Experimental Measurement of Angular Anisoplanatism for Sodium

Laser Guide Star: Synchronized Range Gating Realization

Xi Luo, Xinyang Li, Xiaoyun Wang and Kui Huang

The Laboratory on Adaptive Optics, Institute of Optics and Electronics, Chinese Academy of Sciences, P. O. Box 350,

Shuangliu, Chengdu, Sichuan 610209, China

The Key Laboratory on Adaptive Optics, Chinese Academy of Sciences, P. O. Box 350,

Shuangliu, Chengdu, Sichuan 610209, China

Keywords: Adaptive Optics, Sodium Laser Guide Star, Angular Anisoplanatism, Range Gating Mechanism,

Synchronized Timing Control, Experimental Measurement.

Abstract: Laser Guide Star (LGS) is an ideal synthetic beacon of Adaptive Optics (AO) for compensating for the

atmospheric turbulence induced wave-front distortion of the science object; however the unavoidable

anisoplanatism resulting from different light experience between the LGS and the science object through

turbulent atmosphere will lead to a degradation of compensation performance, especially for the angular

anisoplanatism in sodium LGS AO. By using our developed Hartmann-Shack (HS) wave-front sensor with

accurate range gating mechanism, the return-light spot arrays through turbulent atmosphere from the natural

star and the excited sodium LGS with certain angular offsets can be synchronously collected. Different from

our previously published work (Luo et al., 2018), the experimental set-up, the structural design of the range

gating mechanism, and the timing design of the synchronized control are discussed emphatically in this

paper. The typical experimental measurement result of the angular anisoplanatism for the sodium LGS with

10” angular offsets is just briefly presented, which is basically consistent with our previous numerical

simulation result (Luo et al., 2015). The majority of Zernike-modal de-correlations between the sodium

LGS and the science object occur obviously, as the sodium LGS reference moving outside of the optical

path from the science object to the telescope aperture.

1 INTRODUCTION

Adaptive Optics (AO) applied for compensating for

turbulent atmosphere in real time usually requires a

sufficiently bright reference source in the isoplanatic

patch around the science object to provide a desired

measurement of the wave-front distortion induced

from atmospheric turbulence. The concept of Laser

Guide Star (LGS) has been publicly proposed to

overcome the limitations due to finite sky-coverage

(Foy and Labeyrie, 1985), which is generated by

illuminating a ground-based laser in the specific

atmosphere layer to provide the backscattered light

with information on the wave-front distortion

introduced by atmospheric turbulence, including the

Rayleigh LGS (Fugate et al., 1991) and the sodium

LGS (Humphreys et al., 1991). Profiting from its

higher altitude with better sampling of atmospheric

turbulence, the sodium LGS has been received

worldwide attention since its concept was first put

forward (Fugate et al., 1994; Bonaccini, Hackenberg,

and Avila, 1998; Joyce, et al., 2006).

Anisoplanatism results from different turbulence

experience along the optical path by light from the

LGS and the science object, which is one of the

fundamental limitations to preventing an ideal LGS

AO performance. Since atmospheric turbulence

strength is distributed and varied with altitude in

front of the aperture of receiving telescope,

comparing with focal anisoplanatism just induced

from the finite altitude for the LGS reference

coinciding with the science object, angular

separation (namely, angular anisoplanatism) results

in two lights traversing different regions in

atmospheric turbulence, and arises an deterioration

of the partial Zernike-modal correlations between

the LGS reference and the science object, especially

for the sodium LGS with greater angular separation.

As the theoretical investigation has progressed

(Molodij and Rousset, 1997; Sasiela, 2007), with the

rapid development of the sodium LGS technology

102

Luo, X., Li, X., Wang, X. and Huang, K.

Experimental Measurement of Angular Anisoplanatism for Sodium Laser Guide Star: Synchronized Range Gating Realization.

DOI: 10.5220/0007308401020109

In Proceedings of the 7th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2019), pages 102-109

ISBN: 978-989-758-364-3

and its application in engineering, also the

experimental investigations on the sodium LGS

anisoplanatism have been carried out. For example,

the experimental measurement of anisoplanatic

degradation of K-band Strehl ratio on the 10-m Keck

II telescope (Van Dam et al., 2006), the

experimental measurement of focal anisoplanatism

carried out by China Academy of Engineering

Physics (Chen et al., 2015), etc.. However, to the

best of our knowledgement, there has been no public

report on the quantitative measurements of angular

anisoplanatic error for the sodium LGS in literature.

