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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 4 — Feb. 25, 2013
  • pp: 4367–4375
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Impacts of underwater turbulence on acoustical and optical signals and their linkage

Weilin Hou, Ewa Jarosz, Sarah Woods, Wesley Goode, and Alan Weidemann  »View Author Affiliations


Optics Express, Vol. 21, Issue 4, pp. 4367-4375 (2013)
http://dx.doi.org/10.1364/OE.21.004367


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Abstract

Acoustical and optical signal transmission underwater is of vital interest for both civilian and military applications. The range and signal to noise during the transmission, as a function of system and water optical properties, in terms of absorption and scattering, determines the effectiveness of deployed electro-optical (EO) technology. The impacts from turbulence have been demonstrated to affect system performance comparable to those from particles by recent studies. This paper examines the impacts from underwater turbulence on both acoustic scattering and EO imaging degradation, and establishes a framework that can be used to correlate these. It is hypothesized here that underwater turbulence would influence the acoustic scattering cross section and the optical turbulence intensity coefficient in a similar manner. Data from a recent field campaign, Skaneateles Optical Turbulence Exercise (SOTEX, July, 2010) is used to examine the above relationship. Results presented here show strong correlation between the acoustic scattering cross-sections and the intensity coefficient related to the modulation transfer function of an EO imaging system. This significant finding will pave ways to utilize long range acoustical returns to predict EO system performance.

© 2013 OSA

1. Introduction

Better understanding of the process, and more importantly, developing means to quantify these impacts, is a crucial research element that will benefit the above mentioned visibility applications. One of the issues that hinder the research is to identifying and implementing ways to effectively quantify underwater turbulence structures. The traditional approach to quantify the turbulence structure involves spot sampling techniques with either acoustical scattering properties such as those relying on Doppler effects, or mechanical means involving Piezo electric derived shear probes. While these methods provide the most reliable, direct and accurate assessment to-date, they do not offer the capability of synoptic coverage over distance, nor instantaneous measurements over the light path, which is vital in assessing total impacts on EO signal transmission. One possible solution is to use the scattering properties of the acoustical signal over these microstructures [10

10. S. A. Thorpe and J. M. Brubaker, “Observations of sound reflection by temperature microstructure,” Limnol. Oceanogr. 28(4), 601–613 (1983). [CrossRef]

, 11

11. L. Goodman, “Acoustic scattering from ocean microstructure,” J. Geophys. Res. 95(C7), 11557–11573 (1990). [CrossRef]

], as acoustical signals do provide coverage over longer range, while encountering the same impacts as optical signals.

2. Theoretical background

When it comes to diver visibility, the most prominent issue is the degradation of image quality over distance due to scattering in water. This presents a striking contrast for those of us who are accustomed to the seemingly unlimited visual ranges in air. The cause of the degradation has been mostly attributed to the particles of various origins in the water and it is rightly so. Most research has been focused on reducing the impact of particle scattering by means of discriminating scattering photons involving polarization, range gating, modulation, and by means of restoration via deconvolution [1

1. W. Hou, Z. Lee, and A. D. Weidemann, “Why does the Secchi disk disappear? An imaging perspective,” Opt. Express 15(6), 2791–2802 (2007). [CrossRef] [PubMed]

, 12

12. G. D. Gilbert and J. C. Pernicka, “Improvement of underwater visibility by reduction of backscatter with a circular polarization technique,” Appl. Opt. 6(4), 741–746 (1967). [CrossRef] [PubMed]

16

16. G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging system,” Opt. Eng. 32(9), 2185 (1993). [CrossRef]

]. However, in certain oceanic or lake waters, another factor could come into play. This is the scattering by optical turbulence, which is the result of the variations of the index of refraction of the medium. This scattering is mostly associated with the turbulence structures of the medium, or water body in our case. Degradation of the image quality in a scattering medium involving turbulence has been studied mostly in the atmosphere. These studies are mainly focused on modeling the optical transfer function (OTF), in an effort to restore the images obtained, such as in air reconnaissance or astronomy studies [17

17. D. Sadot, A. Dvir, I. Bergel, and N. Kopeika, “Restoration of thermal images distorted by the atmosphere, based on measured and theoretical atmospheric modulation transfer function,” Opt. Eng. 33, 44–53 (1994). [CrossRef]

