2.1

Pre-Processing of data: identify suitable times and extract data.

As a first step all times where the TDP1-LCT receives light are identified. In order to include also time-spans with deep fades, i.e. light gone for a short time, the script also keeps time-spans where the space segment had seen sufficient light, i.e. being in tracking, but afterwards loses the light – for shorter periods (fades), but also for longer periods.

Once the list of suitable time-spans of the relevant data is identified, the relevant telemetries are extracted out of the available 25 kHz (TDP1) and 5 kHz (T-AOGS) data.

There are two drawbacks of this method: a) if the link budget is very good, and the space segment has already begun tracking while the ground segment is still, semi-manually, correcting it’s pointing, the data is treated as valid, even though it still contains part of the alignment phase. b) power drops seen at the space segment are not only due to the atmosphere: it was a common operational scenario, that the T-AOGS operator switched off the ground OPA for ~1s, during several special tests, e.g. re-starting spatial and frequency acquisition. These times are currently part of the prepossessed data, though they are removed in the final processing via an ignore list and dedicated filtering.

In addition to the pure data pre-processing, special information like the used T-AOGS divergence angle or transmitting path (CPA100 or CPA270) are included in the file information.

2.2

Processing the data within ATLANTIS tool

In its first step the ATLANTIS tool generates what we call CHUNKs: each of the ‘pre-processed-time-spans’ are analysed whether the TPD1-LCT signal is homodyne, heterodyne or unclear and the data are split into CHUNKs of consecutive homodyne signal or consecutive heterodyne signal. The unclear times, which are mainly times where the frequency (re-)acquisition takes place, are ignored because a clear calibration from signal in V to optical power in W cannot be given. The TDP1-LCT detector signal is converted to received optical light, and the data from the T-AOGS are added to the data set of each CHUNK, thus the CHUNKs contain the following data: time, 25 kHz space segment received light and 5 kHz ground segment received signal. Each CHUNK is assigned a unique number.

In the following, each CHUNK is evaluated and characteristic information extracted. These are, besides others: mean power, number of fades (for -3 dB, -6 dB, -10 dB), mean duration of fades (-3 dB, -6 dB, -10 dB), both: at TDP1 and at T-AOGS. In order to make the fade analysis robust against electronic noise, the power signal is low pass filtered; and to be robust against slow power variations during a CHUNK, the -3 dB, -6 dB, and -10 dB is taken relative to a 3 sec local mean values (see also section 4.2). All of this information, together with evaluated T-AOGS data and used setting (e.g. sending aperture) is listed per CHUNK. In addition to a table gathering the information, each CHUNK is visualized with a set of plots: time-line of power, distribution of power, CDF of fade duration etc.

2.3

Filtering options and final processing within ATLANTIS tool

Once all CHUNKs are generated, analysed individually and a table with the main information and characteristic (mean) values are generated, the data can be filtered by all table information. In addition, a CHUNK-ignore list can be used. In a first step this ignore list and filter settings are used to clean up the data from all CHUNKs containing obviously incorrect data. e.g. T-AOGS OPA switched off for 2 s can be seen either in the time-line, but also in a strongly increased mean ‘fade’ duration.

As the pre-processing is not yet optimized, we lose about 5 h at this filtering step, i.e. 10% of the data. But the remaining data are still sufficient for the analysis on ‘big-data’.

4.1

Link: 2018-04-26, T0 = 00:50, T-AOGS aperture = 35 mm, CHUNK#2294

The single CHUNK shown and described here is representative of a well behaved dataset regarding the optical power received at the space terminal TDP1-LCT. The T-AOGS performing the link using the 35 mm sending aperture via the CPA100. The link itself started at 00:50:00 on 2018-04-26. Data recording for this CHUNK began at a time of 01:05:48, which is represented as t = 0 in Figure 2.

This single CHUNK has a mean optical power received within the 135 mm aperture of the LCT in space of 54.7 nW (-42.6 dBm, i.e. 0.38 nW/cm²). The fades statistic is shown in Table 3.

Figure 2.

shows a timeline (left) and a histogram (right) of the received power at the GEO space segment TDP1-LCT. The data are recorded at: 2018-04-26 from 01-05-48 (=0 s in the plot) in a link with T0 = 00:50. The receiver was heterodyne. The T-AOGS configuration was: CPA100 for TX and 35 mm sending aperture i.e. 26 μrad divergence angle. The unique CHUNK number is 2294.

