Lucky image performance simulation on the basis of optical turbulence data obtained on Mt. Shatdzhatmaz
Lucky imaging is a method allowing to achieve difiraction resolution on a moderate ground-based telescopes with the cost of magnitude limitation. To adequately evaluate capabilities of this technique for a given place (Mt. Shatdzhatmaz) we performed a Monte Carlo numerical simulation taking into acc...
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Advances in astronomy and space physics
2011
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| Цитувати: | Lucky image performance simulation on the basis of optical turbulence data obtained on Mt. Shatdzhatmaz / B.S. Safonov // Advances in Astronomy and Space Physics. — 2011. — Т. 1., вип. 1-2. — С. 102-105. — Бібліогр.: 6 назв. — англ. |
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irk-123456789-1190932017-06-04T03:02:48Z Lucky image performance simulation on the basis of optical turbulence data obtained on Mt. Shatdzhatmaz Safonov, B.S. Lucky imaging is a method allowing to achieve difiraction resolution on a moderate ground-based telescopes with the cost of magnitude limitation. To adequately evaluate capabilities of this technique for a given place (Mt. Shatdzhatmaz) we performed a Monte Carlo numerical simulation taking into account properties of optical turbulence measured there. Statistics of lucky imaging isoplanatic angle was evaluated on the basis of these data. Optimal atmospheric conditions for lucky imaging were obtained. 2011 Article Lucky image performance simulation on the basis of optical turbulence data obtained on Mt. Shatdzhatmaz / B.S. Safonov // Advances in Astronomy and Space Physics. — 2011. — Т. 1., вип. 1-2. — С. 102-105. — Бібліогр.: 6 назв. — англ. 987-966-439-367-3 http://dspace.nbuv.gov.ua/handle/123456789/119093 en Advances in Astronomy and Space Physics Advances in astronomy and space physics |
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Lucky imaging is a method allowing to achieve difiraction resolution on a moderate ground-based telescopes with the cost of magnitude limitation. To adequately evaluate capabilities of this technique for a given place (Mt. Shatdzhatmaz) we performed a Monte Carlo numerical simulation taking into account properties of optical turbulence measured there. Statistics of lucky imaging isoplanatic angle was evaluated on the basis of these data. Optimal atmospheric conditions for lucky imaging were obtained. |
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Article |
| author |
Safonov, B.S. |
| spellingShingle |
Safonov, B.S. Lucky image performance simulation on the basis of optical turbulence data obtained on Mt. Shatdzhatmaz Advances in Astronomy and Space Physics |
| author_facet |
Safonov, B.S. |
| author_sort |
Safonov, B.S. |
| title |
Lucky image performance simulation on the basis of optical turbulence data obtained on Mt. Shatdzhatmaz |
| title_short |
Lucky image performance simulation on the basis of optical turbulence data obtained on Mt. Shatdzhatmaz |
| title_full |
Lucky image performance simulation on the basis of optical turbulence data obtained on Mt. Shatdzhatmaz |
| title_fullStr |
Lucky image performance simulation on the basis of optical turbulence data obtained on Mt. Shatdzhatmaz |
| title_full_unstemmed |
Lucky image performance simulation on the basis of optical turbulence data obtained on Mt. Shatdzhatmaz |
| title_sort |
lucky image performance simulation on the basis of optical turbulence data obtained on mt. shatdzhatmaz |
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Advances in astronomy and space physics |
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2011 |
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http://dspace.nbuv.gov.ua/handle/123456789/119093 |
| citation_txt |
Lucky image performance simulation on the basis of optical turbulence data obtained on Mt. Shatdzhatmaz / B.S. Safonov // Advances in Astronomy and Space Physics. — 2011. — Т. 1., вип. 1-2. — С. 102-105. — Бібліогр.: 6 назв. — англ. |
| series |
Advances in Astronomy and Space Physics |
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2025-07-08T15:12:54Z |
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2025-07-08T15:12:54Z |
| _version_ |
1837092123393916928 |
| fulltext |
Lucky image performance simulation on the basis of optical turbulence
data obtained on Mt. Shatdzhatmaz
B. S. Safonov
Sternberg Astronomical Institute, Universitetskij pr-t, 13, 119991, Moscow, Russia
safonov@sai.msu.ru
Lucky imaging is a method allowing to achieve di�raction resolution on a moderate ground-based tele-
scopes with the cost of magnitude limitation. To adequately evaluate capabilities of this technique for a given
place (Mt. Shatdzhatmaz) we performed a Monte Carlo numerical simulation taking into account properties
of optical turbulence measured there. Statistics of lucky imaging isoplanatic angle was evaluated on the basis
of these data. Optimal atmospheric conditions for lucky imaging were obtained.
Introduction
Lucky imaging gained popularity as an alternative to adaptive optics (AO) thanks to simplicity and low
cost comparing with AO. It seems that it has also much larger isoplanatic angle than in the case of simple AO.
Activity in this �eld increased signi�cantly in last several years thanks to appearance of EMCCD technology.