, 18

18. Y. Yitzhaky, I. Dror, and N. Kopeika, “Restoration of atmospherically blurred images according to weather-predicted atmospheric modulation transfer functions,” Opt. Eng. 36(11), 3064–3072 (1997). [CrossRef]

]. Similar effects of underwater turbulence have been postulated to have impacts over long image transmission range [5

5. W. H. Wells, “Theory of small angle scattering,” in AGARD Lec. Series No. 61(NATO, 1973).

], which has been supported by light scattering measurements and simulations [19

19. D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, and C. R. Truman, “Light scattering on oceanic turbulence,” Appl. Opt. 43(30), 5662–5668 (2004). [CrossRef] [PubMed]

]. Under extreme conditions, observations have been made that involves targets with a pathlength of only a few feet [6

6. G. D. Gilbert and R. C. Honey, “Optical turbulence in the sea,” in Underwater photo-optical instrumentation applications. (SPIE, 1972), pp. 49–55.

]. The images obtained under such conditions are often severely degraded or blurred, on par with or more than those caused by particle scattering. A simple underwater imaging model, or SUIM [9

9. W. Hou, “A simple underwater imaging model,” Opt. Lett. 34(17), 2688–2690 (2009). [CrossRef] [PubMed]

], was developed to address this issue and it has been shown that, on average, the relative contribution of different components [1

1. W. Hou, Z. Lee, and A. D. Weidemann, “Why does the Secchi disk disappear? An imaging perspective,” Opt. Express 15(6), 2791–2802 (2007). [CrossRef] [PubMed]

, 2

2. W. Hou, D. J. Gray, A. D. Weidemann, and R. A. Arnone, “Comparison and validation of point spread models for imaging in natural waters,” Opt. Express 16(13), 9958–9965 (2008). [CrossRef] [PubMed]

], namely, path radiance, particle and turbulence scattering, in underwater imaging applications can be expressed in terms of the OTF as
OTF(ψ,r)total=OTF(ψ,r)pathOTF(ψ,r)parOTF(ψ,r)tur=(11+D)exp[cr+br(1e2πθ0ψ2πθ0ψ)]exp(Snψ5/3r)=(11+D)exp{[cb(1e2πθ0ψ2πθ0ψ)+Snψ5/3]r}
(1)
where θ0 relates to the mean scattering angle, c and b are the beam attenuation and scattering coefficients respectively. Ψ is the spatial frequency in cycles per radian, r is the imaging range, and D relates to path radiance. Sn is defined as the optical turbulence intensity coefficient, and contains parameters that are dependent on the structure function [20

20. J. W. Goodman, Statistical Optics (John Wiley & Sons, 1985).

], which can be further expressed as a function of the turbulence dissipation rates of temperature, salinity and kinetic energy, assuming Kolmogorov type power spectrum. For convenience, it is rewritten here as
Sn=3.44(λ¯/R0)5/3=1736K3λ¯1/3
(2)
where K3=B1χε-1/3, and reflects the 3-dimensional optical turbulence strength. λ¯ is the average wavelength of the transmitted light. R0 is the characteristic seeing parameter. B1 is a constant, and assumed to be on the order of unity. The kinetic energy dissipation rate (TKED, ε), typically ranges from 10-3 to 10-11 m2s-3 in natural waters. χ relates to the dissipation rate of temperature (TD) or salinity variances [9

9. W. Hou, “A simple underwater imaging model,” Opt. Lett. 34(17), 2688–2690 (2009). [CrossRef] [PubMed]

].

Since the phase information can be ignored under incoherent imaging conditions, the magnitude of the OTF or the modulation transfer function (MTF) will be used interchangeably here. The above model has been validated using both direct and indirect field measurements [8

8. W. Hou, S. Woods, E. Jarosz, W. Goode, and A. Weidemann, “Optical turbulence on underwater image degradation in natural environments,” Appl. Opt. 51(14), 2678–2686 (2012). [CrossRef] [PubMed]

, 9

9. W. Hou, “A simple underwater imaging model,” Opt. Lett. 34(17), 2688–2690 (2009). [CrossRef] [PubMed]

], and Sn can be used as a proxy for optical turbulence intensity that relates directly with image quality degradation.

