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Influence of gating and of the gate shape on the penetration capacity of range-gated active imaging in scattering environments

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Abstract

Range-gated active imaging is a well-known technique used for night vision or for vision enhancement in scattering environments. A lot of papers have been published, in which the performance enhancement of range gating has been demonstrated. However, there are no studies which systematically investigate and quantify the real gain brought by range gating, in comparison with a classical imaging system, in controlled smoke densities. In this paper, a systematic investigation of the performance enhancement of range-gated viewing is presented in comparison with a color camera representing the human vision. The influence of range gating and of the gate shape is studied. We have been able to demonstrate that a short-wave infrared (SWIR) range-gated active imaging system can enhance by a factor of 6.9 the penetration depth in dense smoke. On the other hand, we have shown that the combination of a short pulse with a short integration time gives better contrasted images in dense scattering media.

© 2015 Optical Society of America

1. Introduction

Range-gated active imaging is a well-known technique mainly used for night-vision applications or to enhance the image quality in vision through scattering environments [1, 2]. It is also a known fact that the so-called “range gating” or “time gating” eliminates the backscattering effects during the propagation of the range gate when illuminating through scattering environments, like rain, snow, fog, mist or smoke. This elimination leads to a significant increase in the vision range in scattering environments. A lot of papers have been published where this fact has been experimentally demonstrated [3], in particular for underwater vision [4, 5].

Despite the fact that some authors estimate that active imaging brings a gain in range between 2 and 3 in scattering environments and in comparison with classical imaging systems [4], there are no studies which systematically investigate and quantify the real gain brought by range gating in comparison with classical imaging systems in different controlled smoke densities. In this paper, we thoroughly examine the performance enhancement of laser range gating in comparison with a color camera representing the human vision. At first, we study the influence of range gating by comparing a long gate with a short gate and we investigate the influence of the gate shape by comparing two types of gated cameras.

2. Principle of range gating and of backscattering elimination

The principle of range-gated active imaging is illustrated in Fig. 1. An active imaging system consists of a sensitive image sensor and a pulsed illumination source. In most cases, the laser divergence (θDiv) and the sensor field of view (θFOV) are matched to maximize the energy balance and, therefore, the range of the system.

 figure: Fig. 1

Fig. 1 Principle of range-gated active imaging.

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The duration of the illuminating light pulse can vary from sub-nanosecond values to several microseconds. These durations correspond to a wave train of a few decimeters to some hundreds of meters. A delay between the sensor gate and the illumination pulse allows the so-called gated viewing process (or range gating, time gating) that delivers the reflectivity of the scene in a given range. Figure 2 illustrates the range-gated imaging process in a time-space diagram [6]. The laser pulse illuminates a certain region in the time-space model. The illumination path represents the light propagating in the positive z-direction during a time equivalent to the pulse width. On the other hand, the sensor collects only the reflected light corresponding to a given gate path (negative z-direction) during the integration time. The imaging zone is the intersection of the illumination and the gate paths. This zone contains all the information which is imaged by the gated viewing process. A projection of this zone onto the z-axis leads to a specific depth-intensity profile or range gate.

 figure: Fig. 2

Fig. 2 Time-space diagram of the active imaging process (here, the laser pulse width and the sensor integration time are equal).

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As illustrated in Fig. 1, the laser pulse which travels through the depth of the scene will hit different objects at different distances (here a tree, then a truck). Owing to the time of flight, the back-reflected photons will arrive back at the sensor at different times. While the photons travel toward the scene and back to the sensor, the camera is closed. Therefore, the sensor is not dazzled by backscattered photons or parasitic light sources. The sensor gate opens after a certain delay and for a short integration time. Thus, only light that arrives at the sensor into the right timing window contributes to the imaging process.

Equation (1) shows that the depth-intensity profile can be calculated as a convolution of the laser pulse (P) and sensor gate functions (G). For a given range gate, τdelay is the sensor delay and 2zc−1, the round-trip time or the photon time of flight (c refers to the speed of light in the medium of propagation).

I(z)=0P(t2zc)G(tτdelay)dt

If the pulse and the gate functions are square-shaped and have equal temporal widths, the resulting depth-intensity profile is triangle-shaped, with rising-edge and falling-edge depths (Δzr, Δzf) depending on the laser pulse width (τpls) [Eq. (2)].