By using our developed HS wave-front sensor with

accurate range gating actualization, the synchronized

experimental measurement of angular anisoplanatic

effect for the sodium LGS can be achieved.

The emphasises of this paper are on the

discussions of the experimental set-up, the structural

design of the range gating mechanism, and the

timing design of the synchronized control. In order

to maintain the integrity of this paper, the typical

experimental results of the wave-front distortion

decomposed Zernike-modal correlations between the

natural star and the sodium LGS reference with 10”

angular offsets, and the angular anisoplanatism

decomposed Zernike-modal relative errors for the

off-axis sodium LGS reference are just briefly

presented. For the detailed disscusion of the

achieved angular anisoplanatism experimental data,

readers could find answer in our previously

published work (Luo et al., 2018).

2 EXPERIMENTAL SET-UP

The experimental set-up of synchronized angular

anisoplanatism measurement for sodium LGS is

outlined in Figure 1, which includes the telescope

with clear aperture of 1m, the pulsed sodium LGS

laser source with wavelength centered on the

mesospheric sodium D

line, the Tilt Mirror (TM)

for pointing control of the sodium LGS laser source

projection to sky, the synchronized control module,

the developed HS wave-front sensor with accurate

range gating mechanism, and the corresponding

processor for the wave-front recovery and the TM

actuation.

As shown in Figure 1, in the experiment, the

telescope works in closed-loop to track an

appropriate natural star in the sky with azimuth

angle A and elevation angle E, and the incident laser

beam of the sodium LGS laser source is reflected off

the TM and projected to the mesospheric layer for

generating the resonant backscattered sodium LGS

with its angular distance θ from the natural star

closed-loop controlled by the TM. On the basis of

the synchronized control reference signal provided

from the HS wave-front sensor, in every laser shot,

the temporal synchronization of the laser source

emission and the resulting resonant backscattered

sodium LGS detection with the HS wave-front

sensor can be achieved via the synchronized control

module. Consequently, two sets of the synchronous

wave-front distortion sequences can be recovered

with the return-light spot arrays through turbulent

atmosphere from the on-axis natural star and the off-

axis sodium LGS. Furthermore, the anisoplanatic

error’s Zernike-modal statistics for the off-axis

sodium LGS can be derived from the two sets of the

recovered wave-front distortion sequences.

2.1 HS Wave-front Sensor with

Accurate Range Gating

Actualization

The schematic diagram of the HS wave-front sensor

is illustrated in Figure 2, along the direction of the

return-light propagation, which consists of the beam

compressing optical system with compression ratio

of 6:1, the mechanical shutter device, the microlens

array, the matched imaging optical system with

magnification of 2:1, and the Charge Coupled

Device (CCD) camera. The corresponding field of

view of each sub-aperture is 21.9”.

In our developed HS wave-front sensor, the

adoption of mechanical shutter technology is an

effective way to selecting the resonant backscatter

from the sodium atoms in the mesospheric layer (at

the altitude of approximately 80~100km), and

meanwhile to obstructing the Rayleigh backscatter

from the air molecules in the short-range atmosphere

(at the altitude of approximately below 30km).

As shown in Figure 2 and Figure 3, the

mechanical shutter device includes the photoelectric

switch sensor, the rotary optical-chopping disc and

its motor driven. The rotary optical-chopping disc is

vertically mounted at the optical focus of entry lens

of the beam compressing optical system. For the

repetitively pulsed sodium resonant backscattered

light unobstructed propagation and collection, there

are a number of slots with central angle φ are

rotational-symmetrically manufactured on the edge

of the optical-chopping disc. In practice, the number

of the slots M depends on the output pulse repetition

frequency of the sodium LGS laser source f and an

appropriate rotational speed of the optical-chopping

disc N (namely, M×N=f). At the same time, the

output pulse-width of the sodium LGS laser source

Experimental Measurement of Angular Anisoplanatism for Sodium Laser Guide Star: Synchronized Range Gating Realization

103

Figure 1: The experimental set-up of synchronized angular anisoplanatism measurement for sodium LGS.

Δt

Pulse

, the sampled thickness of the sodium layer ΔH,

the accommodation to the elevation angle E

variation for the sodium LGS observation, and the

transition time from the open-started state to the

open-completed state of the receiving optical path of

the HS wave-front sensor Δt

rising

must be taken into

account in the design of the central angle φ of every

single slot on the optical-chopping disc (namely,

φ≥(2×ΔH/sinE/c+Δt

pulse

+Δt

rising

) ×N×360).

