Patent Publication Number: US-10317532-B1

Title: Integrative optics system, device, and method

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of application Ser. No. 13/913,090, filed on Jun. 7, 2013, which has been assigned U.S. Pat. No. 9,689,987, issuing on Jun. 27, 2017, which claims the benefit of U.S. Provisional Application No. 61/659,348, filed Jun. 13, 2012; U.S. Provisional Application No. 61/675,256, filed Jul. 24, 2012; and U.S. Provisional Application No. 61/718,154, filed Oct. 24, 2012, which are hereby incorporated herein by reference in their entireties. 
    
    
     STATEMENT OF GOVERNMENT RIGHTS 
     One or more inventions described herein are partially supported by the following contracts for the Department of Navy under the SBIR program: M67854-10-C-6531, N00024-06-C-4121, N00014-09-C-0456, and N00014-05-C-0423. The Government may have partial rights in such inventions. 
    
    
     TECHNICAL FIELD 
     The present invention relates generally to object detection systems, and more particularly, some embodiments relate to systems and methods for long distance optical detection. 
     DESCRIPTION OF THE RELATED ART 
     Clutter can cause serious performance issues in object detection systems, such as radar, LIDAR, sonar, and imaging systems. For example, in littoral environments, wave clutter can severely impede the ability of a radar system to detect objects such as periscopes. 
     BRIEF SUMMARY OF EMBODIMENTS OF THE INVENTION 
     Optical detection systems are provided for detecting objects in the presence of clutter and discriminating between target objects and clutter. In some embodiments, the system is configured for detection of high brightness objects and light sources—for example, non-Lambertian reflectors, such as retroreflectors. 
     In some embodiments, the system mitigates clutter in the scene by reducing false positives or increasing positive predictive values (PPV). Various signals may be used for target discrimination. For example, clutter signal patterns associated with known target types may be detected along with potential target signals. Additionally, specific target signals may be detected. For example, multiple retroreflections from a single ocular body may be detected, and the character of these multiple retrorefelections may be used for target discrimination. 
     In various embodiments, an eye-safe laser is used to emit a diverging laser flash configured to illuminate a detection zone. A pseudoimaging optical receiver system is used to detect reflections from objects in the detection zone. The receiver system includes a time-gated photodetector array that is used to record signatures in a voxel array. A voxel processing module receives the voxel array and detects a reference clutter signal within the array. Potential targets are then detected according to target signals in relation to the reference clutter signal. 
     Further embodiments of the invention use a temporal sequence of voxel-arrays from the same detection zone to implement voxel change detection. Potential target may be detected according to various temporal voxel signatures. More generally, the potential target may detected space/time voxel patterns manifested by voxel coherence. 
     Other features and aspects of the invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, which illustrate, by way of example, the features in accordance with embodiments of the invention. The summary is not intended to limit the scope of the invention, which is defined solely by the claims attached hereto. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention, in accordance with one or more various embodiments, is described in detail with reference to the following figures. The drawings are provided for purposes of illustration only and merely depict typical or example embodiments of the invention. These drawings are provided to facilitate the reader&#39;s understanding of the invention and shall not be considered limiting of the breadth, scope, or applicability of the invention. It should be noted that for clarity and ease of illustration these drawings are not necessarily made to scale. 
       Some of the figures included herein illustrate various embodiments of the invention from different viewing angles. Although the accompanying descriptive text may refer to such views as “top,” “bottom” or “side” views, such references are merely descriptive and do not imply or require that the invention be implemented or used in a particular spatial orientation unless explicitly stated otherwise. 
         FIG. 1  illustrates an example system module. 
         FIG. 2  illustrates an example dual-module system. 
         FIG. 3  illustrates an example system deployment. 
         FIGS. 4A-B  illustrate a top down view of the field of view and detection zone of an example system. 
         FIG. 5  illustrates an example laser source. 
         FIG. 6  illustrates an example laser delivery system. 
         FIG. 7  illustrates an example beam expander. 
         FIG. 8  illustrates an example beam reshuffler. 
         FIG. 9  illustrates an example of system geometry during operation. 
         FIG. 10  illustrates an example fiber optic laser delivery component. 
         FIG. 11A  illustrates an example laser reception system. 
         FIG. 11B  illustrates an example laser reception system. 
         FIG. 110  illustrates an example laser reception system. 
         FIG. 11D  illustrates an example laser reception system. 
         FIG. 12A  illustrates an example sensor layout. 
         FIG. 12B  illustrates an example sensor layout. 
         FIG. 13A  illustrates an example reception optic. 
         FIG. 13B  illustrates an example reception optic. 
         FIG. 130  illustrates an example reception optic. 
         FIG. 13D  illustrates an example reception optic. 
         FIG. 14A  illustrates a tapered fiber optic for laser receivers. 
         FIG. 14B  illustrates a tapered fiber optic for laser receivers. 
         FIG. 15  illustrates an example of system operation during scanning. 
         FIG. 16  illustrates an example of target detection. 
         FIG. 17A  illustrates an example step of target detection methods. 
         FIG. 17B  illustrates an example step of target detection methods. 
         FIG. 18A  illustrates an example step of target detection methods. 
         FIG. 18B  illustrates an example step of target detection methods. 
         FIG. 180  illustrates an example step of target detection methods. 
         FIG. 19  illustrates voxel coherence in a vertical line of voxels. 
         FIG. 20  illustrates an example of horizontal voxel coherency. 
         FIG. 21A  illustrates space-time correlation between voxels. 
         FIG. 21B  illustrates space-time correlation between voxels. 
         FIG. 210  illustrates space-time correlation between voxels. 
         FIG. 21D  illustrates space-time correlation between voxels. 
         FIG. 22  illustrates a inference method of target detection discrimination for periscopes. 
         FIG. 23  illustrates an additional method of target detection discrimination for periscopes. 
         FIG. 24  illustrates an example of rigid foxel group movement. 
         FIG. 25  illustrates a second example of rigid foxel group movement. 
         FIG. 26  illustrates an example of non-rigid foxel group movement. 
         FIG. 27  illustrates an example of velocity flow mapping. 
         FIG. 28  illustrates an example system implementation for trip-wire detection. 
         FIG. 29A  illustrates an example system implementation for fingerprint detection. 
         FIG. 29B  illustrates an example system implementation for fingerprint detection. 
         FIG. 30A  illustrates an example of pulse partition sampling. 
         FIG. 30B  illustrates an example of pulse partition sampling. 
         FIG. 31A  illustrates detection of pulse reflection deformation by various surfaces. 
         FIG. 31B  illustrates detection of pulse reflection deformation by various surfaces. 
         FIG. 31C  illustrates detection of pulse reflection deformation by various surfaces. 
         FIG. 31D  illustrates detection of pulse reflection deformation by various surfaces. 
         FIG. 31E  illustrates detection of pulse reflection deformation by various surfaces. 
         FIG. 31F  illustrates detection of pulse reflection deformation by various surfaces. 
         FIG. 32  illustrates an example computing module that may be used in implementing various features of embodiments of the invention. 
     
    
    
     The figures are not intended to be exhaustive or to limit the invention to the precise form disclosed. It should be understood that the invention can be practiced with modification and alteration, and that the invention be limited only by the claims and the equivalents thereof. 
     DETAILED DESCRIPTION 
     As used herein the term “sensor” or “pixel” refers generally to an element of a sensor array. For example, the term sensor or pixel may refer to an individual photodetector of a photodetector array (“PDA”). In other cases, as indicated by context, the term “sensor” may refer to an entire sensor or pixel array. 
       FIG. 1  illustrates an exemplary integrative optics system. The system comprises a housing  100  mounted on a stabilized platform  101 . One or more detection modules  105  are disposed within the housing. Each detection module  105  comprises a laser emitter  103  and an optical receiver  102 . The module has a total field of view (FOV)  104 . The total field of view is achieved by emitting flashes (or facets) that encompass a sub-range of the total field of view. The emitter  103  and the receiver  102  scan the total field of view using a plurality of facets at different angles. For example, to cover a 180° field of view, the housing may comprise 5 modules  105 , each having a 40° field of view (with some overlap between fields of view). Each module  105  may emit flashes along about 100 facet angles, each flash having a 0.4° field of view. In another embodiment, the modules  105  scan to cover a plurality of views. For example, rather than 5 different modules  105  to cover a 180° field of view, a single module  105  may move to 5 different positions. For example, the stabilizing platform  101  may rotate the housing  100  to the different positions. In some embodiments, the stabilizing platform  101  rotates the housing  100  in a staccato fashion, stopping for each flash and return signal. In other embodiments, the stabilizing platform  101  smoothly rotates, and transforms are performed on the data to compensate for the rotation. 
       FIG. 2  illustrates a second exemplary integrative optics system. In this system, multiple housings  207 ,  206  may house emitters and receivers to provide additional fields of view  203 ,  204 . In this particular implementation, the system  201  is mounted on a semi-platform  205  of a ships mast  202 . In other embodiments, the system  201  may be mounted at other locations. For example, on a stationary tower (for example, on shore) or on an aircraft (for example, a helicopter). 
       FIG. 3  illustrates the system mounted on a marine platform. The FOV  307  of a detection module of the system  201  comprises a plurality of facets  302 ,  303 ,  304 ,  305 . Each module may operate in parallel or serially with other modules to provide the full system FOV. Each facet FOV  302 ,  303 ,  304 ,  305  is provided by a laser flash illuminating a detection volume at a distance from the laser light emitter. In some embodiments, the detection volume is at least 3 km from the laser light emitter. In further embodiments, the laser is eye-safe, having a wavelength greater than 1.3 μm. In other embodiments, the laser has a wavelength greater than 1.5 μm. In still further embodiment, the laser is not eye-safe (for example, the laser may have a wavelength of 1 μm). In such embodiments, a baffle or other shield may be disposed between the system and operating personnel. 
       FIGS. 4A and 4B  illustrate a top down view of the FOV and detection zone of an embodiment. The system  400  has a FOV  401  and is comprises of a plurality of modules. Each module has a FOV  402 , which when combined provide the entire FOV  401 . Each module has an inner detection radius  403  and an outer detection radius  406 , to provide a detection zone  404 . In some embodiments, the detection zone  404  is between an inner radius  403  between 3 and 10 km and outer radius  406  between 10 and 30 km. For example, in a particular embodiment, the detection zone  404  is between 5 km and 15 km. For single facet, its FOV=0.36°, for example, or FOV=0.00628, in radians. This is, for range of R=10 km, equivalent to horizontal range of: 10 4  m×0.00628=62.8 m, per single facet. 
     In still further embodiments, the emitter  103  is optomechanically adjustable to adjust the size or range of the detection zone. Each module&#39;s FOV  402  is provided by the laser flashes  405  that illuminate a detection volume comprising a portion of the detection zone. The number of flashes  405  may vary in different implementations based on factors such as module FOV size, desired operational frequency, available laser power, available detection power, visibility, and other system or environmental factors. In one embodiment, for a detection zone between 5 km and 15 km, with each flash illuminating about 100 m at the 15 km radius, each flash has a horizontal FOV of 0.38° and a vertical FOV of 0.37°. 
     Returning to  FIG. 3 , in the illustrated embodiment, the laser is transported to the emitter in the system head  201  from a laser source proximal to the mast base  301 .  FIG. 5  illustrates a cross section of a system having a laser source  500  proximal to the base  301  of a mast  202 . The laser source  500  emits a pulsed laser beam  501  into laser path  502 . The pulsed laser beam  501  as sufficient peak power to illuminate the detection volume sufficiently for return pulses to be detected by the detector. In one embodiment, the peak laser power P 0  is greater than at least 1 MW. In a particular embodiment, the laser pulse peak power is 6.67×10 6  W. 
     As an example, the following formula relating pulse energy, E O , and repetition frequency, n, into equivalent continuous watt (CW) power,  P  may be applied:
 
   P =E   O   ·n   O   (1)
 
where n O  is nominal repetition frequency:
 
 n   O =100 Hz  (2)
 
Therefore:
 
                     P   o     =         E   o       τ   L       =       P   _         n   o     ⁢     τ   L                   (   3   )               
As an example, assume  P =10 W, and n O =100 Hz, then, E O = P /n o =10 W/100 Hz=100 mJ, and for pulse length, t L =10 nsec, P O =100 mJ/10 nsec=0.1 J/10 −8  sec=10 MW.
 
     In some embodiments, the laser path  502  may be free space, a waveguide, or an optical fiber. As discussed above, in some embodiments, the laser has a peak power greater than 1 MW. Optical fibers have a laser damage threshold which defines the maximum optical intensity in W/cm 2  that can be transmitted in the fiber. In particular embodiments, the laser path  502  comprises a multi-mode fiber with a core diameter of around 300 μm. 
     In one embodiment, the laser damage threshold is about:
 
 I   O =10 GW/cm 2 =10 10  W/cm 2   (4)
 
Then, minimum fiber core diameter, (d F ) min, is
 
                       (     d   F     )     ⁢   min     =         4   ⁢     P   o         π   ⁢           ⁢     I   o                   (   5   )               
where P O  is laser beam nominal power. Assuming, as before, P O =6.67.10 6  W, we obtain
 
( d   F )min=290 μm  (6)
 
, which is a multimode fiber. For a typical multi-mode fiber the numerical aperture is N A =0.4. From this, its etendue is: (2)(290 μm) (0.4)=232 μm, which is much larger than a laser&#39;s single-mode Gaussian beam etendue, ε L , in the form:
 
                     ɛ   L     =       4   ⁢           ⁢   θ   ⁢           ⁢       w   o     ⁡     (     λ     π   ⁢           ⁢     w   o         )         =         4   ⁢   λ     π     ~   λ               (   7   )               
i.e., about 1.6 μm
 
     In other embodiments, the laser beam path comprises a single mode optics. In these embodiments, the laser beam may comprise a Gaussian beam with divergence, 2θ, and beam waist, 2w O . For 2θ=Δϕ=0.38°, w O =(1.6) (32) (10 −4 )/(0.033), =0.155 mm, and 2 w O =310 μm&gt;290 μm. The relation between the beam waist 2 w O  and divergence angle, 2θ in degrees, is summarized in Table 2. 
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Relation between Gaussian Beam Waist, 2 w 0 , and its divergence, 2θ, for λ = 1.6 μm 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 2θ 
                 1° 
                 0.3° 
                 0.1° 
                 0.05° 
                 0.03° 
                 0.01° 
               
               
                 θ [Rad] 
                 0.0087 
                 0.0026 
                 0.00087 
                 0.0004 
                 0.00026 
                 0.000087 
               
               
                 2 w o  [mm] 
                 0.112 
                 0.192 
                 0.59 
                 1.28 
                 1.97 
                 5.89 
               
               
                   
               
            
           
         
       
     
