7.3.1 Estimation of Laser Frequency Drift

It was not possible to record the changes in the frequency of the infrared laser directly since no spectrometer of sufficiently high temporal and chromatic resolution was available; the following indirect method was, therefore, adopted.

The free spectral range of the laser was calculated from measurements of the cavity length as being approximately 0.017 cm^-1 (section 5.1.1.1). Since February 1997 it has been possible to record the laser output power and the temperatures of the cavity, the outer box of the laser system, and the laboratory at set intervals (usually every thirty seconds). When the temperature of the laser cavity changes, for whatever reason, it will expand or contract, causing a corresponding shift in the output frequency of the laser. As the thermal expansion or contraction continues, the output frequency of the laser will continue to change until the frequency shift exceeds the free spectral range of the cavity and a mode hop occurs. As the frequency of the current, oscillating mode approaches the edge of the usable portion of the gain curve, the output power of the laser will drop correspondingly. These characteristic drops in power may be seen in the recorded readings (figure 7-4) and used as markers, indicating the time taken for the laser frequency to decrease by 0.017 cm^-1.

Figure 7-4 shows temperature and power measurements recorded during the intercomparison at Lauder. The upper plot shows the detector output as a function of time; the lower plot shows records of the temperatures of the laboratory (bottom), laser system box (middle) and the laser cavity (top). For the first hour and three quarters (before the temperature control was switched on) the temperature of the laboratory can be seen to fall; this results in the temperature of the laser cavity dropping for some four hours. During this period the laser detector voltage can be seen to drop to approximately half the maximum value on four occasions (corresponding to a frequency drift rate, averaged over one mode, of up to 5x10^-4 cm^-1/min, and with a maximum of greater than 0.0013 cm^-1/min); each dip corresponds to the laser undergoing a mode hop. After the temperature control is switched on the rate of change of the cavity temperature can be seen to drop drastically and only one further mode hop is seen in this record, corresponding to the cavity expanding as it slowly warms up. If we assume that the last mode hop in this record occurs at approximately 8« hours and that at the end of the record (approximately 13« hours) the oscillating mode is at the centre of the gain curve, we can say that the laser has drifted half of its free spectral range in approximately five hours, and hence estimate the long term drift at the end of the record to be less than 3x10^-5 cm^-1/min; this would result in one percent asymmetry (section 4.5) and effectively no broadening (section 4.4) which would permit credible measurements of the instrument line shape to be made.

In the foregoing, it has been assumed that the rate of frequency drift is constant in any given 0.017 cm^-1 interval. This is used in conjunction with the modelling of the effects of frequency drift (section 7.3.2) to assess the degree to which laser drift is responsible for the asymmetry seen in the measurements.

Figure 7-4. Temperature and power data from Lauder (10-min., moving averages). Upper plot indicates laser output power with dips due to mode hopping as a result of the temperature changes shown in the lower plot. In the lower plot the bottom curve indicates the laboratory temperature, the middle one the temperature of the system box and the upper curve indicates the temperature of the spacer bars (section 7.3.1).

Ripples on the power record (figure 7-4) suggest that this assumption of constant drift rate may not be wholly valid. Figure 7-5 shows the correlation between the small temperature fluctuations in the laser cavity (lower plot) and the ripples (upper plot) seen on the power curve in figure 7-4. It can be seen that peaks in the power curve follow peaks in the temperature plot with a time lag of approximately eight minutes, suggesting that the long term frequency drift has short term fluctuations superposed on it. In the assessment of the importance of these ripples, the reduction in laser power over the period of a scan has been used to estimate the apodisation of the interferogram and, hence, the associated frequency drift rate (the effects of a loss of power will be considered further in the next section). The ripples are sufficient to invalidate the line shape measurements as they can give rise to a two percent loss of power during the course of a measurement. Although this reduction will cause only a 0.4% broadening of the spectral line, it corresponds to a drift rate of 6x10^-4 cm^-1/min which will result in an asymmetry of some 19%. Laser spectra recorded at Lauder typically exhibited asymmetries of between 10 and 20% but were not reproducible; some show asymmetry in excess of 30% (figure 7-6).

Figure 7-5 Temperature and power data from Lauder (5-min., moving averages). The upper plot depicts short term ripples in laser output power (long term trend removed) caused by fluctuations in the temperature of the laser cavity (section 7.3.1).

Figure 7-6. Laser measurements from Lauder (15th February 1997) exhibiting 3, 14 and 35% asymmetry (section 7.3.1).