As the optical-chopping disc stably rotates, the

receiving optical path on-off state of the HS wave-

front sensor is periodically modulated, and the

synchronized control reference signal of the same

frequency as the sodium LGS laser source emission

is obtained from the photoelectric switch sensor

reading the slots on the disc, whose duty cycle

equals to (φ×f)/(N×360). Based on this synchronized

control reference signal, the sodium LGS laser

Figure 2: The schematic diagram of the HS wave-front sensor with range gating mechanism.

PHOTOPTICS 2019 - 7th International Conference on Photonics, Optics and Laser Technology

104

Figure 3: The schematic diagram of the mechanical shutter

device.

source emission and the resulting resonant

backscattered sodium LGS detection with the CCD

camera can be temporally synchronized. Within

every launch period of the sodium LGS laser source,

it is synchronously confirmed that the receiving

optical path is not in completely on state until the

resonant backscattered light resulting from the

interaction between the emitted laser pulse and the

mesospheric sodium atoms arrives at the aperture of

the telescope.

2.2 Synchronized Control Process for

Sodium LGS Laser Source

Emission and Its Resulting

Resonant Backscattered Light

Collection

In order to select the resonant backscatter from the

sodium atoms in the mesospheric layer and to

obstruct the Rayleigh backscatter from the air

molecules in the short-range atmosphere by

effectively range gating, the synchronized control

process for the pulsed sodium LGS laser source

emission and its resulting resonant backscattered

light collection is designed.

In Figure 4 the synchronized control process for

the pulsed sodium LGS laser source emission and its

resulting resonant backscattered light collection is

outlined:

(1) Δt

=φ/(N×360) is the high level duration of

the synchronized control reference signal obtained

from the photoelectric switch sensor;

Δt

=2×H

begin

×cscE/c is the arrive time of the

resonant backscattered light from the bottom of the

sodium layer at the altitude of H

begin

after each laser

pulse emitting; Δt

sodium-LGS

=2×ΔH×cscE/c+Δt

pulse

the temporal duration of the resonant backscattered

light resulting from the interaction between the

sodium atoms in the mesospheric layer and the

emitted laser pulse with pulse-width of Δt

pulse

(2) Δt

rising

is the transition time from the open-

started state to the open-completed state of the

receiving optical path of the HS wave-front sensor;

Δt

is the time delay between the rising edge of the

synchronized control reference signal and the open-

completed state of the receiving optical path of the

HS wave-front sensor; both of them can be

accurately measured in advance by high-speed

photodetector and oscilloscope.

(3) Δt

laser-delay

=Δt

‒Δt

is the time delay between

the rising edge of the synchronized control reference

signal and the rising edge of the synchronized

control signal for the pulsed sodium LGS laser

source emission; Δt

CCD-delay

=Δt

is the time delay

between the rising edge of the synchronized control

reference signal and the rising edge of the

synchronized control signal for the sodium LGS

resonant backscattered light exposure by the CCD

camera.

Figure 4: The designed timing diagram of the sodium LGS resonant backscattered light synchronized collection.

Experimental Measurement of Angular Anisoplanatism for Sodium Laser Guide Star: Synchronized Range Gating Realization

105

3 POST-PROCESSING OF

EXPERIMENTAL DATA

Based on the experimental set-up (as shown in

Figure 1), the structural design of the mechanical

shutter device (as shown in Figure 3), and the timing

design of the sodium LGS synchronized collection

(as shown in Figure 4), as time goes by, the

sequences of the return-light spot arrays through

turbulent atmosphere from the natural star and the

sodium LGS with certain angular offsets can be

synchronously collected by the HS wave-front

sensor.

Afterwards, from the mutiple-frame sequences of

the return-light spot arrays collected by the HS

wave-front sensor, the synchronous turbulence-

induced wave-front distortion sequences can be

recovered for the on-axis natural star and the off-

axis sodium LGS, respectively:

   

STAR j STAR j

LGS j LGS j

Rr a Z r









    

     



, , ,

(1)

where R is the clear aperture radium of the telescope,

(r,ϑ) is the j th-order Zernike polynomial (Noll,

1976), a

j-STAR

is the decomposed j th-order Zernike-

modal coefficient of the wave-front distortion of the

on-axis natural star, a

j-LGS

is the decomposed j th-

order Zernike-modal coefficient of the wave-front

distortion of the off-axis sodium LGS, and K is the

corresponding highest-order Zernike mode of the

recovered wave-front distortion by the HS wave-

front sensor (e.g. K=35). The total-tilt terms (e.g.

j=1, 2) for the on-axis natural star, and the total-tilt

and defocus terms (e.g. j=1, 2, 3) for the off-axis

sodium LGS are not included in the recovered wave-

front distortion.

