Diver visibility: Why one cannot see as far?

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CONTRACT NUMBER 4. TITLE AND SUBTITLE Diver Visibility: Why One Can Not See As Far? 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 0602782N 5d. PROJECT NUMBER 6. AUTHOR(S) Weilin Hou, Alan D. Weidemann 5e. TASK NUMBER 5f. WORK UNIT NUMBER 73-6369-09-5 8. PERFORMING ORGANIZATIC M REPORT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Research Laboratory Oceanography Division Stennis Space Center, MS 39529-5004 NRL/PP/7330-09-9 190 10. SPONSOR/MONITOR'S ACIIONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) ONR Office of Naval Research 800 N. Quincy St. Arlington, VA 22217-5660 11. SPONSOR/MONITOR'S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release, distribution is unlimited. 20090814034 13. SUPPLEMENTARY NOTES 14. ABSTRACT Diver visibility has been one of the key research areas in underwater vision and imaging studies. Its applications also extend into imaging sys .•m performance evaluation and prediction, which is important in MIW and ASW operations. These applications are often associated with coastal ocean waters, anc this is generally translated directly into turbidity of the water column. While mostly this is the case, exceptions can lead to erroneous predictions and potcr lially significant consequences. We examine issues associated with such situations, both by model as well as field data, in order to reach better estimates and to i *plore means to compensate for such effects, to enhance diver visibility. Visibility data collected by Navy divers from clean and relatively calm waters outside Pensa ola, during Sept 2001 Gorging Littoral Ocean for Warfighters (GLOW) experiments suggested a closer examination is warranted, as observed diver visibility mea; jred at different spatial frequencies contradicts conventional model predictions. Observation data from two different days, by different divers at different depths were used. The modulation transfer of high frequency components disappears at a level much higher than those predicted by the human vision sensitivity level. Su h contradictions can be resolved, once the effect of the turbulence scattering is considered using a general imaging model. 15. SUBJECT TERMS visibility, scattering, particles, turbulence, underwater, MCM, OTF, MTF 16. SECURITY CLASSIFICATION OF: a. REPORT b. ABSTRACT c. THIS PAGE Unclassified Unclassified Unclassified 17. LIMITATION OF ABSTRACT UL 18. NUMBER 19a. NAME OF RESPONSIBLE PERSON OF Weilin Hou PAGES 19b. TELEPHONE NUMBER (Include area co e) 228-688-5257 Standard Form 2H8 (Rev. 8/98) Prescribed by ANSI Si . Z39.18 Diver visibility: why one can not see as far? Weilin Hou, Alan D. Weidemann Navel Research Laboratory, Code 7334, Stennis Space Center, MS 39529 ABSTRACT Diver visibility has been one of the key research areas in underwater vision and imaging studies. Its applicalions also extend into imaging system performance evaluation and prediction, which is important in MIW and ASW operations. These applications are often associated with coastal ocean waters, and this is generally translated directly into turbidity of the water column. While mostly this is the case, exceptions can lead to erroneous predictions and pi tentially significant consequences. We examine issues associated with such situations, both by model as well as fiek data, in order to reach better estimates and to explore means to compensate for such effects, to enhance diver • isibility. Visibility data collected by Navy divers from clean and relatively calm waters outside Pensacola, during S pt 2001 Gorging Littoral Ocean for Warfighters (GLOW) experiments suggested a closer examination is warranted, as >bserved diver visibility measured at different spatial frequencies contradicts conventional model predictions. Observation data from two different days, by different divers at different depths were used. The modulation transfer of high t equency components disappears at a level much higher than those predicted by the human vision sensitivity lev;l. Such contradictions can be resolved, once the effect of the turbulence scattering is considered using a general imagin model. Keywords: visibility, scattering, particles, turbulence, underwater, MCM, OTF, MTF 1. BACKGROUND Diver visibility is one of the key underwater vision and imaging topics dating back to the early days of oceanographic research. One of the simple approaches to determine diver visibility, or turbidity of the water, the use of Secchi disk, for the past 150 years[l, 2]. The idea was rather intuitive, that the disappearing distan dinner dish would give clue to the turbidity of the water. Its deployment is simple: one lowers the traditional circular disk about 30cm in diameter, from above the water into the water column, and determines the point at disappears from sight. The depth at which the disk can no longer be discerned against the background is defin Secchi disk depth. The physics behind the Secchi disk is the absorption but mostly scattering by the wate constituents to reduce the contrast. The classical work done by Duntley relates such quantities by means of transfer[2], A recent study revealed such links from image formation, or modulation transfer perspective! 