Experimental setup for investigation of laser beampropagation along horizontal urban path

Rui Barrosa, Sarah Kearya, Lydia Yatchevaa, Italo Toselliab, Szymon Gladysza

aFraunhofer Institute of Optronics, System Technologies and Image Exploitation,Gutleuthausstr. 1, 76275 Ettlingen, Germany;

bUniversity of Miami, Coral Gables, Florida,USA;

ABSTRACT

It is well known that a laser beam propagating through optical atmosphere is affected by atmospheric turbulence.In this paper, we describe an experimental double-passage system for laser beam propagation along a horizontalurban path that can be useful for applications such as free-space laser communications. The setup includes atelescope to focus a laser beam on a retro-reflector, which is located 410 meters away, and the optical-test benchwith which we measure intensity and phase fluctuations of the reflected beam. In our measurements scintillationis decreasing with distance from the center of the pupil. This shows the need for further theoretical modellingof double-passage systems.

Keywords: Adaptive optics, atmospheric turbulence, scintillation

1. INTRODUCTION

Atmospheric turbulence is one of the most significant factors limiting the performance of electro optical systemsand thus can severely affect laser beam propagation along horizontal paths especially over urban terrain. Inrecent years, the need to develop new and better devices for applications like active and passive imaging orfree-space laser communications has become a reality. Consequently, a deeper understanding of atmosphericturbulence along horizontal paths, and development of new adaptive optics solutions has become a criticalsubject. In our adaptive optics laboratory, the Mewlon300-AO test-bench setup was built for laser beampropagation experiments along a horizontal urban path (Fig. 1). We want to gather the data for applicationssuch as directed-energy and free-space laser communications.

The project goal is to build an AO double-passage system capable of focusing a laser beam ( ' 632.8 nm)onto a retro-reflector, which is located 410 m away. Currently, we measure intensity fluctuations and wavefrontdistortions of the reflected beam and test the susceptibility of the Shack-Hartmann wavefront sensor (SHWFS)to scintillation. In the future the setup will be used as the main optical system for testing of the holographicwavefront sensor.1

A number of field tests have been executed at Fraunhofer IOSB facilities in the city of Ettlingen (Germany).The measurements were performed over a horizontal path of 410 m. The emitter/receiver system is locatedat our AO laboratory at a height of 12 m and, at approximately the same height, a 1-inch retro-reflector wasinstalled on a church tower. The path covers a large yard, some rooftops, a road and the church garden. Theexperiments were performed during daytime in the summer of 2014.

Rui Barros: Fraunhofer-IOSB, Gutleuthausstrasse 1, Ettlingen, Germany, Telephone: +49 (0)7243 992 206

Figure 1: Mewlon 300 test-bench pointing at the retro-reflector located on the church tower, 410 m away from the AOlaboratory.

2. SYSTEM DESIGN

The concept of our setup is illustrated in Figure 2. The setup was designed and optimized to work in the visiblespectrum ( ' 632.8 nm) for easy calibration. However, for the purpose of free-space laser communications,further modifications should be made in order to work in the near-infrared range ( ' 1.55 m). From an opticalpoint of view, the setup is a double-passage system where a Gaussian beam propagates from a transmitterthrough a random media, and is focused onto a retro-reflector. The beam propagates back through the sameatmospheric turbulence. A SHWFS and a high-speed CMOS camera are placed in conjugated planes with thetelescope entrance pupil in order to measure phase aberrations and intensity fluctuations, respectively.

Figure 2: Optical principle of the Mewlon 300 AO test bench.

2.1 Optical system architecture

Figure 3 depicts the setup used for measuring the intensity fluctuations and phase aberrations at the entrancepupil of the telescope. The system is fed by a 35 mW linearly polarized, red laser beam (output beam) whichby means of a converging lens (L1) is focused in the image plane of the Dall-Kirkham telescope (Mewlon 300)conjugated with the retro-reflector plane located at the tower, 410 m away. The reflected light from the retro-reflector is collected by the telescope and re-collimated by L2. By placing a Pellicle Beamsplitter (BS2) afterL2 it is possible to produce two images of the entrance pupil of the telescope, where one is dedicated to theSHWFS and the other imaged again by a relay system (L3 + L4) onto the camera (Dalsa Genie HM640, C2).Both SHWFS and C2 are placed in conjugated planes with the telescope entrance pupil. Another detector (C1)was placed at the focal plane of L3 in order to simultaneously measure the focal plane image.