     The emitter housing  503  comprises a beam coupler that couples the laser path  502  to the laser emitter  504  and that conditions the beam  501  to be emitted  505 .  FIG. 6  illustrates the beam coupler  601  of the laser housing coupled to the optical fiber laser path  502 . The coupler  601  conditions the beam by expanding the beam to obtain a desired beam profile. 
       FIG. 7  illustrates one embodiment of the coupler  601 . Here, the coupler  601  comprises an entrance interface  702  in contact or coupled to an exit surface of the fiber  502 . The expanded beam fiber coupler  601  comprises a material that has a similar refractive index, n 2 , as the refractive index, n 1 , of the fiber&#39;s  502  core. In some embodiments, the beam coupler  601  is made of the same material as the fiber&#39;s  502  core. In still further embodiments, the beam coupler  601  and fiber  502  core is a continuous volume of material. The similarity of refractive indexes between the fiber  502  core and the beam coupler  601  reduces Fresnel reflection losses at the interface  702 . 
     The coupler  601  has a profile  707  configured to provide a desired intensity distribution  708  at the coupler exit  709 . The desired intensity distribution  708  may be symmetrical or asymmetrical. Symmetrical intensity distributions  708  may include circularly symmetrical distributions, where intensity, I, is a function of radius, r. The intensity distribution  708  arises from total internal reflection (TIR)  705  of rays  704  within the beam coupler  601 . In some embodiments, the intensity distribution  708  is Gaussian. In other embodiments, the intensity distribution  708  follows some other bell-shaped curve. 
     In some embodiments, the coupler exit  709  is optically coupled to the emitter optics directly. In other embodiments, the beam undergoes further conditioning prior to the emitter. In the illustrated embodiment, the coupler exit  709  is optically coupled to a beam shuffler  602 . An embodiment of the beam shuffler  602  is illustrated in  FIG. 8 . 
     The beam shuffler  602  comprises a fiber bundle having an input arrangement  801  and an output arrangement  802 . The fiber bundle comprises a plurality of optical fibers  803  having input surfaces optically coupled to the output surface  709  of the beam coupler  601 . The optical fibers  803  may be made of the same material as the coupler  601 , or other material having a similar index of refraction, n 3 . In some embodiments, the optical fibers  803  lack claddings or have reduced claddings to reduce the space between fibers  803  and reduce light loss at the interface between output surface  709  and the input  801 . 
     The output fiber bundle arrangement  802  differs from the input fiber bundle arrangement  801  in a manner adapted to provide an output intensity distribution  805 . As discussed above, in some embodiments, each module FOV has an inner radius and an outer radius. In some cases, the inner radius and outer radius can differ by several kilometers. Accordingly, if the beam had isotropic intensity, the irradiance of the detection zone near the outer radius could be significantly less than the irradiance near the inner radius. Indeed, any symmetric distribution  708  provides an unequal irradiance throughout the detection zone. To reduce these effects, the output fiber bundle arrangement  802  is configured to provide an asymmetrical spatial intensity profile  805 . The asymmetrical intensity profile is formed because fibers  808 ,  809  with an input near the peak input intensities  806 ,  807  have outputs at locations corresponding to farther detection distances. Any desired output intensity function  805  may be obtained by such reshuffling. For example, the output intensity function  805  may be a monotonically decreasing intensity function. Additionally, in some embodiments, the centers of the fibers  803  are not symmetrically distributed about the center of the input  708 . Accordingly, the input intensity function  708  is sampled by the fiber bundle  801  asymmetrically. This allows the output intensity function  805  to more accurately approximate a desired profile. For example, in the illustrated embodiment, fiber  808  is closer to the peak intensity value than fiber  809 . Accordingly, fiber  808  samples a higher intensity value  806  than intensity value  807  sampled by fiber  809 . In other embodiments, shuffler  602  may include fiber optic couplers joining two input fibers  803  to form a single output fiber  810 . In such embodiments, the exit intensity from the output fiber  810  may be the sum of the input intensities of the two input fibers  803 . 
     After transmission through the emitter optics, the spatial intensity function  805  is transformed into a radiant intensity function. In particular embodiments, the radiant intensity function is or is an approximation of the radiant intensity function (measured in Watts per steradian, or W/sr): 
                         J   ⁡     (   θ   )       ∝     R   2       ;     R   =     h     cos   ⁢           ⁢   θ           ,           (     8   ⁢   ab     )               
where h is the approximate height of the system and θ is the vertical beam angle with respect to the mast.  FIG. 9  illustrates this geometry in the context of an example platform on a mast  902  with inner detection radius R 1  of 5 km and an outer detection radius, R 2  of 15 km. Here, h is the height in the z direction. The x coordinate illustrates distance from the transmitter T x , where y would refer to the lateral coordinate. θ is the vertical angle measured from the mast. At R 1  the angle is θ 1 , at R 2  the angle is θ 2  and the difference between the angles is Δθ. Additionally, β is the complement of θ and measures the angle from sea level to T x .  FIG. 9  further illustrates, an example target A T  just within range of Tx.
 
     In this geometry, the emittance as a function of R is (ignoring atmospheric effects): 
                     E   ⁡     (   R   )       =           J   ⁡     (   θ   )       ⁢   cos   ⁢           ⁢   β       R   2       .             (   9   )               
Accordingly, the radiant intensity given in Eq. (8ab) compensates for the dependence of E(R) on R −2 . For marine platforms: β&lt;&lt;1, so that J(θ) is as follows:
 
                     J   ⁡     (   θ   )       =         P   o     Δϕ     ⁢       F   ⁡     (       θ   1     ,     θ   2       )           cos   2     ⁢   θ                 (   10   )               
where P O  is total beam power, Δϕ is beam azimuthal range of a single facet, and F-factor, is
 
                     F   ⁡     (       θ   1     ,     θ   2       )       =     h       R   2     -     R   1                 (   11   )               
including R-formula, as in Eq. (8b). Eq. (10) includes both R 2 -profile as in Eq. (8a) and power normalization, while
 
                   Δφ   =     w   R             (   12   )               
where w is azimuthal range value. The azimuthal range may vary depending on embodiment, but remains less than a threshold, w T , defined by the implementation. This can be done, at least, in two ways, either keeping Δφ constant, or w constant, where the first case can be preferable in order to keep well-controlled total FOV combined of a number of modules. In such a case, w-value will be variable, equal to w T -value, for R=R 2 :
 
     In other implementations, the system may be mounted at other locations. For example, the system may be mounted on an aircraft or helicopter. In such an example, β may be not be &lt;&lt;1. In these implementations, J(θ) will vary, but may be determined in a straightforward extension of the above analysis. 
     Additionally, although discussed in terms of a multimode fiber delivery path  502 . A coupler  601  and shuffler  602  may likewise be applied in the case of a free space path  502 . Additionally, in embodiments without large power requirements, the path  502  may comprise a single mode fiber. In these embodiments, the coupler  601  and shuffler  602  may or may not be applied, depending on implementation. 
     Returning to  FIGS. 5 and 6 , the output  811  of the beam shuffler is directed into emitter optics  504 . In some embodiments, the emitter optics comprises a collimating lens system.  FIG. 10  illustrates an example collimating lens system. In this figure, the fiber  1010  with core diameter, d F , is illustrated. For example, the fiber  1010  may be the output fiber bundle of the shuffler  602 , or if a shuffler  602  is not employed, the output of the beam expander  601 . In still further embodiments, neither a beam expander  601  nor a shuffler  602  are employed, and the fiber  1010  is the output of the beam path  502 . In one embodiment, d F =(d F ) min =290 μm=0.29 mm, with (N A )=0.4; thus, f#=1.14, and, D/2f=0.44: 
                     f   =         d   F     Δϕ     =         0.29   ⁢           ⁢   mm     0.0066     =     44   ⁢           ⁢   mm           ;     D   =       f     f   #       =         44   ⁢           ⁢   mm     1.14     =     38.6   ⁢           ⁢   mm                   (   13   )               
The following general relation for multi-mode fiber optics applies:
 
                       4   ⁢           ⁢   f   ⁢     #   2       +   1     =     1       (     N   A     )     2               (   14   )               
From this relation: (N A )=0.447 for f#=1, and f#=1.14 for (N A )=0.4, while, the Ettendue theorem has the form:
 
2 d   F ( N   A )=(Δϕ)· D   (15)
 
This is the optical version of the 2 nd  principle of Thermodynamics, which is a consequence of the Liouville Theorem.
 
     Bottom intensity value  1030 , is transformed to the same upper (or, double-rescaled) exit angular intensity value  1030 , as it is shown for the three upper exit values  1030 ; same with intensity values  1031 . This occurs because the spatial intensity values  1032 , for z-coordinated at the exit of fiber core  1010 , are transformed to angular intensity values  1033  at the lens exit, and this relation is inverse (i.e., upside-down). 
     In some embodiments, an actuator  1034  may be coupled to the fiber  1010 . For example, the actuator  1034  may comprise a piezoelectric actuator. This may be used to change the position of the beam axis  1039 , for example, in the z direction. As a result, the scanning range (R 1 , R 2 ) may be modified. For example, the range might be modified from (5 km, 15 km) to (8 km, 18 km). 
     Returning to  FIG. 9 , an example of calculating radiant intensity at the far range of an embodiment is provided. Eq. (10) becomes: 
                     J   ⁡     (   θ   )       =         P   o     Δϕ     ⁢     1       1     cos   ⁢           ⁢     θ   2         -     1     cos   ⁢           ⁢     θ   1             ⁢     (     1       cos   2     ⁢   θ       )               (   16   )               
To calculate the radiant intensity, J(θ), for R=15 km, assuming R 1 =5 km, R 2 =15 km, w=100 m, and P O =6.667·10 6  W, and:
 
                   Δϕ   =       W     R   2       =         100   ⁢           ⁢   m       15   ⁢           ⁢   km       =     0.00666   =     0.382   ⁢   °                   (   17   )               
And, equivalent pulse energy, E O , is (for τ L =6 nsec)
 
 E   O =τ L   ·P   O =(6.667·10 6  W)(6·10 −9  sec)=40 mJ  (18)
 
Also, assuming nominal repetition frequency value of n O =100 Hz, according to Eq. (3), the equivalent continuous-work (CW) power,  P , is
 
   P =P   O   n   O τ L   =E   o   ·n   O =(40·10 −3 J)(100 Hz)=4 W  (19)
 
For R=R 2 =15 km, Eq. (16) becomes
 
                     J   ⁡     (   θ   )       =         P   o     Δϕ     ⁢     (     1       cos   ⁢           ⁢     θ   1       -     cos   ⁢           ⁢     θ   2           )     ⁢     (       cos   ⁢           ⁢     θ   2         cos   ⁢           ⁢     θ   1         )               (   20   )               
where θ 1 =89.43° (5 km) and θ 2 =89.8° (15 km). Using Eq. (17), the value of radiant intensity at the front of the target  901  is:
 
                     J   ⁡     (   θ   )       =           (         6.67   ·     10   6       ⁢           ⁢   W     0.00666     )     ⁢     (     1       cos   ⁢           ⁢   89.43   ⁢   °     -     cos   ⁢           ⁢   89.8   ⁢   °         )     ⁢     (       cos   ⁢           ⁢   89.43   ⁢   °       cos   ⁢           ⁢   89.8   ⁢   °       )       ==       (       10   9     ⁢           ⁢   W     )     ⁢     (   155   )     ⁢     (   2.84   )         =       4.41   ·     10   11       ⁢           ⁢     W   /   sr                 (   21   )               
In some cases, the target  901  is a non-Lambertian reflecting optical system (such as a periscope). Such targets  901  may be called optical-augmented devices (OADs) herein.
 
       FIGS. 11A-D  illustrate various detection subsystems implemented in accordance with various embodiments. Each system&#39;s detection subsystem detects and processes laser pulses reflected from the module&#39;s FOV. In some implementations, a single detection subsystem is sufficient, while in other implementations multiple subsystems or subsystem branches may be employed. 
     The illumination and optical power at the detector relates to the illumination and optical power at the reflector as follows. 
                       η   DR     =         P   5       P   3       =       A   L       π   ⁢           ⁢     R   2     ⁢     sin   2     ⁢   α           ;       A   L     =       π   ⁢           ⁢     D   2       4               (     22   ⁢   ab     )               
where D is the lens diameter, R the distance from reflector to detector, and α is the reflection divergence half-angle. P 5  is the power at the detector while P 3  is the power at the reflector surface. For (Lambertian) clutter reflectors (using prime to distinguish clutter objects):
 
α′=90°  (23)
 
while, for the target (non-Lambertian), α&lt;&lt;1, such as:
 
α=0.25°=0.0044=4.4·10 −3   (24)
 
     From well-known radiometric definitions:
 
 P   5   =E   5   A   5   ;P   3   =E   3   A   3   (25ab)
 
where E is illumination or irradiance. Therefore, substituting Eq. (25b) into Eq. (22a), we obtain
 
                     P   5     =         E   3     ·     A   3     ·     A   L         π   ⁢           ⁢     R   2     ⁢     sin   2     ⁢   α               (   26   )               
introducing focal length of the detection optics and system magnification results in:
 
                     P   5     =         E   3     ·     A   5     ·     A   L         π   ⁢           ⁢     f   2     ⁢     sin   2     ⁢   α               (   27   )               
or,
 
                       P   5       A   5       =       E   5     =         E   3     ·     A   L         π   ⁢           ⁢     f   2     ⁢     sin   2     ⁢   α                 (   28   )               
Introducing brightness (or radiance), B 3 , at the reflector then, the well-known basic radiometric formula results:
 
                     E   5     =         B   3     ·     A   L         f   2               (   29   )               
This formula shows that the retro-reflectors, such as periscopes, which have high brightness, image very well. However, they image into a very small spot, which is typically much smaller than pixel size (linear), a.
 
     An example is a periscope cross-section as a reflector object, with diameter, d=7 cm. Assuming typical: R=10 km, and f=30 cm, then the image sizes is: 
                     s   =       d   m     =         7   ⁢           ⁢   cm       3.33   ·     10   4         =         2.1   ·     10     -   4         ⁢           ⁢   cm     =     2.1   ⁢           ⁢   µm             ,           (   30   )               
where m is demagnification (m=R/f). If a 50 μm sensor (pixel) size is used (i.e., a=50 μm), then:
 
                     a   s     =       50   2.1     =   23.8             (   31   )               
i.e., periscope cross-section cannot be imaged (in other words, the system is a pseudo-imaging system, where the target images do not satisfy the resolving criteria of having images extending across at least two sensors).
 
     The ratio of clutter/target powers, may be written as 
                       P   5       P   5   ′       =           E   3     ⁢     A   5     ⁢     A   L         π   ⁢           ⁢     f   2     ⁢     sin   2     ⁢   α             E   3   ′     ⁢     A   5   ′     ⁢     A   L         π   ⁢           ⁢       f   2     ⁡     (   1   )                     (   32   )               
Additionally:
 
 E   3   =r E   2   ;E   3   ′=r′E   2 ′  (33ab)
 
where subscript “3” denotes the exit plane of the reflector plane, while subscript “2” denotes the entrance plane of the reflector, and r and r′ are Fresnel (energy) effective reflection coefficients for target and clutter, respectively. Thus:
 
                       P   5       P   5   ′       =             rE   2     ⁢     A   5     ⁢     A   L         π   ⁢           ⁢     f   2     ⁢     sin   2     ⁢   α             r   ′     ⁢     E   2   ′     ⁢     A   5   ′     ⁢     A   L         π   ⁢           ⁢       f   2     ⁡     (   1   )             =       (       A   5       A   5   ′       )     ⁢     (     1     sin   ⁢           ⁢   α       )     ⁢     (     r     r   ′       )                 (   34   )               
where, E 2 =E 2 ′ (e.g, the same laser illumination is incident on target and clutter), and clutter reflection beam is imaged, uniformly; i.e., filling up whole pixel area; thus,
 
 A   5   ′=a   2 .  (35)
 
Accordingly:
 
                       P   5       P   5   ′       =       (       A   3       m   2       )     ⁢     (     1     a   2       )     ⁢     (     1       sin   2     ⁢   α       )     ⁢     (     r     r   ′       )               (   36   )               
Introducing the resolving element, as described herein:
 
                         P   5       P   5   ′       =         A   3         (     δ   ⁢           ⁢   l     )     2       ⁢     (     1       sin   2     ⁢   α       )     ⁢     (     r     r   ′       )         ,           (   37   )               
where δl is the pixel resolving element (in other words δl is the size of an object that is imaged to the size of the pixel) (δl=m*A), and, for circular periscopic cross-section with diameter, d:
 
                     A   3     =       π   ⁢           ⁢     d   2       4             (   38   )               
and, Eq. (37) becomes,
 
     
       
         
           
             
               
                 
                   
                     
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                       5 
                     
                     
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                   39 
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     As an example, the resolving element for δl, for a=50 μm, f=20 cm, and R=10 cm is:
 
(δ l )= ma =(50 μm)(5·10 4 )=25·10 5  μm=25·10 2  mm=2.5 m  (40)
 
     To continue this example, the power ratio for (δl)=2.5 m, d=7 cm, and α=1°, assuming: r=r is: 
                       P   5       P   5   ′       =           (     38.46   ⁢           ⁢     cm   2       )         (     2.5   ⁢           ⁢   m     )     2       ⁢     (     3   ⁢     ,     ⁢   283     )       =             (   38.46   )     ⁢     (     10     -   4       )           (   2.5   )     2       ⁢     (     3.28   ·     10   3       )       =         (   20.2   )     ⁢     (     10     -   1       )       =     2.2   .                   (   41   )               
Accordingly, voxel inference (i.e., distinguishing a true target from a potential false target using the presence of a reference clutter signal) may be applied in this example because both powers have comparable values. In general, so long as the power ratio for the clutter signals and potential target signals are within the dynamic range of the detector, both signals may be read by a single detector.
 
     As a contrary example, assume: f=30 cm, a=20 μm, α−0.25°, R=10 km, d=7 cm, and r=r′. Here the power ratio of retroreflected target signal to Lambertian clutter signal is 
                       P   5       P   5   ′       =           38.46   ⁢           ⁢     cm   2           (     66   ⁢           ⁢   cm     )     2       ⁢     (     52   ⁢     ,     ⁢   500     )       =     463.5   ⪢   1               (   42   )               
This power ratio exceeds typical dynamic ranges of available photodetectors, and hence voxel inference cannot be applied using a single detection branch.
 
     Accordingly, for small a-angles and small-δl, the target power is much higher than that for reference clutter; thus, the voxel inference cannot be applied within the single system; otherwise the voxel inference (within the same system) can be applied. 
     This reflects the general fact that minimizing both false negatives and false positives within a single detection system may be contradictory. In general, to minimize false negatives, the target signal is maximized by reducing sensor size, a. This also reduces the NEP (noise equivalent power) of the system. 
     In contrast, to minimize false positives, ability to perform voxel inference is maximized; e.g., both signal and clutter powers are brought within the system detector range. 
     An R* parameter may be defined as the distance, that:
 
 P=P′;r=r′   (43ab)
 
The use of equality for R* is for simplicity of explanation. In general, the relevant distance is where both powers are within the system detection range.
 