1], c in horizontal situations. modern las been e of the y white, which it d as the and its adiative pecially Image formation and transmission in underwater environments are always hindered by the attenuation by watc • and its constituents. Unlike in the atmosphere where visibility can be on the order of miles, the visual range in un lerwater environments is rather limited, at maximum on the order of tens of meters, even in the clearest waters. The c jminant factor is typically not due to absorption, unless visible channels near the red are used. Scattering by w iter and particulates within the water often poses the most challenges, causing photons stray from its designated pith, thus introducing the blur and loss of details within the image. This reduction of details, or high frequency components, prevents retrieval of information needed for detection and more importantly, for clear identification. The main cause of blurry images in water is scattering, ie the photon changes path or direction. This is describe >j by the volume scattering function (VSF) which is the probability of photons being scattered into certain directions. F >r ocean waters, the VSF has a strong scattering peak in very small forward angle. In more turbid waters, the peak broa< ens into larger angles, or higher chance for photons scatter to larger angles, which means more blur[3, 4]. This also leads to multiple scattering, where the same photon being scattered more than once before reaching detector. The esulting distribution is different from that of the single scattering, with even wider peak thus more blur. Such effects can be best described via the point spread function (PSF) of the medium and system, or simply put, the system response to a point source, denoted as h(x,y). The outcome image g(x,y) is the result of the simple convo ution of h(x,y) and original signalf(x,y), adding the noise n(x,y): Ocean Sensing and Monitoring, edited by Weilin (Will) Hou, Proc. of SPIE Vol. 7317, 731701 ©2009SPIE • CCCcode: 0277-786X/09/$18 • doi: 10.1117/12.820810 Proc. of SPIE Vol. 7317 731701-1 g(x,y) = ^f(x„yj)h{x-xl,y-yi)dxidyl+n{x,y), (1) Mathematically, it is easier to manipulate the above relationship in frequency domain, as convolutions represent simple multiplications after Fourier transforms, G{u,v) = F(u,v)H{u,v)+N{u,v). (2) The Fourier transformed PSF is the optical transfer function or OTF, H(u,v). u, v are frequency componen >. When consider only the magnitude of the transform, which is adequate in underwater incoherent imaging applications, it is referred to as modulation transfer function or MTF. We know that the total OTF can be modeled in simple forms with multiplicative components as in all linear systems, while the effect of water involving mostly paniculate scattering can be expressed in a closed formfl, 4, 5] HnaH,r{¥,r) = e-D^\ and D{y/) = C—y—— 27V0o\f/ (3) '-, (4) where c, b are attenuation and scattering coefficients respectively. 90 is related to mean scattering angle. Tlie single scattering albedo a0=b/c is used to describe the amount of scattering, while the optical depth T=c*r (r is ram;e). The angular spatial frequency is expressed in cycles per radian. Degradation of the image quality in a scattering medium involving turbulence has been studied mostly in atnosphere. These studies are mainly focused on modeling the optical transfer function, in an effort to restore the images ( btained. such as in air reconnaissance or astronomy studies [6, 7]. Little has been done regarding the turbulence ei fects on imaging formation in water, mainly due to the dominant particle scattering and strong attenuation associated. 