Δzr=Δzf=cτpls2

If the gate function has a longer temporal width than the pulse function, the resulting depth-intensity profile will have a plateau between the rising and the falling edges [7–9].

Based on these considerations, the sensor signal S in the presence of a scattering material can be described as the addition of the target signal St and of a backscattering function SSCS. Due to the number of particles which are in the range gate in front of the target, the backscattering is more or less important. As described in the literature [10, 11], the signal can be expressed by Eq. (3):

SA(z0)z02ρtI(z0)St+0z0A(z)z2ρSCSI(z)dzSSCS

where z0 is the system-target distance, A(z0) and A(z) are coefficients dependent on the system characteristics and the atmospheric attenuation. Further, the target and environment reflectances are described by ρt, the target reflectance and ρSCS, the local scattering cross-section. Note that, as a first approximation of the diffusion process, we only take into account backscattering and not multiple scattering. Thus, we only consider the scattered signal from 0 to z0 in the line of sight. The scattered signal behind or around the target is not considered in this first approximation, as it can be regarded as multiple scattering and contributes only marginally to the contrast decrease.

Following the argumentation of McManamon [2], the recorded signal can be quantified by the received optical power PR which is described by the lidar equation in Eq. (4). In this equation, PT is the transmitted optical power, Aillum is the illuminated area and Arec the effective receiver area. The target is described by the target reflectance and range, as well as the target size, At. Further, the transmission efficiencies of the atmosphere and of the optical system are described by ηatm and ηsys, respectively.

PR=PTρtAtAillumArecπz02ηatm2ηsys

Some authors have claimed that a short illumination pulse associated with a short sensor integration time significantly increases the image contrast by eliminating backscattering coming from the light propagation [12, 13]. The aim of this paper is to quantify this gain in comparison with classical systems. Our experiments were conducted with an eye-safe active imaging system consisting of a 65 mJ pulsed laser at 1.57 µm (10ns pulse width) for the illumination task and an EB-CMOS SWIR camera [14] or an MCT-APD SWIR sensor [15, 16] as imaging sensors. The two sensors are intensified: the first one by electron bombarding (EB) a CMOS sensor, the second one by coupling a mercury-cadmium-telluride sensor (MCT) to avalanche photodiodes (APDs). During the measurements, the noise limit of the different sensors was never reached as the remaining signal is always above the sensor threshold. The active imaging system was coupled to a color camera to compare the two channels.

3. Experimental study and theoretical analysis

3.1 Description of the ISL test facility and method for the performance assessment of active imaging

In order to produce fog or smoke with different but reproducible densities, we built a 25 m long fog chamber in a concrete tunnel. Constant temperature and humidity guarantee the reproducibility of the experiments and ensure a good stability of the water fog droplets or of the smoke particles during the measurements. Water fog is generated by using a high-pressure nozzle ramp producing an extremely fine water mist, with water particle diameters between 10 and 100 µm. Glycol smoke is generated by a JB Systems FX-700 smoke machine vaporizing a glycol-based fluid, in this case a Universal Effects ST-Smoke Fluid Light. Canister smoke is generated by the combustion of chemical agents such as those in smoke canisters or smoke grenades. In these experiments, we used a Björnax AB Ventilax smoke canister based on potassium chlorate and ammonium chloride. The wavelength transmission spectrum was measured by a portable StellarNet spectrophotometer between 400 nm and 1600 nm. As an example, Fig. 3 shows the transmission spectrum of the canister smoke. It is obvious that the smoke transmission increases in the SWIR wavelengths. The particle size distribution was mainly under 1 µm for the two types of smoke.

 figure: Fig. 3

Fig. 3 Relative transmission spectrum of canister smoke generated by combustion.

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The obscurant is homogenized through the tunnel by using three fans to break up stagnant particles. With this facility, it is possible to generate fogs or smokes of different densities, with visibilities varying from “good visibility” down to one meter visibility. Figure 4 shows the tunnel with 8 contrast panel targets placed at different depths and under different conditions of visibility.

 figure: Fig. 4

Fig. 4 ISL fog tunnel facility with different fog densities (color camera). (a) α = 2.10−4 m−1, (b) α = 0.05 m−1, (c) α = 0.5 m−1.