7.3.2 Modelling the Effects of Laser Frequency Drift.

The single-sided interferogram was represented by a cosinusoidal wave form whose period could be varied smoothly along its length to simulate amplitude fringes resulting from the measurement of an instantaneously monochromatic source whose frequency changes with time. The rate of change of the fringe separation may be varied to simulate different drift rates. The Fourier transformation of this simulated interferogram gives the spectrum of the drifting source. A 'tail' of zeros is added to the interferogram prior to the Fourier transformation, to ensure that the resulting spectrum is sufficiently smooth that the width and asymmetry of the resulting spectrum may be assessed with sufficient accuracy.

By this method, a relationship between the rate of change of the source frequency and the width and degree of asymmetry in the resulting spectral line may be determined.

Figure 7-7 shows the relationship between laser frequency drift and the symmetry of the resulting spectral line for frequency drift rates of up to 9x10^-4 cm^-1/min; asymmetry can be seen to increase linearly with drift rate (asymmetries and widths were calculated at 2x10^-5 cm^-1/min intervals for both plots). The lower plot illustrates the effect of this frequency drift on the full width at half maximum of the laser line, which again increases with drift. The ripples on the lower curve are an artefact resulting from the choice of frequency grid for the simulations. While the use of a fine frequency grid would have produced a smoother curve, these ripples are not big enough to affect the conclusions, and the finer grid would have resulted in an undesirable increase in the computational burden. Figure 7-8 shows the spectra resulting from simulated interferograms with frequency drifts of zero, 10^-4 and 10^-3 cm^-1/min. The first plot shows a symmetrical, unbroadened line; the second is barely broadened and only slightly asymmetric but the third plot, although still barely broadened, shows serious asymmetry, such as seen in some actual measurements (figure 7-6).

In none of these plots has any account been taken of the fact that the laser power will vary as its frequency drifts; this is now considered.

The upper and middle plots in figure 7-9 show the relationship between laser frequency drift and asymmetry (upper) and the full width at half maximum (middle) of the laser line, as did figure 7-7, but in this case the amplitude of the interferogram was modified to simulate the effects of the change in the output power of the laser caused by the oscillating mode moving under the gain curve.

Figure 7-7. Expected changes in symmetry (top) and width (bottom) of measured spectral line as a result of laser drift. The ripples on the lower curve are an artefact resulting from the choice of frequency grid (section 7.3.2).

Figure 7-8. Three simulated spectra illustrating the onset of frequency drift induced asymmetry (section 7.3.2).

The laser drifts (in frequency) as a function of time, and will undergo a mode hop at a certain time determined, in part, by the rate of the drift. Due to the finite time taken to make a measurement with a Fourier spectrometer, and the constant velocity of the moving mirror in 'continuous scan' systems such as the Bruker, it is possible, and at times conceptually helpful, to consider optical path difference and time as equivalent quantities. In view of this it is possible to define the point in time at which the mode hop occurs in terms of an optical path difference. The chosen drift rate was, therefore, used to calculate the optical path difference at which the mode would reach the end of the useful part of the gain curve¹, with the associated loss of power; effectively a form of extinction path difference, qualitatively similar to the field of view effect described in section 3.4.3. It is assumed that at the start of the measurement the laser is tuned to the centre of the gain curve and its output power is, therefore, at a maximum. A squared cosine wave, whose first minimum occurs at this extinction path difference, was then used to modify the interferogram such that its amplitude would drop to zero here; this was believed to provide a good approximation to the actual situation (Joliffe (private communication)). Figure 7-9(c) illustrates how the position of this extinction point varies with laser frequency drift rate. The effect of this loss of power is to apodise the interferogram and thereby cause the onset of broadening of the spectral line to be much more rapid than is implied by the previous, constant-power scenario.

Figure 7-9. Expected changes in symmetry (top) and width (middle) of measured spectral line as a result of laser drift as in figure 7-7 but modified to take account of the laser power dropping during the measurement as a result of frequency drift; lower plot indicates position of next mode hop in terms of maximum optical path difference (180 cm, scanning at 2.5 cms-1) (section 7.3.2).

It can be seen that although the degree of broadening is significantly increased when the decrease in power is taken into consideration (figure 7-9(b)), the asymmetry (figure 7-9(a)) is unchanged but still the dominant effect. When an interferogram is simulated with a drift rate of 0.001 cm^-1/min the associated drop in laser power at 180 cm optical path difference is approximately two percent (giving rise to 0.4% broadening of the spectral line) which is negligible compared to apodisation caused by minor misalignments, such as might be tolerated in the field; the asymmetry resulting from this drift rate is, however, totally unacceptable.