1 his is of little surprise as anyone with experiences in coastal waters, especially those inside a harbor, or estuary a eas like Mississippi, experience first-hand looks of how visibility could quickly reduce to zero in a matter of a few Icet. The same applies to regions of strong re-suspensions from the bottom, both in coastal regions as well as in the c ;ep sea. However, the effects of turbulence have been postulated to have impacts over long image transmission range [5], and supported by light scattering measurements and simulations[8]. Under extreme conditions, observations have be :n made that involves targets with a few feet[9]. The images obtained under such conditions are often severely deg aded or blurred, on par or more than those caused by particles. 2. A DIVER VISIBILITY PARADOX Diver visibility can be measured simply by using Secchi disk as mentioned above, or use more sophisticate involving different spatial frequencies, such as the USAF-type resolution charts (Fig. 1). The benefits of the lat< it provides convenient spatial frequency modulation measurements, which can be used directly with underwater modelsfl]. During Gorging Littoral Ocean for Warfighters (GLOW, Sept, 2001) experiments, measurement wc to estimate diver visibility under different range and optical conditions. Some of the data is shown in Table 1. I targets r is that maging e made It can be readily seen by above visibility model (Eqs. (3) and (4)) that at the range of disappearance, the modulation transfer (Hwalcr) or relative contrast can be as high as 0.24 for high frequency components (Fig.2), which is n direct contradiction of common sense and those of Blackwell's conclusions[10]. In other words, the imaging model prec icts that the diver should still be able to see the high frequency group (finer line pairs), but the diver reported otherwise. The reason behind this contradiction could be the effects of turbulence as postulated above. We will apply a ecently developed imaging model in the following section to solve the puzzle. Proc. of SPIE Vol. 7317 731701-2 N/1 2mm 4 mm 8mm 16mm 32mm 9/21/2001 14 28 38 44 56 9/21/2001 14 28 38 44 56 9/23/2001 20 32 40 48 54 9/23/2001 20 32 40 46 54 dateX, Table 1. Diver observed disappearing distance in feet. /* denotes spatial frequency or line pairs, corrected for water. Each observation series were carried out by different Navy divers. No vision issues are involved. Figure 1. Sample diver visibility panel at close range. Bottom right corner shows the enlarged version of the resolution panel. Picture was taken underwater during GLOW experiment. 3. APPLYING GENERAL UNDERWATER IMAGING EQUATION A general underwater imaging model has been developed, to include the contributions of both particle and tu bulence scattering effects on imaging in the underwater environment[ 11]. For convenience, we will briefly outline the key results before apply the model to the current problem. From Fourier optics, it is commonly known that spatial coherence functions between optical fields of any two pc ints can be used to describe the irradiance distribution of the source image or object[12, 13]. The famous Young into ference experiment can be seen as a special case. The modulation transfer function can be shown as equivalent to th' spatial correlation function on the pupil screen. For a time-varying correlation function under wide-sense stationary conditions. Proc. ofSPIEVol. 7317 731701-3 its ensemble average can be related to the spatial phase structure function when absorption variation can be neglected, such that //.!(x) = rv(i) = exp(-D,(x)/2) (5) DAt) = (0(x)-0(x + te))2 (6) where 0(x)is the phase of the optical field on pupil plane. This is under the assumption that amplitude strucure does not change over the small separation distance under examination. Other preconditions involve small perturb;itions of index of refraction, scale of turbulence compared large to wavelength and log-normal distribution unc:;r weak turbulence can be found in detailed discussions in listed references[13, 14]. Following the Kolmogorov model, for a fully developed turbulent flow, under the inertial regime, the powei spectral density of index of refractions can be expressed in the forms of [15] -11/3 <X>Kn{K,r) = K,(r)K (7) where the superscript K. denotes Kolmogorov spectrum. Kj(r) is equivalent of the structure constant of the ndex of refraction fluctuations, which describes the intensity of the optical turbulence strength (ie index of r fraction fluctuations). It is a function of kinetic energy dissipation rate and the molecular viscosity of the water. The abo "e scalar relationship implies that the turbulence can be considered statistically isotropic, and homogenous (wile-sense stationary). Further, it is important to remember that not all turbulent flows can be described by tr >i above spectrum[14], although experimental evidence suggests the above spectrum can be used in underwater conditions [15]. Following the approach by Fried[16], and relating the spectral power spectrum to the IOR spatial distribution! 