3.1 Telescope mapping

The telescope mapping procedure controls the position of the optical system in all three axes. This procedure is implemented by performing, for a given set of z positions, a series of acquisitions in the horizontal plane (x and y directions). Each x–y plane is scanned starting from a reference position (x₀, y₀) along a spiral path, in order to minimize the necessary motor movements (see example in Fig. 6).

Figure 6Example of telescope mapping geometry in the x–y plane (used for the first measurement session described in this work); x and y relative position of the servomotors in the respective axis.

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Figure 7(a) Expected radii for maximum (r_d−r_i) and partial counts (r_d+r_i) in the signal map for an image of radius r_i and a diaphragm (solid line) of radius r_d for r_i<r_d. (b) Schematic longitudinal view of radiation intensity near the focal plane, diaphragm in a focused (1) and in an out-of-focus (2) position.

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Given the relative dimension of the diaphragm and the optical fibre core and assuming a well-aligned receiving box, the procedure presented in this study takes into account only the characterizable effect of the field stop diaphragm displacement.

Figure 8(a) Simulated signal map for a diaphragm of radius r_d=0.4 mm and an image of radius r_i=0.2 mm. The signal is normalized by the maximum value. (b) Result of a single-plane mapping performed with misaligned optics; here the signal (normalized by the maximum value) is asymmetrically clipped by the optical system between the telescope and the photomultiplier.

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Moving the diaphragm in the x–y plane on a fixed z for an image of radius r_i<r_d, where r_d is the diaphragm radius, approximately constant counts are expected in a circle of radius r_d−r_i and a decrease to zero counts within a radius r_d+r_i (Fig. 7a). This of course under the assumption that all the signal passing through the diaphragm is captured by the PMT. When the signal is clipped in the path between the aperture and the sensor, the obtained mapping could be asymmetric and could diverge from the expected shape. The resulting image could also be affected by inhomogeneities in the PMT sensitivity (Freudenthaler, 2004); the use of optical fibres effectively acts as a light scrambler minimizing the impact of this problem (Sherlock et al., 1999). Small imperfections in the beam cross section, when the image is small and well-focused, should not cause asymmetries in the resulting mapping.

For a fixed range R in lidar-acquired profiles, when changing the z coordinate of the field stop/diaphragm, the image is expected to grow from the minimum in the focused position following the enlargement of the circle of confusion. If the image size is bigger than the receiving optical component (e.g. diaphragm, optical fibre, lens), part of the signal will be lost but the mapping will still be symmetric (Fig. 7b).

From the qualitative analyses of acquired signals from a single telescope mapping, knowing the ideal behaviour, it is possible to diagnose deviations from the nominal positions for all the optical components in the system not taken into account by the simplified model. As an example, Fig. 8 depicts a simulated single-plane mapping in case of good alignment and a real mapping showing problems with the optical alignment (i.e. signal clipping in the optical system between the telescope and the photomultiplier).

The information given by this type of mapping can be used to accurately position the receiving optical system as shown in Sect. 4. Another potential use of the information derived from the mapping is to estimate unknown characteristics of the system.

As an example, the relative tilt between the field of view axis and the laser beam can be computed once the centre of the image in the focal plane (x_c, y_c) is found. For high ranges, this position corresponds to a configuration with parallel beam and field of view axes. If the measurements are done at different positions of the receiving system in the horizontal plane, the relative tilt angle θ_tilt can be calculated for any given position (x, y) with the following formula:

where f is the telescope focal length and D is the geometric distance between the position x, y and the reference position x_c, y_c.

As previously mentioned, a trade-off between obtaining a reasonable signal-to-noise ratio (SNR) in the range of interest and minimizing possible changes in the signals due to atmospheric and system variability is needed.

In order to account for atmospheric/system variability, two approaches have been tested:

• If there is a channel acquiring information at the same wavelength of the channel being mapped but through another telescope, a normalized signal is obtained from the ratio of the profiles from the two channels. For example, the normalized signal $S^{\prime }\left(R\right)=S_{\mathrm{CH}\mathrm{01}}\left(R\right)/S_{\mathrm{CH}\mathrm{02}}\left(R\right)$ used for the mapping of channel 1 described in the following section (Sect. 4.1) is defined as the ratio of the simultaneously acquired measurements from channel 1 and 2 (Table 4).

