Abstract

This paper investigates active and passive short-wave infrared (SWIR) imaging for slant paths close to ground. The main sensor, a gated SWIR camera, was collecting both passive and active images along a 2 km long path over an airfield and also from our rooftop laboratory looking over open fields. For some investigations we also used a gated system working in the near-infrared region and thermal as well as color CCD cameras. The sensor was elevated by a lift in steps from 1.6–13.5 m or placed in a rooftop laboratory 13 m above ground. Targets were resolution charts and man targets. The turbulence was measured along the path with anemometers and scintillometers. The image performance was evaluated by measurement of the image blur and also by performing observer perception tests. The results reveal a strong dependence on the sensor height especially during daytime.

© 2013 Optical Society of America

1. Introduction

It is well known that the atmospheric turbulence will rapidly decrease with height especially during daytime and this fact is of importance when evaluating the active and passive imaging performance close to ground. We should expect that the image quality will improve if the sensor is elevated even by just a few meters.

This study investigates active and passive imaging in the short-wave infrared (SWIR) region around 1.5 μm as well as in the near-infrared (NIR) region around 0.81 μm. Most investigations were performed during daytime to have a wide span of turbulence and to catch the strong turbulence close to ground. The NIR active imaging was only performed during evenings because during daytime the daylight dominated over the laser illumination. Study of range-gated imaging in daytime with high turbulence at the eye safe wavelength of 1.5 μm is motivated from several reasons. One is based on the fact that in the SWIR region, the daytime background is low so the pulsed laser illumination in combination with time gating is effective to separate the target from the background either with the gate around the target or behind showing the target silhouette. The gated imaging also gives a better capability to observe targets in shadows and through windows.

Active imaging experiments with emphasis on turbulence and speckle effects have been studied by several groups. One serious attempt to measure and model active imaging systems was made within a special NATO group [1].

Examples of analysis of turbulence influence from these measurements have been published by the Swedish Defense Research Agency (FOI) [2]. Other examples of experimental work in active imaging involve both monostatic and bistatic measurements [3]. Active imaging of maritime targets has been reported [46]. Other authors have investigated target-induced speckle in active imaging and modeled that [7,8]. A full analytical model of active imaging has been presented in [9] and later extended by [10] for slant-path active imaging. Other examples of studies of active imaging performance in turbulence are shown in [11,12] and [13] demonstrates a turbulence mitigating technique for slant-path imaging using CCD passive sensing. In [14,15], long-range active and passive imaging form an airborne platform are demonstrated. However, there seem to be very few reports on active and passive imaging very close to ground, which motivated this investigation. Some of the key benefits of this investigation are detailed measurements and comparison of short-wave active and passive imaging as a function of height as well as a detailed characterization of the turbulence using different methods.

First, the theory for slant-path imaging is reviewed and then the experimental equipment is presented, which is followed by experimental results and analysis. Finally, a discussion of the results is presented.

A. Theoretical Background

Atmospheric turbulence will degrade both active and passive images. We will therefore start with review of the turbulence behavior close to ground.

1. Turbulence Near Ground

The refractive index structure constant Cn2 measured in m2/3 is known to decrease with height above ground and a classic approximation of the height decay for low altitudes (<1km) is often given by the relation

Cn2(h)=Cn2(1)·hα,
where Cn2(1) is the reference value for the height h=1m and α a parameter that often is set to 4/3 for daytime and 2/3 for nightime conditions. The relation (1) is valid close to ground and is part of a more general height dependence, which according to the Kaimal/Walters–Kunkel profile [16] for the atmospheric boundary layer, i.e., up to the inversion layer, and the Hufnagel–Valley 5/7 profile [17] for the free atmosphere.

