Amplitude-modulated laser imager - OSA Publishing

Amplitude-modulated laser imager Linda Mullen, Alan Laux, Brian Concannon, Eleonora P. Zege, Iosif L. Katsev, and Alexander S. Prikhach

Laser systems have been developed to image underwater objects. However, the performance of these systems can be severely degraded in turbid water. We have developed a technique using modulated light to improve underwater detection and imaging. A program, Modulated Vision System 共MVS兲, which is based on a new theoretical approach, has been developed to predict modulated laser imaging performance. Experiments have been conducted in a controlled laboratory environment to test the accuracy of the theory as a function of system and environmental parameters. Results show a strong correlation between experiment and theory and indicate that the MVS program can be used to predict future system performance. © 2004 Optical Society of America OCIS codes: 010.4450, 120.4820, 280.3420, 010.3310, 010.3640, 290.7050.

1. Introduction

Laser systems have been and are continuing to be developed to detect and identify objects in turbid media 共seawater, clouds, tissue兲. Operating a laser imaging system in such an environment is challenging because light is both absorbed and scattered. Although the optical wavelength is typically selected to minimize absorption, the scattering experienced by an optical signal can severely degrade image quality. In highly turbid media, there may be plenty of light scattered back from the object of interest, but it is buried in the signal returning from the surrounding environment. A method for separating the unscattered 共or minimally scattered兲 image bearing photons from the multiply scattered background light can be used to improve object detection and identification. The focus of this paper is to explore techniques to improve the sensitivity of underwater imaging systems. Several techniques have been developed to reduce the detrimental effects of scattered light. These approaches can be categorized according to the type of L. Mullen 共[email protected]兲, A. Laux, and B. Concannon are with the Electro-Optics and Special Mission Sensors Division, Naval Air Warfare Center, Naval Air Systems Command, 22347 Cedar Point Road, Patuxent River, Maryland 20670-1161. E. P. Zege, I. L. Katsev, and A. S. Prikhach are with the Institute of Physics, Belarus Academy of Sciences, Scaryna Avenue 68, Minsk 220072, Belarus. Received 30 September 2003; revised manuscript received 11 March 2004; accepted 5 April 2004. 0003-6935兾04兾193874-19$15.00兾0 © 2004 Optical Society of America 3874

APPLIED OPTICS 兾 Vol. 43, No. 19 兾 1 July 2004

laser source and receiver combination and the scanning method used to create the image. All systems are capable of creating an image, whether it is a synchronously scanned narrow beam and narrow receiver field of view 共narrow–narrow兲 or a floodilluminated scene with a multiple-pixel receiver 共wide–narrow兲. The decision as to which configuration provides the best performance depends directly on the task at hand 共i.e., above-water or below-water operation, size and depth of underwater object, water optical properties兲. The Laser Line Scan system consists of a wellcollimated continuous-wave source and a narrowfield-of-view receiver that are synchronously scanned over the object of interest.1 The bistatic configuration limits the common volume created by the source and receiver field-of-view overlap and reduces the contribution from scattered light. However, because the system uses a continuous-wave source, no inherent time 共depth兲 information is present in the detected signal, and postprocessing with triangulation methods must be used to obtain target range information. Pulsed laser sources are also used in several underwater laser imaging systems to temporally discriminate against scattered light and to provide target range information. In the operation of a typical range-gated imaging system, a short 共10 –20 ns兲 pulse is transmitted to a distant object, and the receiver is timed to open only when the reflected light returns from the object. A typical configuration is broad-beam illumination of the scene and a gated intensified camera receiver,2 although systems that use photomultiplier tube receivers in both single- and

multiple-pixel configurations have also been demonstrated. The Streak Tube Imaging Lidar uses a pulsed laser transmitter in a scannerless configuration.3 Instead of scanning the laser beam, a fan of light is used to illuminate a volume of water. The streak tube receiver can measure both the amplitude and the range 共time兲 of the collected slit of light, and a three-dimensional image is created when the system is operated from a moving platform. Although the range-gated and Streak Tube Imaging Lidar approaches are effective to minimize background light, the sensitivity is ultimately limited by small-angle forward-scattered light that induces image blurring. A final category of underwater imagers encompasses those that use temporal modulation of the transmitted light and subsequent synchronous detection of the modulation envelope at the receiver. The underwater scannerless range imager uses a radiofrequency modulation source that is coupled to both the timing of the laser transmitter and the gain of the image-intensified CCD receiver.4 Target range information is obtained by measurement of the phase difference between the transmitted and the reflected signals simultaneously for each pixel of the receiver. However, multiple frames are required by use of different modulation schemes to extract the range information and to differentiate changes due to range variations from those due to intensity variations in the scene. Previous configurations used continuouswave sources, but a recent configuration implements a pulsed source and a range-gated receiver to minimize the volumetric backscatter signal.5 Researchers at the Naval Air Systems Command are also developing a system that uses temporal modulation of the transmitted optical signal.6 However, in this approach, the optical receiver consists of a photodetector with sufficient bandwidth to recover the modulation envelope encoded on the optical signal. The resulting radio-frequency signal is then processed by traditional radar signal processing techniques. This approach reduces the contribution by volumetric backscatter by use of a modulation frequency that becomes strongly decorrelated with respect to the transmitted signal because of multiple scattering. A gain in image contrast is achieved when the modulation envelope emanating from an underwater object remains coherent relative to the original modulation signal. The phase information encoded on the detected modulation signal is processed to obtain target range information. This amplitude-modulated imaging approach has been applied to a pulsed laser configuration.7 However, the current focus is to study the application to a continuous-wave synchronous scan configuration because of the availability of off-the-shelf components.8 Although not compatible with realistic scan rates, the current configuration has enabled us to test the effect of modulation frequency on the volumetric backscatter and target signals and the resulting image contrast. Preliminary experiments were conducted in both in situ and laboratory tank environments. In both

cases, interesting features were observed in the data collected in relatively turbid water 共beam attenuation coefficient ⬎1兾m兲 and at short ranges 共2–3 m兲. A model was developed concurrently with the experiments and was incorporated into a program, Modulated Vision System 共MVS兲, to investigate the application of this approach to other system configurations and to understand the underlying physics involved with modulated light beam propagation through water. The MVS program was also used to investigate the origin of the interesting but unexpected experimental results. Our purpose in this paper is to briefly describe the theory that was developed to simulate amplitude-modulated imaging performance and to illustrate its utility in interpreting experimental measurements. Comparisons of experimental and simulated data are shown to demonstrate the accuracy of the theory and its ability to predict future amplitude-modulated system performance. 2. Theoretical Approach