• In the absence of a suitable signal from a second channel, the signal profile from the same channel, acquired periodically in a reference position (e.g. the position chosen with a previous alignment) during the mapping, can be used to normalize the measurements within the interval of time between acquisitions in the reference position. This approach is used in the laser mapping (Sects. 3.2 and 4.2); in this case the normalized signal was calculated as $S^{\prime }\left(R\right)=S_{\mathrm{CH}\mathrm{01}}\left(R\right)/S_{\mathrm{CH}\mathrm{01}}^{\mathrm{ref}}\left(R\right)$.

3.2 Laser mapping

In the case of lidar systems with the capability of electronically controlled azimuth and zenith orientation of the laser beam, an analogous procedure can be implemented, leading to similar insights into the geometry of the system.

For a given telescope-laser relative geometry the overlap function can be estimated through a mapping performed varying the laser beam zenith and azimuth angle. The lowermost range for which the overlap function can be estimated depends on the characteristics of the system being required that the laser beam can be tilted to have some position with full overlap. Moreover, in order to define an absolute maximum with O(R)=1, the size of the image has to be smaller than the diaphragm (i.e. the image is sufficiently focused).

The scan is performed progressively, minimizing the necessary motor movements (Fig. 9) and the subsequent delay between acquisitions. To monitor changes in the atmospheric conditions and in the power output of the laser, an acquisition in a reference laser position (e.g. the setup chosen with the telescope mapping and used for routine measurements) is performed before and after each zenith swipe. This is highlighted in Fig. 9, where at the beginning and at the end of each column (i.e. zenith angle swipe) the laser beam returns to the same pair of zenith and azimuth values. Time-interpolated data acquired in the reference position $S_{\mathrm{CH}\mathrm{01}}^{\mathrm{ref}}\left(R\right)$ are used to normalize the measurements during the mapping.

Figure 9(a) Laser mapping scan geometry, after each zenith scan a measurement in the reference position (black square) is performed. (b) Schematic of the telescope FOV and laser beam for different orientations.

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To estimate the overlap function, for each range value R, the maximum (or the mean of the highest n values if the mapping is performed with sufficient x–y resolution) of the normalized signal $S_{\max }^{\prime }$ is sought. Under the previously stated assumptions, this value should represent the ratio of a full overlap signal and $S_{\mathrm{CH}\mathrm{01}}^{\mathrm{ref}}$ affected by partial overlap. Consequently, for a given range R, the overlap factor in the reference position is $\mathrm{1}/S_{\max }^{\prime }$. We therefore calculate the overlap function O(R) for each R between the minimum range with useful signal and the range in which the full overlap is reached.

4.1 Telescope mapping and alignment

The objective of this telescope mapping session is to optimize the alignment relative to the acquisition of 532 nm elastic backscatter by the 15 cm telescope (CH01). This has been performed in two steps:

• a preliminary mapping with a larger range and a coarser step in the three dimensions to identify the sub-volume of optimal alignment;

• a mapping in the sub-volume identified in the first mapping, close to the optimal position and with finer resolution.

Figure 10Overall view (a) and x–z section (b) of the results of the telescope mapping of the first session (13 January 2021) showing the normalized signal as a function of the x–y–z positions at a chosen range (15 µs – 2250 m a.g.l.).

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Two steps are needed due to the time necessary to perform a scan with both large x–y–z range and step. The first mapping could be skipped if the system was recently aligned.

Figure 11Signal mapping of the first session (13 January 2021) showing the normalized signal for three planes at different z positions and chosen range (15 µs – 2250 m a.g.l.). The position derived from the manual alignment is highlighted by the black square.

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The two sessions were performed on 13 January 2021 (18:01–23:04 UTC) and on 26 January 2021 (17:02–20:01 UTC).

Table 6 reports the characteristics of the performed mapping.

Table 6Characteristics of the two telescope mapping sessions and the laser mapping session; the channels used for the procedure are highlighted in bold.