We argue that the same turbulent microstructures in the ocean could impact the sound propagation and scattering in a somewhat similar manner, despite the differences in pressure versus electromagnetic waves. The turbulence scattering cross-section (σ) for a given sound frequency has been shown to be proportional to the first order derivatives of the one dimensional spectrum ϕ(k) of the sound speed fluctuations [11

11. L. Goodman, “Acoustic scattering from ocean microstructure,” J. Geophys. Res. 95(C7), 11557–11573 (1990). [CrossRef]

, 21

21. T. Ross and R. Lueck, “Sound scattering from oceanic turbulence,” Geophys. Res. Lett. 30(6), 1343 (2003). [CrossRef]

], namely

σ=C1kz32dΦT(kz)dkz.
(3)

A simplified form is used here as we opt to neglect the contribution from salinity for the time being, as data from a freshwater lake will be used, and assume Φ = ΦT (temperature only, omitting subscript T hereon). C1 denotes a numerical constant. The spectrum can be further expressed as a function of kz (vertical wavenumber), ε, χ, in a combined spectra including buoyancy-dominated, inertial and Batchelor subranges [11

11. L. Goodman, “Acoustic scattering from ocean microstructure,” J. Geophys. Res. 95(C7), 11557–11573 (1990). [CrossRef]

]
Φ(kz)=C2[N2χε1kz3+B1χε1/3kz5/3+χ(εν)1/2kz1]exp[q(kzkB)2],
(4)
where kB is the diffusive cutoff wavenumber, associated with the Batchelor subrange boundary, as [22

22. S. Woods, W. Hou, W. Goode, E. Jarosz, and A. Weidemann, “Quantifying turbulence microstructure for improvement of underwater imaging,” in Ocean Sensing and Monitoring, SPIE Defense and Security Symposium, W. Hou, ed. (SPIE, Orlando, FL, 2011).

]:
kB=(12π)(ενDT2)0.25
(5)
ν and DT denote the kinematic viscosity and thermal diffusivity of seawater respectively. N is the buoyancy frequency, q and C2 are numerical constants.

3. Field exercise

3.1 Setup

From above analysis, one could expect to see a meaningful relationship between Sn and σ as expressed in Eqs. (2) and (3). We set out to obtain field data to examine image degradation as a function of the microstructure turbulence. As underwater optical turbulence is primarily a function of the temperature structure, intensified thermoclines in natural environments provide a convenient setup to examine this chaotic process. We thus identified one of the finger lakes in upstate New York, Skaneateles, as our test site for SOTEX (Skaneateles Optical Turbulence EXercise, July, 2010). Figure 1(a)
Fig. 1 (left, a) Bathymetric sketch of Skaneateles Lake showing the approximate location of the two stations: S1 (red circle) near the center of the lake, and S2 (blue triangle) in the northern end of the lake. Map from http://www.ourlake.org/html/skaneateles_lake1.html. (right, b) Temperature profiles corresponding to the dissipation profiles shown in Fig. 2-6 for deployments on July 27 day (solid red), July 28 day (solid green), July 29 day (solid blue), July 29 night (dashed purple), July 30 day (solid black). All profiles are from S1 except for the July 29th daytime deployment, which is from S2.
shows the approximate location of the two sampling stations, the first (S1, red circle) near the center of the lake (42.8668° N, 76.3920° W) over a sloping bottom with an approximate depth of 70m, and the second (S2, blue triangle) at the northern end of the lake (42.9063° N, 76.4058° W) over a flatter bottom with an approximate depth of 50m. The lake is the clearest of all the Finger Lakes, with an average Secchi depth near 8 to 12 m [23

23. S. W. Effler, A. R. Rrestigiacomo, and D. M. O'Donnel, “Water quality and limonological monitoring for Skaneateles Lake: Field Year 2007,” (Upstate Freshwater Institute, 2008), p. 57.