2. Target Speckle Noise

Speckle arises from the interference of coherent or partially coherent light from an irregular surface. A simplified expression for the speckle size in the image plane is given by the resolution (point spread function of the optics) according to

ρsp=1.22λFD,
where F is the receiver focal length, λ the laser wavelength, and D the receiver lens diameter. For F=1.26m, D=20cm, and λ=1.57μm we get a speckle size of about 12 μm. Note that the image plane speckle size is independent of range. A more rigorous treatment is made by Korotkova and Andrews [18] including turbulence. A speckle pattern is also characterized by the speckle intensity distribution and the speckle contrast. The fully developed speckle probability density function is exponential with its mean equal to the standard deviation and the speckle contrast defined by the ratio of mean to standard deviation is thus equal to 1. The speckle contrast for M averaged speckle cells (as for one pixel intensity summed over M frames) is [19]
Csp=1M.
The target surface, the surface tilt, and the laser coherence length also affect the speckle size and contrast. Man-made surfaces are often not ideally diffuse at 1.5 μm. For a target with a glint plus diffuse part (as is often the case for curved surfaces) the probability density distribution for intensity becomes Ricean with the glint to diffuse power ratio as a parameter.

3. Atmospheric Turbulence Effects

Atmospheric influence (especially the turbulence) on optical beam propagation and imaging, is covered by a number of textbooks and review articles [2023]. Recently, new efforts in modeling atmospheric and target speckle effects for range-gated imaging have appeared in a number of publications [2427].

The Fried parameter r0 defines the efficient angular resolution of the receiver with diameter D as δθ=λ/min(r0,D). For a focal plane array or image tube the corresponding angular resolution is θres=max(dpix/F,δθ) with F=focal length. The relevant r0 for this problem is calculated at the receiver plane. Within the validity of the Rytov’s method, i.e., within the nonsaturated scintillation regime, the Fried parameter in spherical wave approximation for the receiving path is given by

r0=2.1·[1.46k20LCn2(z)(1z/L)5/3dz]3/5,
with Cn2(z) being the turbulence strength profile along the path from the target plane (z=0) to the transmitter-receiver plane (z=L) and k the wavenumber, k=2π/λ.

Figure 1 illustrates the improvement in angular resolution due to turbulence blur only versus sensor height for observing a ground target at 1.9 km range. A sensor resolution limit of 16 μrad roughly corresponding to our sensor resolution for the SWIR camera at 1.5 μm and F=1.26m focal length is also indicated. For ground turbulence Cn2<1014m2/3 the angular resolution due to turbulence is less than 10 μrad.

 

Fig. 1. Improvement in angular resolution versus sensor height for observing a ground target at 1.9 km range for different values of the parameter α.

Download Full Size | PPT Slide | PDF

The refractive effects of the turbulent atmosphere will be manifested in effects like beam wander, angle-of-arrival variations, and image dancing, and they are all interrelated. Angle of arrival is the variation of the waveform giving rise to image dancing. The angular variation (jitter) for a spherical wave can be estimated by [21]

σα2.9Cn2LD1/3,
where L is the target range, Cn2 the turbulence structure constant, and D the receiver aperture diameter. We note that the angular jitter is independent of wavelength. For a typical daytime turbulence value, Cn2=1014m2/3 and D=20cm results in a jitter equal to 9–10 μrad for a path length of 1.9 km.

2. Experimental Equipment and Methods

FOI has collected slant- and ground-path active images during two campaigns which are more described in two SPIE (the international society for optics and photonics) papers [28,29].

The two campaigns took place in the summers of 2010 and 2011 at the former airfield Bråvalla in Sweden with the purpose of studying turbulence effects in close to ground paths. We also made measurements from our rooftop laboratory at FOI during 2011 from a height of 13 m above ground looking at targets between 800 m–2.4 km.

A. 2010 Campaign

1. Active Imaging Experiment

The measurements at the airfield included range-gated imaging [gated viewing (GV)] at 1.5 μm as well as passive SWIR imaging during 3 days. The active imaging sensor was placed in a lift and the altitude could be varied between 1.6–12.5 m above ground. The range to the targets was almost 2 km. Figure 2 shows the experimental arrangement and Fig. 3 the size and details of the test panels.

 

Fig. 2. Experimental arrangement with the 1.5 μm laser sensor in the cage and the elevated platform.

Download Full Size | PPT Slide | PDF

 

Fig. 3. Edge and resolution charts. At 1920 m range the bar separation for the three largest bar groups corresponds to 26.3, 37.9, and 52.6 μrad, respectively. The ratio of length to width of all black bars is 15 and the linear scale factor between each bar group is 2. The size of the resolution test panel was 1.3×2.2m and the edge chart was about 2 m in square.

