the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 May 2026
Deriving the telescope focus function for a pulsed coherent Doppler lidar without a reference instrument
Abstract. Obtaining profiles of attenuated backscatter coefficient from the signal-to-noise ratio measured by a pulsed coherent Doppler lidar requires knowledge of the instrument telescope focus function, which is often unknown. Here, we present a methodology for deriving the telescope focus function from horizontally-pointing pulsed coherent Doppler lidar measurements without the use of an external reference. The method relies on the assumption that the horizontal profile of attenuated backscatter coefficient is close to homogeneous, which is tested for using a convolution filter. The methodology was applied to measurements from eight co-located Doppler lidars and the results compared to a methodology for deriving the telescope focus function using vertically-pointing Doppler lidar measurements using an elastic backscatter lidar as reference. The telescope focus functions obtained with the two methodologies show good agreement even for measurement periods as short as two days.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-1140', Anonymous Referee #1, 20 Aug 2026
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CC1: 'Comment on egusphere-2026-1140', Tianwen Wei, 21 Aug 2026
Dear authors,
I have read this preprint and would like to draw attention to a closely related prior study that appears to be absent from the current reference list:
Wei, T., Wang, M., Jiang, P., Wu, K., Zhang, Z., Yuan, J., Xia, H., and Lolli, S.: Retrieving aerosol backscatter coefficient using coherent Doppler wind lidar, Optics Express, 33, 6832-6849, https://doi.org/10.1364/OE.551730, 2025.
Wei et al. (2025) proposed and validated a self-calibration method for the telescope focus function of pulsed coherent Doppler wind lidar using horizontal observations and the assumption of horizontally homogeneous aerosol distribution. In that work, the focus parameters were estimated from the range dependence of the focus-function-corrected CNR or attenuated-backscatter profile under horizontally homogeneous conditions, with profiles affected by aerosol inhomogeneity or strong turbulence excluded from the analysis. The study also discussed the influence of beam focusing, heterodyne efficiency, CNR, lidar constant calibration, lidar-ratio assumptions, and refractive turbulence on aerosol backscatter retrieval.
The present preprint addresses a closely connected topic, namely deriving the telescope focus function from horizontally pointing pulsed coherent Doppler lidar measurements without an external reference instrument, using the assumption that the horizontal attenuated-backscatter profile is close to homogeneous and applying filtering to identify suitable profiles. Compared with Wei et al. (2025), this manuscript adds useful and distinct elements, including an eight-instrument intercomparison during FESSTVaL, comparison with a ceilometer-based vertical method, and an explicit convolution/MSE filtering strategy for selecting suitable horizontal profiles.
I suggest that the revised manuscript cite Wei et al. (2025) and briefly distinguish the two studies in terms of the telescope-focus-function parameterization, treatment of heterodyne efficiency and turbulence, filtering criteria for horizontal homogeneity, validation data sets, and the role of external reference instruments. This addition would give readers a more complete view of the recent development of reference-free and self-calibrated aerosol-backscatter retrieval methods for coherent Doppler wind lidar.
Best regards,
Tianwen Wei
Citation: https://doi.org/10.5194/egusphere-2026-1140-CC1 - RC2: 'Comment on egusphere-2026-1140', Anonymous Referee #2, 31 Aug 2026
Data sets
Doppler lidar data from Falkenberg for Pentikäinen et al. (2026) "Deriving the telescope focus function for a pulsed coherent Doppler lidar without a reference instrument". Compiled by E. O'Connor. R. Leinweber and E. O'Connor https://doi.org/10.57707/fmi-b2share.qssxd-qxt78
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Summary
This paper describes a method for deriving a coherent detection wind lidar telescope focus function using horizontal staring data, as well as vertical staring data paired with another elastic backscatter lidar. This is an important issue for coherent wind lidar which measures signal return intensity relative to instrument noise, and not calibrated attenuated backscatter measured by direct detection lidars that is commonly used for quantitative atmospheric and cloud characterization.
The data, methods, and results presented are sound, and the writing is of high quality. I feel that aspects of the methodology could be described a little more clearly to make the approach accessible to non-experts, with some supporting graphic(s) to clarify some aspects of the methods as described below.
My only question / concern is related to repeated suggestions that there isn’t enough data included here to narrow uncertainty or understand differences between the assorted wind lidars (e.g. Line 150, 219). I see that data is averaged to 1-minute samples, and there are 2-3 days of data included (Line 219). This seems to me to be quite substantial to perform this investigation, especially considering wind profile retrievals from these systems are typically done every 1-2 sec (Line 61). I understand that even though these instruments are pointed in the “same direction”, subtle variability with pointing or other instrument artifacts require more averaging. One would think that averaging to 30 sec would be sufficient which would double the samples. You say that data was previously averaged to 30 mins which is extremely long for these types of lidars. But, regardless even at 1 min, you have over 3000 samples across 2+ days which should be plenty. Please comment on this in the response to me and in the text.
I recommend this paper be published with minor revisions requested above and below
Specific Comments
Line 100-102, you describe that the data are “normalized” but the approach you use to do this is not provided. Please explain this in the text
Lines 107-111, you describe your fitting procedure based on iterative adjustment of f and D, but according to your equation in line 83, Tf is not modulated by f and D. Please clarify
Section 3.3, A schematic diagram illustrating the filtering procedure is needed. The text description alone does not provide enough for me to fully understand what it is you’re doing and why you need to do it, considering that these lidars are basically sampling the same atmospheres especially when averaged to the long time scales you are using.
Line 139, it is unclear what you mean by how the normalized profiles are “compared to unity”.
Lines 161-163, as noted above you say here that there is a “small amount of data” when in my opinion you have an abundance of data.
Line 181, artifacts is misspelled