Airborne observation of the sea shelf and of objectslaying on the sea bottom or submerged in the wateris a much more efficient way to survey an area thanare shipborne methods. For the same viewing anglethe bottom area at a depth z when viewed from analtitude H over the sea surface is about ðH=zÞ2 timesgreater than when viewed from a point on the seasurface. Since the altitudeH is usually much greaterthan the bottom depth, and the speed of a surveyairplane is much greater than that of a ship orunderwater vehicle, the gain in the survey productiv-ity as well as savings in fuel and other resources isconsiderable.However, a major disadvantage of airborne ima-
ging is due to the negative influence of surface waveson image quality. Surface waves introduce additionalnoise due to fluctuations of radiation seen by an ima-ging system. Such fluctuations are produced by the
action of surface waves on the upwelling light re-flected from the bottom, backscattered in the waterbody, and reflected from the surface. Methods ofcomputing wave-produced noises and decreasingtheir effects by choosing the optimal aircraft flightdirections relative to the Sun position and wind di-rection are given in Dolin et al. [1]. Besides, thesea surface waves produce strong distortions in theimage. Light reflected from a submerged object is dis-torted by refraction through the random slopes of therippled sea surface.
When an image is averaged over a time intervalmuch longer than the period of the longest surfacewave in the imaging area, the image distortionmay be easily determined. In this case the averageimage fluctuations appear as blur circles or ellipsesabout points in the image. This averaging leads to adecreased image contrast that can be quantitativelyexpressed by the surface modulation transfer func-tion (MTFs), itself a function of the surface slopedistribution. Using the Cox–Munk wave slope distri-bution, a function of wind velocity, the surface MTFscan be expressed as [2]
where ν ¼ 1=λ is the wave spatial frequency, λ is thewave’s wavelength, n is the air–water refraction in-dex, and σ2 is the surface slope variance as a functionof the surface wind velocity.Thus, for integration times much greater than an
average wave period, the distortion of the image canbe determined by Eq. (1). In this case the image con-trast and hence the viewing distance z will be lessthan if the same object is viewed through a flatsea surface.However, in real airborne imagery, integration
time is quite insignificant due to the high speed de-veloped by aircraft. Here the sea surface is imagedinstantaneously and not stared at for an extensiveperiod of time. The structure of such images may dif-fer significantly from the structure of the imaged ob-ject. For example, the image may become broken andstraight lines may convert into curves. Figure 1,taken from [3], a reference not available to westernreaders, shows photos of an underwater self-luminous test object obtained in the Black Sea.The images were made from a height H ¼ 8m abovethe water surface with an exposure of 1=500 s. Notethat the pictures in Fig. 1 have been resized to thesame size for all depths. The sea surface roughnesswas relatively weak with a wind velocity of about2:5m=s. One can see that increases in the test-objectdepth result in a rapid degradation of the image. Fi-nally information about the test object becomes com-pletely lost at a depth z ¼ 10m. Thus, it may beconcluded that the removal or at least a decreaseof the image distortion produced by surface wavesis an important issue for imaging in the ocean.Recently several publications [4–7] have consid-
ered different theoretical aspects of the problem of
correction of wave-induced image distortion. The cor-rectionmethods are based on having complete or par-tial information about the surface slopes occurring atthe time of the imagery. However, we are not aware ofpublications on the experimental study of such cor-rections. This paper presents the first results ofthe experimental correction of images distorted bywaves obtained using a laboratory-modeling installa-tion (LMI) designed and built for experimentalinvestigations of light and image transfer throughwavy water surfaces at the Laboratory of Oceanand Atmospheric Optics, P. P. Shirshov Institute ofOceanology, St. Petersburg Branch.