], or beam attenuation values less than 0.4m−1 for 532nm in most cases [8

8. W. Hou, S. Woods, E. Jarosz, W. Goode, and A. Weidemann, “Optical turbulence on underwater image degradation in natural environments,” Appl. Opt. 51(14), 2678–2686 (2012). [CrossRef] [PubMed]

], and allowed for imaging under varied turbulent strength, with little scattering contribution from particulates. The strong stratification in July at relatively shallow depth, and low wind and current interference ensure a well-defined thermocline, as demonstrated by the temperature profiles shown in Fig. 1(b). The same features help to form strong structures for optical turbulence in the lake. The optical properties of the water column were measured with a 9-channel absorption and attenuation meter (ac-9, WETLabs), and Laser In Situ Scattering Transmissometer (LISST, Sequoia Scientific).

Turbulence measurements of the water column were carried out by a Vertical Microstructure Profiler (VMP, Rockland Scientific), a 3D acoustic Doppler velocimeter (Vector, Nortek), and a Precision Measurements Engineering (PME) fast Conductivity and Temperature (CT) sensor. To estimate the effects of the optical turbulence in the water column, it is essential to remove any other variations that could contribute to the blurring of the imagery obtained. For this reason, the Image Measurement Assembly for Subsurface Turbulence (IMAST) was designed. The camera and housing, and passive and active imaging targets were attached to a 5m rigid aluminum structure, along with the velocimeter, and a CTD. The two instruments, Vector and CT, are mounted near the center of the IMAST structure, and the heads of the instruments placed in such a way as to sample the same volume of water, thus providing time series of the 3D velocity, temperature, and conductivity fluctuations of the sample water volume. As the two instruments (Vector/CT) are commonly used for laboratory measurements or stationary moorings, the setup requires collection of a time series of velocities at a stationary depth in order to compute the turbulent dissipation rates. Therefore, during deployment, the IMAST profiled the water column by pausing at each depth for ten to fifteen minutes to capture the turbulence statistics.

The VMP profiler, designed to measure microstructures in oceans and lakes up to 500 m, is used to profile the water column for vertical structures. It is equipped with four microstructure sensors: two current shear sensors, one thermistor (FP07), and a micro-conductivity sensor (SBE7). These sensors allow measuring with high accuracy and resolution microscale velocity shear, temperature, and conductivity. Additionally, the VMP profiler has externally attached SeaBird SBE7-3F temperature and SBE-4C conductivity sensors. The profiler also measures pressure and provides dissipation rates as a function of depth.

This allows two different measurement approaches, namely the shear-probe-based, and acoustical-Doppler-based to be compared. Initial results showed comparable TKED dissipation rates between the two configurations [22

22. S. Woods, W. Hou, W. Goode, E. Jarosz, and A. Weidemann, “Quantifying turbulence microstructure for improvement of underwater imaging,” in Ocean Sensing and Monitoring, SPIE Defense and Security Symposium, W. Hou, ed. (SPIE, Orlando, FL, 2011).

]. These provide needed validation amongst our instrumentation setup. We consider the VMP data to be validated in this sense and only VMP data will be used in exploring the relationship for the profile comparison in the following sections.

3.2 VMP turbulence measurements and calculations

During the SOTEX experiment, over 100 VMP profiles were executed and used to estimate turbulent energy (shear data) and temperature (thermistor data) dissipation rates. The turbulent energy dissipation rate, ε, was computed by integrating the shear spectrum from k1 to k2 using the isotropic formula:
ε=152νk1k2φ(k)dk
(6)
where k is the wavenumber, ν is the kinematic molecular viscosity of water, and φ(k) is the shear spectrum. Spectra of the velocity shear were calculated from consecutive segments of 1024 data points, corresponding to a bin height of approximately 0.8 m, with an overlap between adjacent bins of 512 points. The lowest wavenumber k1 was set to 1 cpm, and the highest one (k2) was set to the wavenumber where the shear spectrum has a minimum between the natural spectrum and a high wavenumber peak, but not higher than 30 cpm due to signal to noise levels. Different profiling velocities were employed in order to better quantify dissipation rates of TKED (~70 cm/s) and TD (~30cm/s).