Figure 3: Optical scheme of the Mewlon 300 AO test bench.

In order to isolate the input from the output beam, it was necessary to install a half-wave plate with apolarized beamsplitter (BS1+1/2WP) to rotate the polarization plane of the previously linearly polarized beamof light. By rotation of the half-wave plate, one can select the amount of s-polarized light reflected to thetelescope. After the beamsplitter (BS1) a quarter-wave plate (1/4WP) converts the output s-polarized light intoright circularly polarized light, and upon retro-reflection it will be transformed from right to left-handed andfinally converted again by the quarter-wave plate into p-polarized light that will be transmitted by the polarizedbeamsplitter (BS1) instead of being reflected onto the source.

The wavefront sensor used was the SHSCAM from Optocraft with a 1.4-Megapixel 8-bit greyscale Photonfocussensor, capable of 170 fps at full resolution. The lenslet array is a square pattern of 42x31 lenslet with a pitchof 248 m . For measuring intensity fluctuations at the pupil of the telescope the camera was used running at60 fps.

3. EXPERIMENTAL METHODS AND THEORY

For the purpose of this work, Frieds coherence length (r0) and refractive index structure parameter (C2n) wereestimated using the Zernike mode variances. Measuring scintillation was also a goal of this work in order tounderstand the radial distribution of scintillation in double-passage systems.

3.1 Zernike modes variances

The first 25 Zernike modes2 were recorded with the Shack-Hartmann wavefront sensor, every half hour. Thevariances of Zernike modes are computed and compared to a theoretical model,3 based on propagation throughKolmogorov turbulence. Regardless of propagation geometry the variance of any Zernike mode Zn in radial ordern is:

Zn = 1.095(n+ 1)[ 56 + n][ 73 ][ 236 + n][

176 ]

(D

r0

) 53

(1)

where Zn is the Zernike mode variance in radians squared, D the diameter of the telescope entrance pupiland the Gamma function. The Fried parameter r0 is obtained by best fit to experimental data. Furthermore,the refractive index structure constant C2n is computed by assuming spherical propagation:

C2n = 353 (Lk2r

530 )

1 (2)

L being the path length and k the wave number.

3.2 Scintillation index

A laser beam propagated through atmospheric turbulence will be affected by temporal and spatial irradiancefluctuations commonly referred to as scintillation. One of the most important parameters used to characterizethese irradiance fluctuations is the scintillation index, or normalized variance of intensity, which is defined as4,5

2I =I2 I2

I2 =I2I2 1 (3)

where I is the intensity, I2 is the second moment, I the mean value and I2I2 is the second normalizedmoment of the irradiance.

Scintillation index was computed for an interval of 15 seconds (at 60 fps) individually for each point (pixel) ofthe telescope pupil image (Fig. 4). The central obscuration and spider arms were masked. For each scintillationmap three circles (c1 to c3) with increasing diameters, and centers coincident with the center of the pupil weredefined. For each circle 360 points (scintillation values) were selected along the path of the circumference (Fig. 4).In that way for each increasing diameter we averaged the scintillation index from 360 values (one per degree) allwith the same distance to the center of the pupil.

Figure 4: Scintillation map distribution over the pupil and integrated over 1000 frames with three circles (c1 to c3)defined on it. Measurements from 5th August 2014 at 8:35 am.

4. EXPERIMENTAL RESULTS

4.1 Zernike variance fittingZernike modes were obtained from the SHWF sensor. Figure 5 shows an example of a scintillation focal plane ofthe sensor. Scintillation is one of the main causes of failure of SHWFS in the strong turbulence regime (Fig. 8).

Figure 5: Shack-Hartmann spots recorded on the 5th of August 2014. Scintillation is clearly visible.

For series of 1000 wavefront measurements, the variance of each Zernike mode was computed and comparedwith Equation 1. In each instance, the Fried parameter was obtained by comparing 104 theoretical templatesfor r0 in the range of 0.5-10 cm to the measured values and choosing the best fit (Fig. 6).