The challenge in the development of an accurate theoretical model for modulated light beam propagation is that it is intimately related 共through Fourier transform兲 to short-pulse propagation, which requires a solution of the nonstationary radiative transfer equation. The characteristic parameter of the nonstationary light field is the mean photon residence in the medium, or the mean free time between two scattering events, t ⫽ 1兾c␯, where c is the extinction 共or beam attenuation兲 coefficient and ␯ is the velocity of light in water. If the changes in light source intensity 共i.e., pulse width or modulation wavelength兲 occur in time scales that are much longer than this mean photon residence time, the optical field essentially follows the source power fluctuations and is said to be quasi-stationary. However, if the pulse width or modulation wavelength are on the order of or smaller than this characteristic time, then the light field is essentially nonstationary and must be calculated by means of solving the nonstationary radiative transfer equation. Fortunately, we have developed techniques that help simplify the problem so that a semianalytical solution can be found. In Subsection 2.A the approximations and assumptions that were used to derive this solution are discussed. The basic equations that describe the modulated laser imaging system are then described. Finally, the features of the MVS program that incorporate this theory to predict modulated laser imaging system performance are discussed. A.

Approximations

Multiple scattering in ocean water contributes significantly to both the backscatter and the object signals. Including the effects of multiple scattering is the main challenge when we compute backscattered radiation. Therefore a technique was used that essentially simplifies the estimations of the backscatter signal. This approach includes the effect of multiple scattering in both the object signal and the backscat1 July 2004 兾 Vol. 43, No. 19 兾 APPLIED OPTICS

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ter signal components and the effect of almost all the features of the scattering phase function of water. The one assumption that is made regarding the scattering phase function of water is that it has a sharp peak in the small forward angles, which is characteristic of typical ocean water. It is also assumed that multiple scattering occurs in small angles, and only single scattering into large angles is used to compute the radiance distribution.9 Other approximations used in the theory include the multicomponent approach10 and the small–angle diffusion approximation.11 The multicomponent approach focuses on simplifying the complex nature of the scattering phase function p共␤兲 so that the radiative transfer equation can be broken into smaller, more simple equations that are easier to solve. The small-angle diffusion approximation can be used with the assumption that the phase function is strongly forward peaked and has a sharp maximum at 0 deg and that the angular radiance distribution is described by smooth functions and is not closely correlated with the phase function 共e.g., there are enough scattering events so that the radiance distribution does not follow the phase function兲. The combination of these two approaches provides the transfer characteristics of the scattering medium that include the optical transfer function and the point-spread function. A new model of the point-spread function, which includes the inherent point-spread function singularity at the beam axis, was also developed and employed in the theory.12 In the current version, the temporal stretching of the forward-propagating optical signal is not included. B.

optical signals. The component Pb共r兲 consists of two parts: P b共r, t兲 ⫽ P BSN共r, t兲 ⫹ P bot共r, t兲,

(5)

P BSN共r, t兲 ⫽ P BSN共r兲exp兵i关2␲ft ⫺ ␸ BSN共r兲兴其,

(6)

where

P bot共r, t兲 ⫽ P bot共r兲exp兵i关2␲ft ⫺ ␸ bot共r兲兴其

are the optical powers due to the volumetric backscatter signal and to the diffuse reflection by the sea bottom, respectively. As can be seen from Eq. 共2兲, the power of a valid signal, PVS共r, t兲, is the difference between the total power at the receiver input when an object is present, P共r, t兲, and the power of the background signal that exists when no object is present, Pb共r, t兲. With allowance for the object reflection and a shadow behind the object, we obtain P VS共r, t兲 ⫽ P ob共r, t兲 ⫺ P sh共r, t兲.

P共r兲 ⫽ 兩 P b共r, t兲 ⫹ P VS共r, t兲兩

冋

1 2 ⫽ P b共r兲 1 ⫹ 2 ⫹ cos ␸共r兲 ␩ 共r兲 ␩共r兲

In the modulated laser imaging system, the source power P共t兲 can be described by the following equation: (1)

where f is a specific modulation frequency and t is time. At the receiver end, a high-speed optical detector and a microwave receiver record and process the signal with frequency f for the frame recording time tfr. If there are no objects in the volume intersected by the transmitted beam and receiver field of view, the power of an optical signal at the modulation frequency f at the input of the receiver with the axis directed to any point r at the object plane z ⫽ 0 is the power Pb共r, t兲 of the background. When an object is present, the total signal power at the input of the receiver is P共r, t兲 ⫽ P VS共r, t兲 ⫹ P b共r, t兲,

(2)

(8)

Here Pob共r, t兲 is the signal power reflected by the object. The object partially shields the water layer between it and the bottom. This shielding changes the valid signal and is included by the term Psh共r, t兲 in Eq. 共8兲. It is necessary to stress that the sum of all components of P共r, t兲 at the modulation frequency f includes contributions of both the amplitude and the phase of the background and object signal components. The power of the total signal is

Basic Equations

P共t兲 ⫽ P 0关1 ⫹ exp共i2␲ft兲兴,

(7)

册

1兾2

,

(9)

where ␩共r兲 ⫽ P b共r兲兾P VS共r兲,

(10)

␸共r兲 ⫽ ␸ b共r兲 ⫺ ␸ VS共r兲.