From this work we may conclude that, although the power change associated with changes in the laser frequency do cause a broadening of the spectral line, this effect is not significant since the frequency stability of the laser is critical if serious asymmetric distortions of the spectral line are to be avoided.

Although this work is concerned with modelling the effect of changes in the frequency of the infrared laser during the course of a measurement, the results concerning asymmetry are largely applicable (in a qualitative sense) to the situation in which the frequency of the internal reference laser drifts (for reasons given in section 7.3). Here, however, the relative intensity of the interference fringes are unimportant so long as the contrast between bright and dark is sufficient for the detector system; insufficient contrast will usually result in the measurement being aborted automatically.

7.4 Non-uniform Illumination of the Aperture

The following two hypotheses are fundamental to the design and use of the infrared laser system (section 5.1): firstly that if the field stop is over-filled by the laser in the same way as it is by the sun, then the collimation and alignment of the two beams entering the interferometer will be defined by the collimator and the field stop and they will, therefore, be identical; and secondly that, as a result of the previous, the phase correction calculated for the solar radiation will be equally valid for the laser light. Although both of these fundaments are correct, their full criticality was not realised at the design stage.

It is known that correct calculation of the phase correction for narrow, isolated emission lines is difficult (Mertz [1967], Keens (private communications)) since the lack of signal at adjacent frequencies makes the process highly susceptible to noise and because such lines are themselves essentially noise-like but this problem should not arise if the solar and laser beams are coaxial and have sufficiently similar intensity profiles for the reason proposed above. It has subsequently been pointed out (Delbouille (private communication), Keens (private communication)) that the requirements for similarity of the beam profiles are extremely strict.

The situation where the aperture is unevenly illuminated is qualitatively similar to that where the source is misaligned as described in section 7.2 and mathematically in Saarinen & Kauppinen [1992] but without a significantly more accurate measurement of the laser beam profile it is not possible to assess the extent to which the asymmetries seen are or are not the result of non-uniform illumination of the aperture.

7.5 Conclusions

It has been shown that a laser system such as has been described here (chapter 5) could be used to provide valid simultaneous measurements of the instrument line shape of Fourier spectrometers providing that the laser is sufficiently stable during measurements and that it is properly aligned to the instrument but that this was not accomplished here. It has also been shown that the use of a low pressure gas cell provides a useful check on the laser measurement.

Although thermal drift seriously hampered measurements of the laser system at the Table Mountain and Lauder intercomparisons described here, the laser system was, on occasions, sufficiently stable for repeatable measurements to be made (figure 6-3) but these still exhibit significant asymmetry.

Measurements made of the laser system exhibit serious asymmetry not present in the low pressure hydrogen bromide lines. Six possible causes of this asymmetry have been proposed:
• internal misalignment of the interferometer;
• misalignment of the infrared laser to the spectrometer;
• error in the phase correction for the spectrum;
• 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.

The first and fourth have been discounted on the grounds that they would have similar effects on all spectral features and it has been shown that the possibility of an isolated, uncorrected phase error does not arise due to manner in which the phase correction is carried out in the Bruker.

The effects of changes in the output of the infrared laser have been modelled. It has been demonstrated that frequency drift can give rise to the sort of asymmetry seen in the measurements of the laser and that the drift rates required to produce these distortions were recorded at Lauder. This suggests that laser frequency drift is likely to be a major cause of asymmetry although the presence of asymmetry in measurements taken when the laser frequency appeared to be stable suggests that drift is not the only cause of asymmetry.

It has not been possible to rule out misalignment of the laser system to the spectrometer as a possible cause of asymmetry in the laser lines. It was subsequently ascertained from Bruker that the positioning accuracy of the field stop is poor (Jewkes (private communication)). The twelve apertures are drilled in a disc mounted on a stepper motor enabling the apertures to be changed at will but this system limits the accuracy with which the selected aperture may be positioned to ±50 mm. Since the most frequently used aperture is only 0.65 mm diameter and the smallest one 0.3 mm diameter, this must further call into question the validity of the current method for aligning the laser system to the spectrometer.

Non-uniform illumination of the aperture is another potential cause of asymmetry in the laser lines which it has not been possible to rule out. More accurate measurements of the laser beam profile are required before the effects of possible non-uniform illumination may be quantified.

A more reliable means of aligning the infrared laser system to the spectrometer must be developed if meaningful measurements are to be obtained, in addition to which the frequency of the laser must be prevented from drifting at greater than 3x10^-5 cm^-1/min during measurements.

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