The rate of loss of temperature variance is determined from microstructure measurements of temperature using the very fast-response (glass-enclosed) thermistors. Assuming isotropy, the thermal dissipation rate, χT, was estimated following the below formula [24

24. T. R. Osborn and C. S. Cox, “Oceanic fine structure,” Geophys. Astrophys. Fluid Dyn. 3(1), 321–345 (1972). [CrossRef]

]:
χT=6DT(dT'dz)2¯
(7)
where T’ is the temperature fluctuation, and (dT'dz)2¯ is the bin average of the squared gradient of the temperature variance in the vertical direction, z. An accurate determination of χT requires estimates of spatial temperature gradients with resolution to the Batchelor scale, which is beyond the capability of conventional sensors. Hence, interpolation was made for SOTEX observations by fitting the measured temperature gradient spectra determined over a limited wavenumber range to the universal Batchelor form [25

25. G. K. Batchelor, “Small-scale variation of convected quantities like temperature in turbulence fluid,” J. Fluid Mech. 5, 113–133 (1959). [CrossRef]

]. The cutoff wavenumber is as defined in Eq. (5). Spectra of the temperature gradient were calculated from consecutive segments of 1024 data points with an overlap between adjacent bins of 512 points, corresponding to a mean bin height of approximately 0.45 m.

Sample results from different days can be seen in Figs. 2
Fig. 2 VMP profiles of TKED (ε) and TD rates (χ), optical turbulence intensity (Sn) and acoustical scattering cross section (σ) on July 29, 2010 (Profile#62, left), on July 30, 2010 (Profile#112, right) . The units for ε is m2s−3, while χ is °C2s−1. Sn and σ are not calibrated.
-3
Fig. 3 VMP profiles of TKED (ε) and TD rates (χ), optical turbulence intensity (Sn) and acoustical scattering cross section (σ) on July 30, 2010 (Profile#117, left), on July 30, 2010 (Profile#126, right) . The units for ε are m2s−3, while χ is C2s−1. Sn and σ are not calibrated.
. These are dissipation rate profiles of TKED (ε) and TD (χ, again, for convenience, subscript T is omitted), optical turbulence intensity coefficient (Sn) and acoustical scattering cross section (σ). The units for ε are m2s−3, while those for χ are °C2s−1. Since the main concern here is to examine the relative contribution and correlation between Sn and σ, they are not calibrated and therefore have arbitary units, and are offset by a constant value. Our focus here is to explore the shape of the profiles and examine their correlation, therefore the relative units are acceptable. On the other hand, these values will be offset by a constant in most cases, since they are all dependent upon the sound frequencies in consideration. Nonetheless, the general trend should still hold.

This is indeed the case by examining these figures. One should notice that the general trend of stronger turbulence at or near the thermocline around 10 to 15m, as shown by Fig. 1(b). The strong turbulence layer can be observed in both the TKED and TD rates throughout the exercise. It is encouraging, while not surprising, to see that indeed both the optical turbulence intensity coefficient (Sn), as well as the acoustic scattering cross section (σ), follow the same trend, shown in lower part of Figs. 2-3. As one can observe, this trend is predominantely determined by the temperature dissipation rate structure. This is in part due to the fact that this is a freshwater lake, and thus sound speed is affected by little, if any, conductivity variations. It is reasonable to believe such relationship still holds in the oceanic environment, as the extra term associated with salinity variations to be added in Eq. (3) is similar to the cascade properties of the MTF in Eq. (2) [26

26. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2005).

]. An oceanic research cruise has been scheduled to further test this relationship.

Fig. 5 Optical turbulence intensity (Sn) versus acoustical scattering cross section (σ), for July 30, 2010 (Profile#126, R2 = 0.93, left), for July 30, 2010 (Profile#117, R2 = 0.86, right)

4. Summary

References and links

1.

W. Hou, Z. Lee, and A. D. Weidemann, “Why does the Secchi disk disappear? An imaging perspective,” Opt. Express 15(6), 2791–2802 (2007). [CrossRef] [PubMed]

2.

W. Hou, D. J. Gray, A. D. Weidemann, and R. A. Arnone, “Comparison and validation of point spread models for imaging in natural waters,” Opt. Express 16(13), 9958–9965 (2008). [CrossRef] [PubMed]

3.

