Modeling solar eclipse shadow bands using wave optics simulation through distributed turbulence

Hanyu Zhan; David G. Voelz

doi:10.1364/AO.431996

Applied Optics
Vol. 60,
Issue 27,
pp. 8426-8434
(2021)
•https://doi.org/10.1364/AO.431996

Modeling solar eclipse shadow bands using wave optics simulation through distributed turbulence

Hanyu Zhan and David G. Voelz

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Hanyu Zhan and David G. Voelz, "Modeling solar eclipse shadow bands using wave optics simulation through distributed turbulence," Appl. Opt. 60, 8426-8434 (2021)

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- Atmospheric and Oceanic Optics
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About this Article
History
- Original Manuscript: May 20, 2021
- Revised Manuscript: August 6, 2021
- Manuscript Accepted: August 20, 2021
- Published: September 16, 2021

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Abstract

Thin, wavy ribbons of light known as “shadow bands” can be seen moving and undulating on the ground just preceding and following the occurrence of a total solar eclipse. Using the scattering scintillation theory, Codona [Astron. Astrophys. 164, 415 (1986)] presented theoretical investigations that explain recorded features of shadow bands and suggest the turbulence mainly responsible for the bands is within the bottom 2–3 km of the atmosphere. This paper proposes an approach to model the shadow band phenomena using a numerical wave optics simulation. The simulation approach employs numerical wave optics techniques to model a crescent-shape source, propagation of component plane waves through turbulence phase screens, and observation of the light at the ground. The simulation produces intensity patterns with structures and evolution that are consistent with actual shadow band observations and Codona’s theory. The contribution of the turbulence phase screens as a function of height to the shadow band intensity scintillation index is simulated and excellent correspondence is found with the theory. Finally, the practical utility of the simulation is illustrated by creating intensity frames that show the temporal evolution of the patterns due to wind. The simulation approach is adaptable and can be applied to scintillation and imaging problems involving other incoherent objects or sources that subtend relatively large angles and are observed through atmospheric turbulence.

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Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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			$C_{n}^{2}$
Screen ( $i$ )	$h$ (m)	$Δ z$ (m)	( $m^{- 2 / 3}$ )	( $m^{- 2 / 3}$ )	Samples
6	2500	1000	$5.25 \times 10^{- 17}$	$32 \times 32$	$12800 \times 12800$
5	1750	500	$8.90 \times 10^{- 17}$	$25 \times 25$	$10000 \times 10000$
4	1250	500	$1.30 \times 10^{- 16}$	$21 \times 21$	$8400 \times 8400$
3	550	900	$2.64 \times 10^{- 16}$	$15 \times 15$	$6000 \times 6000$
2	55	90	$2.95 \times 10^{- 15}$	$11 \times 11$	$4400 \times 4400$
1	5	10	$7.00 \times 10^{- 14}$	$11 \times 11$	$4400 \times 4400$

Crescent	$w / C$	$R_{M}$	$R_{S}$	$ε$	$τ$
Wide	0.028	0.278°	0.265°	0.05	0.05
Medium	0.016	0.278°	0.265°	0.05	0.025
Narrow	0.0059	0.278°	0.265°	0.05	0.0057

			$C_{n}^{2}$
Screen ( $i$ )	$h$ (m)	$Δ z$ (m)	( $m^{- 2 / 3}$ )	( $m^{- 2 / 3}$ )	Samples
6	2500	1000	$5.25 \times 10^{- 17}$	$32 \times 32$	$12800 \times 12800$
5	1750	500	$8.90 \times 10^{- 17}$	$25 \times 25$	$10000 \times 10000$
4	1250	500	$1.30 \times 10^{- 16}$	$21 \times 21$	$8400 \times 8400$
3	550	900	$2.64 \times 10^{- 16}$	$15 \times 15$	$6000 \times 6000$
2	55	90	$2.95 \times 10^{- 15}$	$11 \times 11$	$4400 \times 4400$
1	5	10	$7.00 \times 10^{- 14}$	$11 \times 11$	$4400 \times 4400$

Crescent	$w / C$	$R_{M}$	$R_{S}$	$ε$	$τ$
Wide	0.028	0.278°	0.265°	0.05	0.05
Medium	0.016	0.278°	0.265°	0.05	0.025
Narrow	0.0059	0.278°	0.265°	0.05	0.0057

Abstract

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Applied Optics