(11)

If Pbot共r兲 ⬍⬍ PBSN共r兲, we have Pb共r兲 ⬇ PBSN共r兲 and correspondingly ␩共r兲 ⬇ PBSN共r兲兾PVS共r兲, ␸共r兲 ⫽ ␸BSN共r兲 ⫺ ␸VS共r兲. This is the case when the water is turbid or the bottom depth is large so that the backscatter signal dominates the background signal. It is this case that we examine further in Sections 3 and 4 to study particular features of images produced by modulated laser systems. C.

Modulated Vision System Software

P b共r, t兲 ⫽ P b共r兲exp兵i关2␲ft ⫺ ␸ b共r兲兴其,

(3)

P VS共r, t兲 ⫽ P VS共r兲exp兵i关2␲ft ⫺ ␸ VS共r兲兴其,

(4)

The theoretical approach described above provides the backbone for the MVS program, which simulates the performance of underwater, modulated laser imaging systems. This software runs under Windows and has an interactive, user-friendly interface. The inputs to the MVS program include

where Pb共r兲, PVS共r兲 and ␸b共r兲, ␸VS共r兲 are the amplitudes and phase shifts, respectively, of the modulated

1. system configuration 共modulated or nonmodulated, focal-plane array, or synchronous scan兲,

where PVS共r, t兲 is the power of the valid signal due to the underwater object. Here

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2. system geometry 共source–receiver separation, receiver– object distance, object– bottom distance兲, 3. source parameters 共optical power, wavelength, aperture size, divergence, modulation frequency兲, 4. receiver parameters 共aperture, field of view, optical transmission, detector quantum efficiency, number of pixels兲, 5. target characteristics 共size, shape, reflectivity兲, and 6. water characteristics 共beam attenuation coefficient, single-scattering albedo, scattering phase function兲. With these inputs, the program simulates images observed by a modulated or a nonmodulated laser imaging system, including the amplitude and phase signals from both backscatter and targets. Additional program outputs include plots of the frequency dependencies of the total signal, backscatter noise, and image contrast that are useful to understand the effect of modulation frequency on system performance. Results from the MVS program are used in Section 3 to illustrate interesting features of images produced by a modulated laser imaging system. 3. Features of Modulated Vision System Images

In the past, it was observed in both experimental and computer simulation results that under certain conditions maxima and minima were observed in the dependence of signal power on the modulation frequency.8 An explanation for these results was that the reflection of the modulated optical signal from the target interacted with the backscatter signal to produce both constructive and destructive interference of the modulation envelope at the receiver. To understand and explain these interference effects and their influence on the images created by a modulated laser imaging system, two main factors must be considered: 1. dependencies of the backscatter noise phase and amplitude ␸BSN共z, f 兲 and PBSN共z, f 兲 and the valid signal phase and amplitude ␸VS共z, f 兲 and PVS共z, f 兲 on the target depth z and the modulation frequency f for a fixed water clarity 共beam attenuation coefficient c兲; and 2. dependencies of ␸BSN共r兲, PBSN共r兲, PVS共r兲, and ␸VS共r兲 on the coordinate r at the image plane. Plots of the dependencies of ␸BSN共z, f 兲 and ␸VS共z, f 兲 on modulation frequency and depth for a fixed c ⫽ 2.2兾m are shown in Figs. 1共a兲 and 1共b兲, respectively. The data for these graphs were obtained with the MVS program, and we used the values in Table 1 as inputs. In Fig. 1共a兲 the depth was fixed at z ⫽ 2.74 m, and in Fig. 1共b兲 the modulation frequency was set to f ⫽ 33 MHz. It is evident from Fig. 1 that the function ␸VS共z, f 兲 shows much stronger dependencies both on the depth and on the modulation frequency than the function ␸BSN共z, f 兲. Also shown in Fig. 1 is the dependency of ␸BSN共z, f 兲 and ␸VS共z, f 兲 on the beam attenuation coefficient c for z ⫽ 2.74 m and f ⫽

Fig. 1. 共a兲 Dependency of ␸BSN共z, f 兲 and ␸VS共z, f 兲 on modulation frequency for z ⫽ 2.74 m and c ⫽ 2.2兾m. 共b兲 Dependency of ␸BSN共z, f 兲 and ␸VS共z, f 兲 on depth for f ⫽ 33 MHz and c ⫽ 2.2兾m. 共c兲 Dependency of ␸BSN共z, f 兲 and ␸VS共z, f 兲 on the beam attenuation coefficient for z ⫽ 2.74 m and f ⫽ 33 MHz.

33 MHz 关Fig. 1共c兲兴. It is evident that ␸VS共z, f 兲 is constant whereas ␸BSN共z, f 兲 changes only slightly with increasing c. The plots of PBSN共z, f 兲 and PVS共z, f 兲 corresponding to the phase data in Fig. 1 are shown in Fig. 2. It is evident that PVS共z, f 兲 has a stronger dependency on depth and water clarity than PBSN共z, f 兲. However, PVS共z, f 兲 is constant whereas PBSN共z, f 兲 decreases as a function of modulation frequency. This is due to the fact that, as the modulation frequency increases, the backscatter signal becomes 1 July 2004 兾 Vol. 43, No. 19 兾 APPLIED OPTICS

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Table 1. System Configurationa and Environmental Parameters Used as Inputs to the MVS Program to Produce the Results Shown in Figs. 1–11

Parameter System geometry Source–receiver separation Receiver–object distance Source parameters Wavelength Power Aperture size Divergence Modulation frequency Receiver parameters Aperture 共diameter兲 Field of view Target characteristics Size 共diameter of white兲 Reflectivity 共white兾black兲 Water characteristics Beam attenuation coefficient Single-scattering albedo Phase function

Measurement 0.289 m 2.74, 3.5 532 nm 5W 0.01 m 0.3 deg 10–100 MHz 0.0508 m 1.0°, full angle 0.1 m 0.8兾0.01 2.2, 2.6兾m 0.85 Maaloxb

a Modulated and nonmodulated, synchronous scan, continuous wave. b Ref. 13.

decorrelated relative to the transmitted signal because of multiple scattering. The effect of ␸BSN共z, f 兲, PBSN共z, f 兲, ␸VS共z, f 兲, and PVS共z, f 兲 on the total power received by the modulated system is now examined in more detail. A.