2. Experimental Technique and Wave Parameters inthe Laboratory Basin
The design of the LMI is shown in Fig. 2. The mainpart of the LMI is a basin (1) with a water surfacearea of 1:15m× 0:55m and a depth of 0:3m. A glasswindow of 33 cm × 36 cm (6) is at the center of the ba-sin bottom. Four fans (16) for the generation of wavesare fixed above the water surface. The voltage of thefans’ power supply can be controlled to vary the airspeed from 1.3 to 4:5m=s. A rotary apparatus (2) forholding a variety of sources and receivers is mountedover the center of the water surface. It is used to fix,move, and rotate different light sources including la-sers, wide parallel beam sources (4), and sensors in-cluding photo- or TV cameras (5) with steel bars (14)and (17). The distance between the camera and thewater surface can be changed by a special unit (15).The source of diffuse light (3) consists of a lamp (13),a condenser (11), a unit for changing filters (12), a flatmirror (10), an opal glass (9), and a transparent glass(8). The diffuse source is placed under the bottomglass window. A unit (3) allows the observation ofa variety of test objects (7) through the water layer.
Fig. 1. Photos of an underwater self-luminous test object obtained in the Black Sea from a height of H ¼ 8m with an exposure timeof 1=500 s through a wavy sea surface with a wind velocity of 2:5m=s. The depths of the test object are 1m (a), 5m (b), and 10m(c), respectively.
Two identical four-electrode wavemeters were de-signed for measuring the properties of the surfacewaves. Each wavemeter measures the water levelat four closely spaced points separated by about2:5mm. This makes it possible to estimate thetwo-dimensional wind–wave spectrum and the slopedistribution function. The relative position of thewavemeters is varied to estimate the wave spatialcorrelation function.One of the key factors in laboratory experiments on
wavy water surfaces is the method of generatingwaves. It is natural to consider a method as suitableif well-known laws for wavy surface properties arefulfilled. We used the dependence of the wavy surfaceslope variance on the wind speed as a criterion of the“quality” of the generated waves. As is known, thevariance of the sea surface slope is linear with re-spect to the wind speed per the Cox–Munk approxi-mation [8]. Thus we performed a series ofmeasurements of the water surface slope distribu-tions for different wind speeds. The variance becamelinear with wind speed when the speed reached
3:5m=s. Thus we set the range of the wind speedin our experiment to vary from 3.5 to 4:5m=s, with4:5m=s being the maximum speed possible.
A criterion of laboratory-modeling quality is thefulfillment of the condition that theMTFsm of the sys-tem, i.e., the turbid medium and the water surface, isa product of the MTFm of the turbid media and theMTFs of the water surface [1,9]:
MTFsm ¼ MTFm ×MTFs: ð2ÞTheMTFðvÞ of any linear medium is determined as
the ratio of the apparent, Ca, and inherent, Ci, con-trast modulation indices of an extensive sinusoidaltest object of a given spatial frequency, ν, observedwith a long exposure time through the medium.Generally the MTFðvÞ ¼ CaðvÞ=CiðvÞ, where Ca ¼ðLa1 − La2Þ=ðLa1 þ La2Þ, Ci ¼ ðLi1 − Li2Þ=ðLi1 þ Li2Þ,and Li1 and La1 are the maximum and Li2 and La2minimum radiances of the sinusoidal test objectand its image, respectively. We obtained the imageof this sinusoidal test object with a spatial frequencyv ¼ 25m−1 viewed through four media. These were 1,tap water with a flat surface; 2, tap water with awavy surface; 3, tap water with milk to produce morescattering and a flat surface; and 4, tap water withmilk and a wavy surface. The measured radiance dis-tributions of the sinusoidal test object and its imagein the x direction were processed to obtain the follow-ing values of the apparent contrast modulation indexfor the four media: 1, Ca1 ¼ 0:704; 2, Ca2 ¼ 0:161; 3,Ca3 ¼ 0:556; and 4, Ca4 ¼ 0:125. Thus for the wavysurface alone the experimental MTFs ¼ Ca2=Ca1 ¼0:229. The MTFm for the turbid medium alone wasdetermined by two different ways. The first MTFMTFm ¼ Ca3=Ca1 ¼ 0:790. The second MTFm ¼Ca4=Ca2 ¼ 0:776. The mean of these two measure-ments was MTFm ¼ 0:783. Now the total MTFsm ofthe wavy surfaceþ the turbid mediumwasmeasuredas MTFsm ¼ Ca4=Ca1 ¼ 0:178. A separate multiplica-tion of the surface and media MTFs, where MTFs ¼0:229 and mean MTFm ¼ 0:783 gives MTFs×MTFm ¼ 0:179, which is well within the limits ofmeasurement accuracy of the measured totalMTFsm ¼ 0:178. This verifies the validity of Eq. (2)and the reliability of the modeling. Note that thewind speed was constant for all measurementsof MTFs.