K. J. Voss, “Simple empirical model of the oceanic point spread function,” Appl. Opt. 30(18), 2647–2651 (1991). [CrossRef] [PubMed]

4.

W. Hou and A. Weidemann, “Diver visibility: why one can not see as far?” in SPIE Proc. 7317, W. Hou, ed. (SPIE, Orlando, FL, USA, 2009).

5.

W. H. Wells, “Theory of small angle scattering,” in AGARD Lec. Series No. 61(NATO, 1973).

6.

G. D. Gilbert and R. C. Honey, “Optical turbulence in the sea,” in Underwater photo-optical instrumentation applications. (SPIE, 1972), pp. 49–55.

7.

R. C. Honey and G. P. Sorenson, “Optical absorption and turbulenced induced narrow angle forward scatter in the sea,” in AGARD Conference Proceeding No.77 on Electromagnetics of the sea(1970).

8.

W. Hou, S. Woods, E. Jarosz, W. Goode, and A. Weidemann, “Optical turbulence on underwater image degradation in natural environments,” Appl. Opt. 51(14), 2678–2686 (2012). [CrossRef] [PubMed]

9.

W. Hou, “A simple underwater imaging model,” Opt. Lett. 34(17), 2688–2690 (2009). [CrossRef] [PubMed]

10.

S. A. Thorpe and J. M. Brubaker, “Observations of sound reflection by temperature microstructure,” Limnol. Oceanogr. 28(4), 601–613 (1983). [CrossRef]

11.

L. Goodman, “Acoustic scattering from ocean microstructure,” J. Geophys. Res. 95(C7), 11557–11573 (1990). [CrossRef]

12.

G. D. Gilbert and J. C. Pernicka, “Improvement of underwater visibility by reduction of backscatter with a circular polarization technique,” Appl. Opt. 6(4), 741–746 (1967). [CrossRef] [PubMed]

13.

W. Hou, A. Weidemann, D. Gray, and G. R. Fournier, “Imagery-derived modulation transfer function and its applications for underwater imaging,” in Applications of Digital Image Processing XXX, A. G. Tescher, ed. (SPIE, San Diego, 2007), pp. 6696221–6696228.

14.

P. C. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D. L. Jordan, and J. G. Walker, “Improving visibility depth in passive underwater imaging by use of polarization,” Appl. Opt. 42(15), 2794–2803 (2003). [CrossRef] [PubMed]

15.

L. Mullen, A. Laux, B. M. Concannon, E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Amplitude-modulated laser imager,” Appl. Opt. 43(19), 3874–3892 (2004). [CrossRef] [PubMed]

16.

G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging system,” Opt. Eng. 32(9), 2185 (1993). [CrossRef]

17.

D. Sadot, A. Dvir, I. Bergel, and N. Kopeika, “Restoration of thermal images distorted by the atmosphere, based on measured and theoretical atmospheric modulation transfer function,” Opt. Eng. 33, 44–53 (1994). [CrossRef]

18.

Y. Yitzhaky, I. Dror, and N. Kopeika, “Restoration of atmospherically blurred images according to weather-predicted atmospheric modulation transfer functions,” Opt. Eng. 36(11), 3064–3072 (1997). [CrossRef]

19.

D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, and C. R. Truman, “Light scattering on oceanic turbulence,” Appl. Opt. 43(30), 5662–5668 (2004). [CrossRef] [PubMed]

20.

J. W. Goodman, Statistical Optics (John Wiley & Sons, 1985).

21.

T. Ross and R. Lueck, “Sound scattering from oceanic turbulence,” Geophys. Res. Lett. 30(6), 1343 (2003). [CrossRef]

22.

S. Woods, W. Hou, W. Goode, E. Jarosz, and A. Weidemann, “Quantifying turbulence microstructure for improvement of underwater imaging,” in Ocean Sensing and Monitoring, SPIE Defense and Security Symposium, W. Hou, ed. (SPIE, Orlando, FL, 2011).

23.

S. W. Effler, A. R. Rrestigiacomo, and D. M. O'Donnel, “Water quality and limonological monitoring for Skaneateles Lake: Field Year 2007,” (Upstate Freshwater Institute, 2008), p. 57.

24.