Download Full Size | PPT Slide | PDF

The eye-safe 1.5 μm GV sensor use the Intevac tube technology. The operator running the GV camera controls the system via a LabView program. In this program it is possible to acquire active or passive images and measuring range with a laser range finder. In active mode the operator manually sets the gate delay and width or uses the automatic ranging mode where the gate delay is continuously updated from the laser range data. This automatic range mode makes it possible to track moving objects in depth. In the range step mode it is possible to acquire image sequences where the gate steps trough the target saving a requested number of images at each step.

In these trials the system was equipped with a 1260 mm focal length telescope. The laser divergence can be adapted to the target range. For measurements at 2 km a divergence of 5.5 mrad was used in order to cover the 6 mrad field of view of the sensor. The laser illuminator is a range finder developed by SAAB with a pulse energy of about 20 mJ. The laser typically runs at a pulse repetition frequency (prf) of 10 Hz. The laser pulse width is approximately 20 ns. The Intevac camera sensor is of the Electron Bombardment CMOS type with 640*480 elements (pixel size 12*12μm) and is sensitive between 950–1650 nm. The quantum efficiency is about 25% and the limiting resolution 28lp/mm (line pairs/mm). The dark current is of the order of 1 electron per pixel per μs and the sensitivity is down to the single photon level. The dynamic range is 16 bits. The gate widths of the camera from approximately 150 ns and with a gate rise and a fall time of about 75 ns. The gated systems at 1.5 μm could be run both in passive and active modes. Typically a gate width of 200 ns was used for active imaging and an integration time of 3 μs for the passive mode.

The targets are depicted in Fig. 3. The left is a black and white contrast screen. The right target is a resolution chart reminding of the well-known Air Force resolution chart. The size of the largest bars are 10cm×50cm and the size of the patterns decrease with a factor of 2. The reflection at 1.5 μm is measured to 3.2% and 80.8%, respectively, for the black and white parts.

The targets were measured with the sensor in the aerial work platform from five height steps, 2.1, 4.9, 7.3, 9.8, and 12.2 m. At each height step four sequences were acquired. A passive sequence with the sun illuminated targets and a second passive sequence viewing the headlights on the car, these datasets are used for measuring the turbulence-influenced angular jitter. The two last sequences at each height were active imaging of the two test panels. During most of the measurements an anemometer was mounted on the aerial work platform.

The car beside the second reference target was oriented to get a target with specular reflection points from the headlights, which were used for estimation of angular jitter.

2. Turbulence Measurements

The turbulence was measured during the field trials along the runway using a scintillometer (Scintec BLS2000, wavelength 0.8 μm) and three ultrasonic anemometers (Gill Instruments, Windmaster). The instruments were initially distributed as shown in Fig. 4 with one anemometer each at point A (close to the elevated platform), B2, and B, and the scintillometer path from C to A. The scintillometer transmitter was placed at the target at point C and the receiver was placed at point A, giving a distance of 1900 m. The direction was chosen to avoid disturbing sunshine into the receiver. The scintillometer, both transmitter and receiver, was at a height of 1.5 m.

 

Fig. 4. Drawing of the air field and the position of the experimental setup at the second day in the September 2010 campaign.

Download Full Size | PPT Slide | PDF

The first day (7 September 2010) the anemometers were placed near point A, and at B and B2. The anemometer at A was placed about 50 m in to the grass field. The distance from point A, to the anemometer at B2 was 546 m and to 1059 m. All the anemometers were raised to about 2 m height above ground. In the afternoon the anemometer at A was moved to the aerial elevated platform together with the GV system, approximately in line with point A. During the second and third day the anemometer was mounted on the GV elevator at a height 1.55 m above the GV system and raised to different levels and the anemometer at point B2 was moved to point B near the container and raised to 7.3 m. During the third day the anemometer at A was placed all day on the GV elevator (same position as the second day), which meant that the height above ground varied.

Using an ultrasonic anemometer the sound velocity is measured as function of time along a short path (about 0.3 m) in three dimensions. The sonic temperatures are deduced out of the sound velocity with 20 Hz. The power spectral density of the sonic temperature was computed and data were average in 1 min bins. The sonic temperature structure constant, CT2, is then computed from the power spectral density and wind velocity choosing the CT2 at the frequency equal to one [30]. The turbulence refractive index structure constant, Cn2, can be described as a function of variation of temperature and humidity [31]. By assuming the influences of humidity during dry condition are negligible the Cn2 can be given as function of temperature and CT2, as suggested by Potvin et al. [32].