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In the fog tunnel, the 8 contrast targets are placed at the following distances from the imaging system: 2.4 m; 5.4 m; 8.4 m; 11.4 m; 14.4 m; 17.4 m; 20.4 m; 24.4 m. The performance assessment will consist in a comparison between the active imaging system and the color camera which has a performance comparable to the human vision. The images recorded by the color camera are used to measure the visibility of the smoke. As defined by Koschmieder [17], the atmospheric visibility V (m) is related to the attenuation coefficient α (m−1) by the law:

V=1αln(C0Cth)
where C0 corresponds to the B/W (black and white) target contrast (C0 = 1) and Cth is set equal to 0.05, i.e. the human eye's minimal perceptible contrast as defined by the CIE (International Commission on Illumination). With these values the relation between visibility and attenuation becomes very simple and can be written as:

V=3α

Knowing the distance of each target in the tunnel, the color images give a precise estimation of the visibility/attenuation of the obscurant during the experiments. By definition and according to Eq. (5), a classical vision system (human eye, color or video camera) will have a visibility limit at 3 attenuation lengths, where the attenuation length is defined by the visibility multiplied by the attenuation coefficient (dimensionless parameter).

V.α=3

The images recorded with the range-gated imaging system are used to quantify the gain brought by range gating [18]. The contrast of each target is analyzed at different fog densities varying from “without fog”, i.e. α 10−4 m−1, to “very dense fog”, i.e. α1 1 m−1. Figure 5 recapitulates the results of these investigations on one of the experiments with a glycol smoke obscurant. In this example, the laser pulse duration was of 10 ns and the exposure time of the intensified camera was set to 500 ns.

 figure: Fig. 5

Fig. 5 (a) Measured contrast of the contrast panels at different ranges and at different fog densities (varying from α = 10−4 m−1 without fog to α1 = 0.75 m−1 with very dense fog). (b) The same data represented vs the attenuation length in x-axis, clearly shows the gain brought by active imaging in comparison with the Koschmieder law.

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The contrast is determined by applying the well-known contrast formula, where m¯w and m¯b are the averages of the pixels grey levels in the white part and in the black part of the contrast targets, respectively.

C=m¯wm¯bm¯w+m¯b

In Fig. 5(a) each curve corresponds to an experiment at a given smoke density. Without smoke, the contrast of each panel is more or less constant over the different ranges. When the fog density increases, it is clearly visible that the contrast of the different panels decreases. By plotting the contrast values (normalized to the higher contrast reached on the first panel without smoke) against the attenuation length (visibility * attenuation, dimensionless parameter) as depicted in Fig. 5(b), a more general representation of the results can be given. Here, the gain obtained by laser gated viewing in comparison with the Koschmieder law is clearly visible. The minimum contrast of 5% that can be resolved by the human eye is attained, by definition, for an attenuation length of 3. At this value, the active imaging system can give comparable images for an attenuation length of 8. Consequently, the technique of active imaging increases the distance of visibility by a factor of 2.7. Although this factor is specific to the investigated system and the type of smoke, it can be considered to be a representative gain value, when comparing active imaging with classical imaging systems [4].

By introducing the sensor signals for the white side and for the black side of the target panels in Eq. (8), as being m¯wSw+SSCS and m¯bSb+SSCS, respectively, the contrast formula can be rewritten as:

CSwSbSw+Sb+2SSCS
Here, it is clearly visible that the contrast is reduced by the backscattering of light in front of the target. This simple scattering model does not take into account multiple scattering effects but is sufficient to describe the contrast decrease in very dense smoke.

3.2. Influence of the gate length

As mentioned above, it is well-known that the image quality enhancement brought by active imaging in scattering environments is related to the possibility of eliminating the backscattering effects through a synchronization between the laser illumination and the camera integration time. In order to be able to evaluate the gain obtained by range-gated active imaging, we conducted two new types of experiments. We acquired images at different smoke densities with a long gate and a short gate. The principle of these experiments is described in Fig. 6.

 figure: Fig. 6

Fig. 6 Principle of the experiments with a long gate (a) and a short gate (b).

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For the long gate, the camera integration time was set to be longer than 500 ns (the laser pulse duration has a fixed value of 10 ns). In this way, the range gate covered the 8 B/W contrast targets. For the short gate, the camera integration time was set to 70 ns, i.e. the minimum value of the EB-CMOS camera. This small range gate was shifted in depth to perform a tomography of the scene. In this case, only the maximum contrast obtained on each panel was taken into account during our image analysis.