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With these settings, each acquisition for the mapping procedure took about 38 s of which 30 s are the effective acquisition time and 8 s are dedicated to the data transfer and the movement of the motors that can be performed one motor at a time.

From the results, which are depicted in Figs. 10 and 11, it is clear that the telescope in the manually optimized configuration (x=9.40 mm, y=10.50 mm, z=10.50 mm, highlighted in Fig. 11a), despite being not far from the optimal x–y position, is highly out of focus due to its z position. The overall intensity of the signal in the x–y plane increases, changing the z position (Fig. 11b), as the now focused image passes through the diaphragm without being clipped. Moving further in the z axis, the signal starts again to decrease (Fig. 11c). No clear asymmetries in the signal are found. The presumed optimal position resulting from this session is x=9.40 mm, y=10.60 mm, z=8.50 mm.

The slight shift of the image centre (i.e. the centre of the area with maximum values) at different z positions is caused by incoming light rays tilted with respect to the z axis. Moreover, looking at the uppermost useful range, for x–y positions at the centre of the image the beam and telescope axis (more precisely the FOV axis) should be approximately parallel. Assuming the z axis as vertical, this information can be used to estimate the tilt of the laser beam dividing the x–y shift of the centre of the image by the z displacement, resulting in a tilt of ∼ 50 mrad.

Figure 12Signal mapping (CH01 photon-counting signal) of the second session (26 January 2021) at same z and different ranges (a: 5.0 µs – 750 m; b: 10.0 µs – 1500 m; c: 20.0 µs – 3000 m). Here the signal is not normalized due to the lack of sufficient SNR from the second channel in the lower range (highly incomplete overlap).

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The second session was performed with finer steps and centred around the presumed optimal position. In Fig. 12 is plotted the signal intensity S at different ranges and a fixed z coordinate. In this case, the signal has not been normalized due to highly incomplete overlap of the second channel in the low range. The atmospheric and power variability has been monitored qualitatively with channel-2 measurements at higher ranges. In the x–y plane, as expected, the image shifts at different altitudes. No evident asymmetries are present in the signal map.

Through this session, a definitive and well-aligned position can be selected in the x–y plane as a trade-off between maximizing counts in the lower range (optimizing the signal in the partial overlap range and lowering the full overlap height) and maintaining the beam in the telescope FOV at high ranges.

In the z coordinate, the optimal position is selected evaluating the normalized signals at a medium range around the selected x and y position. As shown in Fig. 13, the curve has a plateau in which the maximum value is reached (i.e. the image is sufficiently focused and inside the diaphragm). The selection of a position in the higher-value portion of the plateau corresponds to a diaphragm position that better captures the signal in the lowermost range (the focus shifts from infinity to lower ranges).

Based on the above considerations the derived optimal position is x=9.45 mm, y=10.55 mm, z=8.30 mm.

As mentioned in Sect. 3.1, measuring the angular distance between the selected position and the centre of the image at high ranges (Eq. 3), the relative tilt between the telescope FOV axis and the laser beam is about 0.3 mrad.

Figure 13Normalized signal at a chosen range (20 µs – 3000 m) for different x and y positions as a function of z; data from both mapping sessions (dashed line for the first session, solid line for the second). A plateau is reached approximately between z=7 mm and z=9 mm. Each colour corresponds to different x and y positions as indicated in the legend of the plot.

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4.2 Alignment validation

The selected alignment configuration was validated through a telecover test and direct comparison of the signal profiles in the different positions.

The telecover test, described by Freudenthaler et al. (2018), is a quality assurance tool used for lidar system misalignment diagnostic and evaluation of the full overlap range. Lidar profiles taken with different sectors of the telescope aperture are compared to each other. For well-designed and correctly aligned systems, the normalized signals should only show differences in the partial overlap range.

Measurements were carried out during a single night session (2 February 2021, 18:55–21:26 UTC). Progressively the following measurements were performed (see Fig. 14): a telecover test in the non-optimized starting position (a), a full telescope measurement in the same position (b) and one in the optimized position (c), and finally a telecover test in the optimized position (d). Standard acquisition times were used (60 s), with an integration time of 10 min for each telecover test sector or comparison profile.