An example of Cn2 as function of time measured at three different points along the runway (point A, B, and B2) is shown in Fig. 5. The anemometer at point A was moved to the GV elevator after 14:00 giving lower values of Cn2 during periods due to the higher level.

 

Fig. 5. Cn2 as function of time measured using three different ultrasonic anemometer along the runway, 7 September 2010.

Download Full Size | PPT Slide | PDF

Due to the neglected influence of humidity on Cn2 the anemometer data should in general have lower values compared with data from the scintillometer. The different ways to measure turbulence, one by the average scintillation over 1.9 km and one by using the other instrument to measure the temperature variance along a very short path (0.3 m) are quite different in nature. Likewise are the position and height of the instruments also different, the scintillometer with a path about 1.2 m above the ground and the anemometers about 2 m height.

In Fig. 6, the scintillometer data are compared with data from two anemometers, one near the receiver, about 50 m in front of receiver at point A and one (B) halfway down the runway.

 

Fig. 6. Comparison between measured Cn2 along the runway measured with the scintillometer (crosses) and measured with two ultrasonic anemometers halfway down the runway. Measurement performed 7 September 2010.

Download Full Size | PPT Slide | PDF

3. Other Meteorological Measurements

A weather station of the type Vaisala Milos was placed just close to the aerial platform and the scintillometer receiver at point A. The weather during the field trials was dominated by high-pressure clear weather with scattered clouds all three days. The wind direction changed during different days but the wind speeds were low. The measured average wind speed each day was 1.1m/s, 2.8m/s, and 3.6m/s, respectively. The temperature was relatively constant during the trials (daytime) and the average temperature measured 14.7°C, 16°C, and 17°C, respectively, with the highest standard deviation of 1.3°C. The relative humidity (RH) started out to be about 80%–90% in the morning. During the middle of the day the RH dropped and was as low as 50%.

B. 2011 Campaign

During June 2011 a number of parallel laser imaging experiments were taking place at the same airfield Bråvalla to get more data for slant paths and to improve some of the techniques for turbulence measurements. These experiments also included persons as targets and compared the recognition of their objects and activities with the resolution information obtained from resolution targets. We also included an NIR imaging system (Obzerv with 808 nm wavelength). Besides range-gated and passive imaging at 1.5 μm and 808 nm, these experiments also investigated turbulence influence on the performance for a scanning slit ladar and a time-correlated single-photon detection ladar [33,34]. Later during the autumn we also made complementing measurements from the rooftop laboratory at FOI.

1. Active Imaging Experiment

The Obzerv 750 Night Vision Camera [35] (Fig. 7) has an aperture of 104 mm using a custom variant of Generation III Intensifier tube and a laser diode illuminator operating at 808 nm. The system also has a bore-sighted color camera for daytime use. The system has an optical magnification between 4.5 to 73 times and an FOV between 0.5*0.37deg to 8*6deg. The Obzerv camera was only used for horizontal experiments at the airfield but later together with the 1.5 μm system from our rooftop laboratory situated about 13 m above ground.

 

Fig. 7. Two active imaging systems. Left, the Intevac tube with a F=1260mm telescope and a Saab laser range finder at 1.5 μm, and right, the Obzerve system (white box).

Download Full Size | PPT Slide | PDF

The same test targets as shown in Fig. 3 were used. Two headlights put on tripods were used for estimating the angle of arrival giving an independent estimate of the turbulence. We also used persons holding various objects and also using them in simulated activities (Fig. 8).

 

Fig. 8. Person holding different objects to be identified statically and in conjunction with associated activities.

Download Full Size | PPT Slide | PDF

The measurements at the airfield occurred during two days at the airfield, the 13th and 14th of July 2011. The measurements from the rooftop laboratory at FOI occurred at several occasions. No measurements of the turbulence were made because the influence from it was considered to be limited as the sensor was operating during darkness and from 13 m above ground.