Constructive and Destructive Interference

The total power P共z, f 兲 received from an underwater target at r ⫽ 0 corresponding to the data shown in Figs. 1共a兲 and 2共a兲 is plotted in Fig. 3共a兲 as a function of modulation frequency. In Fig. 3共a兲 it is evident that P共z, f 兲 is not a smooth function of modulation frequency, but rather it has a certain periodic dependency with several extrema. Because it has already been determined that both PVS共z, f 兲 and PBSN共z, f 兲 are relatively linear functions of modulation frequency 关see Fig. 2共a兲兴, the fluctuations observed in Fig. 3共a兲 must be due to the interaction between these two signal components. It is well known that electromagnetic waves that are overlapped in the same region of space can either reinforce 共constructive interference兲 or cancel each other 共destructive interference兲.14 The condition for constructive interference is that the two waves are in phase 共0-deg phase difference兲 or that the phase difference between the two waves is a multiple of 360 deg. Destructive interference will occur for waves that are opposite in phase 共180-deg phase difference兲 or have phase differences equal to an odd multiple of 180 deg. The phase difference between the backscatter noise and valid signals ␸ ⫽ ␸BSN共z, f 兲 ⫺ ␸VS共z, f 兲 corresponding to the data in Fig. 3共a兲 is shown in Fig. 3共b兲 to illustrate this point. Also plotted in Fig. 3共b兲 is the amplitude ratio between the backscatter and the valid signals ␩ ⫽ PBSN共z, f 兲兾PVS共z, f 兲. At the frequency correspond3878


Fig. 2. 共a兲–共c兲 PBSN共z, f 兲 and PVS共z, f 兲 corresponding to the phase data in Fig. 1.

ing to ␸ ⫽ 180 deg 共 f ⫽ 33 MHz兲, the total power P共z, f 兲 reaches a minimum value because of destructive interference between the backscatter and the valid signal components. The effect of constructive interference is also evident in the plot of P共z, f 兲 where the power reaches a maximum at the frequency corresponding to ␸ ⫽ 360 deg 共 f ⫽ 62 MHz兲. Although a second minimum is observed at the frequency corresponding to ␸ ⫽ 540 deg 共 f ⫽ 88 MHz兲, it is less pronounced than the minimum occurring at ␸ ⫽ 180 because the ratio between the two waves, ␩, decreases from ␩ ⫽ 0.6 to 0.2. The effects of destructive interference are the most prominent when the

Fig. 3. 共a兲 Total power P共z, f 兲 as a function of modulation frequency for the data in Fig. 1共a兲 and 2共a兲. The power was normalized relative to the power at f ⫽ 10 MHz. The dashed lines indicate the frequencies at which destructive and constructive interference occurs. 共b兲 ␸ ⫽ ␸BSN共z, f 兲 ⫺ ␸VS共z, f 兲共left axis兲 and ␩ ⫽ PBSN共z, f 兲兾PVS共z, f 兲共right axis兲 as a function of modulation frequency calculated from the data in Figs. 1共a兲 and 2共a兲. The dashed lines indicate the frequencies at which destructive and constructive interference occurs.

two waves are close in amplitude because complete cancellation occurs when ␩ ⫽ 1. The effect of object depth on P共z, f 兲, ␸, and ␩ is shown in Fig. 4 where the data from Fig. 3 are plotted along with the data corresponding to an increased object depth of z ⫽ 3.25 m. Because the effect of the increased depth is to change the phase and amplitude relationships between the backscatter and the valid signals 关as shown in Fig. 4共b兲兴, the frequencies at which constructive and destructive interference are observed change as well as the relative signal amplitude. The effect of a change in water clarity c on P共 z, f 兲 is shown in Fig. 5. Here it is evident that with an increase in c the locations of the extrema change only slightly, but the signal level decreases relative to the signal for c ⫽ 2.2兾m. This is due to the fact that an increase in c produces only a slight change in the relative phase between the backscatter and the valid signals but results in an increase in the ratio between the backscatter and the valid signal amplitudes 关as shown in Fig. 5共b兲兴. Furthermore, the destructive interference at f ⫽ 88 MHz is enhanced because of the

Fig. 4. 共a兲 and 共b兲 Data from Figs. 3共a兲 and 3共b兲 plotted along with the data corresponding to an increased object depth of z ⫽ 3.25 m.

fact that at this frequency the backscatter and valid signal amplitudes are approximately equal 共␩ ⬇ 1兲, and almost complete cancellation occurs. To summarize, the relative phase between the backscatter and the valid signals ␸ determines the frequency at which constructive and destructive interference occurs, whereas the amplitude ratio between the two signals ␩ affects the overall magnitude of P共z, f 兲. The effect of these dependencies on both the target contrast and the images produced by the modulated laser imaging system is discussed in Subsections 3.B and 3.C. B.

Target Contrast

A figure of merit used to quantify the effect of the backscatter and the valid signals on the system sensitivity is the contrast of the target at the target center 共at r ⫽ 0兲: k共 z, f 兲 ⫽

P共 z, f 兲 ⫺ P BSN共 z, f 兲 , P共 z, f 兲 ⫹ P BSN共 z, f 兲

(12)

where P共z, f 兲 and PBSN共z, f 兲 are the powers of the total signal and the backscatter signal at the center of the target at depth z and modulation frequency f, respectively. Plots of k共z, f 兲 for the data shown in Figs. 1 and 2 are shown in Fig. 6. From this graph it is apparent that the plots of k共 z, f 兲 as a function of modulation frequency exhibit similar characteristics 1 July 2004 兾 Vol. 43, No. 19 兾 APPLIED OPTICS

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Fig. 6. Contrast k共z, f 兲 as a function of modulation frequency for the data in Figs. 3–5.