     As an example, typical conditions might be d=7 cm, α=1°, f=20 cm, and a=50 μm. The R* value is obtained from 
                 (     δ   ⁢           ⁢   l     )     2     =         (       π   ⁢           ⁢     d   2       4     )         sin   2     ⁢   α       =         (     38.48   ⁢           ⁢     cm   2       )     ⁢     (     3   ⁢     ,     ⁢   283     )       =       126   ⁢     ,     ⁢   330   ⁢           ⁢     cm   2       =       126   ⁢     ,     ⁢     330   ·     10     -   4         ⁢           ⁢     m   2       =     12.63   ⁢           ⁢     m   2                     
Thus,
 
(δ l )=3.55 m  (44)
 
and,
 
             m   =       (       δ   ⁢           ⁢   l     a     )     =         3.55   ⁢           ⁢   m       50   ⁢           ⁢   µm       =           3.55   ·     10   6       ⁢           ⁢   µm       50   ⁢           ⁢   µm       =     7.1   ·     10   4                   
thus, the R*-value, is
 
 R*=f·m =(20 cm)(7.1·10 4 )=142·10 4  cm=142·10 2  m=14.2 km  (45)
 
Less than this distance, P&gt;P′, while greater than this distance, P′&gt;P.
 
From Eq. 39:
 
                       R   *     =             A   3         sin   ⁢           ⁢   α       ⁢     (     f   a     )       =           π   ⁢           ⁢     d   2       4       ⁢     (     1     sin   ⁢           ⁢   α       )     ⁢     (     f   a     )           ⁢     
     ⁢     and   ⁢     :               (   46   )                 R   *     =           π     2     ⁢     (     d     sin   ⁢           ⁢   α       )     ⁢     (     f   a     )       =       (   0.89   )     ⁢     (     d     sin   ⁢           ⁢   α       )     ⁢     (     f   a     )                 (   47   )               
To increase the ability to perform voxel inference, the reference clutter signal must be reduced in respect to target signal by reducing the R* value. Therefore, according to Eq. (47), adjustment of following parameters in the following manner minimizes R* value:
 
 d     ;α     ;f     ;a         (48abcd)
 
Conditions (48ab) are fixed for specific target (e.g., periscope) types, so system parameters determining Eq. (48cd) may be modified. Reducing f-value, is equivalent to reducing system sensitivity because reducing f value is equivalent to reducing D value in the f# (i.e., weakening light collection). Accordingly, preferably, the sensor (i.e., pixel) size a is increased to reduce R*. Additionally, a second system having a different a value will have a different R* value. Accordingly, in some implementations, two parallel detection systems are used for distances shorter than R&lt;R*.
 
     Minimizing both false negatives and false positives at the same time is a central challenge with the IOS. This is done by maximizing the strength of the laser beam reflected from the periscopic target, and, at the same time, providing voxel inference (i.e., to process information from clutter correlated to the target, which includes, for example, the body of periscope, wave disturbance by the submarine, etc.) The first task leading to minimization of false negatives [target misses] is detecting the signal from the target. This is performed, in one embodiment, for example, by elements  1103  and  1104  in the upper branch of the detection system of  FIG. 11D . It can also be performed by the corresponding elements in the upper branch of  FIGS. 11B and 11C . 
     The second task [signal from correlated clutter] leading to minimization of false positives [false alarms] relates to detecting a signal from correlative clutter. This task is performed, for example, by elements  1109 ,  1103 ′ and  1104 ′ in the lower branch of detection system in  FIG. 11D  (or in the corresponding elements of  FIGS. 11B and 110 ). In ideal case, the powers attained in both branches are the same or close to each other, which means that P=P′ as in equation 43a. The equality is realized at a distance, R=R*, as in equation 47. For R&gt;R*, we obtain P smaller than P′, while for R&lt;R* we obtain P&gt;P′. Therefore and because P is typically larger than P′, a goal of the system is to minimize the R* value to increase the range of operation of voxel inference. However, in circumstances where P′ is larger than P, the system can be configured to provide the inverse operation. 
     According to equation 47, the only parameters that can be controlled or varied by modifying the system are f and a, where f is focal length, and a is the linear pixel size. In order to increase the value of P′ in the lower branch of  FIG. 11D , we need to increase the a value or reduce the f value, or both. This leads to increasing the pixel resolving element defined by equation 40. For too small a, which is pixel linear size, a larger pixel size is used in detector array PDA  1103 ′ in the lower branch. In some embodiments, the pixel size used in PDA  1103 ′ is chosen as greater than the pixel size in PDA  1103 . Accordingly, various embodiments use two pixel sizes—a smaller pixel size in the upper branch, and a larger in the lower branch 
     Depending on system configuration and constraints, component availabilities and other design considerations, it may not always be possible or practical to implement detectors  1103 ,  1103 ′ with actual pixel sizes meeting this constraint. Accordingly, in some embodiments, a pixel cluster concept can be applied in the lower branch in which multiple adjacent pixels are clustered together to yield a larger effective pixel size. For example, four (2×2), nine (3×3), (they need not be in a ‘square’ array) or more pixels can be configured to work in coordination as one single pixel. This electronically increases pixel size in the lower branch. 
     The pupil  1109  in the lower branch of  FIG. 11D  may be included to provide an equivalent decrease of diameter, D, of the collection lens. Then, keeping as typically fixed f#=f/D can allow a decrease in the f value of the same amount, or approximately the same. For example, if D is decreased 1.5 times, then the f value can also be decreased 1.5 times. Thus, we obtain cumulating effect of decreasing R* value, thus minimizing both false negatives and false positives. This is because there could be a lot of strong reflective signals, but by using the second parallel branch with a regulated pupil  1109 , false signals that do not have properly correlative clutter can be reduced or eliminated. This means reducing or even eliminating false alarms. 
     The detection subsystem may comprise a filter  1101 . The filter  1101  passes the laser wavelength while blocking other light. This reduces, minimizes, or eliminates optical noise. For example, such optical noise might arise from unwanted solar reflections, or other light sources. Because the laser beam is practically monochromatic, the filter  1101  may be a narrow wavelength filter. For example, the filter  1101  may comprise an interference passband filter, such as a Bragg filter. These filters demonstrate a “blue-shift” effect for slanted beams, the form: λ=λ O √{square root over (1−sin 2  α/n 2 )}, where a is the slant angle λ O  is interference wavelength under normal incidence (α=0). This blue-shift effect can be quite significant for narrow passband filters and moderate incidence angles. However, as discussed above, in some embodiments, each flash FOV may be less than 1°, for example 0.36°. The blue shift effect in these cases is small enough that the interference filter performance is not compromised. For example, for α=0.36°, Δλ=0.012 nm. 
     In further embodiments, the filter  1101  may comprise a polarizing filter. As discussed above, in some embodiments, the emitted light beam may have a polarization signature. The filter  1101  may be configured to allow only light having that polarization signature to pass. For example, if the emitted beam is TH-polarized, the filter  1101  may comprise a TH-polarization filter. Man-made targets may be more likely to reflect light without change in polarization when compared to natural clutter, such as waves and plant matter. Accordingly, filter  1101  may increase the likelihood of target detection by reducing clutter signatures. 
     In still further embodiments, the filter  1101  may comprise a non-uniform neutral density filter. A non-uniform neutral density filter  1101  may be used instead of or to augment the normalizing system of the emitter. For example, the non-uniform neutral density filter  1101  may reduce the optical signal from close objects to normalize the received signal. 
     In the illustrated embodiment, the detection optics  1102  is optically coupled to the filter  1101 . In some embodiments, the detection optics  1102  is disposed behind the filter  1101  in the optical path. In other embodiments, the detection optics  1102  may be in front of the filter  1101 . The detection optics  1102  is configured to transfer received light to the detector  1103  in a pseudo-imaging manner. In still further embodiments, a filter  1101  is not employed. 
     In some embodiments, the detection system comprises a pupil  1109  coupled to, or integrated with, the optics  1102 . In the optical path, the pupil  1109  may be behind or in front of optics  1102 . The pupil  1109  may be used in the system to control the effective aperture, and thus, f#, of the optics system  1102 . In embodiments having a pupil  1109 , the pupil  1109  may be used to control the instantaneous dynamic range of the detection system. In some instances, reflected signals may exceed the system dynamic range—for example, if an object with a strong reflected (e.g., a non-Lambertian reflector) signal is near clutter with weaker reflected signal (e.g. a painted marine vessel). In such a case, the pupil may be used to reduce the light gathering ability of the optics system  1102 , to bring the reflected signals within the dynamic range of the detector  1103 . 
     In some embodiments, the pupil  1109  is adjustable, and to control the f# of the system, the detection optics  1102  has an adjustable focal length, f. For example, in some embodiments, the f# may be between 1 and 5. In systems without a pupil  1109  or with a fixed pupil  1109 , the focal length f of the detection optics  1102  may also be fixed to set the desired f#. 
     As discussed below, the detector  1103  may comprise a one or two dimensional array of individual sensors  1106  separated by gaps ( FIG. 12A ). Alternatively, the detector  1103  may comprise an array of rows of gapless one dimensional sensor  1106  arrays ( FIG. 12B ). The detection optics  1102  is configured to transmit light to the detector  1106  in a manner that avoids a possible detection signal falling into the gaps between sensors  1106 . 
     In the case of long distance detection, such as optical periscope detection (OPD), the photodetector array  1103  creates potential problem with missing periscope target during pseudo-imaging operation. This is because, the periscopic target is very small, with 10 cm-diameter, for example. In such a case, its image, at very long distances (e.g., R=10 km), is very small, down to even 0.1 μm size. Then, if photodetector array  1103  filling factor, F (i.e, the ratio between sensor area to total array area), is not perfect (i.e., F=100%), this target image can be missed in the space between sensors  1106 . This is illustrated in  FIG. 12A , where a is the sensor  1106  size, and δa is the half-pitch between sensors. Thus, the filling factor, is: 
                   F   =       a     a   +     δ   ⁢           ⁢   a         =     1     1   +       δ   ⁢           ⁢   a     a                   (   49   )               
In  FIG. 12A , a photodetector 2D geometry is shown with a less than 100% filling factor (F&lt;1). In such, if imaging optics with high resolution were used, the periscopic target image  1107  can be missed in the gap between sensors  1106 . Assuming, for example, a=20 μm, and δa=0.1 μm, e relative pixel space is: (δa/a)=0.01/20=0.005, and F=0.995=99.5%; i.e., even for such high filling factor, a small target can be missed.
 
     In one embodiment, this problem is solved by increasing the size of the target signal at the detector  1103 .  FIGS. 13A-D  illustrate an embodiment of detector optics  1103  that increases the size of the target signal. The optics system  1103  comprises a lens, lens system, catoptric system, or catadioptric system the aberrates the image by de-focusing of image plane; i.e., providing that the image, equation is not well satisfied. Then, by artificially increasing target signal sizes to 1 μm, for example, F=0.95=95%, and the previous filling factor (F=99.5%) may be satisfactory. Imaging optics in this highly-aberrated mode satisfy both the etendue theorem (or, Liouville theorem) for concentrator optics, and, at the same time, optimize detector optics for maximum power collection (and maximum electrical SNR). For example, in the illustrated embodiment, the detector  1102  may be positioned closer to or farther from the optics system  1103  than the focal length of the optics system  1103 . In other embodiments, the optics system  1103  may have a predetermined type and magnitude of aberration to produce the desired target signal sizes. In one embodiment, the detection optics  1102  produces an image with a circle of confusion having a diameter as large or larger than a distance between adjacent photodetectors  1106  of the photodetector array  1103  (i.e., a radius greater than or equal to δa). For example, the radius of the circle of confusion may be one, two, or three times larger than δa. In other embodiments, the circle of confusion is determined according to the photodetector  1106  size a. For example, the diameter of the circle of confusion may be equal to a. In one embodiment, each sensor  1106  comprises an avalanche photo diode (APD), with a being about 25 μm. In a further embodiment, the point spread function (PSF) exceeds the Airy ring by a factor of 5-10 (turning a 2 μm target image into a 10 20 μm-spot). In addition to reducing the risk that a target signal will fall on dead space between pixels, the aberrated imaging system may disperse the signal across multiple pixels, reducing overload when a strong target signal is present. 
     According to the Nyquist resolution criteria, the smallest resolving object should produce an image across at least two pixels  1106  of the array  1103 . If, for example, this object is a periscope cross-section, with 10 cm diameter, then for detection optics  1102 , with focal length f=30 cm and distance, R=10 km, the system demagnification, m=R/f=10 km/30 cm=3.33*10 4 . Then, the Nyquist-satisfying pixel size is equal to 5 cm/3.33*10 4 =1.5 microns, i.e, smaller than the Raleigh resolution (1.22*λ*f#=1.59 microns, for f#=1 and λ=1.3 microns), and which is comparable with speckle size for this system. Thus, in typical conditions, such small objects cannot be imaged without significant speckle-sized distortion. Therefore, the integrative optics system is “pseudo-imaging” rather than an imaging system. In other words, the optics  1102  produces images of targets that do not satisfy the Nyquist criteria for imaging a target. 
     In various embodiments, the f# of the optics system is as small as possible. For example, the f# may be between 1 and 0.5. However, in other embodiments, f#s between 1 and 5, or even higher may be employed. 
     The size of the detector  1103  may depend on considerations such as the sensor  1106  size, the effective diameter of the optics system and the distance from the detector  1103  to the optics (which may differ from the focal length for de-focusing embodiments). For a lens system with an effective diameter of D=30 cm, for example, f=30 cm, while Δϕ=0.38°=0.0066; thus, Δϕ/2=0.0033, and
 
 d=Δϕ×f =(0.0066)(30 cm)=1.98 mm  (50)
 
and, for vertical FOV (Δθ=0.37°), d=1.94 mm for 50 μm APD sensors (e.g.,  1106 ,  FIGS. 12A &amp;B). Then, 1.98 mm=1980 μm; thus, the number of horizontal APD sensors is
 
                     2   ⁢     N   x       =       1980   50     =   40             (   51   )               
and, the number of vertical APD sensors is (e.g, in a APD detector array  1103  ( FIG. 12A )
 
     
       
         
           
             
               
                 
                   
                     2 
                     ⁢ 
                     
                       N 
                       y 
                     
                   
                   = 
                   
                     
                       1940 
                       50 
                     
                     = 
                     39. 
                   
                 
               
               
                 
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                   52 
                   ) 
                 
               
             
           
         
       
     
     In some embodiments, the ratio of the sensed energy from a potential target to the sensed energy from the surrounding clutter is used a parameter for target detection. The sensed area per image sensor  1106  (i.e., the area illuminated by a flash whose reflection impinges on a sensor  1106 ) is correlated to the sensed energy from the surrounding clutter. This parameter is dependent on factors such as de-magnification, FOV, sensor size, and distance from the sensed area to the system. 
     In  FIG. 13B , the detection optics system  1103  comprise a compound parabolic concentrator  1301 . In the illustrated embodiment, the detector  1102  is coupled to the absorber plane  1302  of the concentrator  1301 . In other embodiments, the detection optics system  1103  may further comprise one or more lenses  1303  disposed between the concentrator  1301  and the detector  1102  ( FIG. 3C ). In still further embodiments, the detection optics system  1103  may comprise an array of concentrators  1301  disposed behind a lens or other optics system  1303 . Individual sensors  1106  of the detector  1102  may be disposed at corresponding absorber planes  1302  of the array of concentrators  1301  ( FIG. 13D ). 
     As illustrated in  FIGS. 14A and 14B , in a further embodiment, the detection optics system  1103  comprises one or more tapered optical fibers  1401 . For example, the optics system  1103  may comprise an array of tapered optical fibers  1401 , each tapered fiber  1401  having an output at a sensor  1106 . This system directs more light onto the sensors  1106 , avoiding signal falling in the dead space between sensors. In some embodiments, the tapered optical fibers  1401  may be utilized in conjunction with or in replacement to, the concentrators  1301  and the lens system  1103 . 
     As discussed above, the detector  1103  may comprise a plurality of individual sensors  1106  arranged in various one or two dimensional pixel arrays. The sensors  1106  are selected to have a sufficient specific detectivity. Typically, in semiconductor detectors  1106 , the NEP (noise equivalent power) is defined by so-called specific detectivity, D*, in W −1  cm Hz 1/2 , by the following formula: 
                     (   NEP   )     =         A   ·   B         D   *               (   53   )               
where A is the photodetection area in cm 2  and B is the bandwidth in Hz. For semi-conductor detectors, D* is, approximately, proportional to wavelength, up to cutoff wavelength, λ cutoff, defined by energy gap, Eg, as: λ cutoff=hc/Eg, where h is the Planck constant and c is the speed of light. For Avalanche Photodiodes (APD), the speed is very high (even in picoseconds), but (NEP) is limited by Johnson (thermal) noise, where
 
                       r   .   m   .   s     =       〈     i   n   2     〉     =       4   ⁢           ⁢   kTB     R         ,           (   54   )               
where &lt; &gt; is the statistical ensemble average, i n  is the noise current, k is the Boltzmann constant, T is the temperature in Kelvins (K°) and R is the resistance (typically, R ˜20Ω). Then for typical applications, D* ˜1.9·10 11  Hz 1/2  cm W −1 , and, for pulse laser with pulse length: δt=6 ns, the bandwidth B=1/δt=1.67·10 8  Hz; and for APD pixel size: √{square root over (A)}=25 μm=25·10 −4  cm and √{square root over (B)}=1.3·10 4  Hz 1/2 , from Eq. (35):
 