13], the OTF of optical turbulence in underwater environments can be derived as[l 1] f OTF(y/,r) = exp -3.44 x vH> 5 1 v^y (8) = exp(-S„^V) where 3 5 r0 = 0.0239 4TT~ (9) k2K}r 1735^/L1 (10) The key parameter that relates to turbulence structure is rth or Fries parameter[17], which is a function of integn ed turbulent structure constant (K3 or C„ in equivalent atmospheric terms ), range of propagation (r) and the optica wavelength involved. The general underwater imaging equation accounts for both particle and turbulence scattering, and takes the form: Proc. ofSPIEVol. 7317 731701-4 OTF(v,r),nlal = OTF{y,r)OTF(y,r) cxp -ar + br l-e -2 nOtfp 27t60y/ -2 nO^y/ = exp -ar - br \-e InO^y 'exp(-SyV) (11) -sy!ir It is easy to see that OTF(0,r)=exp(-ar). It is also worth mentioning that in practice, the OTF is often normalised by its DC component. This can be important in situations especially when automatic gain control is applied. Assuming that the turbulence structures during GLOW is isotropic and homogenous, and in fully developed inert al stage, a characteristic seeing parameter for underwater imaging can be introduced (R0), which is equivalent of Fried par imeter at lm distance in waterfl 1]. If one can assume that the discrepancies between observation and model is solely th; t of the effects by turbulence, such effects can be estimated by taking away the effects of particle scattering from the tota Blackwell criterion (ie 2%). This sets R,r0.004. 1fj Spatial frequency (cyc/rad) Figure 2. Effects of turbulence and particle scattering on OTF. Top to bottom: turbulence scattc ing, particle scattering, and the combined (multiplicative) effects. The effects of turbulence on underwater imaging has been discussed and demonstrated previously[9 , albeit qualitatively. It has long been postulated that such effects will only pose significant challenge once high a solution imaging becomes an issue, or in extreme turbulent environments[3]. Using results above (Eq.l 1), we can riK> el what happened during GLOW experiment using sample values from Sept 21, 2001 field measurements. The range is set at 5m. The water has a total attenuation coefficient of 0.3m"1. If only particle scattering were present, the mclulation Proc. ofSPIE Vol. 7317 731701-5 transfer of high frequency components disappears at a level following that of Eq. (4), and shown by the middle (green color) curve in Figure 2. This value (0.24) is much higher than those predicted by the human vision sensitivity level[ 10]. Such contradictions can be resolved, once the effect of the turbulence scattering is considered (blue or top curve), and properly included (red or bottom curve). Figure 3 includes all observations shown in Table 1, using particle-scattering only data from Sept 23 for clarity. < )ne can see that with only one exception of Sept 21 observation, all relative contrast values are around 0.02, in line with Blackwell criterion. Contrasting to the total contribution of both particle and turbulence scattering, the particle-only results clearly show high contrast values at high spatial frequencies. 0.35 0.3 • 921 total * 923 total 923 part 0.25 o 0.2 0.15 O 0.1 O 0.05 0 O : 0 •* 500 .* 1000 . 1500 * • * 2000 250C Spatial frequency (cyc/rad) Figure 3. Combined effects of particle and turbulence scattering in terms of contrast threshold from divci observations from two different days (see text for details). 3. CONCLUSION This paper discusses the effects of turbulence on imaging outcome in natural environments. Specific lly, we demonstrate that the previous diver visibility model based only on particle scattering can lead to erroneous predictions under certain conditions. When the accumulative effects of turbulence scattering is included, by using tlK general underwater imaging equation which is based on Kolmogorov power spectrum, we are able to explain the > bserved discrepancy, assuming weak path radiance contribution. Further validation of the theory is necessary, especial y under different turbulence conditions and particulars concentration. The application range of the developed theory sh< uld also be tested, along with different turbulence models and subregimes. Proc. ofSPIE Vol. 7317 731701-6 4. ACKNOWLEDGEMENTS This research was supported by NRL core project 73-6369, "Increasing EO Imaging Resolution in Underwater Environment via Adaptive Coherent Integration". 5. REFERENCES [I] [2] 131 [4] [5] [6] [8] [9] [10] [II] [12] [13] [14] [15] [16] [17] W. 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