T. R. Osborn and C. S. Cox, “Oceanic fine structure,” Geophys. Astrophys. Fluid Dyn. 3(1), 321–345 (1972). [CrossRef]

25.

G. K. Batchelor, “Small-scale variation of convected quantities like temperature in turbulence fluid,” J. Fluid Mech. 5, 113–133 (1959). [CrossRef]

26.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2005).

OCIS Codes
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(010.7060) Atmospheric and oceanic optics : Turbulence
(110.4850) Imaging systems : Optical transfer functions
(330.6130) Vision, color, and visual optics : Spatial resolution
(010.7295) Atmospheric and oceanic optics : Visibility and imaging

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: January 11, 2013
Manuscript Accepted: January 14, 2013
Published: February 12, 2013

Virtual Issues
Vol. 8, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Weilin Hou, Ewa Jarosz, Sarah Woods, Wesley Goode, and Alan Weidemann, "Impacts of underwater turbulence on acoustical and optical signals and their linkage," Opt. Express 21, 4367-4375 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-4367


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References

  1. W. Hou, Z. Lee, and A. D. Weidemann, “Why does the Secchi disk disappear? An imaging perspective,” Opt. Express15(6), 2791–2802 (2007). [CrossRef] [PubMed]
  2. W. Hou, D. J. Gray, A. D. Weidemann, and R. A. Arnone, “Comparison and validation of point spread models for imaging in natural waters,” Opt. Express16(13), 9958–9965 (2008). [CrossRef] [PubMed]
  3. K. J. Voss, “Simple empirical model of the oceanic point spread function,” Appl. Opt.30(18), 2647–2651 (1991). [CrossRef] [PubMed]
  4. W. Hou and A. Weidemann, “Diver visibility: why one can not see as far?” in SPIE Proc. 7317, W. Hou, ed. (SPIE, Orlando, FL, USA, 2009).
  5. W. H. Wells, “Theory of small angle scattering,” in AGARD Lec. Series No. 61(NATO, 1973).
  6. G. D. Gilbert and R. C. Honey, “Optical turbulence in the sea,” in Underwater photo-optical instrumentation applications. (SPIE, 1972), pp. 49–55.
  7. R. C. Honey and G. P. Sorenson, “Optical absorption and turbulenced induced narrow angle forward scatter in the sea,” in AGARD Conference Proceeding No.77 on Electromagnetics of the sea(1970).
  8. W. Hou, S. Woods, E. Jarosz, W. Goode, and A. Weidemann, “Optical turbulence on underwater image degradation in natural environments,” Appl. Opt.51(14), 2678–2686 (2012). [CrossRef] [PubMed]
  9. W. Hou, “A simple underwater imaging model,” Opt. Lett.34(17), 2688–2690 (2009). [CrossRef] [PubMed]
  10. S. A. Thorpe and J. M. Brubaker, “Observations of sound reflection by temperature microstructure,” Limnol. Oceanogr.28(4), 601–613 (1983). [CrossRef]
  11. L. Goodman, “Acoustic scattering from ocean microstructure,” J. Geophys. Res.95(C7), 11557–11573 (1990). [CrossRef]
  12. G. D. Gilbert and J. C. Pernicka, “Improvement of underwater visibility by reduction of backscatter with a circular polarization technique,” Appl. Opt.6(4), 741–746 (1967). [CrossRef] [PubMed]
  13. W. Hou, A. Weidemann, D. Gray, and G. R. Fournier, “Imagery-derived modulation transfer function and its applications for underwater imaging,” in Applications of Digital Image Processing XXX, A. G. Tescher, ed. (SPIE, San Diego, 2007), pp. 6696221–6696228.
  14. P. C. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D. L. Jordan, and J. G. Walker, “Improving visibility depth in passive underwater imaging by use of polarization,” Appl. Opt.42(15), 2794–2803 (2003). [CrossRef] [PubMed]
  15. L. Mullen, A. Laux, B. M. Concannon, E. P. Zege, I. L. Katsev, and A. S. Prikhach, “Amplitude-modulated laser imager,” Appl. Opt.43(19), 3874–3892 (2004). [CrossRef] [PubMed]
  16. G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging system,” Opt. Eng.32(9), 2185 (1993). [CrossRef]
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