kconstr grows with decreasing depth, increasing modulation frequency or decreasing beam attenuation. This is shown in Fig. 6 where kconstr increases with decreasing depth and decreasing beam attenuation. 2. Case 2: ␸ ⫽ ␸BSN共z, f 兲 ⫺ ␸VS共z, f 兲 ⫽ ␲ When the two signals are opposite in phase 共odd multiples of 180 deg兲, destructive interference occurs. Two situations are possible in this case: 1. When 兩PBSN兩 ⬍ 兩PVS兩共i.e., ␩ ⬍ 1兲, the contrast corresponding to destructive interference becomes Fig. 5. 共a兲 and 共b兲 Data from Figs. 3共a兲 and 3共b兲 plotted along with the data corresponding to an increased beam attenuation coefficient of c ⫽ 2.6兾m.

to the plots of P共z, f 兲 in Figs. 3–5. In certain cases, destructive interference between the backscatter and the valid signals produces negative contrast, whereas constructive interference between these two signal components results in improved contrast relative to the contrast at f ⫽ 10 MHz. To better understand the effect of the relationships between the relative phase ␸ ⫽ ␸BSN共z, f 兲 ⫺ ␸VS共z, f 兲 and the amplitude ratio ␩ ⫽ PBSN共z, f 兲兾PVS共z, f 兲 on the target contrast k共z, f 兲, the two extreme points, where the phase shift between the backscatter and the valid signals is equal to ␸ ⫽ 0 or ␸ ⫽ ␲, is now examined in more detail. 1. Case 1: ␸ ⫽ ␸BSN共z, f 兲 ⫺ ␸VS共z, f 兲 ⫽ 0 When the phases of the backscatter and valid signals are equal 共or a multiple of 360 deg兲, constructive interference occurs: k constr ⫽

兩 P VS兩 1 ⫽ , 兩 P VS兩 ⫹ 2兩 P BSN兩 1 ⫹ 2␩

(13)

(14)

In this case, the contrast is positive 共kconstr ⬎ 0兲 for any ␩. The value of ␩ decreases and the contrast 3880


兩 P VS兩 ⫺ 2兩 P BSN兩 ⫽ 1 ⫺ 2␩. 兩 P VS兩

(15)

Equation 共15兲 shows that the contrast kdestr ⬎ 0 at ␩ ⬍ 0.5, which would occur at shallow depths or clear water when the valid signal is large or for high modulation frequencies when the backscatter signal is strongly decorrelated. The negative contrast kdestr ⬍ 0 is produced when ␩ ⬎ 0.5, which requires comparatively large depths, more turbid water, or low modulation frequencies. For example, for the data corresponding to c ⫽ 2.2兾m and z ⫽ 2.74 m in Figs. 3 and 6, kdestr ⬎ 0 at f ⫽ 88 MHz when ␩ ⫽ 0.19, whereas kdestr ⬍ 0 at f ⫽ 33 MHz when ␩ ⫽ 0.67. 2. When 兩PBSN兩 ⬎ 兩PVS兩共i.e., ␩ ⬎ 1兲, the contrast corresponding to destructive interference is k destr ⫽

兩 P VS兩 1 ⫽⫺ . 2兩 P BSN兩 ⫺ 兩 P VS兩 2␩ ⫺ 1

(16)

In this case, the contrast kdestr is negative for any ␩ ⬎ 1. This is the case in Figs. 4 and 6 for z ⫽ 3.25 m: kdestr ⬍ 0 when ␩ ⫽ 4.9 and kdestr ⬎ 0 for ␩ ⫽ 1.8. In summary, when ␸ ⫽ ␸BSN共z, f 兲 ⫺ ␸VS共z, f 兲 ⫽ ␲, k destr ⬎ 0 at ␩ ⬍ 0.5, k destr ⬍ 0 at ␩ ⬎ 0.5.

where 兩 P BSN兩 ␩⫽ . 兩 P VS兩

k destr ⫽

(17)

In Fig. 7 the value of kdestr is plotted as a function of ␩. When the target dominates the signal, the contrast kdestr is high and positive. This situation would occur for shallow target depths or for high modulation frequencies when the backscatter is strongly decorrelated. However, as the backscatter

Fig. 7. Plot of kdestr as a function of ␩ ⫽ PBSN共z, f 兲兾PVS共z, f 兲.

and target signals approach one another because of decreasing water clarity, increasing depth, or for low modulation frequencies, the contrast becomes negative and approaches a minimum when ␩ ⫽ 1. As ␩ grows because of larger target depths, the contrast approaches zero but remains negative. C.

Object Images

The effect of these variances in target contrast on the images produced by the modulated laser system can be better understood when we study the dependence of the backscatter and valid signals on the spatial coordinate r in the target plane. Within the smallangle approximation, the phases of the backscatter and valid signals are independent of the spatial coordinate r: ␸VS共r兲 ⫽ const and ␸BSN共r兲 ⬇ const. This is the case for a synchronous scan configuration where the receiver field of view is narrow or the target takes up a significant portion of the receiver field of view at the object plane. Therefore, within this assumption, the difference in phases between the backscatter and the valid signals is ␸共r兲 ⫽ ␸ BSN共r兲 ⫺ ␸ VS共r兲 ⬇ const.

(18)

Again, two extremes must be considered: ␸共r兲 ⫽ 0 and ␸共r兲 ⫽ ␲. The modulation frequencies that correspond to the phase difference ␸共r兲 ⫽ 0 when k ⫽ kconstr and the phase difference ␸共r兲 ⫽ ␲ when k ⫽ kdestr can be found when we plot the contrast as a function of modulation frequency 共as shown in Fig. 6兲. The MVS program can then be used to illustrate the effect of these interference effects on the object image. For example, the images corresponding to the data shown in Fig. 3 are shown in Fig. 8. Also shown in Fig. 8 are the normalized energy distribution and the ratio of backscatter to valid signal energy ␩ as a function of pixel number 共spatial position r兲. Here the water-free and continuous-wave images are shown for reference, and the constructive and destructive images are those we obtained by using the modulation frequencies corresponding to kconstr and kdestr in Fig. 6, respectively. The constructive image shows an improved contrast between the white circular object and the black background relative to the continuous-wave image. The destructive image shows a dark ring around the white object and a

