Atmospheric temperature measurement using a pure rotational Raman lidar: comment John A. Cooney

Drexel University, Department of Physics & Atmospheric Science, Philadelphia, Pennsylvania 19104. Received 4 November 1983. 0003-6935/84/050653-02$02.00/0. © 1984 Optical Society of America The authors of this paper1 are to be congratulated. The

success of the effort along with the punctilious attention to detail shown therein has greatly enhanced the development of methods for acquisition of accurate atmospheric temper­ature profiles.

The purpose of this Letter is to comment on the severity of the elastic cross talk entering the Raman channels and to suggest why such cross talk is a matter of somewhat less con­cern than the authors suppose.

As noted in Ref. 1 the presence of an enhanced aerosol overburden increases both the elastic backscatter and trans­mission losses. Due to the finite rejection of radiation at the elastic wavelength (Rayleigh and Mie backscatter) in the Raman channels some of the so-called online radiation pen­etrates and becomes part of the signal acquired in the Raman channel. The greater the aerosol overburden the greater the penetration into the Raman channel and so the greater the amount of unwanted signal which can act to reduce the ac­curacy of the measurement.

It is noted in Ref. 1 that because of the ratio of the Raman to Rayleigh cross section along with nominal overburdens (≃10.0-km visibility), and because of the need to keep the errors on the temperature measurement below the 1.0% level, transmission of the elastic line in the Raman channel must be of the order of 10~6. For the small wavelength intervals which separate the pertinent Raman lines from the elastic line re­jection by factors of 106 are quite difficult to achieve by ordi­nary narrowband interference filters. When using a ruby laser (6943 Å) as the existing source useful Raman lines suggest that the Raman channels be set in the vicinity of 6910 and 5990 Å. Interference filters were used in a series of ex­periments2 which led to temperature uncertainties of ≃1.0 K and an absolute temperature difference of mean value in­tegrated all along the profile to 2.3 km of ≃2.5 K between lidar and radiosonde methods of profile acquisition. Here, how­ever, the filter rejection was only ~105.

The seeming inconsistency of the 1% error requirement of 106 rejection, on the one hand, and the <1% error obtained using a filter with rejection of 105, on the other, is resolved in the following way. The temperature measurement itself is given by the ratio of the intensities in the two Raman chan­nels. For the moment assume for the sake of clarity of ex-

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position that the only source of deviation from an errorless Raman signal is due to this elastic intrusion. Let the channel I signal be I1 = A1 + ε1, where A1 is the errorless measurement of the Raman signal in Raman channel I, and ε1 is the elastic intrusion. Similarly for channel II, let I2 = A2 + εz∙ The error ε1, is assumed to be <10% to A. The temperature Tm mea­sured at altitude is proportional to the measured ratio of I1/I2 at altitude. Hence

(where ε1/Ai∙ is the fractional error in channel i). It should be noted that unlike a random noise source the εi

are simply related to one another by a constant as they both arise from the identical elastic scatter radiation. Statistically speaking, although the Rayleigh signal carries with it random fluctuations, because the information desired arises from the ratio as above, the cross-correlation for zero delay time is and remains equal to unity. Thus the following becomes legiti­mate:

If things are arranged so that ε1/A1 = ε2/A2 (or nearly so), the error remaining is of second order. Thus a 10% error becomes a 1.0% error and so on. Such an analysis would not be legiti­mate for independent or even partially correlated noise sources, but it is clear that the elastic intrusion into both Raman channels arises from precisely the same signal.

In actual field operation to get a measurement of the size of the elastic intrusion if any, an additional filter into each Raman channel was imposed momentarily but was centered at the elastic line. In the usual case with very little Rayleigh intrusion the entire signal would disappear. When Rayleigh intrusion was significant (e.g., cloud return) some signal would remain in the Raman channel, and the size of the Rayleigh intrusion would then be measured. The Raman portion of the return would be completely obliterated by the lower transmission of the elastic centered filter at the Raman wavelengths.

These considerations have modest theoretical significance but are of great practical value. They permit the use of less than Draconian measures to arrive at sufficient relative spectural purity. Filters cost hundreds of dollars, whereas double monochromators cost many thousands. Furthermore, the additional throughput of the filter further enhances the SNR of the measurement.

References 1. Y. Arshinov et al., Appl. Opt. 22, 2984 (1983). 2. J. Gill et al.,J. Appl. Meteorol. 8, 225 (1979).

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