Figure 7 shows the results for the SWIR eye-safe active imaging system used with different densities of glycol-based smoke. The 5% visibility limit was reached at 7.8 attenuation lengths when using a long range gate and at 15.7 attenuation lengths when using a small range gate. In comparison with the capacity of a classical system (Koschmieder), the gain achieved by active imaging was of 2.6 for a long range gate and of 5.2 for a short range gate. For canister smoke, the 5% visibility limit was reached at 8.8 attenuation lengths when using a long range gate and at 20.8 attenuation lengths when using a small range gate. In comparison with the capacity of a classical system, the visibility in smoke was improved by a factor of 2.9 for a long range gate and of 6.9 for a short range gate.

 figure: Fig. 7

Fig. 7 Long gate and short gate gains against attenuation length for two types of obscurants.

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This result is interesting for two reasons: the gap between the Beer-Lambert law (color camera) and the long gate curve (1.5 µm active imaging system) can be explained as the result of a better smoke penetration capacity of the SWIR wavelengths in comparison with the visible wavelengths [see Fig. 3]. This fact is also due to a longer wavelength for which the diffusion is nearly ten times lower than in the visible spectrum. The second gap between the long gate curve and the short gate one, clearly shows the influence of gate ranging. This supplementary factor, due to gating, can be understood as a lower contribution of the scattering function (SSCS) to the sensor signal which increases the contrast values [see Eq. (9)]. It is worth noticing here that a range-gated active imaging system at SWIR wavelengths is able to reach 15.7-20.8 attenuation lengths, which gives an increase by a factor of 5.2-6.9 in comparison with a classical vision system. As explained before, the global performance comes from the inherent capacity of the 1.5 µm wavelength to penetrate through smoke [19, Fig. 3], which brings a factor of 2.6-2.9 without range gating and a supplementary factor of 2-2.4 due to range gating.

In a range-gated system, the second important point is the temporal form of the gate. In the next section, the influence of the temporal shape of the gate on the penetration capacity in scattering media will be evaluated.

3.3. Influence of the rising edge of the gate

As previously mentioned, the intensity profile of the range gate is given by the convolution of the laser pulse shape and the opening/closing function of the sensor. In [7–9] the authors have studied the range gate form for temporal rectangle-shaped laser pulses and camera integration functions. Busck [7] has clearly shown that the rising edge of the gate depends more specifically on the falling edge of the laser pulse and on the opening edge of the camera. The faster the falling edge of the laser and the opening edge of the camera, the sharper the rising edge of the range gate. Here, Eqs. (3) and (9) show again that the scattering part (SSCS) in the sensor signal is lower with a fast gate. Figure 8 illustrates this fact and shows that a faster rising edge of the gate illuminates a lower number of particles which reflect back the illumination light in the range gate.

 figure: Fig. 8

Fig. 8 The slope of the rising edge of the gate determines the level of back-reflection in front of a target.

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In order to experimentally study the influence of this parameter, we compared two SWIR gated cameras: an EB-CMOS camera and an MCT-APD camera. The MCT-APD camera is capable of very short integration times, as short as 20 ns. In comparison with the EB-CMOS camera, this integration time is shorter by a factor of 7.5 than the 150 ns of the EB-CMOS camera. Figure 9 shows a simulation with a modelisation of the rising edge of the range gate for an active imaging system at 1.5 µm associated with an EB-CMOS sensor or with an MCT-APD camera. This simulation shows that the rising edge is 12 m long with the EB-CMOS sensor and 3 m long with the MCT-APD sensor.

 figure: Fig. 9

Fig. 9 Gate temporal intensity-variation: result of the convolution of the laser pulse and the camera shutter functions.

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This simulated gate shapes can be experimentally measured by illuminating a long and homogeneous object present in the scene. In our case, we used the side wall of the tunnel and we analyzed the real intensity distribution along the depth of the light gate. This measurement presented in Fig. 10 confirms the above simulation: the gate rising edge is 12 m with the EB-CMOS sensor and 3 m long with the MCT-APD sensor.

 figure: Fig. 10

Fig. 10 Experimental acquisition of the gate intensity variation function.