corresponding dip in the energy distribution at the transition between the object and the background. Also, the contrast between the object center 共which is dominated by the white object reflectivity兲 and the black background 共which is dominated by backscatter noise兲 is negative. From the plot of ␩ as a function of pixel number in Fig. 8, it is evident that 0.5 ⬍ ␩ ⬍ 1 in the center of the target at r ⫽ 0. The fact that ␩ ⬎ 0.5 explains the negative contrast between the white object and the black background because we found that kdestr ⬍ 0 for ␩ ⬎ 0.5 共see Fig. 6兲. As the distance increases from the target center, the valid signal begins to decrease and ␩共r ⬎ 0兲 increases. As the valid signal level approaches the backscatter signal level, ␩共r ⬎ 0兲 approaches a value of ␩共r ⬎ 0兲 ⫽ 1 that produces the dark ring in the object image. For increasing r past the boundary of the white object, ␩共r ⬎ 0兲 ⬎ 1 and the backscatter signal begins to dominate the image. To study the effect of the value of ␩共r ⫽ 0兲 on the resulting destructive images, the albedo of the white target in Fig. 8 was varied while all other parameters remained unchanged. The results are shown in Fig. 9 where the destructive images and the corresponding normalized energy distributions and ␩共r兲 are shown for target albedos ranging from 1 to 0.4. As the albedo decreases, the valid signal also decreases and ␩共r ⫽ 0兲 increases. However, only when ␩共r ⫽ 0兲 ⬍ 1 does the dip in the energy distribution occur somewhere in the vicinity of the white object boundary. These results show that, for destructive images where ␩共r ⫽ 0兲 ⬍ 1, the effect of a change in target albedo for r ⬎ 0 共i.e., change in reflectivity between the white object and the black background兲 is that a minimum in the received photon energy is observed when ␩ ⫽ 1. This explains the outline-emphasizing effect observed in some images produced by the modulated laser imaging system. Other factors that affect the value of ␩共r ⫽ 0兲 include the object depth and the water beam attenuation coefficient. The images produced for an increased object depth 共data in Fig. 4兲 along with the corresponding normalized energy distributions and ␩共r兲 are shown in Fig. 10. The data in Fig. 10 show that in this case ␩共r ⫽ 0兲 ⬎ 1 for the images produced with modulation frequencies corresponding to kdestr 共 f ⫽ 26 and 72 MHz兲. Therefore these images lack the dip in the energy distribution and corresponding dark ring in the object image at the target boundary. However, the contrast between the white target and the black background is negative because kdestr ⬍ 0 for ␩ ⬎ 0.5. A similar situation exists for the images obtained with an increased beam attenuation coefficient 共data from Fig. 5兲, which are shown in Fig. 11. Here, because ␩共r ⫽ 0兲 ⬎ 1 for f ⫽ 32 MHz, the corresponding image also lacks the outlineemphasizing features observed in Fig. 9. However, because ␩共r ⫽ 0兲 ⬍ 1 at f ⫽ 88 MHz, a slight discontinuity is observed in the normalized energy profile 1 July 2004 兾 Vol. 43, No. 19 兾 APPLIED OPTICS

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Fig. 8. Images corresponding to the data shown in Figs. 3 and 6. CW, continuous wave. The water-free 共WF兲 image is also shown for comparison. The graphs below the computer-generated images show the normalized energy 共black curve, left axis兲 and ␩ ⫽ PBSN共z, f 兲兾PVS共z, f 兲共gray curve, right axis兲 plotted as a function of position r.

when ␩ ⫽ 1. It is important to note that in Figs. 10 and 11 the constructive images have improved contrast between the white target and the black background relative to the continuous-wave images. We have shown that the interference between the backscatter and the valid signals produces interest3882


ing features in images produced by a modulated laser imaging system. These features can be explained when we examine the amplitude and phase relationship between the backscatter and the valid signals. The two extreme cases, when the relative phase between the two signals is equal to 0 or ␲, lead to the

Fig. 9. Effect of a change in target albedo on the object image. The albedo of the white portion of the target was varied while all other parameters remained the same as in Fig. 8.

most interesting results, including outline emphasizing of the target albedo patterns, contrast inversion, and contrast enhancement. These features are the most pronounced when the backscatter and valid signals are close in amplitude, which is the situation that typically results in poor image contrast in a tra-

ditional, unmodulated laser imaging system. In Section 4 an experimental setup is described that has been used to validate the MVS program predictions. Results are then shown that compare the experimental and theoretical data for a certain range of environmental and system parameters. 1 July 2004 兾 Vol. 43, No. 19 兾 APPLIED OPTICS

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Fig. 10. Images corresponding to the data shown in Figs. 4 and 6. CW, continuous wave.

4. Validation of Modulated Vision System Results

Controlled laboratory tank experiments were conducted to validate the MVS program results for a fixed set of system and environmental parameters. The experimental setup included a 5-W, 532-nm laser that was modulated by an external electro-optic modulator at frequencies from 10 to 100 MHz. The op3884


tical receiver was a photomultiplier tube with an S20 photocathode and a gain of approximately 40,000. A bias T was connected to the output of the photomultiplier tube so that both the dc current and the ac modulation could be measured separately. A network analyzer was used to drive the electro-optic modulator, to monitor the modulated signal power,

Fig. 11. Images corresponding to the data shown in Figs. 5 and 6. CW, continuous wave.

and to measure the difference in phase between the transmitted and the detected modulated optical signals. The Aqua Tunnel water tank facility at the Naval Air Systems Command was used for the laboratory measurements. The scattering properties of ocean water were simulated by the addition of Maalox antacid, and a WETLabs AC-9 instrument

was used to measure the optical properties of the water for each Maalox concentration. The scattering phase function of Maalox was measured independently and was also used as an input to the program.13 Other details of the experimental setup have been described elsewhere.8 A diagram of the experimental setup is shown in Fig. 12, and the val1 July 2004 兾 Vol. 43, No. 19 兾 APPLIED OPTICS

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Table 2. System Configurationa and Environmental Parameters Corresponding to the Experimental Setup Shown in Fig. 12 and Used as Inputs to the MVS Program

Parameter System geometry Source–receiver separation Receiver–object distance Source parameters Wavelength Power Aperture size Divergence Modulation frequency Receiver parameters Aperture 共diameter兲 Field of view Target characteristics Size 共diameter of white兲 Reflectivity 共white兾black兲 Water characteristics Beam attenuation coefficient Single-scattering albedo Phase function

Fig. 12. Diagram of the experimental setup used to validate the MVS simulation predictions.

ues of the experimental parameters used as inputs to the MVS program are listed in Table 2. In the experiment, the target shown in Fig. 12 was scanned across the plane of intersection of the source and receiver to obtain one slice of the target image 共represented by the large dotted line兲 at each modulation frequency. Because the MVS program has the capability to process a slice of the target image, the two data sets were compared directly. A.