                       (   NEP   )     o     =           A   ·   B         D   *       =           (       25   ·     10     -   4         ⁢           ⁢   cm     )     ⁢     (       1.3   ·     10   4       ⁢           ⁢     Hz     1   /   2         )           1.9   ·     10   19       ⁢           ⁢     Hz     1   /   2       ⁢   cm   ⁢           ⁢     W     -   1           =       1.68   ·     10     -   10         ⁢           ⁢   W                 (   55   )               
In other embodiments, the sensors  1106  may comprise photomultipliers. With photomultipliers with very high gain ˜10 7 , the dark current noise dominates, and:
 
                       (   NEP   )       DARK   ⁢           ⁢     CURRENT   ⁡     (     D   ⁢           ⁢   C     )           =         4   ·     10     -   17         η     ⁢     B     ⁢   W             (   56   )               
where η-quantum efficiency. Then, for η=0.8 and √{square root over (B)}=1.3·10 4  Hz 1/2 :
 
                         (   NEP   )       D   ⁢           ⁢   C       ≅         4   ·     10     -   17       ·   1.3   ·     10   4       ⁢           ⁢   W     0.8       =         6.5   ·     10     -   13         ⁢           ⁢   W     =     0.65   ⁢           ⁢   pW               (   57   )               
Accordingly, for typical embodiments, the NEP is assumed to be approximately:
 
( NEP ) O =0.5pW=0.5·10 −12  W=0.5·10 −18 MW=−183.01 dBM  (58)
 
     In further embodiments, the detector  1103  may comprise a CCD array. CODs have slower responses than APDs but NEP is lower and CCD pixel sizes are smaller. For example, for KODAK KAF-50100 Image Sensor, pixel sizes are 6 μm×6 μm, and Maximum Data Rate, B=18 MHz; i.e., (100)/(18)=5.5 slower than required for some implementations. In particular, implementations using laser pulses with approximately 10 nsec length are equivalent to B=100 MHz. By comparison, CCD speed limitation allows to measure only laser pulses 5.5-times longer; i.e., 16.5 m vs. 3 m for APD devices (since, cδt=(3*10 8  m/s)(10 −8  m)=3 m). On the other hand, the SNR-value is much better. This is, because, the CCDs are limited by dark current noise rather than by Johnson noise as the APDs are. As a result, their D*-values are much higher: about 10 12  W −1  cm Hz 1/2  vs. 10 9  W −1  cm Hz 1/2  for APDs. 
     In still further embodiments, the detector  1103  may comprise a solid state photomultiplier array. 
     The detection system further comprises detector electronics  1104  coupled to the detector  1103 . In some embodiments, the detector electronics  1104  may comprise normalizing electronics. For example, the normalizing electronics may be used to normalize the gain settings across the detector to supplement or replace the normalizing system of the emitter. For example, a non-linear detector response, following a general square-root function or sigmoid function curve may be applied so that detector elements receiving light from closer objects have lower gain than detector elements receiving light from farther objects. 
     In some embodiments, the detector electronics further comprise RISC processor arrays  1104 . Each RISC processor  1108  of array  1104  is coupled to a plurality of sensors  1106  of detector  1103 . In some embodiments, each RISC processor  1108  of array  1104  is coupled to a 3×2 grid of six sensors  1106 . In embodiments employing a 39×40 array of 50 μm APD sensors, an array of 256 RISC processors allows 255 RISC processors to be coupled to 6 APDs each, and one RISC processor  1108  to be coupled to 7 APDs. Each RISC processor  1108  receives a set of readouts from its connected APDs and performs a set number of operations on the set of readouts. In other embodiments, the detector electronics  1104  may comprise any other combination of analog or digital electronics systems. 
     In one embodiment, the RISC processors  1108  perform novelty filtering on their readouts. During the novelty filtering operation, each readout x i  is translated by some predetermined amount Δx to form a set of translated readouts x iO =x j +Δx. In other words, the x iO  has the same coordinates as x i , but its value is the value of x j  at Δx away. In some embodiments, the translation is performed using shift registers or other memory devices coupled to the processors  1108 . When the translated readouts are formed, the RISC processors  1108  send the translated readout values to the appropriate RISC processors. For example, if Δx is one unit down, then the RISC processor connected to the APD at (1,1) would send the readout from (1,1) to the RISC processor connected to the APD at (1,2). 
     Next, during the novelty filtering operation, each RISC processor subtracts x i −x io . If each readout is a binary value (for example, if the APD readout is treated as 1 if the APD detects more than a threshold amount of light and 0 if the detected amount of light is less than the threshold), this value will be 1 at edges of objects and 0 within and outside objects. In some embodiments, the RISC processor array  1104  outputs the subtracted readouts as a set of detected edges. In further embodiments, the RISC processor array  1104  performs further calculations. 
     In one embodiment, the RISC processor array  1104  calculates the squared Euclidean distance d E   2 , in the form; shown in N-space: 
                     d   E   2     =       ∑     i   =   1     N     ⁢         (       x   i     -     x     i   ⁢           ⁢   o         )     2     .               (   59   )               
This value d E   2  may be output by the RISC processor array  1104 . In various implementations, the squared Euclidean distance may be calculated for an entire sensor readout, for a row of sensors, for a column of sensors, or for a block of sensors connected by detected edges.
 
     These examples are intra-frame calculations (i.e., calculations performed on a single readout of the detector  1103 ). In further embodiments, the RISC processor array  1104  may perform inter-frame calculations (i.e., calculations performed on multiple readouts of the detector  1103 ). Examples of such inter-frame calculations are described in further detail below. 
     The RISC processor array  1104  is coupled to a detection processor  1105 . The detection processor  1105  receives data from the RISC processor array  1104  and performs various detection algorithms to determine if a target is detected. Examples of such detection algorithms are described in further detail below. 
     In further embodiments, parallel detection systems may be used to measure return flashes.  FIG. 11B  illustrates such an embodiment. In this embodiment, a first detection subsystem  1000  is configured to detect possible target signals, while a second detection subsystem  1120  is configured to detect possible reference clutter signals. In some implementations, the possible target signals are signals with high power reflections from non-Lambertian reflectors. For example, possible target signals may arise from ocular retroreflectors, such as binoculars or periscopes, or from other environmental features, such as caustics caused by waves. Reference clutter signals may comprise clutter signals that characteristically occur in proximity to true target signals. For example, for a periscope target, the reference clutter signals may comprise characteristic reflections from the periscope body or the submarine body. The reference clutter signals may be used by the signals to determine which of the possible target signals are true target signals. Such an implementation may be employed, for example, if the reflection signal strength from clutter objects, and in particular, reference clutter objects, is significantly different than the reflection signal strength from possible target objects. For example, if the reflection coefficient from a potential target object is much greater than the reflection coefficient from the surrounding reference clutter, a single detector  1103  may not be able to detect both signals. 
     In this embodiment, if filters  1101  and  1111  are employed, they may have similar filter characteristics. Subsystem  1000  is configured to have less greater light gathering ability, in order to detect the weaker of the potential target signals and clutter signals. Accordingly, the system  1000  lacks a pupil. Additionally, the detector  1103  may have larger sensor sizes than detector  1113 , such as 50 μm compared to 25 μm (linear size). The detection optics  1112  may vary from detection optics  1102  to accommodate the pupil  1119 . For example, the focal length of detection optics  1112  may be longer than the focal length of detection optics  1102  to accommodate the reduced diameter caused by pupil  1119 . 
     The detector electronics  1104 ,  1114  may be any combination of digital or analog circuitry, including RISC processors, sufficient to provide the voxel readouts to the detection processor  1105 . Additionally, in some embodiments, detectors  1103  and  1113  may share some detector electronics  1104 ,  1114 , components, for example, to combine the signals prior to providing the signals to detection processor  1105 . 
       FIG. 15  illustrates a method of operation of a system module, such as module  206 ,  207 . In step  1501 , the system emits a first pulse to illuminate a first facet of the module&#39;s field of view. As discussed above, field of view of the module is divided into facets, with each facet illuminated by a single laser flash. For example, a system providing a 360° field of view may comprise 10 modules, each with a 36° field of view. Additionally, each module may use 100 facet flashes to cover the 36° field of view, so that each facet flash illuminates at least 0.36°. In some embodiments, the laser has an energy of about 40 mJ per pulse and an effective pulse length of τ L =6 ns, providing a pulse power of about 6.667*10 6  W. In embodiments employing eye-safe lasers, the laser wavelength may be greater than 1 μm, and in particular, greater than 1.3 μm, or greater than 1.6 μm. In some embodiments, the module emits multiple pulses per facet. In these cases, step  1501  may be repeated multiple times. 
     In step  1502 , the system stabilizes the emitter and detector while detecting return pulses from objects within the facet field of view. As discussed above (for example, see  FIG. 9 ) the area of detection is often an annular section, for example, with an inner radius around 5 km and an outer radius around 15 km. Accordingly, in this example, return pulses from objects within the detection zone may take between 10 km/c≈0.033 ms and 30 km/c≈1 ms. The module is stabilized for the total time of possible return pulses so that sensors within the detector do not receive signals from objects at multiple locations within the detection zone. 
     The step  1502  of receiving return pulses further comprises time-gating the sensor readouts. Time gating the sensor readouts allows the system to determine the distance from the module to the object or clutter that reflected the laser pulse. Then, the minimum quantum of distance, δz, resolved by each laser pulse, is: δz=(0.5)cδt, where c=3·10 8  m/sec is speed of light in air (vacuum) and δt is the pulse width (for example, full width at half maximum). For example, for δt=10 nsec=10 −8  sec: δz=1.5 m, while for δt=1 nsec, δz=15 cm. The step of gating  1502  may comprise gating the detector at any rate up to the pulse repetition rate to obtain a desired distance resolution. The set of time gated sensor readouts, indexed by time, will be termed a set of voxels. Each pixel (i.e., sensor) has its voxel derivatives; each voxel with sizes: a x , a y , δz, where a x , a y —are pixel sizes, while δz is the temporal (i.e., distance) resolution. It should be noted that this is an approximation based on a system mounted at height h that is small compared to the distance R between the system and the target. Systems, such as aircraft or helicopter mounted systems, where the height h is large or on the order of R. δz may be replaced with δR, which provides non-orthogonal voxels, with sizes a x , a y , δR. Alternatively, such systems may translate the δR values to δz values. In these systems β ( FIG. 9 ) may be large, requiring an appropriate modification to the energy detection normalization set-up. 
     The module waits for at least the maximum return time for pulses to return from the farthest range of the detection zone. Then, in step  1503 , the module translate the next facet and repeats the method. For ranges on the order of 15 km, the maximum return times will be around 0.1 msec. Accordingly, the maximum repetition rate is about 10 kHz for one laser pulse per facet. However, lasers meeting the requisite power parameters typically have maximum repetition rates of about 100-200 Hz. Additionally, in some embodiments, multiple pulses are emitted per facet. A 100 Hz laser frequency allows emission of one pulse per facet and a scan rate of 100 facets per second. Allowing a module with a 38° field of view and 100 facets to have a scan rate of 1 scan/sec. 
     In this example, with one module FOV per second, (f=1 Hz) assuming horizontal mechanical tracking with N=100 channels, there are n −1 =10 msec between facets, which is achievable by current mechanical systems. Total return time, Δt, is much smaller than tracking-step-time (TST):
 
(Δ t )&lt;&lt;(TST)= n   −1   (60)
 
since Δt=10 −4  sec, while (TST)=10 −2  sec. Therefore, the mechanical tracking system can be relatively stable, since, there is a lot of time for stabilization. In this example, 99% of the time, the laser is not operating; so, this time can be used for stabilization purposes.
 
       FIG. 16  illustrates a method of target detection implemented by a system module. For example, this method may be performed by a detection processor  1105 , RISC array  1104 , or detection processor  1105  in combination with RISC array  1104 . In step  1601 , a set of voxels are obtained for processing. In some implementations, the set of voxels are a set of voxels from one facet of the module. In other implementations, the set of voxels may be obtained from some or all of the facets of the module. In some embodiments, the set of voxels may have been previously novelty filtered or otherwise processed by RISC array  1104 . 
     In some cases, the set of voxels obtained in step  1601  depends on the environmental visibility. The atmospheric attenuation, T A , may impact the detection range or the total detection space. T A  is the atmospheric attenuation in the form:
 
 T   A   =e   −σR   (61)
 
where R-distance from laser delivery sub-system to the target, and σ is atmospheric attenuation coefficient, based on the following well-known phenomenological formula (defined as distance, V, where image contrast is reduced to 1%):
 
                   σ   =       3.912   V     ⁢       (       λ   550     λ     )     q               (   62   )               
where V is called visibility, λ 550 , is the reference wavelength at λ=550, λ is the system laser wavelength, and q=q(V) is a power factor. (It should be noted that function: y=a x , where a&lt;1, is a monotonically-decreasing function of x. Therefore, the λ-power factor in Eq. (35) is monotonically-deceasing function of q.) Since, q-factor is monotonically-decreasing function of V, therefore, the attenuation coefficient, σ, is a faster decreasing function of V, than V −1 .
 
     As an example, in a system where λ=1.6 μm:
 
λ&gt;550 nm  (63)
 
The well-known phenomenological formula of dependence: q=q(V) has the form
 
             q   =     {           1.6   ,             for   ⁢           ⁢   V     &gt;     50   ⁢           ⁢   km                 1.3   ,             for   ⁢           ⁢   6   ⁢           ⁢   km     &lt;   V   &lt;     50   ⁢           ⁢   km                     0.16   ⁢           ⁢   V     +   0.34     ,             for   ⁢           ⁢   1   ⁢           ⁢   km     &lt;   V   &lt;     6   ⁢           ⁢   km                   V   -   0.5     ,             for   ⁢           ⁢   0.5   ⁢           ⁢   km     &lt;   V   &lt;     1   ⁢           ⁢   km                 0   ,             for   ⁢           ⁢   V     &lt;     0.5   ⁢           ⁢   km                     
The visibilities of equivalent atmospheric conditions are summarized in Table 3.
 
                     TABLE 3                  Visibilities and Equivalent Atmospheric Conditions                         #   Atmospheric Conditions   Visibilities               1.   Exceptionally Clear   V &gt; 50 km       2.   Very Clear   20 km ≤ V ≤ 50 km       3.   Clear   10 km ≤ V ≤ 20 km       4.   Light Haze    4 km ≤ V ≤ 10 km       5.   Haze   2 km ≤ V ≤ 4 km       6.   Thin Fog   1 km ≤ V ≤ 2 km       7.   Light Fog   0.5 km ≤ V ≤ 1 km         8.   Moderate Fog   0.1 km ≤ V ≤ 0.5 km                    
According to simulations, the atmospheric attenuation coefficient relation:
 
σ=σ( V ,λ)  (65)
 
includes both atmospheric absorption and atmospheric scattering, mostly represented by so-called Mie scattering. This modeling should be understood in such a sense that only “ballistic” photons reach photodetector array while both absorbed and scattered photons do not reach the receiver sub-system.
 
     The attenuation coefficient value, 2σ, can be presented as a function of visibility, V, for specific wavelength, λ, in the look-up table form, as shown in Table 4, for λ=1.6 μm, in the visibility range; V=1 km-6 km. According to Table 3, it is equivalent to thin fog (1 km≤V≤2 km), through haze (2 km≤V≤4 km), and part of light haze (4 km≤V≤10 km). 
     