Cameras manufactured using this technology have a remarkable feature � negligibly small readout noise.
It allows to divide a single long exposure into a set of shorter ones, process them separately and than sum
them up. In case of lucky imaging the basic algorithm of such a processing look like the following [5]:
1. Obtain a set of short-exposure images. Exposure time have to be short enough to freeze the image
boiling due to the optical turbulence (OT) in atmosphere � usually it is 30− 70 ms.
2. Choose a reference star to work with. Most convenient option is a bright star near the frame center.
3. Choose a certain portion of the best frames. Ratio of number of these frames to the total number of
frames is called frame selection ratio (FSR). Usually Strehl ratio is used as a �gure-of-merit of quality
of frames.
4. Sum up processed frames using well-known shift-and-add algorithm. Centering is carried out by the
reference star image.
Image obtained as a result of this summation has improved angular resolution [1, 5].
Lucky imaging like other similar techniques � speckle interferometry, AO � su�ers from anisoplanatism.
For lucky imaging it lies in the degrading of the point spread function (PSF) in restored image with the
increasing of distance to the reference star. Isoplanatic angle is an angle at which Strehl ratio is reduced in
e time comparing to that of reference star (see Fig. 1).
The main purpose of this work was to determine this isoplanatic angle for a given telescope and given
conditions of OT in the atmosphere. Unfortunately it is impossible to do it analytically. We performed
the Monte Carlo numerical simulation of light propagation in turbulent atmosphere according to principles
described in [1, 4].
In this simulation the atmosphere is represented by several in�nitely thin layers with von Karman power
spectrum Φ(k) = 0.023r
−5/3
0 (k2 + k2
0)
−11/6, where r0 is Fried radius, k is the spatial frequency and k0
relates to outer scale k0 = 1/L0, where outer scale L0 is the upper limit of sizes of turbulence eddies.
Wavefront undergoes pure phase distortion on these turbulent layers and propagates between them within
the approximation of geometrical optics. To simulate wind the turbulent layers are translated as a whole
(Taylor hypothesis). PSF is calculated as a square of Fourier transform of wavefront on telescope pupil. Basic
parameters of simulation are: size of phase screen 512 × 2048 px, scale 0.025 m/px, wavelength 806 nm1,
1I-band is widely used in lucky imaging because one should go to longer wavelength as far as possible to reduce OT e�ects and I-band
is the most red band allowed by commercially available EMCCD cameras
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Advances in Astronomy and Space Physics B. S. Safonov
outer scale 25 m, telescope diameter 2.5 m, central obscuration 0.43. Fried radiuses r0 of turbulence pro�les
are set according to optical turbulence pro�le (OTP) data which is described in the next section.
Figure 1: All graphs are computed for pro�le BB, thick horizontal line corresponds to 1/e level. Left top:
dependence of Strehl ratio in restored image on distance to reference star for di�erent FSRs. Left bottom:
the same for normalized Strehl ratio. Right top: dependence of Strehl ratio in restored image on distance to
reference star for FSR=5% and for di�erent exposures. Right bottom: the same for normalized Strehl ratio.
Optical turbulence pro�le data
For simulation we used OT data set obtained on Mt. Shatdzhatmaz (2127 m above see level) in 2007-2009
[2] with MASS/DIMM device [3]. This summit is selected as a place of installation of 2.5-m telescope of
Sternberg Astronomical Institute and located on Northen Caucasus near the Kislovodsk city.
For the period between October 2007 and November 2009 85000 OTPs were obtained. Each pro�le
consists of 13 turbulent layers at heights 0, 0.5, 0.7, 1.0, 1.4, 2.0, 2.8, 4.0, 5.6, 8.0, 11.3, 16.0, 22.6 km. These
data already can be used as input for the simulation. However simulation run for one pro�le takes about
several hours to complete so we cannot process all pro�les individually. Also it is well-known that OTP is
highly variable and cannot be represented by a single arbitrary pro�le from data set [6]. Because of this we
reduced the data set to 9 typical OTP using method described in [6].
Firstly, we selected 9 subsets from initial data set, each of them coded by two letters running over 3
values: A, B, C (this results in 9 combinations: AA, AB, AC, BA, BB, BC, CA, CB, CC). These subsets
consist of pro�les having similar values of OT intesity of 0-km layer (ground layer) JGL and of total intensity
of remaining layers � free atmosphere JFA. First letter in the code indicates conditions in ground layer: A
� good, B � median, C � bad, second one indicates conditions in free atmosphere in the same way. The
following inequalities are conditions of falling of certain OTP in ij-subset: pGL(NiL) < JGL < pGL(NiU ) and
pFA(NjL) < JFA < pFA(NjU ), where pGL(N) and pFA(N) is N -th percentiles of distribution of JGL and
JFA, correspondingly. Also, NAL = 20%, NAU = 30%, NBL = 45%, NBU = 55%, NCL = 60%, NCU = 70%.
Finally for each subset we computed the median pro�le. General parameters of resulting typical pro�les are
shown in Table 1. The free atmosphere part of typical pro�les are shown in Fig. 2.