Target Contrast

In the experiment we calculated the target contrast k共z, f 兲 by using Eq. 共12兲. The relative phase differences between the modulator drive signal and both the total signal and the backscatter signal were also measured. To calculate the phase difference between the backscatter and valid signals ␸ ⫽ ␸BSN共z, f 兲 ⫺ ␸VS共z, f 兲, the phase of the target in clear water 共i.e., no Maalox added to the tank water兲 at each depth was measured and subtracted from the recorded backscatter phase. The results are shown in Fig. 13 for three different water clarities, c ⫽ 1.2兾m, c ⫽ 2.1兾m, and c ⫽ 2.5兾m, at a target depth of 2.74 m. Also shown in Fig. 13 are the MVS program results we obtained by using the relevant experimental parameters as inputs. For the cleanest water 共c ⫽ 1.2兾 m兲, both the experiment and the model show high contrast that is relatively independent of modulation frequency. However, for c ⫽ 1.2兾m and c ⫽ 2.5兾m, the contrast shows evidence of constructive and destructive interference effects. The corresponding phase data in Fig. 13共b兲 show that the frequencies at which constructive and destructive interference is observed in the experimental and model data correlates with the conditions when ␸ ⫽ 180 and ␸ ⫽ 360, respectively. The agreement between the model and the experiment is quite good, especially at modulation frequencies exceeding 50 MHz. The effect of a change in target depth on the target contrast is shown in Fig. 14. Here the depth was 3886


Measurement 0.289 m 2.74, 1.83 m 532 nm 5W 0.01 m 0.3 deg 10–100 MHz 0.0508 m 1.0°, full angle 0.1 m 0.8兾0.01 1.2, 2.1, 2.5, 3.7兾m 0.85 Maaloxb

a Modulated and nonmodulated, synchronous scan, continuous wave. b Ref. 13.

decreased to z ⫽ 1.83 m, and the water clarity was increased to achieve a value of cz ⫽ 6.77 within the range of the data shown in Fig. 13. The data from Fig. 13 are also shown for reference. The effect of the decreased target depth was to change the slope of ␸共z, f 兲 as a function of modulation frequency, as expected. This slope change affected the frequencies at which constructive and destructive interference occurred. Both the amplitude 共contrast兲 and the phase data again show good agreement between the model and the experiment. B.

Images

As stated above, in the experiment we obtained image slices of the underwater target by scanning the target across the intersection of the laser and receiver field of view and measuring the total received power at each position and at each modulation frequency. The image slices produced by the MVS program were reduced in resolution to contain only those points measured by the experimental setup. The results corresponding to the data in Figs. 13 and 14 are shown in Figs. 15–18 where the constructive and destructive images are those obtained with a modulation frequency corresponding to ␸ ⫽ 360 and ␸ ⫽ 180, respectively. The fullresolution, two-dimensional images 共64 ⫻ 64 pixels兲 produced by the MVS program are also shown for reference, as is the continuous-wave 共no modulation兲 image. In the destructive image graphs, the value of the amplitude ratio between the backscatter and the valid signals ␩共r兲 ⫽ PBSN共r兲兾PVS共r兲 is also shown for reference. We obtained an estima-

Fig. 13. Model 共black curves兲 and experimental 共gray curves兲 results for the 共a兲 target contrast, k共z, f 兲 and 共b兲 phase difference between the backscatter and the valid signals ␸ ⫽ ␸BSN共z, f 兲 ⫺ ␸VS共z, f 兲 for three different water clarities.

Fig. 14. Data from Fig. 13 plotted along with the results obtained with a decreased target depth of z ⫽ 1.83 m and an increased beam attenuation of c ⫽ 3.7兾m 共model data results in black, experimental results in gray兲.

tion of ␩共r兲 for the experimental data by solving Eq. 共9兲 for ␩: ␩共r兲 ⫽ 关1 ⫺ ␰共r兲兴 ⫺1,

P BSN共r兲 ⬎ P VS共r兲

␩共r兲 ⫽ 关1 ⫹ ␰共r兲兴 ⫺1,

P VS共r兲 ⬎ P BSN共r兲 ,

(19)

where ␰共r兲 is the ratio between the total power and the backscatter noise power at the modulation frequency corresponding to ␸ ⫽ 180. The images obtained with c ⫽ 1.2兾m and z ⫽ 2.74 m 共Fig. 15兲 show high contrast between the black and the white portions of the target for all three cases 共continuous wave, constructive, and destructive兲. The plot of ␩共r兲 for the destructive data shows that 0 ⬍ ␩共r兲 ⬍ 0.5, which explains the positive destructive image contrast because kdestr ⬎ 0 for ␩ ⬍ 0.5. However, for the data shown in Fig. 16 corresponding to an increased beam attenuation of c ⫽ 2.1兾m, the effects of constructive and destructive interference are observed. The constructive image shows improved contrast relative to the continuous-wave image. The destructive image shows the outlineemphasizing feature discussed above. For both the model and the experimental results, ␩共r ⫽ 0兲 ⬍ 1 and the dip in the plot of P共r兲 occurs in the vicinity of ␩ ⫽ 1. These are the conditions described above that lead to the dark ring observed in the object image. This outline-emphasizing feature disappears when