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Figure 11 shows the experimental comparison between the two sensors. In this case, in order to have comparable results between the two cameras which have different sensitivities, it is necessary to work with a lower laser energy to avoid saturation effects on the EB-CMOS camera. This fact explains that, at the 5% visibility limit, the gain due to range gating is only of 4.1-4.5 for glycol smoke and of 6.1-7.1 for the smoke canister. But the important result is that at the 5% visibility limit, there is only a small difference between the two systems. However, the sharpness of the rising edge is clearly visible in the shape of the curve. It can be observed that the system equipped with the MCT-APD camera gives better contrasted images than the system with the EB-CMOS camera.

 figure: Fig. 11

Fig. 11 Target contrast versus attenuation length for a system using the EB-CMOS camera and a system using the MCT-APD camera.

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For a given smoke density, the optical contrast on each target, when the gate is at its optimum position, is better for the MCT-APD camera than for the EB-CMOS camera. As an example, Fig. 12 clearly shows this contrast enhancement for the fourth target panel indicated by the red arrows. The contrast is better when the rising edge of the range gate is shorter.

 figure: Fig. 12

Fig. 12 Illustration of the curves shown in Fig. 11.

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It can clearly be observed that a sharp range gate (combination of a short pulse with a fast sensor shutter for the sensor) increases the contrast of the object by decreasing backscattering in front of the object. With a longer gate, when the maximum of the gate function is placed on the fourth target panel, the third and the second panels are also illuminated by the rising edge of the gate, which decreases the contrast as a result of the higher backscattering in front of the object.

4. Conclusion

In this paper, we have experimentally investigated the importance of range gating and of the gate rising slope in the penetration capacity of range-gated active imaging systems in scattering media. It has been proven that a SWIR gated-viewing system using the latest technology can increase the visibility in canister smoke by a factor of 6.9 (20.8 attenuation lengths). However, this gain is dependent on the type of obscurant. Additionally, the slope of the rising part of the gate is also important. It has been shown that the combination of a short pulse with a fast sensor shutter gives better contrasted images in dense scattering media. The next step in this work will be to compare the performance of different active imaging systems at different wavelengths in different types of scattering media, where the absorption and the diffusion parts of the global attenuation are varying.

Acknowledgments

Authors would like to thank Y. Reibel and X. Lefoul from SOFRADIR, E.de Borniol and J. Rothman from CETI-Leti, S. Bernard from ONERA and DGA (Délégation Générale de l'Armement) who have permitted us to use an experimental version of the MCT-APC MEDIA camera.

References and links

1. V. Molebny, G. Kamerman, and O. Steinvall, “Laser radar: from early history to new trends,” Proc. SPIE 7835, 783502 (2010). [CrossRef]  

2. P. F. McManamon, “Review of ladar: a historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng. 51(6), 060901 (2012). [CrossRef]  

3. O. K. Steinvall, H. Olsson, G. Bolander, C. A. Groenwall, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE 3707, 432–448 (1999). [CrossRef]  

4. G. R. Fournier, D. Bonnier, L. J. Forand, and P. W. Pace, “Range-gated underwater laser imaging system,” Opt. Eng. 32(9), 2185–2190 (1993). [CrossRef]  

5. J. S. Jaffe, K. D. Moore, J. McLean, and M. P. Strand, “Underwater optical imaging: Status and prospects,” J. Oceanogr. 14, 66 (2001).

6. L. F. Gillespie, “Apparent illuminance as a function of range in gated, laser night-viewing systems,” J. Opt. Soc. Am. A 56(7), 883 (1966). [CrossRef]  

7. J. Busck, “Underwater 3-D optical imaging with a gated viewing laser radar,” Opt. Eng. 44(11), 116001 (2005). [CrossRef]  

8. P. Andersson, “Long-range three-dimensional imaging using range-gated laser radar images,” Opt. Eng. 45(3), 034301 (2006). [CrossRef]  

9. D. Monnin, A. Schneider, F. Christnacher, and Y. Lutz, “A 3D outdoor scene scanner based on a night-vision range-gated active imaging system,” in Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT’06), ed. (IEEE Computer Society, 2006). [CrossRef]  

10. H. Steingold and R. E. Strauch, “Backscatter effects in active night vision systems,” Appl. Opt. 8(1), 147–154 (1969). [CrossRef]   [PubMed]  