       
         
           
               
             
               
                 TABLE 4a 
               
               
                   
               
               
                 Look-Up Table for 2σ, Versus Visibility Range: 1-2 km 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 V [km] 
                 1.1 
                 1.2 
                 1.3 
                 1.4 
                 1.5 
                 1.6 
                 1.7 
                 1.8 
                 1.9 
                 2.0 
               
               
                 q 
                 0.52 
                 0.53 
                 0.55 
                 0.56 
                 0.58 
                 0.60 
                 0.61 
                 0.63 
                 0.64 
                 0.66 
               
               
                 2σ [km −1 ] 
                 4.08 
                 3.70 
                 3.35 
                 3.07 
                 2.81 
                 2.58 
                 2.40 
                 2.22 
                 2.08 
                 1.93 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4b 
               
               
                   
               
               
                 Same as 2a, for V = 2-3 km 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 V [km] 
                 2.1 
                 2.2 
                 2.3 
                 2.4 
                 2.5 
                 2.6 
                 2.7 
                 2.8 
                 2.9 
                 3.0 
               
               
                 q 
                 0.68 
                 0.69 
                 0.71 
                 0.72 
                 0.74 
                 0.76 
                 0.77 
                 0.79 
                 0.80 
                 0.82 
               
               
                 2σ 
                 1.80 
                 1.70 
                 1.59 
                 1.51 
                 1.42 
                 1.34 
                 1.27 
                 1.20 
                 1.15 
                 1.09 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4c 
               
               
                   
               
               
                 Same as 2a, for V = 3-4 km 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 V [km] 
                 3.1 
                 3.2 
                 3.3 
                 3.4 
                 3.5 
                 3.6 
                 3.7 
                 3.8 
                 3.9 
                 4.0 
               
               
                 q 
                 0.84 
                 0.85 
                 0.87 
                 0.88 
                 0.90 
                 0.92 
                 0.93 
                 0.95 
                 0.96 
                 0.98 
               
               
                 2σ [km −1 ] 
                 1.02 
                 0.98 
                 0.93 
                 0.89 
                 0.85 
                 0.81 
                 0.77 
                 0.74 
                 0.71 
                 0.68 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4d 
               
               
                   
               
               
                 Same as 2a, for V = 4-5 km 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 V [km] 
                 4.1 
                 4.2 
                 4.3 
                 4.4 
                 4.5 
                 4.6 
                 4.7 
                 4.8 
                 4.9 
                 5.0 
               
               
                 q 
                 1.00 
                 1.01 
                 1.03 
                 1.04 
                 1.06 
                 1.08 
                 1.09 
                 1.11 
                 1.12 
                 1.14 
               
               
                 2σ [km −1 ] 
                 0.65 
                 0.63 
                 0.60 
                 0.58 
                 0.55 
                 0.53 
                 0.51 
                 0.49 
                 0.48 
                 0.46 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4e 
               
               
                   
               
               
                 Same as 2a, for V = 5-6 km 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 V [km] 
                 5.1 
                 5.2 
                 5.3 
                 5.4 
                 5.5 
                 5.6 
                 5.7 
                 5.8 
                 5.9 
                 6.0 
               
               
                 q 
                 1.16 
                 1.17 
                 1.19 
                 1.20 
                 1.22 
                 1.24 
                 1.25 
                 1.27 
                 1.28 
                 1.30 
               
               
                 2σ [km −1 ] 
                 0.44 
                 0.43 
                 0.41 
                 0.40 
                 0.38 
                 0.37 
                 0.36 
                 0.34 
                 0.33 
                 0.32 
               
               
                   
               
            
           
         
       
     
     The system may handle the impact of visibility in various ways. For example, the step of obtaining voxels  1601  may comprise obtaining a reduced set of voxels in lower visibilities. As another example, the step of obtaining voxels  1601  may comprise angling the system to provide a detection range (e.g.  402 ,  FIG. 4B ) that is closer to the system, so that the entire available detection range ( 402 ) is visible. 
     Step  1601  may also include an automatic dynamic range adjustment procedure. For example, the system may adjust the pupil  1109  (if present), activate a second detection system having a different dynamic range, or activate a splitter  1110  (if present). If a second detector (from a second detection system or from a second detector  1103 ′) is used, the system builds the voxel space from the combined signals of the two detectors. 
     In step  1602 , a clutter signal is obtained from the set of voxels. For example, in a system deployed on a ship mast, a clutter signal will occur at the voxels corresponding to sea level. As described above, measured distance is a function of laser pulse return time and gating speed.  FIG. 17B  illustrates a “light line” of sea level clutter measured because of this relationship.  FIG. 17A  illustrates the corresponding system geometry. The system  1748  is at a height h above sea level. The system emits a laser pulse (including optical ray  1479 ) that reflects off of sea level clutter creating “light line”  1753 , which manifests a plane of clutter signals in the three-dimensional set of voxels. 
     In step  1603 , voxels are missing from the expected clutter signal are detected. For example, in a clutter plane created by sea level, missing voxels are created by objects (such as targets or other clutter objects) blocking the laser pulse and causing an early return pulse or by absorbing the laser pulse, causing a late or non-existent return pulse. For example, in  FIGS. 17A  and B, the optical ray  1749  is not reflected at sea level  1751 , but rather at the sea clutter (sea wave) at point  1750 . At  FIG. 17B , expected clutter at light line  1753  is broken in point  1754 . As illustrated in  FIG. 17B , all reflection points at the sea level are located on light line with their z-coordinate on z-axis. However, because of light line symmetry breaking, the reflection point “moves” from point  1754  to point  1755 , with z 1 , z 2 -coordinates shown both in  FIGS. 17  A and B, where (arrows  1756  and  1757  have equivalent interpretation):
 
Δ z=z   2   −z   1   (66)
 
     In  FIG. 17B , projection of points  1754  and  1755  (or, their equivalents  1750  and  1751  shown in  FIG. 17A ) on ct-axis is such that their distance, at ct-axis is 2Δz, while their distance at z-axis is only Δz, which explains 26.56°-angle value of line  1753 , since tan 26.56°=0.5. 
     The light line symmetry breaking situation becomes more complex in the case of other targets. For example,  FIGS. 18A-C  illustrate the situation of light line symmetry breaking in periscope detection. In  FIG. 18A , three points A, B, C are shown, including the periscopic entrance/exit A; a low-brightness target at the periscopic surface B, (which acts as a reference clutter reflecting object) and a clutter point C. Clutter point C is illustrated in  FIG. 18B  where optical ray  1860  passes point C, reflecting at distant point  1861  (z 4 -coordinate). Therefore, this clutter object has the largest coordinate: ct 3 , as  1862 , with smaller ct-coordinate  1863  for A-point, and smallest one  1864 , for B-point. 
     For clutter point, C, the symmetry is not broken, because C-point is located at light line  1865 . The most broken light line symmetry is for low-brightness point B, since, this breaking value is: 2Δz, where Δz=z 2 −z 1 . High-brightness A-point has symmetry breaking less than 2(z 3 −z 1 ), because there is pulse time delay due to optical ray penetrating the periscope&#39;s interior. Assuming that the optical ray is reflected at the periscope and at its eye piece, this extra time delay is 2L, in ct-coordinates, where L is the periscope length. However, in the case of reflection from intermediate retro-surface, with distance, L′, from periscope point A, this extra time delay will be 2L′, in ct-coordinates, where L′&lt;L, where L-periscope length. 
     The number of t-cell units: δz=(cδt)/2, this extra time-delay provides is as follows. For typical marine (mast) platforms (h=50 m), and typical R-distances, (R=10 km), and for typical A-point height (H=3 m), the |z 3 −z 1 |-distance is about 600 m, and δz=1.5 m, for δt=10 nsec. Therefore, for periscope length; L=12 m: 
                         (         z   3     -     z   1         δ   ⁢           ⁢   z       )     =         600   ⁢           ⁢   m       1.5   ⁢           ⁢   m       =   400       ;       L     δ   ⁢           ⁢   z       =         12   ⁢           ⁢   m       1.5   ⁢           ⁢   m       =   8       ;     ⁢     
     ⁢         (       z   3     -     z   1     -   L     )       δ   ⁢           ⁢   z       =   392             (     67   ⁢   abc     )               
Therefore, the value of periscope length in t-cell units is 8; i.e., location of point A is separated by 8-number of t-cells (or, 8-number of voxels) from point, B. This is a significant value, which can be used as an extra temporal signature of periscopic target, even for single-pulse reflection.
 
     The clutter point C is separated far from points A and B, in t-cell units, since, according to Eq. (67a), for |z 4 −z 1 |≅|z 3 −z 1 |, we have about 400-units separation. Therefore, the related clutter is separated quite far from periscopic points&#39; location, in t-cell units; thus, providing significant t-cell or, voxel or-units, separation. Accordingly, if target point, A, is located at (m+8)th voxel, for example, by using Eq. (39), the low-brightness periscopic point, B, is located at mth voxel, while C-point is located at (m+392)th voxel, according to Eq. (67). Therefore, the noise signals from reflective points, B and C, do not bias target signal from high-brightness point, A. In various embodiments, targets may be detected using the t-cell separation of signals from background clutter signals as determined from the voxel readouts. 
     Returning to  FIG. 16 , in step  1604 , the voxel set is evaluated to determine the location in voxel space of reflections causing the missing voxels in the clutter signal. These voxels are identified as potential target signals. The potential target signals may be located in front of or behind their corresponding clutter signal (i.e., the target may reflect rays that return prior to rays striking surrounding clutter or the target may reflect rays that return after rays striking surrounding clutter). In some embodiments, this may comprise searching for the nearest voxel in or-units to a voxel missing from the clutter signal. 
     In other embodiments, step  1604  may comprise detect voxel coherency signals.  FIG. 19  illustrates voxel coherence in a vertical line of voxels. Typically, the pixel optical power of an image of integrated clutter, such as that of sea level, or Lambertian solid state (false) target such as a boat, a ship, a rock, is comparable with the optical power from strong non-Lambertian target such as retro-reflection from a periscope. Such integrated clutter can be used as temporal reference for establishing IOS voxel coherency, as shown in  FIG. 19 . This integrated clutter may be used as a temporal reference because the location of Lambertian objects and non-Lambertian target in voxel space are usually located in different time-resolution voxel coordinates. 
     Vertical voxel coherency is illustrated in  FIG. 19 . A target comprises periscope  1900 , with its entrance  1901 , and its side  1902 . The side  1902  represents integrated Lambertian solid-state clutter working here as a voxel reference. Four (4) vertical pixels are considered for the sake of explanation, their object-inverse areas are  1903 ,  1904 ,  1905 , and  1906  (i.e., each pixel&#39;s vertical field of view (inverted)), respectively. Their voxel sets (derivatives) are represented by two exemplary columns  1907  and  1908 . Time coordinate  1909  illustrates that voxel column  1908  occurs later on the time scale than column  1907  (i.e., voxels in column  1908  measure signals that are farther than voxels in column  1907 ). Periscope  1900  total length is L  1910 , while its frontal horizontal length is l  1911 . For sake of simplicity, only one retro-reflection is assumed to occur from retroreflective surface  1912 . Therefore, using vertical line  1913 , with its bottom point  1914 , at sea level, the extra time delay for incident ray  1915  and its retroreflected ray  1916 , is: 2L=cΔt 1 , where Δt 1  is total extra return-time for ray passing whole periscope interior, reflected from retro-surface  1912  and passing backward through periscope interior. For laser pulse, with temporal length, δt, representing voxel length in light units, δz (where: δz=(0.5)cδt), this extra time delay Δt 1 , is equal to the following number of light units: N 1 =L/δz. For example, for δz=1.5 m and L=12 m, we obtain: N 1 =12/1.5=8. Using the same reasoning, the extra time delay for Lambertian clutter  1902 , is: N 2 =l/δz. For example, for l=30 cm: N 2 =0.3/1.5=0.2; i.e., practically the same time cell as without any extra delay. Therefore, the retroreflected signal  1916  comes 8-light units (or 8 voxels columns in the δz direction) later than reflected signal  1917 , while the general formula; is: ΔN=N 1 −N 2 =8−0.2≅8. The voxel column  1907  represents extra-time delay for reflected ray  1917 , while the voxel column  1908  represents extra-time delay for reflected ray  1916 . Thus, voxels  1918  and  1921  have signals, while voxels  1919 , and  1920  are empty. Similarly, for column  1908 , only voxel  1922  has a signal. 
     The temporal relation between voxel columns  1907  and  1908  represents an example of voxel coherency. By retrieving and analyzing all voxels from these columns, the system can identify two meaningful voxels  1918  and  1922 , representing the information about mutual location of two reflected signals  1916  and  1917 . In turn, the system can perform reasoning about presence of periscope  1900 , in respect to reference clutter  1902 . We see that this specific periscopic information can be obtained without using distinctive periscope optical signals, due to reference clutter  1902  which has comparable pixel signal power with high-brightness retro-reflected signal  1916 . 
     Voxel coherency analysis may also be applied using all available dimensions of the voxel space.  FIG. 20  illustrates an example of horizontal voxel coherency. Indeed, in some embodiments, rather than a two dimensional sensor array, a one dimensional sensor array is used. The one dimensional sensor array is arranged horizontally, in which case, only horizontal voxel coherency analysis is available. 
       FIG. 20  presents a case of horizontal voxel coherency involving a periscope  2000 , and retro-reflected beam from only one retroreflective surface  2001 . Point A is at the periscope entrance with incident ray  2002  and retroreflected ray  2003 . In this figure, we consider three reflective objects A, B, C, representing: high brightness retro-reflective object, A, reference solid clutter B, and the 2 nd  reference sea clutter C, respectively. The slant of ray  2019 ,  2003 ,  2015  has slant angle, β. β is shown, out of scale, because, in practice, for the marine (mast) platforms, this slant is very small (β&lt;&lt;1). Three exemplary voxel horizontal arrays,  2004 ,  2005 , and  2006 , are shown, representing the same horizontal pixel array, but different arrival times: t 1 , t 2 , t 3  out of scale (i.e., difference between them is not the same). Signal-filled voxels are  2007 ,  2008 ,  2009 ,  2011 , and  2012 , while empty voxels are  2013 ,  2014 ,  2015 ,  2016 ,  2017 ,  2018 , and  2010 . 
     The incident ray  2013  strikes solid reference clutter  2014 , and its reflected ray is  2015 . This reflected ray  2015  has the earliest arrival time, t 1 , represented by voxel array  2004 . The retro-reflected ray  2003  has the second arrival time, t 2 , represented by voxel array  2005 . The 3rd incident ray  2019  is reflected at sea point C, denoted as  2021 , and incoming as reflected ray  2019 , much later than other reflected rays  2003  and  2015 , at arrival time, t 3 , represented as voxel array  2006 . The distance between bottom point, B′, denoted as  2020  and C-reflection point,  2021 , is very large, say 600 m, for example. Therefore, from general formula: (t 3 −t 2 )=(2×600 m)/(3·10 8  m/sec)=4.10 −6  sec, while for spatial voxel quant of δz=1.5 m, this distance, in light units, is: (N 3 −N 2 )=(600 m)/(1.5 m)=400; i.e., very large, in comparison with periscope return time for example (eight (8) light units); thus, (N 2 −N 1 )=8. Therefore, voxel arrays  2004  and  2005  are relatively close to each other (N 2 − N 1 =8), while voxel arrays  2005  and  2006  are far away (N 3 −N 2 )=400. 
     The horizontal voxel coherency signature is represented by graphical voxel pattern of three horizontal voxel arrays  2004 ,  2005 , and  2006 , in respect to signal-filled voxels and empty voxels. In particular, horizontal voxel array  2006  demonstrates a characteristic missing-tooth pattern, with “missing” voxel (or “hole”)  2010 , while this missing voxel is located at other voxel array  2005 , at voxel  2008 . The second reference voxel is  2007 , represents solid (hard) reference clutter B. This clutter plays a dual role, not only as regular clutter (a noise) but also as reference object, allowing the system to identify (ID) periscopic target  2000  as well us to find its location, with single time cell accuracy (˜1.5 m). This is done even without two-pulse operation. In further embodiments, the reference clutter may additionally or alternatively comprise the ground, clouds, or distant background objects. 
     In general, detectable targets will show significant space time voxel coherency.  FIGS. 21  A-D illustrate some general space-time voxel coherency. All these clutter/target objects are represented by related voxel intensity values:
 
 I=I ( i,j,m )  (68)
 
where; i, j, m—are integers, defining given voxel index; e.g.,
 
 I   i,j,m   =I   2,5,151   =I (2,5,151)=2.5·10 −5  W/cm 2   (69)
 
where: i-index defines voxel&#39;s x-coordinate (horizontal); j-index defines voxel&#39;s y-coordinate (vertical); and, m-index defines voxel&#39;s ct-coordinate (in light units).
 