4.2.1 Profile comparison

Figure 15a shows the direct comparison of the background subtracted signal profiles in the non-optimized starting position and in the optimized position. Higher signal is found in the whole optimized profile (>50 % relative normalized difference), confirming the successful alignment procedure and no signal loss in the high range (Fig. 15b). The negative difference in the lowermost range is well below the full overlap height (i.e. <500 m) and can be explained considering that the large and less focused image of the non-optimized position can maintain a partial overlap with the telescope FOV for a wider vertical range.

Figure 14Validation measurement session (2 February 2021). Telecover (a) and full telescope measurement in the non-optimized position (b) and in the optimized position (d and c, respectively).

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Figure 15Background subtracted counts (a) and relative difference between the normalized signal $\mathrm{CH}\mathrm{01}/\mathrm{CH}\mathrm{02}$ profiles (b) in the selected position (x=9.45 mm y=10.55 mm z=8.30 mm) and the starting one (x=9.40 mm y=10.50 mm z=10.50 mm).

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Figure 16Telecover test results for the positions selected with manual (a) and mapping-based (b) alignment procedures.

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Figure 17Laser mapping signal (CH01 analogue signal before normalization with the reference position signal) at three different ranges expressed as delays at the top of the bin (a: 2.0 µs – 300 m; b: 3.0 µs – 450 m; c: 8.0 µs – 1200 m). The reference position (Az = 7.73, Zen =7.97) is highlighted by the black square. Measurements in this position are acquired every zenith acquisition sequence and are represented in the lower array.

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4.3 Laser mapping and overlap estimation

Once an optimized position has been selected and verified (see Sect. 4.1 and 4.2), a laser beam mapping with the purpose of estimating the overlap function was performed (15 February 2021, 18:39–19:37 UTC). The characteristics of the mapping are reported in Table 6. In Fig. 17 the mapped analogue signal at three different ranges is shown. As in the telescope mapping, a range-dependent shift of the signal away from the reference position is visible in the lowermost range.

From this data, the overlap function using the methodology presented in Sect. 3.2 is calculated. The first five highest values are used for the calculation of $S_{\max }^{\prime }$ at each range. In order to evaluate the possible impact of the dead-time effect in the PC mode (Donovan et al., 1993; Cairo et al., 1996), the analysis was performed also using data acquired in the analogue mode. Figure 18 shows the estimated overlap function from analogue (A) and photon-counting (PC) data; the resulting uncertainty is evaluated by the propagation of the signal uncertainties. As a reference, Fig. 18 also shows the overlap function computed with an analytical model with uniform beam energy distribution (Stelmaszczyk et al., 2005) and a Monte Carlo integration of Halldórsson and Langerholc (1978) equations with Gaussian beam energy distribution. Both models use the relative inclination of the laser beam estimated via the telescope mapping (see Sect. 4.1).

Figure 18Estimated overlap function using analogue (A) and photon-counting (PC) data compared to the overlap function calculated from models with the assumption of a uniform/Gaussian beam, diaphragm in the focal plane, and tilted beam (0.3 mrad).

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The function O(R) reaches unity in the expected range and the experimental results are in agreement with the models. Photon-counting data were corrected for trigger delays (Freudenthaler et al., 2018) as described in Appendix A. One evident feature is that after having reached the maximum (at 500–800 m) the values start to slowly decrease. This underestimation of the retrieved overlap function in the high ranges can be explained by the methodology chosen for the maxima selection. In particular, the systematic overestimation of the maxima $S_{\max }^{\prime }$ (due to the shot noise) becomes relevant only above the range of interest (i.e. where O(R) has already reached unity). The difference between the modelled/retrieved full overlap height and the one found via the telecover test could be due to aerosol variability in the latter or slight instabilities of the system beam/telescope alignment and needs to be further investigated.

As an example of the application, Fig. 19 shows an uncorrected aerosol backscattering profile and the corrected one using the PC-retrieved overlap function applied from 200 to 500 m for channel 1 (11 February 2021, 19:45–20:44 UTC). Both the uncertainty associated with the overlap for the first four bins and the retrieval algorithm uncertainty have been taken into account for the corrected profile. Applying the overlap correction allows the extension of the useful range of the aerosol backscattering profile down to 200 m.