Measurement of the Optical Turbulence Produced by a Multirotor Unmanned Aerial Vehicle

At present, new approaches for the use of Multirotor Unmanned Aerial Vehicle or multirotor drones in high precision optical applications are rising. However, the optical turbulence effects generated by multirotor drones are not entirely understood. These optical effects can reduce the performance of the optical instruments that they transport. This paper presents measurements of the wavefront deformation generated by the temperature fluctuations and the airflow of a drone's propulsion system. To do so, we used a single arm of a DJI S800 EVO Hexacopter (professional drone) and measured its operating temperature with a commercial infrared camera. The resulting temperature variation, between a switched-off propulsion system at room temperature and one running at its maximum performance, was 34.2{\deg} C. Later, we performed two different interferometric tests, Takeda's method, and the phase-shifting technique, using a ZYGO interferometer. These tests show that the total deformation over an incident wavefront to the propeller airflow is lower than 0.074 \lambda PV and 0.007 \lambda RMS (HeNe laser, \lambda=633nm). We conclude that the optical turbulence produced by a drone propulsion system is negligible.


Measurement of the Optical Turbulence Produced by a Multirotor Unmanned Aerial Vehicle
Raúl Rodríguez García, Luis Carlos Alvarez Nuñez, and Salvador Cuevas Abstract-At present, new approaches for the use of Multirotor Unmanned Aerial Vehicle or multirotor drones in high precision optical applications are rising. However, the optical turbulence effects generated by multirotor drones are not entirely understood. These optical effects can reduce the performance of the optical instruments that they transport. This paper presents measurements of the wavefront deformation generated by the temperature fluctuations and the airflow of a drone's propulsion system. To do so, we used a single arm of a DJI S800 EVO Hexacopter (professional drone) and measured its operating temperature with a commercial infrared camera. The resulting temperature variation, between a switched-off propulsion system at room temperature and one running at its maximum performance, was 34.2 C. Later, we performed two different interferometric tests, Takeda's method, and the phase-shifting technique, using a ZYGO interferometer. These tests show that the total deformation over an incident wavefront to the propeller airflow is lower than 0.074 λ PV and 0.007 λ RMS (HeNe laser, λ=633nm). We conclude that the optical turbulence produced by a drone propulsion system is negligible.

I. INTRODUCTION
The development of multirotor drones has been astounding, and today we can find them in a great variety of scientific applications [1]. The crucial point of this expansion has been the implementation of more robust and precise flight controllers, as well as the improvement of the battery technologies. These have increased drone's maneuverability (even automatically) and flight time, thereby easing their professional use. applications involving the use of high precision optics, such as in astronomical instrumentation. Here, multirotor drones need to carry a light source that will use as a reference source for astronomical telescopes applications. An example of these applications can be: the maintenance of telescopes, optical characterization or adaptive optics [3] [4] [5].
In optical instrumentation, there are several reasons why an optical system cannot reach its ideal performance. Sometimes inhere in their design and manufacturing parameters, and other times are resulting from external factors such as vibrations, temperature variations of their optomechanical components, and optical turbulence. The latter is produced by random variations in the refractive index of air due to changes in its density or temperature. These variations result in lower quality of the images obtained by the optical instruments. These If the size of atmospheric cells is larger than the input pupil diameter, a perfect optical system will produce Point Spread Function (PSF) images determined by the diffraction limit of the pupil. When the size of atmospheric cells is smaller than the pupil diameter, such that the number of encircled cells is bigger than 3-4, the PSF energy will be transferred from the central core to the diffraction rings at a rate of change Nevertheless, the best approach is by measuring the optical turbulence produced by a drone propeller and its motor. That means to measure directly the wavefront distortions using instruments and techniques with enough optical sensitivity. The purpose of this paper is to determine the atmospheric turbulence produced by a drone's propulsion system. To this end, we conducted three different optical tests: a Schlieren imaging test, and two interferometry tests (using the Takeda method and the phase-shifting technique). Additionally, we measured the temperature of the motor and the surrounding air using a thermal imaging infrared camera. These type of cameras have an appropriate image resolution (320 X 240 pixels) and temperature sensitivity of around 0.1C per pixel. Section II shows the measurements of the increase of temperature of the motor, running at its maximum power, using an infrared camera. Section III addresses the analysis of the distribution of turbulent airflow with Schlieren imaging test. Section IV presents the development of an experiment using two different interferometric tests. This was because the propulsion system generated many vibrations and we wanted to be sure about the obtained results from this experiment.
Finally, we give a summary and our conclusions in Section V.

II. MOTOR TEMPERATURE VARIATION
To evaluate the change in temperature of drone's propulsion system, we used a single arm of a DJI S800 EVO drone (see figure 1). Its features are described below: • Motor.  C after ten minutes of use at its maximum power [7]. This temperature value is consistent with our measurements. Fig. 2. Difference in the temperature of the motor when it was switched-off (left) and after five minutes of operation at its maximum speed (right).

III. DISTRIBUTION OF TURBULENT FLOW
To better understand the distribution of the heated air flux produced by the propulsion system, we performed a Schlieren test. This kind of test has been widely used to study air flux related problems [8]. For this test, we used the largest mirror available in our laboratory (60 cm), since the area covered by the rotating propeller is 40 cm in diameter. In this qualitative test, we ran the motor to its maximum speed for about five minutes and then we reduced this speed by half to perceive the optical effects of turbulence.