Figure 6: Zernike variances obtained from 1000 wavefronts. Line: theoretical variances for best-fitting r0 (6th August

2014).

Good correspondence between theoretically computed variances and experimentally obtained values allowsfor a fairly precise estimation of the Fried parameter. Figure 7 shows the estimated behavior of r0 and C2n forthe 6th of August experiment.

Figure 7: Estimated r0 (left) and C2n (right) on the August 6

th 2014.

It is important to note that for the application of a Shack-Hartmann wavefront sensor in horizontal ground-level turbulence measurements, in contrast to e.g. astronomical adaptive optics, scintillation plays a role. Wave-front reconstruction failed for a significant portion of the measurements (5 to 15%) because of partial obscurationsof the pupil caused by scintillation. Figure 8 show the number of errors for 6th of August. For the purpose ofscintillation resistent wavefront sensing we are developing a new, holography-based sensor.1

Figure 8: Percent of failed wavefront reconstruction measurements due to scintillation.

4.2 Scintillation index

The radial dependence of scintillation has been a topic of extensive research.5 Here, we measured this dependenceto confirm or to show shortcomings of the current theory.

Figure 9: Left: single frame of the telescope pupil for an exposure time of 0.5 ms at 60 fps. Right: map of the intensitydistribution over the pupil integrated over 1000 frames. Measurements from 5th August 2014 at 13:15 pm.

In order to measure intensity fluctuations at the pupil of the telescope the 8-bit Dalsa Genie HM640 camerawas used, with 640x480 pixels running at 60 fps. First, we confirmed the gaussian form of the return beam (Fig. 9).Secondly, we computed scintillation index for each pixel, over 1000 intensity measurements with exposures timesbetween 0.3 and 0.5 ms depending on the weather conditions (Fig. 10). These measurements were repeated overthe whole day at 30 minutes intervals.

Figure 10: Left: scintillation map over the telescope pupil computed for 1000 frames. Right: Corresponding 3D plot.Measurements from 5th of August 2014 at 13:15 pm.

Quite surprisingly, we have measured scintillation decreasing with distance away from the center (Fig. 11).This effect is barely touched upon in the literature.5 In most cases of interest, scintillation is predicted to behigher at the edges of the image than at the center. Only in the case of a double-passage system with a verysmall target/reflector (point target) does the theory predict scintillation decreasing with off-axis distance. Thefunctional dependence however has not been developed/published, to our knowledge.

Figure 11: Cross-sections of the scintillation index distribution along two angles: 135 deg and 45 deg respectively.

Another study was performed where for all sets of measurements during one day three different annuli withincreasing diameters were defined over the pupil (Fig. 4) and 360 positions (one per degree) were selected foreach. Scintillation was averaged for each annulus (Fig. 12).

Figure 12: Study of scintillation for three different annuli with increasing diameters vs time. Measurements from 6th ofAugust 2014.

From the plots one can see that most of the time scintillation is radially decreasing between 5 to 25% fromthe center to the boundaries of the telescope pupil.

We also compared C2n evolution over time with evolution of the scintillation index. Results show, not sur-prisingly, correlation between C2n and scintillation (Fig. 13).

Figure 13: Comparison between C2n and Scintillation index evolution over time. Measurements from 6th August 2014

4.3 Conclusions and outlook

While the Zernike fitting approach does deliver results within the expected range, further verification of theaccuracy of the estimated r0 and C2n is necessary. Among other things, the assumption of Kolmogorov turbulencenear the ground has to be investigated.6 Future steps would include long-term monitoring of turbulence over anurban path as well as correlation analysis with weather conditions.

Concerning the observed decrease of scintillation with off-axis distance, we plan to check the applicabilityof the point target hypothesis to our experiment. We also plan to test our setup in a more controllableenvironment like a turbulence simulator.7

4.4 Acknowledgments

The authors acknowledge the support of the following project from BAAINBw/WTD91. They are also gratefulto Erik Sucher and Andreas Zepp for their technical support and to Stephanie Wollgarten for data processingand review of the paper.

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