3. Methods of Image Correction
A principal idea common to all known methods ofcorrecting images distorted by a wavy water surfaceconsists of using information about the surface slopespatial distribution within the surface area responsi-ble for the distortion to correct the image. Figure 3generally sketches out the wavy surface imaging pro-blem. The imaging system consists of an objectivelens and an imaging photodetector. In the absenceof waves, i.e., a flat surface, the point r01 of the photo-detector receives light from the object point r0. How-ever, when the water surface is wavy, light reaching
Fig. 2. Design of the laboratory-modeling installation (LMI).1, basin; 2, rotary-coordinating unit; 3, source of diffuse light;4, light source of wide parallel beam with a unit for changing fil-ters; 5, photo- or TV camera; 6, bottom glass window; 7, test object;8, glass; 9, opal glass; 10, flat mirror; 11, condenser; 12, unit forchanging filters; 13, lamp; 14, unit for mounting and adjustinga light source; 15, unit for moving the photo- or TVcamera;16, fan; 17, steel bar. All sizes are given in millimeters.
the photodetector point r01 comes from a differentobject point r1 along the same ray 1. The distortionoccurs because the system registers the point r1 as ifit was the point r0. To correct the image it is neces-sary to move the image element r01 formed by ray 1 tothe point r02, the image point where the object point r1would be projected for a flat air–water interface, i.e.,to the image element formed by ray 2. Such a correc-tion is possible by using Snell’s refraction law if thevector of the surface slope η is known at the point rswhere ray 1 intersects the surface.A detailed theoretical analysis performed by Dolin
et al. [4–6] showed that various methods of image cor-rection are possible provided that some or all of theinformation about the spatial distribution of waveslopes is available. Specifically, they emphasizedthe importance of an optical system’s resolution foraccurate image correction. They also analyzed differ-ent methods of interpolating surface slope values inthe intervals between points of known slopes. An-other method of correction was suggested and pa-tented (but not published) by Levin at the end ofthe 1970s. His main idea was to use the glitter areasof a sea surface to find those patches of an image thatwere formed by light rays passing the water surface
without a change of direction. A detailed theory ofthis method with reference to Levin’s original expo-sition was given byWeber [7]. To achieve a correctionby this method, an imaging system must include apulsed light source, e.g., a broad beam laser, whichilluminates both the object and the sea surface witha light pulse of a few nanoseconds duration at a pulsefrequency of about 50Hz and two time-gated co-located receivers. One receiver is gated on whenthe pulse reflected by the observed object arrives.The second receiver is gated on when the pulse re-flected by the surface reaches the receiver. Thustwo image frames are obtained, the first one contain-ing the distorted image of the object and the secondcontaining the surface glitter pattern whose ele-ments are the images of surface patches normal toincident rays. Note that the second frame imagingthe surface contains a rather small number of “light-er” patches associated with glitters, while the rest ofthe elements of this frame are “dark” as light re-flected by the surface elements not normal to the re-ceiver and transmitter rays does not enter thereceiver. This small number of glitter patches corre-sponds to the undistorted elements of the first framecontaining the object’s image which are formed bylight rays passed through surface elements normalto these rays. We can use this glitter pattern as amask, e.g., to multiply the video signals of two framesto get one resultant frame in which only the undis-torted elements of the object’s instantaneous imageare present. This resultant frame is a fragment of un-disturbed image. Since the wave state of the surfacechanges in time, each new pair of the two receivers’frames formed by the next laser pulse gives a newfragment of the undisturbed image. The whole undis-turbed image can be obtained by accumulating aseries of such undistorted image fragments.
Our laboratory experiments on image transferthrough wavy air–water interfaces and image correc-tion are based on some features of both methods con-sidered above. Particularly we adopted Levin’s ideaof using glitter information and accumulation of aseries of instantaneous frames for image correction,and the idea of Dolin et al. of moving image pixels tothe “right” places, on the basis of glitter information.