the beam attenuation coefficient increases to c ⫽ 2.5兾m 共Fig. 17兲. In this case, ␩ ⬎ 1 for all r, which results in kdestr ⬍ 0. Although the experimental destructive data are rather noisy, they still show the same trend toward negative contrast as is shown in the model data. For both the model and the experiment, the contrast of the constructive image is enhanced relative to the destructive image. The outline-emphasizing feature reappears when the target depth is decreased to z ⫽ 1.83 m and the beam attenuation coefficient is increased to c ⫽ 3.7兾m 共Fig. 18兲. Here, ␩共r ⫽ 0兲 ⬍ 1 and slowly increases for r ⬎ 0. The location of the dip in the plot of P共r兲 again occurs in the vicinity where ␩ ⫽ 1. The constructive image again shows improved contrast relative to the nonmodulated continuous-wave image. Although the model and experimental results shown in Figs. 13–18 are a small subset of the data that are possible with various system and environmental parameters, they do validate the theoretical predictions of the effect of constructive and destructive interference on the target contrast and the images obtained with a modulated laser imaging system. The good correlation between the model and the experimental data give confidence that the 1 July 2004 兾 Vol. 43, No. 19 兾 APPLIED OPTICS

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Fig. 15. Model 共black兲 and experimental 共gray兲 images for c ⫽ 1.2兾m and z ⫽ 2.74 m 关the values for ␩共r兲 are plotted on the right axis for the destructive images and are indicated by filled diamonds兴. CW, continuous wave.

MVS program can be used to study the effect of other system and environmental characteristics on the system performance. 5. Conclusions

A technique with an amplitude-modulated laser transmitter has been developed to improve underwater imaging. The theory required to predict the ef3888


fect of system and environmental parameters on the propagation of a modulated optical signal has been derived and incorporated into a software program, Modulated Vision System 共MVS兲. The MVS program was used to gain insight into the origin of variations in target contrast as a function of modulation frequency and other interesting features, such as outline enhancing and contrast inversion, that were ob-


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served in experimental measurements. It was found that the signal amplitude fluctuations as a function of modulation frequency were caused by constructive and destructive interference of the modulation envelope between the backscatter and the target return signals. The accuracy of the MVS program with inputs was validated with controlled laboratory tank measurements. The good agreement between the experimental results and the MVS program predictions gave us confidence in the accuracy of the theory derived for prediction of modulated laser imaging system performance. In the future, other features will be added to the MVS program to improve its accuracy, including realistic system noise and the effects of the forward-scattered light temporal spreading. The program can then be used to quantify the relative performance of continuous-wave, modulated continuous-wave, pulsed, and modulated pulse configurations in terms of signal-to-noise ratio and target contrast for a variety of environmental and system parameters. This future research will help determine the benefits and limitations of the amplitude-modulated imaging approach and will be used to optimize the system design for a desired range of system performance criteria. References 1. M. P. Strand, “Underwater electro-optical system for mine identification,” in Detection Technologies for Mines and Minelike Targets, A. C. Dubey, I. Cindrich, J. M. Ralston, and K. A. Rigano, eds., Proc. SPIE 2496, 487– 497 共1995兲. 2. G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging system,” Opt. Eng. 32, 2185–2190 共1993兲. 3. J. W. McLean, “High-resolution 3D underwater imaging,” in Airborne and In-Water Underwater Imaging, G. D. Gilbert, ed., Proc. SPIE 3761, 10 –19 共1999兲.

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4. M. W. Scott, “Range imaging laser radar,” U.S. patent 4,935,616 共19 June 1990兲. 5. J. W. Rish, S. M. Lebien, R. O. Nellums, J. Foster, J. W. Edwards, and B. T. Blume, “Performance of a gated scannerless optical range imager against volume and bottom targets in a controlled underwater environment,” in Information Systems for Divers and Autonomous Underwater Vehicles Operating in Very Shallow Water and Surf Zone Regions II, J. L. WoodPutnam, ed., Proc. SPIE 4039, 114 –123 共2000兲. 6. L. Mullen, V. M. Contarino, and P. R. Herczfeld, “Modulator lidar system,” U.S. patent 5,822,047 共13 October 1998兲. 7. L. Mullen, V. M. Contarino, and P. R. Herczfeld, “Hybrid lidarradar ocean experiment,” IEEE Trans. Microwave Theory Tech. 44, 2703–2710 共1996兲. 8. L. Mullen, E. Zege, I. Katsev, and A. Prikhach, “Modulated lidar system: experiment and theory,” in Ocean Optics: Remote Sensing and Underwater Imaging, R. J. Frouin and G. D. Gilbert, eds., Proc. SPIE 4488, 25–35 共2001兲. 9. I. L. Katsev, E. P. Zege, A. S. Prikhach, and I. N. Polonsky, “Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems,” J. Opt. Soc. Am. A 14, 1338 –1346 共1997兲. 10. E. P. Zege, I. L. Katsev, and I. N. Polonsky, “Multicomponent approach to light propagation in clouds and mists,” Appl. Opt. 32, 2803–2812 共1993兲. 11. E. P. Zege, A. P. Ivanov, and I. L. Katsev, Image Transfer Through a Scattering Medium 共Springer-Verlag, Heidelberg, Germany, 1991兲. 12. E. P. Zege, I. L. Katsev, A. S. Prikhach, G. D. Ludbrook, and P. Bruscaglioni, “Analytical and computer modeling of the ocean lidar performance,” in 12th International Workshop on Lidar Multiple Scattering Experiments, C. Werner, U. G. Oppel, and T. Rother, eds., Proc. SPIE 5059, 189 –199 共2002兲. 13. J. Prentice, A. Laux, B. Concannon, L. Mullen, V. Contarino, and A. Weidemann, “Comparison of Monte Carlo model predictions with tank beam spread experiments using a Maalox phase function obtained with volume scattering function instruments,” presented at the 2002 Ocean Sciences Meeting, Honolulu, Hawaii, 11–15 February 2002. 14. F. W. Sears, M. W. Zemansky, and H. D. Young, University Physics 共Addison-Wesley, New York, 1987兲.