Table 3.

fades statistic of a sample link, CHUNK#2294, with mean power of 54.67 nW (42.6 dBm)

4.2

Link: 2018-04-16, T0 = 21:00, T-AOGS aperture = 48 mm, CHUNK#2082

The single CHUNK shown and described here shows a different, not so smooth behaviour within the optical power received at the space terminal TDP1-LCT. This time the T-AOGS performed the link using the 48 mm transmitter aperture. The link itself started at 21:00:00 on 2018-04-16 and t = 0 in figure 3 represents: 21:05:59. This single CHUNK has a mean optical power received within the 135mm aperture of the LCT in space of 50.86 nW (-42.9 dBm, i.e. 0.36 nW/cm2).

In the zoom (Figure 3, right) it can be seen that the mean power drifts and also varies abruptly about ~3 dB several times for about 0.2 s. This type of power variations is unexpected and is currently under investigation. Whether it is correlated with T-AOGS pointing (not actively changed here) or weather (which was changing that night) cannot be distinguished yet. Nevertheless: such data are also included within the remaining set of ‘good data’ and part of the big data analysis.

In order to measure fades independent of low frequency power variations (e.g. pointing drift) within a CHUNK, the - 3dB, -6dB, -10dB thresholds are not static, but relative to a 3 s averaged mean power. The behaviour of the local mean power in 3 s and the corresponding -3dB, -6dB and -10dB thresholds are also given in Figure 3. (this way of analysis is used for all CHUNKs). It can be seen (Figure 3, right) that the local mean power in 3 s is almost not affected by the 3 dB drops of 0.2 s – thus this type of intensity drops will increase the fade statistics.

The fades statistic as evaluated with the ATLANTIS tool of this single CHUNK is shown in Table 4.

Figure 3.

Timeline (left) and a zoom (right) of data recorded at 2018-04-16 from 21-05-56 with T0 = 21:00 (CHUNK #2082). The TDP1 tracking detector is in homodyne. The T-AOGS configuration is: TX with CPA100 and aperture 48mm, i.e. divergence angle of 19 μrad (including 20% broadening due to truncation).

Table 4.

fades statistic of a sample link, CHUNK#2028 with mean power 50.86 nW

Comparing the fades statistics of the two CHUNKs (Table 3 and Table 4), which is not only a comparison of a link performed within 35 mm or 48 mm T-AOGS aperture but also between a ‘good behaviour’ and a ‘power variation in the range of 3dB, potentially due to changing attenuation within optical channel’, it can be seen that the amount of -3dB fades are increased by 40%, the amount of -6dB fades are increased by even 70%, while the amount of 10dB fades is not affected.

5.1

Mean power at TDP1 depending on TX beam of T-AOGS

The optical power seen at the space segment depends on the ground segment transmit (TX) beam divergence, it’s pointing accuracy and the transmission of the optical channel. When analysing only mean power values, the dynamic (fades, surges) is averaged. Only beam-shape, pointing and the pure attenuation of the optical channel remain. Figure 4 shows histograms of the mean power derived from each CHUNK (see also Figure 2, right), separated by the different T-AOGS TX apertures and thus beam divergences. Without atmosphere, pointing error, and aging of the T-AOGS, each CHUNK would have the same mean power. The broadening of the distribution is caused by a slight ageing of the T-AOGS transmit path, the different atmospheric transmission, and, most significantly, T-AOGS pointing error. Due to the way the T-AOGS is built (ref. 2, 3, 4) the pointing error can easily have a semi-constant value of up to 10μrad. This explains the slope to less power, as seen for all histograms. Also, the link was used for other purposes and for some of the datasets the main goal was not to achieve an optimal link budget.

The CHUNK mean power distribution for the 95 mm T-AOGS TX aperture (Figure 4, blue) shows, besides a pure statistic due to few links, that the broadening due to miss-pointing is huge.

In Table 5. the mean power seen in Figure 4 is given and the relation between each other, here relative to 35 mm T-AOGS TX aperture is derived. It is compared with the relation of the different antenna gains.