2. Turbulence and Weather Registrations

The turbulence was measured with the same equipment as during the 2010 campaign and the equipment was position approximately as in Fig. 4. Weather parameters such as insolation, temperature, humidity, visibility, and wind speed were monitored using a weather station. The weather situation during the trials was dominated by high pressure and clear sky. Intermittently scattered clouds appeared. The average wind speed was in the range 1 to 7m/s. The wind direction was in most cases nearly perpendicular to the propagation path. Typical temperatures varied between 14°C–20°C. The relative humidity was high in the morning (80%–90%) but lower in the afternoon (approximately 50%).

The scintillation level was well correlated with the sun irradiance as expected. Typical ranges of registered structure constant were, 2×1014 to 5×1013m2/3, i.e., moderate to strong turbulence conditions. An example showing the Cn2 registered with the three anemometers is depicted in Fig. 9. Typically some differences in the measurements between the A, B2=AB, and B locations along the propagation path were observed but the general trend was the same.

 

Fig. 9. Example of Cn2 data registered using ultrasound anemometers at position A, AB=B2, and B during 14 June 2011.

Download Full Size | PPT Slide | PDF

3. Experimental Results and Analysis of the 2010 Data Collection

A. 2010 Campaign

During day 1, 7 September 2010, the laser imaging measurements took place between 11 AM to 6 PM. The number of registrations from different elevations were in total 128 with 100 consecutive frames in every registration. At a laser prf of about 10 Hz, the length of each registration in time was 10 s. Typical ground values of the turbulence vales Cn2 were between 1013 and 1014m2/3.

Figure 10 shows one typical example of images for a horizontal path and a low turbulence situation at the time 14:54:11 on 7 September 2010 and onwards. The anemometers showed a turbulence level of about 1014m2/3. The Fried parameter value for this turbulence level and 1.9 km range indicates a resolution about 10 μrad. The resolution given by the intensifier tube is 28lp/mm, corresponding to a resolution of about 18 μrad. From Fig. 10 we can see the bars down to a separation corresponding to 18.4 μrad both in the passive and active images. The figure also indicates the quality improvement for frame averaging in active images during low turbulence. This improvement is mainly manifested as an intensity smoothing rather than an angular resolution improvement.

 

Fig. 10. Series of images for a low turbulence situation and a horizontal 1.9 km path at 2.1 m above ground. Left: a passive image of the whole FOV and next close-up images of the 2.2*1.3m bar pattern target, partly occluded by grass at the bottom. The angular resolution in the passive and active images are about equal and the improvement of active image averaging is mainly seen as an intensity smoothing. Time 14:54:11 on 7 September 2010. Mean turbulence from anemometers Cn2=1014m2/3.

Download Full Size | PPT Slide | PDF

Figure 11 illustrates one example of how the image quality can be strongly approved by lifting the sensor to heights about 5–12 m looking at the bar target at ground level 1.9 km away. In order to quantify this effect better we analyzed all images both passive and active by measuring the bar pattern modulation for single images as well as for consecutive frame-averaged images using 3, 5, or 10 images. By interpolation we observe the angular resolution values (spatial frequency) for which the modulation was dropping to a value of 2%, which is considered to correspond to the resolution limit [36]. For active imaging we sometimes did not see a whole bar pattern and in such a case the modulation was estimated from the visible bars.

 

Fig. 11. Above the passive image of the scene and the bar target at about 16:42:30 on 7 September 2011 and below examples of single active frames from increasing heights between the time 16:44:24 to 17:11:47. At the higher elevations of the sensor there is a clear improvement in angular resolution, from about 50 μrad at 2.1 m to better than 18 μrad at 12.2 m.

Download Full Size | PPT Slide | PDF

Figure 12 shows some time series (S1–S4) where El. refers to the elevated anemometer and Gr. to the mean value of the two ground-based anemometers. In all sequences the turbulence for the elevated was found to be lower than the corresponding ground values as expected. Although the scatter in data for the evaluated angular resolution is rather high, the trend is clear that it is improved for slant paths with the elevated sensor.

 

Fig. 12. Left: measured turbulence from the anemometer data, 7 September 2010. El. refers to the elevated anemometer (=sensor height) and Gr. to the mean value of the two ground-based anemometers. S1–S4 refer to different time series of measurements (S1: 14:49–15:11, S2: 15:49–16:19, S3: 16:42–17:12, S4: 17:24–17:46). Right: the resolution evaluated from the bar patterns for the corresponding time series.