11. M. Laurenzis, F. Christnacher, D. Monnin, and Th. Scholz, “Investigation of range-gated imaging in scattering environments,” Opt. Eng. 51(6), 061303 (2012). [CrossRef]  

12. M. E. Zevallos, S. K. Gayen, M. Alrubaiee, and R. R. Alfano, “Time-gated backscattered ballistic light imaging of objects in turbid water,” Appl. Phys. Lett. 86(1), 011115 (2005). [CrossRef]  

13. E. A. McLean, H. R. Burris Jr, and M. P. Strand, “Short-pulse range-gated optical imaging in turbid water,” Appl. Opt. 34(21), 4343–4351 (1995). [CrossRef]   [PubMed]  

14. “LIVAR M506: High Sensitivity, Short Wave Infrared (SWIR) Gated Camera,” (Intevac) http://www.intevac.com/intevacphotonics/livar-506/

15. J. Rothman, E. de Borniol, K. Foubert, L. Mollard, N. Péré-Laperne, F. Salvetti, A. Kerlain, and Y. Reibel, “HgCdTe APDs for space applications,” presented at the International Conference on Space Optic (ICSO 2014), Tenerife, Canary Islands, Spain, 7–10 Oct. 2014.

16. E. de Borniol, J. Rothman, F. Salveti, and P. Feautrier, “SWIR HgCdTe avalanche photodiode focal plan arrays performances evaluation,” presented at the International Conference on Space Optic (ICSO 2014), Tenerife, Canary Islands, Spain, 7–10 Oct. 2014.

17. H. Koschmieder, “Theorie der horizontalen Sichtweite,” Beitr. Phys. fr. Atm. 12, 33–55 and 171–181 (1924).

18. F. Christnacher, M. Laurenzis, and S. Schertzer, “Theoretical and experimental comparison of flash and accumulation mode in range-gated active imaging,” Opt. Eng. 53(4), 043106 (2014). [CrossRef]  

19. “SWIR Image Gallery”, (Sensors Unlimited, UTC Aerospace Systems), http://www.sensorsinc.com/gallery/images

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Figures (12)

Fig. 1
Fig. 1 Principle of range-gated active imaging.
Fig. 2
Fig. 2 Time-space diagram of the active imaging process (here, the laser pulse width and the sensor integration time are equal).
Fig. 3
Fig. 3 Relative transmission spectrum of canister smoke generated by combustion.
Fig. 4
Fig. 4 ISL fog tunnel facility with different fog densities (color camera). (a) α = 2.10−4 m−1, (b) α = 0.05 m−1, (c) α = 0.5 m−1.
Fig. 5
Fig. 5 (a) Measured contrast of the contrast panels at different ranges and at different fog densities (varying from α = 10−4 m−1 without fog to α1 = 0.75 m−1 with very dense fog). (b) The same data represented vs the attenuation length in x-axis, clearly shows the gain brought by active imaging in comparison with the Koschmieder law.
Fig. 6
Fig. 6 Principle of the experiments with a long gate (a) and a short gate (b).
Fig. 7
Fig. 7 Long gate and short gate gains against attenuation length for two types of obscurants.
Fig. 8
Fig. 8 The slope of the rising edge of the gate determines the level of back-reflection in front of a target.
Fig. 9
Fig. 9 Gate temporal intensity-variation: result of the convolution of the laser pulse and the camera shutter functions.
Fig. 10
Fig. 10 Experimental acquisition of the gate intensity variation function.
Fig. 11
Fig. 11 Target contrast versus attenuation length for a system using the EB-CMOS camera and a system using the MCT-APD camera.
Fig. 12
Fig. 12 Illustration of the curves shown in Fig. 11.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

I( z )= 0 P( t 2z c ) G( t τ delay )dt
Δ z r =Δ z f = c τ pls 2
S A( z 0 ) z 0 2 ρ t I( z 0 ) S t + 0 z 0 A(z) z 2 ρ SCS I(z) dz S SCS
P R = P T ρ t A t A illum A rec π z 0 2 η atm 2 η sys
V= 1 α ln( C 0 C th )
V= 3 α
V.α=3
C= m ¯ w m ¯ b m ¯ w + m ¯ b
C S w S b S w + S b +2 S SCS
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