The change in mean power fits almost to the theoretical factor. Additionally, one can see that the seen gain due to larger sending aperture, i.e. smaller beam divergence, is slightly less that calculated. This fits well to the influence of TX/RX misalignment and thus pointing errors, having a stronger influence for narrower beams.

Figure 4.

Distribution of the mean optical power at the space segment TDP1 derived of each CHUNK, separated by the used transmit aperture of the ground segment T-AOGS. The broadening shows the variation in the attenuation of the optical channel and the T-AOGS miss-pointing for the different CHUNKs.

Table 5.

Comparison of mean power seen at the TDP1-LCT for different T-AOGS TX apertures, the relative increase due to larger sending apertures, i.e. smaller beam divergence, and the comparison with the potential gain based on calculated antenna gain.

5.2

uplink: fade statistic, depending on TX divergence of T-AOGS

Evaluating the full set of data, only filtered by the different T-AOGS TX divergence angles, average fade statistics have been derived. The statistics do not distinguish between day or night, or season of the year. As the distribution of data over the day and over the year is not balanced (see Figure 1), this average is also not fully balanced. In contrast to the single CHUNKs shown in section 3, or the data from one summer campaign shown in [7] the observed results or not any more single examples, but an overview based on large statistics. Only the numbers for links with the 95 mm T-AOGS transmitter aperture should be considered carefully: only a few links during noticeable good weather conditions were performed. The resulting fade statistics can be seen within Table 6, and cumulative density functions (CDF) are given in Figure 5.

Table 6.

fades statistics: data separated by T-AOGS TX aperture, heterodyne and homodyne CHUNKs, data for 95 mm is not probing so many different times of the day – and might this be inaccurate.

Figure 5.

The cumulated density function of the numbers of fades relative to the fade duration, as seen at the space segment is shown. The CDF differs depending on the ground segments sending aperture (35 mm left, 48 mm middle, 95 mm right). the CDF is given for the three depth of the fades: -3dB, -6dB and -10dB relative to the actual mean power.

Comparing the fade statistics seen at TDP1 for different T-AOGS TX apertures in Table 6: The difference between 35mm and 48mm is only marginal. The mean fade duration increases by about 10%, the number of fades per second increases by 10% (-3dB), 20% (-6dB), 40% (-10dB). Seeing the increase of -10dB fades of 40% when changing from 35mm aperture to 48mm aperture makes it obvious that, the overall link-budget, if sensitive to fades, is not necessarily improved with a larger sending aperture. The statistics on 95 mm sending aperture is very poor (only few links performed most of them in excellent weather condition). Nevertheless, it can be seen that, relative to 35 mm the mean fades times increases by 50% (-3 dB), 70% (-6 dB), 90% (-10 dB), whereas the number of fades per second decrease for -3 dB by 30%, but increase for -10 dB by 60%. This shows that the fades get stronger with narrower beam, in-line with the expected behaviour.

Figure 5 shows the CDF of the fades relative to the fade duration, and separated to the three different T-AOGS sending apertures used. Also here it can be seen, that narrowing the beam shifts the fade duration to longer values. Less space between -3dB, -6dB and -10dB indicates that the fades get steeper: if a fade occurs it is most likely not only a -3dB fades but immediately also a -10dB fade

In order to see, which times are necessary to bridge 90%, 99% or even 99.9% of all fades, e.g. with an appropriate interleaver code, the relevant times are extracted from Figure 5 and given in Table 7.

Table 7.

Extracted values from CDFs in Figure 5.

5.3

Fried Parameter r₀ measured at T-AOGS

In the following section the measured Fried Parameter during operation of the T-AOGS from 2016 to 2019 at the Observatorio del Teide (Tenerife, Spain) is shown. Additionally two different calculation methods for the value are compared to each other. The Fried Parameter r₀ is a measure of the strength of atmospheric turbulence. A smaller value represents stronger turbulence than higher values. The calculation of the Fried Parameter in the T-AOGS fits the measured wave front to the theoretical Zernike mode variance spectrum. This fit can sometimes be poor due to vibrations of the T-AOGS or local dome seeing, which may not adhere to the expected statistics. This leads to an error in the calculation, which should be considered in the comparison with other calculation methods of the theoretical r0.