Download Full Size | PPT Slide | PDF

Figure 13 shows the correlation between the resolution obtained for one frame active imaging versus the angular jitter as obtained from the mutual change in distance between the two car lights, based on Eq. (5) and horizontal paths. The car lights were a bit too strong, which caused the sensor to saturate in the middle of the “blobs”.

 

Fig. 13. Relation between angular jitter measured from the relative movement of two car lights and the angular resolution for single active images.

Download Full Size | PPT Slide | PDF

During day 2, September 8, 2010, the laser imaging measurements took place between 11:15 AM and 2:30 PM. The number of registrations from different elevations were in total 122 with 100 consecutive frames in every registration. At a laser prf of about 10 Hz the length of each registration in time was 10 s.

Figure 14 shows the turbulence values obtained from the anemometers of which one was place at the elevated sensor position and the other two close to the ground. Note that the turbulence varies rather irregular with height on this day in opposite of the situation in day 1, 2010. There is a clear tendency, however, that the position A data show a smaller turbulence values than position B and B2, which is expected due to the height differences. One of the explanations for the irregular behavior of the turbulence versus height is the time delay between the different altitudes. One sequence of data could take more than 10 min during which the turbulence could change. Figure 15 shows the angular resolution versus height for the time sequences S1–S4 with turbulence according to Fig. 14. The passive images show a better tendency to improve in sharpness with height than what was found for the active images. This might reflect the increased noise in the active images due to speckle.

 

Fig. 14. Measured turbulence from the anemometer data, 8 September 2010. El. refers to the elevated anemometer (=sensor height) and Gr. to the mean value of the two ground-based anemometers. S1–S4 refer to different time series of measurements (S1: 11:29–11:37, S2: 11:47–12:10, S3: 13:21–13:32, S4: 14:06–14:16). Note that the turbulence varies rather irregular with height on this day in opposite of the situation during 7 September 2010.

Download Full Size | PPT Slide | PDF

 

Fig. 15. Angular resolution for different heights and three frames averaged. Left, active and right, passive operation.

Download Full Size | PPT Slide | PDF

4. Experimental Results and Analysis of the 2011 Data Collection

During day 1, 13 June 2011, the measurements were concentrated to horizontal imaging about 1.5 m above ground and involved imaging a man. The relevant range-gated results came from our 1.5 μm sensor, which can reject the low daylight background for this wavelength. The Obzerv system was in practice only used for the passive mode as the active mode could not reject the daylight to fully make use of the laser illumination. Figure 16 shows registration from the Obzerv color video and a passive image intensifier capture as well as passive and three active images with the 1.5 μm system using the Intevac tube and a 500 mm lens. Note that the imitated weapon shows a high contrast against the clothes, which generally show a high reflectivity at 1.5 μm. The weapon appears to be more easily classified in the active images as compared with the passive images.

 

Fig. 16. Man at 876 m range with a toy weapon. The turbulence level around 1.5×1013m2/3. Note that the 1.5 μm images in the lower row seem to be somewhat less blurry than those from the visible-NIR region.

Download Full Size | PPT Slide | PDF

Active imaging has a drawback for low-reflectivity objects sticking out from the body in that they may disappear against the background. Silhouette images in active imaging will reduce this problem provided that there is enough background reflectivity. This is investigated in separate experiment discussed below.

During day 2 we continued to collect data along the 876 m distance close to ground. The aim was to collect not only static scenes but also person activities for later observer tests. The turbulence level during day 2 was about the same as for day 1 with the exception of some clouds at noon giving lower turbulence levels.

In the afternoon of day 2 we tested active/passive imaging at 1.5μm/SWIR at 2 km range using the test target and the man (cf. Figs. 17 and 18). Different sensor heights between 1.6–12.8 m were examined.

 

Fig. 17. Images (three frame stabilized average) of active 1.5 μm (above) and passive SWIR images (below) of the resolution chart at 1.92 km range for the sensor heights of 1.6, 5.15, 7.65, 10.35, and 13.15 m, respectively (left to right). Focal length 1260 mm. Collection time period 3:52–4:11 PM, 14 June 2011.

Download Full Size | PPT Slide | PDF

 

Fig. 18. Same as in Fig. 17 but at a later time (7:04–7:23 PM, 14 June 2011) when the ground turbulence measured by the scintillometer was between 47×1014m2/3.