Consequently, the recovered wave-front

distortion decomposed Zernike-modal correlations

between the on-axis natural star and the off-axis

sodium LGS, and the angular anisoplanatism

decomposed Zernike-modal relative errors for the

off-axis sodium LGS can be calculated by the

equation (2) and equation (3), respectively:

 

j STAR j LGS

COV a ,a

r j 4







(2)

 

j STAR

j STAR j LGS

ε j 4









(3)

where COV denotes the covariance, and < > denotes

the ensemble average.

4 TYPICAL EXPERIMENTAL

RESULTS

In this section, for the integrity of this paper, we just

briefly present the typical experimental result of

angular anisoplanatism measurement for the sodium

LGS with 10” angular offsets, which has been

partially published in our previous work (Luo et al.,

2018).

Figure 5: The typical single frame of the return-light spots

arrays from the natural star and the sodium LGS with 10”

angular offsets (Luo et al., 2018).

begin

is chosen to be 75km for timing rejection

of the Rayleigh back scattering. The typical single

frame of the return-light spot arrays through

turbulent atmosphere from the natural star with

azimuth angle A of 70

and elevation angle E of 75

and the sodium LGS with 10” angular offsets is

shown in Figure 5 (Luo et al., 2018), the whole

return-light spot arrays from the natural star are

located at the center of the sub-apertures, and the

whole return-light spot arrays from the sodium LGS

with 10” angular offsets are located at the bottom

right of the sub-apertures.

The first 20th Zernike-modal correlations of the

recovered wave-front distortion between the on-axis

natural star and the off-axis sodium LGS with 10”

angular offsets are calculated and shown in Figure 6.

Good correlations only exist in the low-order

Zernike modes of the two types of wave-front

distortions from the on-axis natural star and the off-

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106

Figure 6: The typical experimental result of the first 20th Zernike-modal correlations of the recovered wave-front distortion

between the on-axis natural star and the off-axis sodium LGS with 10” angular offsets.

Experimental Measurement of Angular Anisoplanatism for Sodium Laser Guide Star: Synchronized Range Gating Realization

107

axis sodium LGS, respectively (e.g., the average of

the Zernike-modal correlation <r

>=0.70 for j=4~9).

Increasing the Zernike-modal order j means

deteriorating correlation r

, the average of the

Zernike-modal correlation <r

>=0.46 for j=10~15,

but the average of the Zernike-modal correlation

>=0.33 for j=16~20.

Figure 7: The typical experimental result of the angular

anisoplanatism decomposed Zernike-modal relative errors

for the off-axis sodium LGS with 10” angular offsets (Luo

et al., 2018).

The corresponding angular anisoplanatism

decomposed Zernike-modal relative errors for the

off-axis sodium LGS are calculated and illustrated in

Figure 7 (Luo et al., 2018). Resulting from improper

turbulent atmosphere probing with the off-axis

sodium LGS as reference on the outside of the

optical path from the natural star to the telescope

aperture, obvious de-correlations occur between the

majority of Zernike modes of the two types of wave-

front distortions from the on-axis natural star and the

off-axis sodium LGS, and the corresponding angular

anisoplanatism decomposed Zernike-modal relative

errors are bigger than one. This phenomenon is

basically consistent with our previous numerical

simulation work (Luo et al., 2015).

5 CONCLUSIONS

By means of the structural design of the range gating

mechanism accompanied with the synchronized

timing design of the sodium LGS excitation and

collection, the synchronized return-light spot arrays

through turbulent atmosphere from the science

object and the excited sodium LGS with certain

angular offsets can be collected by using our

developed HS wave-front sensor, which provides a

convenient way to experimental measurement of the

angular anisoplanatism for LGS. Further

investigation in this area will be carried out in the

future.

ACKNOWLEDGEMENTS

This work has been supported by the Young

Scientists Fund of the National Natural Science

Foundation of China (Grant No. 61505215).

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