     In  FIGS. 21A-D , illustrations of space-time correlation between voxels&#39; intensities, as defined by Eqs. (40-41), are shown. The location of reflective point, B, has longitudinal coordinate, z=z 1 , indexed by m=1, in  FIG. 21A , where pixel fragment of 16-number of voxels,  2080 , is shown, with exemplary ith-indexes: 7, 8, 9, 10, and jth-indexes: 5, 6, 7, 8. In  FIGS. 21B, 21C, and 21D , the voxels with the same i, j-indexes, but different m-indexes, are shown. 
     Returning to  FIG. 21A , the lowest jth index: 5 represents sea level, at z=z 1 , illustrated by three (3) wavy voxels  2101 , including also low-brightness periscopic reference clutter (ie., the body of the periscope), B, denoted as  2102 , which covers two y-levels (˜5 m height). This is a kind of integrated clutter filling all pixel size, (for example, for f=20 cm, R=10 km, the resolving element is about 2.5 m×2.5 m), however, its optical power/intensity is medium-range, comparable with integrated sea clutter intensity range. Therefore, both “wavy” and “horizontal” lines&#39; voxel marks represent comparable medium-range intensity. In contrast, “empty” voxels, as  2103 , represent low intensity levels. 
     In  FIG. 21B , the optical beam reflected from periscopic interior, represented by high-brightness target, A, is shown  2104 , detected by voxel with coordinates: (9, 7, 8). The voxel  2104 , as representing high-brightness target, is marked by crossed double-diagonal lines. Now, voxels  2105  are empty, with low intensity levels (from only stray light); because, the beam was reflected earlier, detected by  2102  voxels. 
     In  FIG. 210 , z=z 2  longitudinal coordinate is represented. Therefore, the beam is reflected from integrated sea clutter (if, it is located at sea level), represented by “wavy” voxels,  2106 , while voxel,  2107 , is empty, because the related beam has been detected by upper voxel,  2102  (with coordinates: 9, 6, 1. Its m=200, assuming that target B&#39;s height is half distance of that of target A (i.e., equal to H/2). 
     In  FIG. 21D , the integrated sea clutter at sea level, is reflected, represented by “wavy” voxels  2108 , while voxel,  2109 , is empty, because the related beam has been detected by pixel,  2104 , in  FIG. 21B . 
     In summary of  FIGS. 21A-D , voxels such as  2101 ,  2102 ,  2104 ,  2105 ,  2106 ,  2107 ,  2108 , and  2109 , are correlated by some space-time relation, representing certain anomalous event, namely, laser reflection off a target (such as a periscope). Otherwise, all voxels with the following j-coordinates:
 
 j= 5, in FIG.  21 A;  j= 6, in FIG.  21 C,  j= 7, in FIG.  21 D  (70)
 
will be filled by light reflected from sea level, assuming sea clutter at sea level. The exception would be sea waves with amplitudes exceeding 2.5 m (assuming exemplary conditions). These waves start to occupy some voxel, with jth coordinates, higher than those in Eq. (42), such as j=6, in  FIG. 21A ; or j=7, in  FIG. 210 , for example. However, such waves would typically not provide the voxel coherency signals associated with targets.
 
     In some implementations, the signal from high-brightness targets (such as non-Lambertian reflectors) will tend to be smaller than the signal from surrounding clutter. This is because, although high-brightness targets reflect a greater amount of light per unit area back to the system, the clutter signal will be integrated over a much larger area. The system parameters may be set so that the upper range of the dynamic range of the detector  1103  encompasses the expected signal from large area clutter. In some embodiments, for example where some target signals may be greater than their reference clutter signals (for example, an ocular target on a vessel with light absorbing paint), some system parameters may be adjusted. For example, a pupil  1109  may be used to reduce the light gathering ability of the system to bring the target signal within the dynamic range of the detector. 
     In some embodiments, a second detection system may be employed in parallel.  FIG. 110  illustrates such an embodiment. For example, a first detection system with a high light gathering ability may be used to detect low brightness signals while a second detection system may have a reduced light gathering ability to detect high brightness signals. 
     Alternatively, a splitter  1110  may allow two detectors  1103 ,  1103 ′ and detector electronics  1104 ,  1104 ′ to operate in parallel. One detector  1103 ′ may be configured to detect higher brightness signals than the other  1103 , for example by having larger sensor sizes or by having more sensitive sensors. In this case, each RISC  1108 ,  1108 ′ array  1104 ,  1104 ′ provides its output to the detection processor  1105  and the detection processor  1105  builds a combined voxel space from the two outputs. 
     In a further embodiment, the pupil  1109  is on only one branch of the detection subsystem.  FIG. 11D  illustrates such an embodiment. Here, compared to  FIG. 110 , the pupil  1109  is after the splitter  1110 . 
     In these embodiments, detectors  1103  and  1103 ′ may have different sensor sizes to accommodate the changes in light gathering ability introduced by the pupil  1109 . As discussed herein, photodetectors  1103  and  1103 ′ may be various types of detectors. For example, they may be APDs or solid-state photomultipliers, satisfying performance conditions such as sufficiently low NEP (preferably on the picowatt order), sufficiently high speed (for example, greater than 100 MHz), and availability in an array configuration (either one-dimensional or two-dimensional). 
     In still further embodiments, further photo detection branches may be employed. For example, three or four photo detection branches may be employed. 
     In other embodiments, for example, those using binary detection signals instead of multi-valued detection signals, high brightness signals are allowed to saturate the detector. Accordingly, the gain of the detector is set for expected low signal levels, such as signals expected from low reflective reference clutter objects, such as absorptive vessel bodies. 
     Returning to  FIG. 16 , in step  1605 , bright voxels are detected. Bright voxels are those voxels having a signal greater than clutter signal. For example, bright voxels may be defined as voxels having a signal some predetermined amount more than a clutter signal. The clutter signal threshold may be determined by averaging the clutter signals received during the current voxel readout, or over some period of operating time. Bright voxels may be created by reflections from various targets. For example, bright voxels may be created by reflections off of one or more retroreflective surfaces. For example, voxels  2104  from  FIG. 21B, 2008  from  FIGS. 20, and 1922  from  FIG. 19  may be bright voxels. 
     In step  1606 , a reference voxel set (RVS) corresponding to the bright voxel is detected from the voxel readout. The reference voxel set comprises clutter signals from clutter surrounding the target (for example, the clutter signals surrounding the missing voxels detected in step  1603 ). The reference voxel set may further comprise voxels nearby the bright voxel that may be reflected by other parts of the target. Such other voxels will have signal levels commensurate with clutter signals, but will be within some predetermined distance of the bright voxels. 
     In step  1607 , the reference voxel set and its relationship to the bright voxel is analyzed for target detection. For example, in one embodiment the distance between the bright voxel and all or a portion of the reference voxel set is determined. For example, in  FIGS. 21A-D  the distance between missing voxel  2102  and its gap  2107 , is significant and equal to Δm=200−1=199, while, in the case of typical sea waves, such distances will be rather small (because, their heights are rather smaller). Based on the analysis, targets may be detected and identified. For example, periscopes or other ocular devices may be detected. 
     In some implementations, various truthing experiments may be performed to determine a figure of merit (FoM) necessary for step  1607  to detect and identify a target. An example of such an analysis would be optical periscope detection, against sea clutter and other false targets. The FoM may be developed pursuant to probability of false alarm (PFA), false alarm rate (FAR), false positives, false negatives, and other considerations. The FoM may be developed using a statistical analysis, based on Bayesian inference (BI). For example, various mock-ups of different target types and different reference clutter types (such as different periscopes on different submarines) may be used to determine appropriate reference clutter and target signals. In particular, these truthing experiments may be used to maximize the PPV of the system. 
     For the sake of explanation and to simplify Bayesian inference (BI), two binary events are considered: signal, or true target; and, noise (clutter), or false target. The event of detection of a signal is denoted S; and, the sensor readout corresponding to the event as S′. Similarly N (event) and N′ (sensor readout) will denote noise. Then, two absolute probabilities: p(S), and p(N), mean probability of signal and noise, respectively, with conservation relation:
 
 p ( S )+ p ( N )=1  (71)
 
because there are only two exclusive events. There are four conditional (direct) probabilities:
 
 p ( S′|S )−probability of detection (PoD)  (72a)
 
 p ( N′|N )−probability of rejection (PoR)  (72b)
 
 p ( S′|N )−probability of false positives  (77c)
 
 p ( N′|S )−probability of false negatives  (77d)
 
For example, p(S′|S) means the probability, that, under signal event, sensor readout will also show signal. Also, p(S′|N) is probability that positive readout (S) is false (since event is noise). Therefore, it can be also called probability of false alarm (PFA); or, the false alarm rate (FAR).
 
     In the case of the BI, inverse conditional probabilities can be mathematically derived from the absolute and direct conditional probabilities. For example, positive predictive value (PPV) is: p(S|S′); i.e., probability of signal event, assuming, that signal readout did occur. According to the Bayesian paradox:
 
(PPV)= p ( S|S ′)  (78a)
 
(PPV)&lt;(PoD)  (78b)
 
The PPV figure is defined as (assuming large number of samples):
 
                   PPV   =       Number   ⁢           ⁢   of   ⁢           ⁢   True   ⁢           ⁢   Alarms       Number   ⁢           ⁢   of   ⁢           ⁢   All   ⁢           ⁢   Alarms               (   79   )               
Therefore, the PPV may be utilized as a FoM for periscopic target truthing (or experimental validation) experiments; i.e., for testing a system while simulating (or, real) true targets (periscopes) and false targets (oculars, small boats, sea clutter, etc.) and with possible increasing P(S) to higher values than in likely real-world scenarios (for training purposes).
 
     In general, it is desirable to minimize p(S′|N) and p(N′|S) while maximizing PPV. Additionally, as false negatives represent missed targets, it is desirable to obtain a very low amount of false negatives. This can be done independently of PoD by minimizing false positive with respect to p(S): p(S′|N)&lt;p(S). 
       FIG. 22  illustrates a method of target detection discrimination for periscopes through inference. In typical environments where periscopes  2205  are present, various clutter objects may also be present. For example, sea spikes, breaking waves, and other natural water formations  2201 , and small boats and other moving objects  2202 , rocks and other stationary objects  2203  may be present in the environment. Additionally, objects such as monoculars or other ocular devices  2204  (e.g., an OAD  901  ( FIG. 9 )) may have some similar characteristics to periscope  2205  that would make them difficult to discriminate from periscopes  2205 . 
     In step  2206 , sensor readouts are evaluated to detect a retroreflective effect to discriminate non-ocular clutter  2207  from ocular potential targets  2208 . Retroreflection occurs when a refracting optical element and a reflective surface are arranged so that the focal surface of the refractive element coincides with the reflective surface. Optical systems, such as periscopes, binoculars, cameras, monoculars, other optical devices, and eyes, often exhibit retroreflection, at least for incident rays within the field of view of the optical system. The light reflected from a retroreflectors is reflected back to its source with little divergence or no divergence. In some cases, the light reflected back from a retroreflector may have a beam divergence of 0.25° or less. However, in other cases, the light reflected back from a retroreflector may have a greater beam divergence. Accordingly, the retroreflected signal from ocular potential targets  2208  will be greater than the non-ocular clutter  2207 , which typically exhibit Lambertian, near-Lambertian, or other divergent scattering. Accordingly, for voxels away from the clutter plane caused by sea level, signal strength may be used to discriminate between non-ocular clutter  2207  and ocular potential targets  2208 . Any signals from non-ocular clutter  2207  may be rejected  2212 . In some embodiments, the voxel readouts include measured signal strength. In other embodiments, the voxel readouts are binary, with a signal detected if measured signal strength is above a threshold. This threshold may be set to a value likely to exclude non-ocular clutter  2207  from ocular potential targets  2208 . 
     Omnipulse discrimination  2210  may be used to distinguish between ocular clutter  2209  (such as optical device  2204 ) and periscope targets  2211 . Omnipulse discrimination  2210  refers to using the tendency of a periscope to produce multiple retroreflective return signals for target discrimination.  FIG. 23  illustrates this method. The omnipulse method is illustrated for two return-pulses, for simplicity. Assuming laser pulse temporal length, δt, and its spatial length, δl, we have:
 
δ t=cδt   (80)
 
For example, for δt=10 nsec, δl=3 m, but for δt=1 nsec, δl=30 cm.
 
     In  FIG. 23 , the incident laser pulse,  2300 , is incident at the entrance/exit of perioscope,  2301 , penetrating perioscope interior,  2302 . Then, it is reflected from the 1 st  retro-surface (which is any focal plane), such as reticle (2a),  2303 ; then, passing ΔL-distance (with L-periscope length), and reflecting from the 2 nd  retro-surface, such as eye piece, (3a),  2304 . As a result, two return pulses,  2305  and  2306  occur. More than two retroreflective return pulses may occur, including pulses for all possible (relay) focal planes. Such surfaces do not need to have central reflection interface, since, vignetting retro-reflection may occur (reflections from boundaries is sufficient.) In order to obtain the pulse separation, the following condition has to be satisfied: 
     
       
         
           
             
               
                 
                   
                     
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     For example, for δt=10 nsec, Eq. (81) yields: ΔL&gt;1.5 m; but, for δt=1 nsec, ΔL&gt;15 cm. Therefore by reducing laser pulse temporal length, δt, can increase the omnipulse resolution, since, for δt=1 nsec, the separation between two retro-surfaces must be larger than only 15 cm. Eq. (81) can be generalized for a number of retro-surfaces larger than two; assuming condition (81) satisfied for any two sequent retro-surfaces. 
     Returning to  FIG. 22 , omnipulse discrimination  2210  may be used to distinguish and reject  2213  ocular clutter  2209  from periscopic targets  2211 , which cause the occurrence of a detection event  2214 . An omnipulse signature is typically characterized by multiple return pulses from a single x,y, location but with different return pulse times (and hence, different z locations in the voxel readout). In one embodiment, omnipulse signatures may be determined for various different periscope types. These omnipulse signatures may be detected in the voxel readouts and used for target identification. In another embodiment, any reading have the characteriscs of an omnipulse is viewed as a potential target. Various other inferential rules, such as use of reference integrated clutter may then be applied to distinguish between a false positive and true positive. 
     Returning to  FIG. 16 , in some implementations step  1601  comprises obtaining multiple voxel readouts from different times. This allows detection of changes in the detection zone. When multiple time indexed voxel readouts are accumulated, the resultant space may be indexed using four dimensions. The set of four-tuple indexed voxels obtained from multiple readouts from the modules field of view is termed the set of 4D voxels, or hypervoxels. The set of hypervoxels may be obtained by sending next PFF (Pulse Facet Flash), and observe state change from one time moment, t 1 , to other time moment, t 2 , where:
 
Δ t=t   2   −t   1   ;t   2   &gt;t   1   (82)
 
Where, Δt is time difference between those moments. Furthermore, multiple PFFs, in time moments: t 1 , t 2 , t 3 , etc, (either periodically, or not) may be sent to build as large a hypervoxel space as desired. For simplicity of explanation, it is assumed that PFFs are sent periodically. However, the non-periodic case is a straightforward extension In the periodic case:
 
Δ t=t   2   −t   1   =t   3   −t   2   =t   4   −t   3 = . . .   (83)
 
Previously, three voxel indices were employed: i, j, m, related to (x,y,z)—coordinates, respectively. Now, four voxel indices are related to four voxel coordinates: (x, y, z, t), in the form:
 
( x,y,z,t )⇒( i,j,m,k )  (84)
 
where index, k, where k=1, 2, 3, . . . , is related to new time coordinate, t, related to different PFFs, obtained from different time moments: t 1 , t 2 , t 3 , etc.
 
     Therefore, in the case of voxel change detection, Voxel Change Coherency (VCC) may be employed in the method. Voxel change coherence is determined in four-dimensional (4D) space (x, y, z, t), defined by Eq. (84), which is a kind of hyperspace. 
     The 4D voxels, or hypervoxels, are: elements, quants, or units of 4D space (x, y, z, y), characterizing voxel change coherency (VCC), in the form of indexing: (i, j, m, k), as described in Eq. (82-84). In this case, (x,y)-arc lateral pixel coordinates, z—is longitudinal voxel coordinate, and t—is (independent) time coordinate. In fact, there are two time coordinates: t, and t′, the latter one being dependent (connected) time coordinate, connected with z-coordinate, by relation: 2z=ct′ (t′-coordinate has, previously, been denoted by t). The sub-set of 4D hyperspace: (x, y, z, t) is called cross-section, and can be itself 3D space, or 2D space. Any subset of 4D space: (x, y, z, t), with constant one coordinate (such, as t, for example), is 3D space cross-section. The 3D voxels discussed above are related to 3D space cross-section: (x, y, z, t O ), in the form:
 
( x,y,z,t )/ t=t   o =CONSTANT  (85)
 
i.e., for single, PFF (Pulse Facet Flash). Then, 4D hypervoxels are reduced to 3D voxels, quantizing space: (x,y,z).
 
     In kinematics, the general movement of material point (a point object) is described by three (3) equations in 4D space (x, y, z, t), in the form:
 
 x=x ( t ), y=y ( t ), z=z ( t )  (86abc)
 
and, the momentary (instant) speed (velocity) vector, is
 
                       v   →     =       lim       Δ   ⁢           ⁢   t     ⁢           -&gt;   0       ⁢       Δ   ⁢           ⁢     r   →         Δ   ⁢           ⁢   t           ;       r   →     =       r   →     ⁡     (     x   ,   y   ,   z     )                 (     87   ⁢   ab     )               
where: {right arrow over (r)}={right arrow over (r)}(x,y,z) is directional vector. Parametrically, the movement:
 
 {right arrow over (r)}={right arrow over (r)} ( t )  (88)
 
where {right arrow over (r)} is directional vector, {right arrow over (v)}—its instant speed, and (x,y,z)—are its coordinates as functions of time, t. In the VCC case, this movement is described by four discrete coordinates: (x, y, z, t), indexed by: (i, j, k, m). Then, instead of momentary (instant) vector, {right arrow over (v)}, there is an almost momentary, or momentary-mean (MM) vector, {right arrow over (v)}′, which, further, will be denoted as, simply, {right arrow over (v)}′, in the form of ratio of Δ{right arrow over (r)} and Δt:
 
                           v   →     ′     ⇒     v   →       =       Δ   ⁢           ⁢     r   →         Δ   ⁢           ⁢   t         ;       Δ   ⁢           ⁢     r   →       =     (       Δ   ⁢           ⁢   x     ,     Δ   ⁢           ⁢   y     ,     Δ   ⁢           ⁢   z       )               (     89   ⁢   ab     )               
where, arrow shows changing of symbolics: from {right arrow over (v)}′ to {right arrow over (v)}.
 