Download Full Size | PPT Slide | PDF

Examples of images for different slant paths are found in Fig. 19. Note how low the image resolution is for the horizontal path at 2 km range. The Cn2 ground value measured by the scintillometer during the measurement time period (3:52–4:11 PM, 14 June 2011) was found to be between 23×1014m2/3.

 

Fig. 19. Man with an RPG weapon in different positions at a range of 2 km. The active (above) and passive images were collected with different sensor heights (1.6, 5.15, 7.65, and 10.35 m). The measurements were collected between 6:07 and 6:33 PM 14 June 2011.

Download Full Size | PPT Slide | PDF

In parallel with the imaging of the resolution charts, the man was also imaged both in dynamic and static positions at 2 km during different slant-path and turbulence levels. Figure 19 gives some examples of active/passive imaging for different sensor heights. There is an interest to compare the resolution derived from the test targets with actual objects in the hand of a person.

A. Test from FOI Rooftop Laboratory, 2011

During a few evenings tests were also performed from the FOI rooftop laboratory. The aim of these tests was to collect both direct illumination and silhouette images of a person holding different objects and using them in simulated activities. Both the Obzerv and the 1.5 μm sensors were used. These images will be more discussed with regard to the observer tests in the analysis section below. The target ranges varied from 850 to 2442 m. The turbulence was low due to the slant path and late evenings for the data collections. Examples of images are shown in Figs. 20 and 21.

 

Fig. 20. (Left two): a man with a shovel imaged at 1.5 μm and (right two) at 0.8 μm. Face reflection is very low at 1.5 μm. Both pair of images show the advantage of silhouette detection for visualizing the shovel. Range 850 m.

Download Full Size | PPT Slide | PDF

 

Fig. 21. Above: the Obzerv system showing images at 2442 m of a man holding a weapon. Below: the same for the 1.5 μm system. Both sensors had a nominal angular resolution about 16 μrad. The sensors were placed 13 m above ground.

Download Full Size | PPT Slide | PDF

The Obzerv system at 0.8 and the 1.5 μm Intevac systems differed in performance especially at the long slant-path range of 2442 m. The nominal resolution set by the focal length and pixel size was about 16 μrad for both sensors. The shorter wavelength Obzerv system gave, however, somewhat more “noisy” imager when compared with the 1.5 μm system using the Intevac camera. The aperture size for the Obzerv system was 10 cm and for the 1.5 μm system 20 cm. The difference in performance may be attributed to atmospheric effects and the SNR (Fig. 21).

B. Active and Passive Frame Averaging Versus Resolution from the Bar Target Images

The example results below all belong to the analysis of the data during the day 14 June 2011 obtained by analyzing the 1.5 μm sensor only. The angular resolution was obtained by measuring the modular transfer function (MTF) from the different bars and the extrapolation to the spatial frequency where MTF=0.02. This extrapolation was done with a spline method. The resolution is somewhat better for passive imaging as expected but this is somewhat reduced when three frames are integrated. The result is also in accordance with the finding from the 2010 campaign. The resolution is most often worse for single-frame active images than for single-frame passive images. This can be attributed to the speckle noise in active imaging related to both turbulence and target-induced speckles. For frame averaging of three and five frames the resolution in passive images and actives images are more equal due to smearing out the speckle noise in active imaging but also introducing an uncertainty due to the stabilization method, which also can give some smearing.

C. Resolution Using the Edge Response

We used one black and white target and one white target to investigate the resolution by other techniques using the edge response. The edge response can be deduced from the MTF, written as [36]

MTF=exp[3.44·(λf/r0)5/3],
where λ is the laser wavelength, f the spatial frequency, and r0 the Fried parameter given by Eq. (4). Figure 22 shows passive and active images from the two target boards. The smaller size white target board to the left was placed about 10 m in front of the black and white target to the right and at a range of 1130 m from the sensor. This arrangement was made to investigate if there was any difference between the edge sharpness obtained from the edge due to the time gating or due to the black and white contrast in the same z plane.

 

Fig. 22. Two pairs of passive (left) and active images at 1.5 μm from the targets boards at 1130 m range. The smaller size white target board to the left was placed 10 m in front of the black and white target. Left, the sensor at 1.6 m above ground and right, the sensor at 7.65 m height. The ground value of the turbulence was between 13×1013m2/3.

