be adequate to prevent this happening, as mentioned earlier (section 5.6), the method does rely on the output power of the laser remaining constant during the alignment process. Since we cannot be absolutely confident that the power did remain constant throughout, it is not possible to totally discount misalignment of the laser system to the interferometer as a possible cause of asymmetry. It has subsequently been pointed out (Delbouille (private communication), Keens (private communication)) that the requirements for coalignment of the beams are extremely strict.

It might also be supposed that misalignments of the laser system upstream of the scatter plate and hemisphere will cause a loss of output and may lead to a non-uniform distribution of radiation across the output beam which would invalidate the line shape measurements and could lead to asymmetry. This is highly unlikely in practice since the output power level is highly sensitive to misalignment of the beam incident on the scatter plate, with the power dropping sharply if the incident beam moves away from the centre of the parent sphere.

7.3 Frequency Drift

The equipment involves two lasers: the internal reference (or counting) laser (633 nm helium:neon) for the spectrometer and the external infrared laser used for instrument line shape measurement (section 5.1). If the frequency of either laser was to change during the course of a measurement, asymmetry would result.

The counting laser is used to regulate the movement of the travelling mirror and the sampling rate of the detector electronics. It passes through the interferometer in the same manner as the infrared radiation to be measured (at the edge of the beam splitter, small windows in the coatings are provided for this purpose) but is collected by a separate detector. These electronics are triggered by intensity minima, and so by counting the fringes due to the reference beam (whose frequency is preset) the speed and position of the mirror may be calculated and, hence, the position of fringes in the measured interferogram determined.

It follows that the frequency calibration of the instrument depends fundamentally on the frequency of the reference laser being set correctly, since all the calculations are based on the true frequency of the laser being equal to the preset value. If the frequency changes during the course of a measurement this will lead to errors in the determination of fringe positions in the interferogram since these will still be based on the assumption of a stable reference. The effect is illustrated in figure 7-3. The upper plot represents (solid line) a fringe pattern due to a monochromatic source, whose frequency decreases during the measurement. Given this interferogram alone, there is no way of telling whether it is a true representation of a source whose frequency is changing with time, or whether the source frequency was stable but the reference laser has drifted, giving rise to errors in the calculation of the optical path difference corresponding to each fringe. The dotted curve represents a perfect measurement of a stable source whose frequency is equal to that corresponding to the first samples in the interferogram.

Figure 7-3. Illustration of the laser drift as a source of phase error. In both plots the solid curves represent an interferogram of decreasing frequency while the dotted curves have constant period (section 7.3).

The solid line in the lower plot has the same meaning as that in the upper plot, again representing a fringe pattern due to a monochromatic source, whose frequency decreases during the measurement, but this time the dotted curve represents the fringe pattern due to a supposed monochromatic source whose frequency is stable at that indicated by the last recorded points on the interferogram. When this frequency is used, and we require the actual interferogram and the one implied by the last samples to coincide at those last data points, we find that the reconstructed fringe pattern (dotted curve) does not have a maximum at zero optical path difference; a phase error seems to have occurred.

In the case of the reference laser drifting in frequency, all spectral features may be affected, but if it is the source that has changed frequency, then only that line will be distorted. It is extremely unlikely that the frequency of the reference laser in the Bruker drifted at any time, since it is designed to be stable to 1 MHz/min (3.3x10^-5 cm^-1/min) (Jewkes (private communication)), and there is no evidence of any significant phase errors elsewhere in the spectra. The infrared laser was essentially free-running, having no form of active frequency stabilisation, and hence could well drift if the temperature of the laboratory was not held constant; indeed the temperature records from Lauder (section 6.3) suggest that there were small but measurable temperature variations in the laser cavity which gave rise to changes in the laser output. Section 7.3.1 is devoted to the assessment of the effects of temperature drift in the laser cavity.

It should be noted that errors caused by frequency drift in the source are spectrally indistinguishable from localised errors in the phase correction (section 7.1) (Blavier (private communication)).

Summary
Acknowlegements
Contents
Chapters: 1, 2, 3, 4, 5, 6, 7, 8
Appendices
References