     The 4D resolution of material point movement, described by MM-velocity vector, {right arrow over (v)}, is characterized by pixel sizes: a x , a y , δz—longitudinal resolution, and time coordinate change, Δt. 
     In the lateral movement case, described by (x,y)-coordinate, and their indices: (i,j), the lateral resolving elements: δ x , and δ y , are derived from the following relations:
 
 a   x   =m   x   δx;a=m   y   δy   (90ab))
 
where: m x , m y  is x, y—IOS system magnification, or, rather de-magnification, because: m x &lt;&lt;1, and m y &lt;&lt;1.
 
     In the longitudinal movement case, described by z-coordinate, the longitudinal resolving element, δz, is
 
δ z =(0.5) cδt   B   (91)
 
where: δt B =B −1 , and, in ideal case: δt B =δt L , where B—photodetector bandwidth, and δt L —laser pulse temporal length.
 
     The time resolving element, Δt, is defined by Eq. (82). In summary, 4D resolution of 3D movement in hypervoxel space: (x, y, z, t), which is time-space, is defined by lateral, longitudinal, and time resolving elements:
 
(δ x,δy,δz,Δt ).  (92)
 
Therefore, MM-velocity vector resolution is also described by these four (4) resolving elements.
 
     When hypervoxels are introduced in step  1601 , the analysis may comprise analyzing movement in the hypervoxel space.  FIGS. 24-26  illustrate examples of movement in hypervoxel space. 
     The term foxel refers to a signal-filled voxel, while the empty voxel, “left” by this foxel, will be called a hole, resulting in foxel-hole pair. When the dynamic cases in time-space (x, y, z, t), foxel-hole pair movement (FH-Pair movement) will occur. Such FH-Pair movement can be either rigid, or elastic. In the 1 st  (rigid, solid state) case, the distance between foxel and hole remains constant at a time, t, while in the 2 nd  (elastic) case, this distance changes with time.  FIG. 24  illustrates an example of rigid foxel group movement. Here, the 3D cross-section-set (CSS) is illustrated, for m=m O =constant, and variable k-index for four k-values: k=1, 2, 3, 4. 
     Here, foxels  2400 ,  2401 , and  2402  move rigidly. At t=t 1 , these foxels have the following pixel (x,y)-locations: for  2400  (i=3, j=4); for  2401  (i=3, j=3); for  2402  (i=4, j=3). At t=t 2 , these (i,j)-locations are: (2,4), (2,3), and (3,3)—respectively. At t=t 3 , (or, k=3), the locations are: (1,4), (1,3), and (2,3). At t=t 4  (k=4), the locations are: (3,2), (3,1), and (4,1). Therefore, for this foxel rigid group, t first, i.e., for t 1 ≤t≤t 3 , the lateral movement from right to left, along x-coordinate which is decreasing, with the following MM-velocity vector: 
                       v   →     =       v   →     ⁡     (         v   x     ⁢   0     ,   0     )         ;       v   x     =     -       δ   ⁢           ⁢   x       Δ   ⁢           ⁢   t           ;       Δ   ⁢           ⁢   t     =         t   2     -     t   1       =       t   3     -     t   2                   (     93   ⁢   abc     )               
where: δx=a x /m x , where a x  is x-pixel size, and m x  is system-de-magnification (m x &lt;&lt;1). It should be emphasized that, in this particular PFF (Pulse Facet Flash) case, the absolute distance, z, from an object to platform is known (by measuring beam return time). For example, for z=1 km, and f=50 cm (focal length), we obtain: m x   −1 =(1 km)/(50 cm)=1000/0.5=2000, and m x =1/2000=5·10 −4 . Then, for a x =20 μm, for example: δx=a x m x   −1 =(2000) (20 μm)=(2000) (20·10 −4  cm)=4 cm; i.e., x-resolving element size is 4 cm. Then, for Δt=0.1 sec. for example:
 
| v   x   |=v =(4 cm)/(0.1) sec=40 cm/sec.  (94)
 
Therefore, by this kind of “forensic” analysis, the system can determine an approximate speed of a given group of foxels:  2400 ,  2401 ,  2402 . This foxel group represents some object with “L”-profile, as with sizes: L x , L y , where L x =L y =L, and L=2δx=8 cm. At t=t 4  (k=4), this foxel group suddenly move to the right-bottom corner. Therefore, for t 3 ≤t≤t 4 , its MM-velocity vector, {right arrow over (v)}, is
 
                         v   →     =     (       v   x     ,     v   y     ,   0     )       ;       v   x     =       Δ   ⁢           ⁢   x       Δ   ⁢           ⁢   t           ,         v   y     =       Δ   ⁢           ⁢   y       Δ   ⁢           ⁢   t         ;       Δ   ⁢           ⁢   t     =       t   4     -     t   3                   (     95   ⁢   abcd     )               
where Δx=3δx=12 cm, Δy=−|Δy|=−12 cm, and,
 
     
       
         
           
             
               
                 
                   v 
                   = 
                   
                     
                       
                         
                           
                             ( 
                             
                               Δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               x 
                             
                             ) 
                           
                           2 
                         
                         + 
                         
                           
                             ( 
                             
                               Δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               y 
                             
                             ) 
                           
                           2 
                         
                       
                     
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       t 
                     
                   
                 
               
               
                 
                   ( 
                   96 
                   ) 
                 
               
             
           
         
       
     
     For example, for Δt=0.1 sec: v=(17 cm/0.1 sec=1.7 m/sec. In summary, at first, this L-object moves with 40 cm/sec-speed into opposite x-axis direction, and then, it moves, diagonally, into “south-east,” with higher 1.7 m/sec-speed. Additionally, a 2 nd  group of foxels:  2003 ,  2004 , and  2005 , which arrived at t−t 1  (k=1), and then, disappear from this set of voxels. Then, the system would search this group in other sets of voxels. Accordingly, during the analysis step, various foxel groups may be identified and tracked. Their movement patterns may be used for target identification. 
       FIG. 25  illustrates an example of rigid foxel-hole pair movement in a different projection of the hypervoxel space in two dimensions. This figure represents the rigid foxel-hole (FH)-pair that moves, longitudinally, with Δm=9 (between m=101 and m=110, for example), and Δk=2 (from k=2, to k=4). Assuming that: Δt=t 4 −t 2 =1 sec, for example, and δz=10 cm: Δz=Δmδz=(9)(10 cm)=90 cm; thus, the longitudinal speed of this pair is: 90 cm/sec. The FH-pair is rigid, because, a longitudinal distance between foxel  2510 , and its “hole”  2511  is constant (Δm′=4, between m=105 and m=101, or, between m=114 and m=110). Also, the integrated clutter (RIC), marked by foxels:  2512 ,  2513 , and  2514 , is at the constant distance from foxel  2510 , confirming that the FH-pair is rigid, indeed. 
       FIG. 26  illustrates an example of non-rigid Foxel-Hole (FH) Pair movement,  FIG. 26  includes two diagonal columns, indexed by k=1, and k=2, respectively. The (identical) 2D-cross-sections of lateral (x,y)-pixels are only shown (six of them), with indices: i=5, 6, 7, 8; and j=11, 12, 13, 14. The 1 st  diagonal column (k=1) is represented by three (3) 2D lateral cross-section-sets (CSS), indexed by m=10, 12, and 20. The same m-indices (10, 12, 20) are representing the 2 nd  column (k=2). Of course, k=1 represents earlier time than k=2, as illustrated by the direction of t-axis. The foxel-group of four (4) foxels, marked by:  2620 ,  2621 ,  2622 ,  2623 , is moving through the following (i, j, m, k)—transformation; related to foxels:  2620 ,  2621 ,  2622 ,  2623 : 
                     {     i   ,   j   ,   m   ,   k     }     :             {           6   ,   12   ,   10   ,   1               7   ,   12   ,   10   ,   1               6   ,   11   ,   10   ,   1               7   ,   11   ,   10   ,   1           }                 Column   ⁢           ⁢   k     =   1           ⇒           {           7   ,   13   ,   12   ,   2               8   ,   13   ,   12   ,   2               7   ,   12   ,   12   ,   2               8   ,   12   ,   12   ,   2           }                 Column   ⁢           ⁢   k     =   2                     (   97   )               
The hole-group of four (4) holes, marked by:  2624 ,  2625 ,  2626 ,  2627 , is moving through the following (i, j, m, k)—transformation:
 
     
       
         
           
             
               
                 
                   
                     { 
                     
                       i 
                       , 
                       j 
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                       m 
                       , 
                       k 
                     
                     } 
                   
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                                     6 
                                     , 
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                             } 
                           
                         
                       
                       
                         
                           
                             
                               Column 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
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                             1 
                           
                         
                       
                     
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                                     7 
                                     , 
                                     13 
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                                     8 
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                                     , 
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                                     7 
                                     , 
                                     12 
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                                     8 
                                     , 
                                     12 
                                     , 
                                     20 
                                     , 
                                     2 
                                   
                                 
                               
                             
                             } 
                           
                         
                       
                       
                         
                           
                             
                               Column 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               k 
                             
                             = 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   98 
                   ) 
                 
               
             
           
         
       
     
     Comparing Eq. (97) and (98), both foxels and holes have the same lateral (i,j)-indices for both columns: k=1 and k=2. For example, for the 1 st  column (k=1), the foxel  2620 , and its hole  2624 , have the same indices: (6, 12); the same with k=2, where this FH-pair has indices (7, 13). However, their longitudinal m-indices are different: 10 vs. 20, for the 1 st  column, and 12 vs. 20, for the 2 nd  column. 
     Therefore, this FH-pair is elastic one. Also, crossed voxels (foxels) in 2D CSS, denoted by k=1 and m=20, as well as in 2D CSS, with k=2, m=20, represent the RIC (Reference Integrated Clutter), because, their m-index does not change (m=20=constant). In contrast, the foxels in 2D CSS, represented by (m, k)=(10, 1), and (m, k)=(12, 2), do change their longitudinal position. Thus, they represent a moving object, while the RIC represents only its (moving) (x,y)-projection. Accordingly, systems may detect reference clutter signals (e.g., perform step  1602  of  FIG. 16 ) by performing hypervoxel analyses. 
     The moment of the object represented by foxels:  2620 ,  2621 ,  2622 ,  2623 , has an MM-velocity vector, {right arrow over (v)}, with all three non-zero coordinates: {right arrow over (v)}′=(v x , v y , v z ). For example, for Δt-representing time difference from k=1 to k=2, equal to: Δt=1 sec, and for lateral resolving element: δx=δy=10 cm, its x-movement is represented by Δi=1, only (e.g., from i=6, to i=7). Therefore: 
                     v   x     =         Δ   ⁢           ⁢   x       Δ   ⁢           ⁢   t       =         δ   ⁢           ⁢   x       Δ   ⁢           ⁢   t       =     10   ⁢           ⁢     cm   /   sec                   (   99   )               
Same with y-movement (Δj=1); thus, also:
 
 v   y   =v   x =10 cm/sec  (100)
 
In order to estimate its longitudinal movement, Δm=2 (from m=10, to m=12). Thus, according to the orientation of right-hand (x,y,z)-coordinate system its:
 
Δ z=− 2δ z   (101)
 
and, for δz=20 cm, for example:
 
 v   z =−20 cm/sec  (102)
 
Accordingly its velocity vector is:
 
 {right arrow over (v)} =(10 cm/sec,10 cm/sec,−20 cm/sec)  (103)
 
     The object with size (2δx, 2δy) has a velocity vector, described by Eq. (103). Its movement is represented by (i, j, m, k)—discrete coordinates (indices) through transformation from column (k=1) table to column (k=2) table, as in Eq. (97), while its lateral (x,y)-projection, represented by RIC (Reference Integrated Clutter), moves through transformation of tables in Eq. (98). However, the specific MM-velocity vector values can be found only when the 4D resolution is known, represented by four (4) resolving elements: δx, δy, δz, and Δt. 
     In some implementations, the hypervoxel analysis may be used to perform detection without the use of reference clutter signals. 
     An example of a detection and analysis method is described with reference to  FIG. 27 . For sake of TOI extraction from RIC, the system performs a technique based on use of a RISC processor array, assuming hyper-voxel 4D space, by voxel-by-voxel 3D frame comparison (subtraction) at two different times t 1  and t 2 . Additionally, the RISC array may perform a 3D frame virtual translation by shift register. The 1 st  operation is for 3D velocity flow mapping, while the 2 nd  operation is for the COI contour extraction. Both operations are possible, however, only the 1 st  operation is discussed here, for simplicity. 
     As an example, a 100×100 photodetector array, per facet; thus, for 100-facets per second, the frame has: 100×100×100=10 6 -pixels. Additionally, with gating there is also signal return z-coordinate. Assume long-range IOS geometry, as in  FIGS. 3 and 4 . Then, for typical facet angular acceptance of 0.4°-per facet, and marine platform with 50 m—mast, and R=10 km—nominal distance, vertical coverage is of distances between R=5 km and R=15 km. Therefore, for single facet, the 1 st  pulse arrives from R=5 km distance, and the last one from R=15 km distance. Assuming laser pulse length, τ L =10 nsec=10 −8  sec, the average number of temporal cells, N t , is 
                     N   t     =         Δ   ⁢           ⁢   R       c   ·     τ   L         =         10   ⁢           ⁢   km         (       3   ·     10   5       ⁢           ⁢     km   /   sec       )     ⁢     (       10     -   8       ⁢           ⁢   sec     )         =         (     1   3     )     ⁢     (     10     -   4       )     ⁢     (     10   8     )       ≅   3000                 (   104   )               
Then, the total number of parallel voxels, is
 
 n   3D =(10 6 )(3·10 3 )=3·10 9   (105)
 
     Using a 200 MHz-speed 256-RISC processor array, with total RISC operation time of 4 msec per 8.3 Mb-parallel pixels as an example, for 3·10 9 -number of parallel calculations, this time, t RISC , is 
     
       
         
           
             
               
                 
                   
                     t 
                     RISC 
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                         ( 
                         
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                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             3 
                             · 
                             
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                               9 
                             
                           
                           
                             8.3 
                             · 
                             
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                         ) 
                       
                     
                     = 
                     
                       
                         
                           ( 
                           
                             12 
                             8.3 
                           
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                         ⁢ 
                         sec 
                       
                       = 
                       
                         1.45 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           sec 
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   106 
                   ) 
                 
               
             
           
         
       
     
     In this method, further the system identifies all COIs, by using virtual 3D frame shift. Then, the system attaches a velocity vector to each COI, by using voxel-by-voxel comparison, and Euclidean distance computing, using RISC processor array. Then, Cluster Voxel Velocity (CV2) flow mapping, or CV2-flow mapping, may be obtained as in  FIG. 27 . 
     In  FIG. 27  a portion  2730  of a cluster voxel velocity (CV2) flow mapping, or, shortly, CV2-flow mapping of COIs is illustrated, by comparing two 3D voxel frames, at times t 1  and t 2 , in (x,y,z)-coordinate system  2731 ; i.e., this illustration is in 3D, not in 2D. In this example, one velocity vector  2732  is longer than another one  2733 . This is because the vector module  2732  is larger than vector value  2733 . The dot  2734  denotes the COI-location. By using more such time-comparisons: t 2  vs. t 1 , t 3  vs. t 2 , etc., and using the velocity formulas, the system can determine and analyze the kinematics of these clusters; and, then, make recognition between TOIs and RICs. For the velocities of sea wave spikes, at littoral waters, for example, they are rather random in value and direction, in contrast to those of ships which are rather regular, in both value and direction. Also, such static RICs as rocks, for example, will have zero-velocities. Accordingly, this movement may be used as an additional signature for distinction between TOIs and RICs. 
     The system and methods detailed above can be applied to other applications then those reflected to marine augmented target with high brightness in retro-reflection. In other words, those targets do not need to be reflective non-Lambertian (RNL) ones only, especially when shorter distances are included. Also, since the VC is based on general integrated reference reflection clutter (IRRC), the IRRC does not need to be sea waves, but, also flat, or folded ground, for example. 
     One such application is the detection of a tripwire above ground. In such a case, such low-contrast (e.g., plastic) trip-wire can be almost invisible to human eye. In this case, the reference clutter signal can result from the ground behind such a wire, as shown in  FIG. 28 . In this figure, the pulse facet flash (PFF) detection of such trip-wire is shown, using the ground level as IRRC, for example. The PFF vertical cross-section is marked by crossed-area  2800 . The PFF is illuminating some ground region,  2801 , shown as flat one, for simplicity, and the incident rays,  2802 ,  2803 ,  2804 , and  2805 , are reflected (returned) at some points such as A′, B′, C′, and D′, where points A′, C′, and D′ are located on the ground, while point B is the point located above the ground, possibly a target. If this target is the wire cross-section, with wire direction perpendicular the figure; then it is single-point, B, marked as  2806 . Otherwise, at skew position, the wire will be represented by some line. The broken line  2807  shows that there is no connection, at this point, between point B, and its ground projection, B′. 
     In order to explain some quantitative parameter values, a reference geometry is introduced, assuming, for example, OA′=50 m, and OD′=100 m. In order to calculate, unknown B′C-distance, as an example: h=3 m, and BB′=20 cm (marked by  2807 ). Then, the unknown B′C-value, denoted as, w, can be estimated from the following trigonometric similarly relation: 
                       h     OC   ′       =       BB   ′         B   ′     ⁢     C   ′           ;       OC   ′     =       OB   ′     +       B   ′     ⁢     C   ′                   (   107   )               
Assuming typical BB′-value of 10 cm, Eq. (72) becomes (w=B′C):
 
                     h       OB   ′     +   w       =       BB   ′     w             (   108   )               
Solving this equation, in respect to unknown: w-value, where: h=3 m, BB′=10 cm, OB′=70 m (so, A′B′=20 m): w=B′C′=2.4 m.
 