A. Schlieren Test Setup
We implemented the Schlieren test with a double pass coincident setup (see figure 3) with a spherical mirror 60 cm of diameter and 4.4 m of focal distance. The drone propulsion system was in front of the mirror at a distance of 50 cm.
At this distance, we positioned the propulsion system above and below to the mirror image formed on the camera's CCD (Schlieren test area). This configuration would allow the air flux to cross through the total test area. The light source was a circular pinhole of 1 mm in diameter illuminated by a white LED (1 W high power). We acquired the images using a Canon T3i camera with a 22,3 X 14,9 mm CMOS detector and a 50 mm objective lens focused on the motor.

B. Results of the Schlieren Test
First, we placed the propulsion system above the test area.
In this configuration, the downward air produced by the propellers crossed the entire mirror. Nevertheless, we could not detect any variation (turbulence) in the Schlieren image. Next, we placed the propulsion system below the test area, under the assumption that the heated air was probably going to move upwards. Again, we could not detect any turbulence after running the motor for five minutes. Nonetheless, only when we switched off the motor, the camera registered fluctuations produced by the ascending heat (see figure 4). It was not possible to see optical turbulence using the Schlieren test. Therefore, it was not possible to detect its distribution. These preliminary results led us to infer that the turbulence must be close to the motor. Hence, for the interferometric tests, we decided to place the propulsion system as close as possible to the light beam (see figure 5).

IV. WAVEFRONT MEASUREMENTS
This section describes the experiment that we implemented to estimate the optical turbulence produced by the drone's propulsion system. We proposed to use interferometric methods since they are the best ways to detect and quantitatively measure the smallest variations (smaller than λ/10) of wavefront respect to a reference surface.
To measure wavefront distortions, we did two interferometric tests using a 6 inches Fizeau interferometer (ZYGO interferometer) with a high-performance transmission flat (λ/20).
It should be mentioned that the interferometer of our optical laboratory is certified by the National Institute of Standards and Technology (NIST). The first interferometric test was the Fourier interferometric fringe pattern analysis, also known in optics as the Takeda's method [9]. The second test was using the phase-shifting technique made directly by ZYGO software.
We used MATLAB to process and display the phase maps (hover mode) to perform some task.

A. Experiment Setup
In the experiment setup, an external 4 inches flat reference mirror (λ/12 PV) reflected the light beam from the interferometer by the same optical path. This arrangement allows us to have a reference wavefront. Figure 5 shows a layout of the performed experiment.  It is important to have a considerable number of fringes so that the algorithm can work correctly [10]. We modified the number of obtained fringes by small adjustments in the tilt of the external flat reference mirror. Figure 7 shows an example of a fringe pattern obtained for Takeda's method test. We implemented Takeda's method in MATLAB, to get the phase-maps from the interferograms. It is worth mentioning that we needed to calibrate our software to get the actual values of Peak to Valley and RMS from the phase-maps' measurements.
We did the calibration of our software by comparing one of its post-processed phase-maps with one obtained by a standard measurement of ZYGO interferometer (phase-shifting).
Both of them were from the flat reference mirror under the same conditions. In the calibration process, we performed the measurements without the influence of the propulsion system and in a controlled temperature environment. Figure 8 shows the phase-map of the flat reference mirror obtained by the two previously described measurements over the same test area. Here, the wavefront errors after the calibration were the same, 0.077 λ PV and 0.013 λ RMS. We ran the propulsion system for five minutes at its maximum speed an then we reduced this speed by half. Then, we took eight interferograms over the next five minutes to be post-processed.

C. Analysis with the Phase-Shifting Technique
Complementary to this work, we verified the results obtained by Takeda's method. To do this, we performed direct interferometric measurements with the ZYGO instrument.
However, even though the motor was isolated from the optical table, the propulsion system produced vibrations by the ejected air from the propeller to the optical table. We made standard phase-shifting measurements, but the resulted phase-maps were distorted. Figure 9 shows the distortion of the obtained phase-map. Here, the wavefront errors were of 0.237 λ PV and 0.032 λ RMS. In order to eliminate the effects of vibrations, we modified the acquisition time parameter of the interferometer camera from 2000 µs (default value) to 5 µs. However, when conducting various measurements on the reference flat mirror, we found variations in the resulting phase-maps, even without the impact of the propulsion system. We attributed these variations to the reduction of the signal-to-noise ratio resulting from the modification of the exposure time.
Similarly to in the Takeda's test, we isolated the effects of turbulence subtracting the instrumental error from each of the measurements. In this case, the instrumental error was the average of ten short exposure phase-maps made with the ZYGO interferometer software. Then this error was subtracted from each measurement using the ZYGO software too.
In figure 11 we show the results of the phase-shifting technique measurements. In this case, we have a mean PV of 0.046 λ (λ/21) and min/max RMS values of 0.007 and 0.009 λ, respectively, with a mean RMS of 0.007 λ, equivalent to a Strehl Ratio of 0.998.  We measured the temperature of a drone propulsion system (motor, propeller, and electronics) using an infrared camera.
We obtained a gradient of 34.2 C after running the propulsion system at its maximum speed for 5 minutes.
We conducted a Schlieren test to determine the distribution of turbulence flow. In this test, we did not see the optical turbulence. However, we observed optical disturbances produced by the heat of the motor when we switched-off the propulsion system after running the test.
We also conducted two interferometric tests using a ZYGO As a result of our experiment, we can affirm that the propulsion system does not produce significant optical turbulence. Therefore, drones can be used in high-precision optical applications.