4.5 Two-color photometry

The small total optical output of elves makes spectroscopic studies at high time resolution exceedingly difficult, as mentioned in Section 3.3. For instance, an ${\rm N}_2(1{\rm P})$ surface brightness between 650 and 750 nm wavelength of 1 MR lasting 0.1 ms, or an integrated energy of $\sim$2 pJ/cm$^2$/str, amounts to 10$^1$ to 10$^4$ photons for each spectral peak shown in Figure 3.6 on page  for an aperture similar to those of the Fly's Eye but for a field-of-view encompassing the entire elve. For a narrow slit field-of-view, the counts are much fewer.

Instead of resolving the details of the shape of the emission spectrum, two-color photometric observations have been made (see Section 3.3.3). For instance, the ratio between emissions from the first positive and second positive bands of N$_2$ is much higher for elves (and sprites) than for the broadband emissions of lightning. Such spectral ratios have been used [Armstrong et al., 2000; Armstrong et al., 1998a; Uchida et al., 1999; Barrington-Leigh and Inan, 1999] as another criterion for discriminating between elves and scattered light from lightning.

Figure 4.8 shows the sferic and photometric signals recorded for an elve event at 09:40:15 UT on 11 August 1997. The NLDN simultaneously recorded a negative CG discharge with current 155 kA, located 571 km away at a bearing of 82$^\circ$ east of geographic north. The central pixel (P5) of the Fly's Eye was pointed at a bearing of 86$^\circ$ and an elevation of 11$^\circ$. The polarity of the CG lightning is unambiguously confirmed by that of the received sferic.

This event exhibits an interesting double-pulse structure and is unusually bright, showing strong emission outside the ${\rm N}_2(1{\rm P})$ band. The dotted trace in the top panel of Figure 4.8 shows the absolute magnitude of the greater than 1 kHz component of the sferic, to emphasize that the optical pulses occur on the same time scale as the amplitude variations in the sferic. This result suggests that the fine structure of the EMP electric field waveform may be manifested in the optical emission signature.

The dashed trace shown in Figure 4.8 is the response of P12, a blue photometer with a rectangular field-of-view containing that of P8, but approximately 3 times as large in each dimension. A second blue photometer, P10, had a similar relationship to the red photometer P2. Only a handful of events during the study period were bright enough to be detected by our blue photometers and, as shown below, the data are inadequate for determination of in situ parameters. Because this was a significant experimental shortcoming, some relevant details of the spectral band comparison are included below.

Figure 4.15: Predicted optical ratio of blue to red photometer signals as a function of electric field. Optical transmission was calculated for a viewing elevation of 3.5$^\circ$

In order to make a comparison between optical signal levels seen in the bandpasses of the blue and red filters, we consider the spectral bands ${\rm N}_2(1{\rm P})$ and ${\rm N}_2(2{\rm P})$. The dashed line in Figure 4.15 shows the state excitation ratio $n_\ensuremath{{{\rm B}^3\Pi_{\rm g}}} / n_\ensuremath{{{\rm C}^3\Pi_{\rm u}}}$ predicted by equation (2.18) for different electric fields, with the effects of quenching neglected. The dotted line shows the ratio of emissions $I_k=A_kn_k$ from these states. The solid line shows the ratio of predicted signal intensities in the red and blue photometers of the Fly's Eye for a viewing elevation of 3.5$^\circ$. This ratio results from performing the integrations in equation (3.8), and takes into account the shape of the spectra, the filter transmittances, the photocathode response, and the atmospheric transmission. The considerable variation of the observed ratio of the intensities in the two bands over the electric field values shown indicates that the Fly's Eye's two-colored photometry is a promising tool for remotely probing the electric field that is the ultimate cause of the optical emissions.

Figure: Sensitivity of the Fly's Eye to ${\rm N}_2(1{\rm P})$ and ${\rm N}_2(2{\rm P})$ as a function of viewing elevation angle.

Unfortunately, the observed ratio of the intensities in the two bands also varies strongly as a function of viewing elevation. Figure 4.16 shows the relationship between photometer signal intensity and the source band brightness for different viewing elevations typical for measurements of elves. Here the varying atmospheric attenuation as experienced from the altitude of Langmuir Laboratory is calculated using the MODTRAN3 model described in Section 3.2.2. The solid line gives the ratio between the dashed and dotted lines and represents the transformation between the red to blue signal ratio in the Fly's Eye and the deduced source emission ratio. It varies by an order of magnitude over 3$^\circ$ of elevation, equivalent to the elevation span in the fields-of-view of P10 and P12.

At low viewing elevations the attenuation of blue light becomes extreme and is also highly dependent on atmospheric conditions and aerosol content. As a result, refraction effects may also play a large role. Several bright elve events from 27 August 1998 produced a measureable signal in one or both blue photometers and are listed below. The intensities shown in Table 4.1 are averaged over the respective fields-of-view, which are $\sim$9 times larger in the case of the blue photometers, and the elevations correspond to the center of the fields-of-view. The lightning events occurred at ranges of approximately 650 km to 750 km. The deduced band emission ratio varies primarily in accordance with the viewing elevation angle, suggesting that the fields-of-view are too large in elevation or that the atmosphere (aerosol content) was not well described by the MODTRAN calculation.

Table 4.1: Inconclusive spectral ratio data for elves.

Event (UT)	Photometers	Red	Blue	Elevation	Emission ratio $\left(\frac{I_{{\rm N}\!_2\!1\!{\rm P}}}{I_{{\rm N}\!_2\!2\!{\rm P}}}\right)$
03:49:49	P2/P10	1190 kR	1.3 kR	6.8$^\circ$	68.8
03:49:49	P8/P12	1175 kR	1.1 kR	5.8$^\circ$	62.1
06:24:36	P8/P12	996 kR	1.2 kR	2.2$^\circ$	3.5
06:34:39	P2/P10	292 kR	1.2 kR	3.2$^\circ$	3.0
08:17:15	P2/P10	2314 kR	2.8 kR	3.6$^\circ$	14.8
08:17:15	P8/P12	1803 kR	3.3 kR	2.6$^\circ$	3.6
08:36:25	P2/P10	1622 kR	1.8 kR	3.6$^\circ$	16.0
08:36:25	P8/P12	1782 kR	2.9 kR	2.6$^\circ$	4.0
08:41:38	P2/P10	622 kR	1.1 kR	3.6$^\circ$	10.1
08:41:38	P8/P12	1419 kR	2.0 kR	2.6$^\circ$	4.5