It can be easily seen that the shape of pro�les does not depend on intensity of ground layer that can be
expected due to the fact that free atmosphere and ground layer are mutually independent [6]. Meanwhile
there is a noticeable di�erence in shapes of pro�les having di�erent free atmosphere integrals. This fact was
already discovered for several sites [6].
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Advances in Astronomy and Space Physics B. S. Safonov
Table 1: General parameters of typical optical turbulence pro�les. Seeing β, Fried radius r0, conventional isoplanatic
patch θ0, and lucky imaging isoplanatic angle θLI are computed for I-band
pro�le JGL10−13 JFA10−13 β D/r0 θ0 θLI(FSR = 5%)
code [m2/3] [m2/3] [arcsec] [arcsec] [arcsec]
AA 1.90 0.89 0.532 8.16 4.44 13.6
AB 1.91 1.50 0.600 9.20 3.72 11.4
AC 1.89 2.70 0.716 11.0 3.08 9.0
BA 3.12 0.89 0.660 10.1 4.58 14.0
BB 3.12 1.49 0.718 11.0 3.74 10.4
BC 3.13 2.72 0.828 12.7 3.15 8.5
CA 5.19 0.89 0.847 13.0 4.56 12.6
CB 5.20 1.56 0.904 13.9 3.90 10.3
CC 5.22 2.88 1.007 15.5 3.23 7.7
Results
We used 9 typical OTPs as a model of atmosphere for the simulation. For each of them 50 realizations of
turbulent atmosphere were obtained. In each realization we considered 30 moments with interval of 50 ms,
which corresponds to shift of each layer of 0.2D, where D is the telescope diameter (all layers are supposed
moving with speed of 10 m/s). For each moment instantaneous PSFs were computed for reference star and
for 12 stars on distances 3, 6, 9, 12, 15, 20, 25, 30, 40, 50, 65, 80 arcseconds to it. These data were then
processed using lucky imaging procedure described in introduction with di�erent FSR: 1%, 5%, 20%, 50%,
100%.
To measure the quality of restored images we used Strehl ratio as in [1, 5]. On the left top panel of
Fig. 1 an example of dependence of Strehl ratio on distance to reference star for di�erent FSR is shown. To
compare rate of reducing of Strehl ratio for di�erent FSRs it is convenient to normalize Strehl ratio by its
value in reference star image (see Fig. 1, left bottom). In this representation cases of di�erent FSRs become
visually indistinguishable.
In Fig. 3 and Table 1 we summarize the values of isoplanatic angles for di�erent turbulent pro�les and
FSRs. Isoplanatic angle for our mountain varies within the range of 7− 16 arcseconds and depends mainly
on OT in free atmosphere. Fig. 3 also clearly demonstrates that there is no considerable dependence of
isoplanatic angle on FSR.
Figure 2: Typical optical turbulence pro�les, free atmosphere part. Ground layer is not depicted because it
has much greater value.
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Advances in Astronomy and Space Physics B. S. Safonov
To make this simulation more practical we introduced a �nite exposure in it. In real lucky image or
speckle interferometry observation exposure is rarely short enough to neglect it. One can expect that �nite
exposure will blur the PSF and reduce the Strehl ratio. The simulation proves this fact as can be seen on
the right top panel of Fig. 1. Strehl ratio is reduced indeed but the e�ect is greater for higher Strehl. It
leads to the fact that formally isoplanatic angle is increased (see right bottom panel of Fig 1).
Figure 3: Isoplanatic angle for lucky imaging derived according to [5]. For pro�les parameters see Table 1.
Conclusions
• Lucky imaging isoplanatic angle varies from 7 to 16 arcseconds and depends mainly on the intensity of
OT in free atmosphere.
• Finiteness of exposure leads to reduction of Strehl ratio of image in all �elds, especially near the reference
star. It results in isoplanatic angle of 20− 30 arcseconds.
• This simulation also explains observed values of isoplanatic angle [5] without additional assumptions
like seeing variations.
• Practical conclusions: there is no sense in construction of camera for lucky imaging with �eld of view
more than 60 arcseconds. During selection of observational programs required large isoplanatic angle
current intensity of OT in free atmosphere is pivotal.
Acknowledgement
I would like to thank Dr. Kornilov V. G. and Dr. Tokovinin A. A. for valuable discussions.
References
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[2] Kornilov V., Shatsky N., Voziakova O. et al. Submitted to Mon. Notic. Roy. Astron. Soc.
[3] Kornilov V., Tokovinin A., Shatsky N. et al. Mon. Notic. Roy. Astron. Soc., V. 382, pp. 1268-1278 (2007)
[4] Lane R. G., Glindemann A., Dainty J. C. Waves in Random Media 2, pp. 209-224 (1992)
[5] Law N. M., Mackay C. D., Baldwin J. E. Astron. & Astrophys., V. 446, pp. 739-745 (2006)
[6] Tokovinin A., Travouillon T. Mon. Notic. Roy. Astron. Soc., V. 365, pp. 1235-1242 (2006)
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