4. Outline of the Experiment
Figure 5 sketches the experimental setup and proce-dure. The LMI was equipped with a color digital cam-era [(6) in Fig. 4], which simultaneously formsimages of the underwater test object (4) illuminatedfrom below by diffuse green light and of the glitterpattern on the surface illuminated by a wide area col-limated light beam from a source of red light (5). Thegreen and red spectral ranges were isolated by ap-propriate spectral filters in the two sources of light.Processing the glitter pattern made it possible to de-termine the surface slope values at the specularpoints within the surface area associated with imagedistortion. For each instantaneous image the slopeinformation was used to obtain a portion of the image
Fig. 3. Scheme of observation through a wavy water surface.N isthe normal to the surface at the point rs with the slope η, throughwhich the object point r1 is observed.
producing corrected image fragments. The totalcorrected image was formed by accumulating a setof these corrected fragments.We sequentially used two black and white striped
underwater test objects, one having strips of constantwidth as shown in the Fig. 5(a) and the other withstrips of varying width as shown in Fig. 6(a). The op-tical axis of the camera was directed at nadir throughthe center of the test object. Photographic exposurewas 1=400 s. Such exposure corresponds to thecondition of a “frozen” surface. For this exposure timeeach instantaneous photograph was a superpositionof a wave distorted image of the test object and of nor-mal surface glitter points. The camera height overthe water surface was about 0:5m. The size of testobjects was 16 cm × 16 cm.Since the fixed geometry of the experiment is
known, for each glitter point presented at the imagewe can find the value of the slope η in the point rs ofthe surface (see Fig. 3) from which the reflected glit-ter ray came to the camera lens.Using Snell’s refraction law at small angles, we can
find the object element r1 from which the ray 1 comesto the point of image r10 ¼ f j1⊥, where f is the lens
focal distance and j1⊥ is the horizontal componentof the unit vector j1 of the ray 1 (see Fig. 3) after re-fraction at the point of the surface with slope η. Forthe one-dimensional case depicted in Fig. 3 Snell’slaw gives the following equation:
j1⊥ ¼ r1 þ zηð1 − n−1ÞH þ z=n
; ð3Þ
from which the value of r1 may be found using knownvalues of j1⊥, z, η, n, and H. Next, the image elementof the point r02 was moved into the point r02 ¼ f j2⊥,where
j2⊥ ¼ r1H þ z=n
: ð4Þ
This point is the one where the element r1 would beprojected if viewed through a flat surface (see ray 2 inFig. 3). Note that strictly speaking each point of anobject in the image converts in the light circle causedby scattering in water. By the image point we meanthe circle center formed by unscattered light. For ourexperiment this effect can be ignored since the opti-cal depth of the water layer between the object andthe water surface was rather small.
This procedure is repeated for all glitter points ofan instantaneous photograph. As a result, the pro-cessing of a single instantaneous photograph pro-duces a sharply defined partial image. Repeat ofthis procedure for many photographs (about 300 inour experiments) and automatic accumulation ofall of 300 frames provides satisfactory reconstructionof image of an object. Note that a wavy surface can
Fig. 4. Scheme of the experiment: 1, water surface; 2, glass;3, diffuse light source; 4, test object; 5, source of the parallel lightbeam; 6, digital photo camera.
Fig. 5. Images of the test object with constant width of thestrips: original image (a), single instantaneous image (b), correctedimage (c).
Fig. 6. Images of a test object with varying width of the strips:original image (a), single instantaneous image (b), accumulatedimage without correction (c), corrected image (d).
cause many different rays from different points of theobject to fall on a single point of the image. To miti-gate this problem, our processing algorithm chooseselements with maximum intensity, while ignoringthe rest. This procedure provides the homogeneityof the object stripes.The image of the test object took 4% of the whole
frame (about 200,000 pixels), the averaged number ofglitter points falling on the instantaneous imageof the object was about 1200 pixels (around 0.6% ofimage of object). In the reconstructed image about10% of the image area in Fig. 5(b) and about 35%in Fig. 6(b) no input data were obtained, while about600 pixels (50% of the both images of object) obtainedmore than one input.