     In order to identify target, B, as a wire, however, vertical voxel coherency (VVC) is used. Still further confirmation will be provided by horizontal voxel coherency (HVC). Therefore, the 2D photodetector pixel array (or, 2D PPA) is preferable. 2D PPA with moderate 60×40-pixel resolution is assumed for sake of simplicity of explanation. First, horizontal pixel resolution for single facet, with typical narrow FOV=3° is estimated. Then, at 100 m-distance, the horizontal range is about 10.5 m; thus, horizontal object resolving element is: (105 cm)/(60)=1.75 cm. For simplicity, vertical angular size of the PPF is assumed to be similar to that of horizontal; i.e., 413=6°, marked as  2808 . 
     Another example of system generalization is the changes in soil density. Changes in density in highly-porous soils (e.g., highly-humid, or poorly settled dirt) that be partially penetrated by high pulse-power IR-beam may be detected. Assuming: 10 MW-pulse optical power and super-high-sensitivity of photodetector array, with noise equivalent power of 0.1 pW, for example, extremely high detection dynamic range of 10 7 /10 −13 =10 20 =200 dB is obtained. In this application, voxel temporal resolution is also high, with δz=100 μm=0.1 mm, for example. Then, laser pulse temporal length, δt, must be 0.67 psec obtained from relation: δz=(0.5)c·δt, or 0.67·10 −12  sec. In such a case, from voxel distance, the soil penetration profile:
 
 z=z ( x,y )  (109)
 
The profile varies with internal structure, modified by, perhaps man-made modification, either by introducing more humidity, or by digging in ground. The profile; z=z(x,y), is obtained from photodetector pixel structure, while longitudinal resolution is defined by δz-value which is proportional to laser pulse length, δt.
 
     A third additional application is the detection of finger-prints. The applied laser pulse beam has a pulse length, δt, and equivalent longitudinal resolution, δz, defined by relation: δz=(0.5)cδt. Additionally, eye-safe infrared beams may be used with wavelengths of greater than 1.3 or 1.5 μm. In  FIGS. 29A-B , the finger papillary lines are shown, marked as  2920 , and the finger-print cross-section profile  2921 , is shown in including the PFF,  2922 , represented by incident rays  2923 ,  2924 ,  2925 ,  2926  and their reflected rays  2927 ,  2928 . If the laser pulse longitudinal resolution, δz, or  2929  is sufficiently high, the reflected rays  2927  and  2928  will belong to different voxels. In such case, if also vertical pixel resolution, δy, or  2930 , is sufficiently high then three dimensional (x,y,z)-mapping of finger prints, such as (x,y), or  2931  is obtained. As a result, by using standard software, we can obtain the finger print profile, where z-axis is marked as  2932 , while (x,y)-mapping is marked as  2931 . Then, by using the second standard finger-print software, we can find all characteristic fiducial markings, such as  2933 , for example, and, as a result, reconstruct whole finger characteristic. 
     Since, for typical finger print profile sizes, δz ˜200-400 μm, and δy ˜300 μm, the system comprises a pixel array zoomed on finger-region. Thus, for typical rather small pixel-numbers, for such long wavelengths (˜1.5 μm), in the range: 60×40, for example, the system employs a second standard camera, in order to find region of interest (ROI), which is human hand with visible finger prints, we need to either manually, or automatically, find the ROI. In the latter case, the system applies some standard pattern recognition algorithm. 
     A further application may be the detection of objects under the ground. Here, the system applies soil profilimetry in connection with detection of trip wires described with respect to  FIG. 28 . 
     As described above, various application time gate the sensor to provide voxel readouts. In some embodiments, the time gating may be performed at a faster rate to sample the reflected laser pulses. This may be used to provide pulse partition voxel coherency (PPVC), related to laser pulse partition/sampling as shown in  FIGS. 30A-B . The laser pulse  3000 , with pulse temporal length, (δt) L , is sampled, with sampling constant (δt) B , and temporal samples  3001  (crossed area). As a result, the continuous instant power, P, line  3002 , is replaced by discrete, “stairs”—line  3003 , characterized by Momentary/Mean-power, {right arrow over (P)},  3004 . This laser pulse partition/sampling process is shown with continuous instant/momentary power, P, and discrete, momentary-mean (M2)-power,  P . Here sampling  3005  is performed such that areas  3006  and  3007  are equal. (This procedure is similar to Riemann-limit integration, for mathematical integrals.) M2-power, power values,  P , are those measured by photodetector gating process, with photodetector pixel bandwidth, B, where 
                     B   =     1       (     δ   ⁢           ⁢   t     )     B         ;         (     δ   ⁢           ⁢   t     )     B     &lt;       (     δ   ⁢           ⁢   t     )     L               (   110   )               
where (δt) L  is laser pulse temporal length, previously denoted as (δt). Of course, when (δt) B →0 (or, B→∞), then, the discrete M2-power line  3003 , becomes continuous (analog) line  3002 .
 
     It should be noted that the analog instant (optical) power line  3002  can be only measured as discrete M2-power line  3003 , while inequality (Eq. 110) can be written as: 
                       (     δ   ⁢           ⁢   t     )     B     =         (     δ   ⁢           ⁢   t     )     L     m             (   111   )               
where m is integer: m=1, 2, 3, . . . . For example, for pulse length: (δt) L =10 nsec=10 −8  sec, and m=10, (δt) B =1 nsec=10 −9  sec, and, according to Eq. (77), B=1 GHz.
 
     Such pulse sampling allows the system to measure reflected pulses, with higher precision than, without sampling. For example, if soil penetration depth is equal to:
 
Δ z=k (δ z ) B   ;k= 1,2,3, . . .   (112)
 
where (δt) B  is voxel resolving element, determined by relation:
 
2(δ z ) B =( C/n )(δ t ) B   (113)
 
where C is light speed in air, and n—soil refractive index; then, reflected pulse will be deformed, respectively.
 
     Various targets may be detected according to their temporal signatures of reflected pulse and related pulse partition voxel coherency (PPVC), which is a generalization of voxel coherency (VC). For sake of explanation rectangular pulse are illustrated instead of analog (Gaussian) pulse. Then, the reflected pulse from hard interface, as in  FIG. 31A , will be (almost) un-deformed,  3100 , while pulse reflected also from soft interface,  3101  as in  FIG. 31B , will have tail,  3102 . In  FIG. 31C , the reflection from partially-transparent two hard interfaces is shown, with incident pulse,  3103 , marked by left-to right arrow,  3104 , is shown, including reflected pulse,  3105 , marked by right-to-left arrow,  3106 . 2 nd  reflected pulse,  3107 , is lower than the 1 st  reflected pulse,  3108 , with separation, Δz, denoted as  3109 , and its equivalent temporal separation, equal to: (2Δz·n)/c, marked as  3110 . In  FIG. 31D , the reflected pulse signature  3111 , is shown, versus incident pulse,  3112 , out of scale, for closer separation,  3113 . Then, the reflected pulse signature has an extra top addition,  3113 , assuming incoherent superposition (beam intensities, not amplitudes, are added). In  FIG. 31E , the reflection from two hard interfaces,  3114  and  3115 , is shown, with attenuation in region  3116 , without reflection from soft interface, however. This is, because we assume that there is no reflection/scattering centers, in region  3116 . In contrast, in  FIG. 31F , such centers exit in soft interface region,  3117 . As a result, in addition to two strong reflection signatures,  3118  and  3119 , we have also weak reflection tail,  3120 . 
     As used herein, the term module might describe a given unit of functionality that can be performed in accordance with one or more embodiments of the present invention. As used herein, a module might be implemented utilizing any form of hardware, software, or a combination thereof. For example, one or more processors, controllers, ASICs, PLAs, PALs, CPLDs, FPGAs, logical components, software routines or other mechanisms might be implemented to make up a module. In implementation, the various modules described herein might be implemented as discrete modules or the functions and features described can be shared in part or in total among one or more modules. In other words, as would be apparent to one of ordinary skill in the art after reading this description, the various features and functionality described herein may be implemented in any given application and can be implemented in one or more separate or shared modules in various combinations and permutations. Even though various features or elements of functionality may be individually described or claimed as separate modules, one of ordinary skill in the art will understand that these features and functionality can be shared among one or more common software and hardware elements, and such description shall not require or imply that separate hardware or software components are used to implement such features or functionality. 
     Where components or modules of the invention are implemented in whole or in part using software, in one embodiment, these software elements can be implemented to operate with a computing or processing module capable of carrying out the functionality described with respect thereto. One such example computing module is shown in  FIG. 32 . Various embodiments are described in terms of this example-computing module  3200 . After reading this description, it will become apparent to a person skilled in the relevant art how to implement the invention using other computing modules or architectures. 
     Referring now to  FIG. 32 , computing module  3200  may represent, for example, computing or processing capabilities found within desktop, laptop and notebook computers; hand-held computing devices (PDA&#39;s, smart phones, cell phones, palmtops, etc.); mainframes, supercomputers, workstations or servers; or any other type of special-purpose or general-purpose computing devices as may be desirable or appropriate for a given application or environment. Computing module  3200  might also represent computing capabilities embedded within or otherwise available to a given device. For example, a computing module might be found in other electronic devices such as, for example, digital cameras, navigation systems, cellular telephones, portable computing devices, modems, routers, WAPs, terminals and other electronic devices that might include some form of processing capability. 
     Computing module  3200  might include, for example, one or more processors, controllers, control modules, or other processing devices, such as a processor  3204 . Processor  3204  might be implemented using a general-purpose or special-purpose processing engine such as, for example, a microprocessor, controller, or other control logic. In the illustrated example, processor  3204  is connected to a bus  3202 , although any communication medium can be used to facilitate interaction with other components of computing module  3200  or to communicate externally. 
     Computing module  3200  might also include one or more memory modules, simply referred to herein as main memory  3208 . For example, preferably random access memory (RAM) or other dynamic memory, might be used for storing information and instructions to be executed by processor  3204 . Main memory  3208  might also be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor  3204 . Computing module  3200  might likewise include a read only memory (“ROM”) or other static storage device coupled to bus  3202  for storing static information and instructions for processor  3204 . 
     The computing module  3200  might also include one or more various forms of information storage mechanism  3210 , which might include, for example, a media drive  3212  and a storage unit interface  3220 . The media drive  3212  might include a drive or other mechanism to support fixed or removable storage media  3214 . For example, a hard disk drive, a floppy disk drive, a magnetic tape drive, an optical disk drive, a CD or DVD drive (R or RW), or other removable or fixed media drive might be provided. Accordingly, storage media  3214  might include, for example, a hard disk, a floppy disk, magnetic tape, cartridge, optical disk, a CD or DVD, or other fixed or removable medium that is read by, written to or accessed by media drive  3212 . As these examples illustrate, the storage media  3214  can include a computer usable storage medium having stored therein computer software or data. 
     In alternative embodiments, information storage mechanism  3210  might include other similar instrumentalities for allowing computer programs or other instructions or data to be loaded into computing module  3200 . Such instrumentalities might include, for example, a fixed or removable storage unit  3222  and an interface  3220 . Examples of such storage units  3222  and interfaces  3220  can include a program cartridge and cartridge interface, a removable memory (for example, a flash memory or other removable memory module) and memory slot, a PCMCIA slot and card, and other fixed or removable storage units  3222  and interfaces  3220  that allow software and data to be transferred from the storage unit  3222  to computing module  3200 . 
     Computing module  3200  might also include a communications interface  3224 . Communications interface  3224  might be used to allow software and data to be transferred between computing module  3200  and external devices. Examples of communications interface  3224  might include a modem or softmodem, a network interface (such as an Ethernet, network interface card, WiMedia, IEEE 802.XX or other interface), a communications port (such as for example, a USB port, IR port, RS232 port Bluetooth® interface, or other port), or other communications interface. Software and data transferred via communications interface  3224  might typically be carried on signals, which can be electronic, electromagnetic (which includes optical) or other signals capable of being exchanged by a given communications interface  3224 . These signals might be provided to communications interface  3224  via a channel  3228 . This channel  3228  might carry signals and might be implemented using a wired or wireless communication medium. Some examples of a channel might include a phone line, a cellular link, an RF link, an optical link, a network interface, a local or wide area network, and other wired or wireless communications channels. 
     In this document, the terms “computer program medium” and “computer usable medium” are used to generally refer to media such as, for example, memory  3208 , storage unit  3220 , media  3214 , and channel  3228 . These and other various forms of computer program media or computer usable media may be involved in carrying one or more sequences of one or more instructions to a processing device for execution. Such instructions embodied on the medium, are generally referred to as “computer program code” or a “computer program product” (which may be grouped in the form of computer programs or other groupings). When executed, such instructions might enable the computing module  3200  to perform features or functions of the present invention as discussed herein. 
     While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not of limitation. Likewise, the various diagrams may depict an example architectural or other configuration for the invention, which is done to aid in understanding the features and functionality that can be included in the invention. The invention is not restricted to the illustrated example architectures or configurations, but the desired features can be implemented using a variety of alternative architectures and configurations. Indeed, it will be apparent to one of skill in the art how alternative functional, logical or physical partitioning and configurations can be implemented to implement the desired features of the present invention. Also, a multitude of different constituent module names other than those depicted herein can be applied to the various partitions. Additionally, with regard to flow diagrams, operational descriptions and method claims, the order in which the steps are presented herein shall not mandate that various embodiments be implemented to perform the recited functionality in the same order unless the context dictates otherwise. 
     Although the invention is described above in terms of various exemplary embodiments and implementations, it should be understood that the various features, aspects and functionality described in one or more of the individual embodiments are not limited in their applicability to the particular embodiment with which they are described, but instead can be applied, alone or in various combinations, to one or more of the other embodiments of the invention, whether or not such embodiments are described and whether or not such features are presented as being a part of a described embodiment. Thus, the breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments. 
     Terms and phrases used in this document, and variations thereof, unless otherwise expressly stated, should be construed as open ended as opposed to limiting. As examples of the foregoing: the term “including” should be read as meaning “including, without limitation” or the like; the term “example” is used to provide exemplary instances of the item in discussion, not an exhaustive or limiting list thereof; the terms “a” or “an” should be read as meaning “at least one,” “one or more” or the like; and adjectives such as “conventional,” “traditional,” “normal,” “standard,” “known” and terms of similar meaning should not be construed as limiting the item described to a given time period or to an item available as of a given time, but instead should be read to encompass conventional, traditional, normal, or standard technologies that may be available or known now or at any time in the future. Likewise, where this document refers to technologies that would be apparent or known to one of ordinary skill in the art, such technologies encompass those apparent or known to the skilled artisan now or at any time in the future. 
     The presence of broadening words and phrases such as “one or more,” “at least,” “but not limited to” or other like phrases in some instances shall not be read to mean that the narrower case is intended or required in instances where such broadening phrases may be absent. The use of the term “module” does not imply that the components or functionality described or claimed as part of the module are all configured in a common package. Indeed, any or all of the various components of a module, whether control logic or other components, can be combined in a single package or separately maintained and can further be distributed in multiple groupings or packages or across multiple locations. 
     Additionally, the various embodiments set forth herein are described in terms of exemplary block diagrams, flow charts and other illustrations. As will become apparent to one of ordinary skill in the art after reading this document, the illustrated embodiments and their various alternatives can be implemented without confinement to the illustrated examples. For example, block diagrams and their accompanying description should not be construed as mandating a particular architecture or configuration.