In contrast to the above automated extraction of data for the analysis of the following data the time spans with sufficient light and signal on the T-AOGS are chosen manually. For each of these times a mean value of the Fried Parameter is evaluated. Within Figure 6 mean values summarizing the data of a full link are shown as blue points versus the time of the day.

Figure 6.

Fried Parameter r0 as measured with the T-AOGS versus time of day in sidereal time. blue: mean value of a single link. red: mean value and median within 2 h time-window, shifted in 10 minutes interval. Sunrise is at 6:00, sunset is at 18:00.

There are times with more data, e.g. early afternoon, and times with less data, e.g. during lunch break but also late in the night. In order to obtain a mean behaviour over the day the single data points are subsumed in the following way: a sliding window of two hours that is shifted in ten minutes intervals is used to calculate a median and a standard deviation, given as solid red line and reddish area.

The values of r0 during the day (from 9:00 to 15:00 sidereal time) is almost constant, with a low value. During the night from 18:00 to 06:00 local sidereal time the value is also almost constant but about a factor 2 larger, i.e. less turbulence and with larger turbulence cells within the atmosphere. It is interesting to consider the time before and after sunset and sunrise, where the r0 rises. This has already seen and reported¹⁰, but only based on few data and the statistics becomes clearer in the presented data. In the morning r0 starts to increase shortly before sunrise and reaches a maximum (factor 2) about 1 h hour after sunrise. With higher altitude of the sun the r0 starts decreasing. 2 h after sunrise it is back to the ‘night value’ and further decreases to the ‘day-value’. In the evening the main changes happen in the two hours before sun-set: r₀ increases by a factor of 2, from the ‘day level’ to the ‘night level’ with a short peak around sun-set itself.

It is not investigated how much of the behaviour originates from the local atmosphere, i.e. turbulence coming from the ground and the T-AOGS itself due to the changing thermal conditions and how much of the behaviour originates in higher layers over the ground (often termed the “free-atmosphere”).

5.4

Comparison of Zernike based r0 calculation used in the T-AOGS and an alternative “Slope Covariance” based method

The T-AOGS’ internal Fried Parameter calculation is performed by fitting the measured wave-front to an atmospheric model of spatial modes. In this process, the wave-front must be “pseudo open-loop” reconstructed to determine the wave-front observed at the telescope aperture, rather than the residual wave-front as recorded by the Shack-Hartmann wave-front sensor post adaptive optics correction. The variance of the computed spatial modes is compared to a theoretical spectrum to determine the r₀ measurement. This process is subject to some errors during reconstruction of spatial modes and can be biased by vibrations of the T-AOGS and noise on the wave-front sensor.

An alternative method¹⁰ of r₀ calculation was also performed on the recorded data. Here the covariance of pseudo open-loop Shack-Hartmann wave-front sensor measurements is considered and also fitted to a theoretical distribution. In this method, errors in spatial mode reconstruction are avoided and it is also possible to avoid bias due to sensor noise by neglecting the auto-covariance between sub-apertures in the fitting algorithm.

Figure 7.

Comparison of two way to calculate r0: either via covariance subaperture or via dynamic modes.

In Figure 7 it can be seen that the r0 values with the actual calculation method of the T-AOGS is slightly larger and has a higher variation than the alternative method using the covariance between sub-aperture measurements. In general the mean over several minutes has an discrepancy smaller than 1 cm.

5.5

Correlation between r0 in down-link and intensity fluctuations in the uplink

Figure 8 shows the scintillation seen at the space segment TDP1 versus the actual Fried Parameter as measured with the T-AOGS. According to the theory there is no direct correlation. The data show a slight dependency. While a small r₀ indicates smaller turbulence cells in the atmosphere, the mean scintillation seen in space is larger. Nevertheless the scintillation spread, for a given r₀, still by a factor of 2 to 3.

The ‘dip’ and ‘spike’ seen in the median scintillation at r0 = 2 cm and r0 = 27 cm are cause by small statistics and maybe indicated areas where the r₀ calculation is not reliable.

Figure 8.

Scintillation seen at the space segment TDP1 versus Fried Parameter measured on ground with the T-AOGS. Blue: single measurements, performed with 35 mm and 48 mm T-AOGS TX aperture. Red: the calculated median with variance.