5. Results
Experimental results are presented in Figs. 5 and 6.Figures 5(a) and 6(a) show the images obtainedthrough flat water surfaces of the two test objectsused. Figures 5(b) and 6(b) present examples ofthe instantaneous images of the objects distortedby wavy water surfaces. Figures 5(c) and 6(d) showthe images corrected in accordance with the proce-dure described above. The image given in Fig. 6(c)was obtained as a result of accumulating instanta-neous images without processing. The image is thephoto of the test object shown in Fig. 6(a) done witha long exposure time of 5 s. Note that this image sum-marizes many (about 1000) different random frames,one of which is shown in Fig. 6(b). Note also that theradiance distribution in this imagemay be calculatedfrom the radiance distribution in the undistorted im-age of Figs. 6(a) by use of MTFs expressed by Eq. (1).One can see that corrected images are quite close
to the initial undistorted ones. It is clear also thataccumulation without correction (Fig. 6(c)) gives apoorer image quality than with correction especiallyfor smaller widths of the object strips.
6. Summary
Measurement results obtained using the laboratory-modeling installation (LMI), including corrections ofwavy surface distorted images, cannot be directly ap-plied to imaging through a real wavy sea surface.This is because it is impossible to control and makewaves in the laboratory like real sea waves. Never-theless, the laboratory experiments make it possibleto obtain insight into some real world wave problems.Laboratory generated waves can have stationarityand homogeneity not present in natural sea waves,
while illumination and observation conditions andwater properties can be controlled in a mannerhardly possible in at-sea experiments. Our experi-ment is to our knowledge the first to demonstrate,in principle, the possibility of correcting wave-induced distortion in an image of an underwaterobject. It also hints at planning in situ at-seaexperiments.
The results of this experiment were presentedat the International Conference “Current Problemsin Optics of Natural Waters” (ONW’2007) at theInstitute of Applied Physics RAS (Nizhniy Novgorod,Russia, 2007) [10]. We are grateful to Gary Gilbertfor many helpful comments and the generous editingof this manuscript. This work was supported by Of-fice of Naval Research (ONR) grant N000140610741through United States Civilian Research and Devel-opment Foundation Project RU61-1619-NN-06 andthe Russian Foundation for Basic Research, project07-05-00099.
References1. L. Dolin, G. Gilbert, I. Levin, and A. Luchinin, Theory of Ima-
ging through Wavy Sea Surface (Institute of Applied PhysicsRAS, 2006).
2. Yu.-A. R. Mullamaa, “Effect of wavy sea surface on thevisibility of underwater objects,” Izv. Atmos. Ocean. Phys.11, 199–205 (1975).
3. L. S. Dolin and I. M. Levin, Spravochnik po Teorii PodvodnogoVideniya. (Handbook of the Theory of Underwater Vision)(Gidrometeoizdat, 1991) (in Russian).
4. L. S. Dolin, A. G. Luchinin, and D. G. Turlaev, “Algorithm ofrecovering underwater object images distorted by surfacewaving,” Izv. Atmos. Ocean. Phys. 40, 842–850 (2004).
5. A. G. Luchinin, L. S. Dolin, and D. G. Turlaev, “Correction ofimages of submerged objects on the basis of incomplete infor-mation about surface roughness,” Izv. Atmos. Ocean. Phys. 41,272–277 (2005).
6. L. S. Dolin, A. G. Luchinin, V. I. Titov, and D. G. Turlaev, “Cor-recting images of underwater objects distorted by sea surfaceroughness,” Proc. SPIE 6615, 66150K (2007).
7. V. Weber, “Observation of underwater object through glitterpart of the sea surface,” Izv. Vyssh. Uchebn. Zaved., Radiofiz.48, 38–52 (2005).
8. C. Cox and W. Munk, “Measurements of the roughness of thesea surface from photographs of the sun glitter,” J. Opt. Soc.Am. 44, 838–850 (1954).
9. R. E. Walker, Marine Light Field Statistics (Wiley, 1994)10. V. Ju. Osadchy, V. V. Savchenko, I. M. Levin, O. N. Frantsuzov,
and N. N. Rybalka, “Correction of image distorted by wavywater surface,” in Proceedings of the International Conference“Current Problems in Optics of Natural Waters” (ONW’2007)(Institute of Applied Physics, 2007), pp. 91–93.