Download Full Size | PPT Slide | PDF

We did not find any clear difference between the sharpness measured from the edge created by “time gating out” the left white target versus the edge due to the black and white target. Figure 23 shows the relation between the angular resolution estimated from the edge response of the black and white target versus the one obtained from the resolution chart. The relative large spread in the data can probably be attributed to the speckle noise in single images. For 3–5 frame averaging this spread is reduced. In Fig. 23, we have omitted the resolution estimated for the sensor height of 1.6 m when the turbulence was strong and it was very uncertain to estimate the resolution especially from the resolution chart.

 

Fig. 23. Estimated angular resolution for single active images using the resolution chart versus edge response from the black and white board. The relatively large spread in data is probably due to the speckle noise.

Download Full Size | PPT Slide | PDF

D. Turbulence and Image Jitter

The refractive effects of the turbulent atmosphere will be manifested in effects like beam wander, angle-of-arrival variations, and image dancing and they are all interrelated. Angle of arrival is the variation of the waveform giving rise to image dancing. The angular variation (jitter) is given by Eq. (5). We measured this jitter by evaluating the movement of two lights relative to each other. In the 2010 tests we used car lights but these light sources were too strong and made the estimate of the accurate light positions uncertain.

This time we replaced the car lights with smaller light bulbs, which led to more accurate reading of their positions. Figure 24 illustrates the good correspondence between the measured image jitter and that obtained from Eq. (5) using the path length L=1910m and the receiver diameter D=0.2m.

 

Fig. 24. Left diagram shows the good correspondence between the estimated image jitter from the relative motion of the two lights versus the theoretical values obtained from Eq. (5) using turbulence values from the scintillometer and the three anemometers. The R2 of the linear fits ranged between 0.62–0.92. Right shows calculated image jitter values for different turbulence values from the scintillometer and the anemometers. The anemometer positions A, AB, and B correspond approximately the positions A, B2, and B in Fig. 4.

Download Full Size | PPT Slide | PDF

The jitter followed the expected decay with the sensor height above ground. Some deviation from that decay was observed for the vertical jitter, as seen in Fig. 25.

 

Fig. 25. Height variation of the horizontal (left) and vertical (right) image jitter. Note the increase in image jitter for the height of 10.35 m. The inserted circles reflect the jitter magnitude in an xy diagram.

Download Full Size | PPT Slide | PDF

Figure 26 illustrates the relation between measured angular resolution from three stabilized active images versus the measured image jitter. Though the spread in data is relatively large it is obvious that the measurement of the image jitter is indicative of the level of turbulence along the path and maybe used in processing to mitigate the turbulence effects on the image quality.

 

Fig. 26. Measured angular resolution for three frame stabilized active images versus measured image jitter.

Download Full Size | PPT Slide | PDF

E. Image Resolution Versus Sensor Height

We tried to compare the angular resolution versus sensor height with what should be expected from the model according to Eq. (1).

Figure 27 shows the comparison between the resolution obtained from the resolution chart with that calculated using the exponent α=4/3 and 2/3 in Eq. (1). There is a discrepancy between the observed resolution at 1.6 m sensor height and that calculated using the turbulence value from the scintillometer for α=4/3 or 2/3. Observing the resolution chart for daytime imaging at 1.6 m sensor height over the 2 km path resulted in a very blurry image (cf. Fig. 19) and consequently a very uncertain resolution value. The corresponding measurement during the evening (Fig. 27, right part) gave a good correspondence between measurements and theory. In this case the turbulence was lower than during daytime giving an easier interpretation from the resolution chart. Using the edge response it was easier to estimate the resolution in strong turbulence, which resulted in a much better correspondence between measurement and theory (Fig. 28).

 

Fig. 27. Left: Measured angular resolution for three frame stabilized active images versus sensor height [black squares] versus theoretical values based on the conventional choice of α=4/3 (daytime) or α=2/3 (night time). Right: During the evening the choice of α=2/3 gave a good correspondence with the measured and theoretical angular resolution.

Download Full Size | PPT Slide | PDF

 

Fig. 28. Measured angular resolution for three frame stabilized active images versus sensor height [black squares] versus theoretical values based on the conventional choice of α=4/3 (daytime) or α=2/3 (night time). The resolution was measured from the edge response of the black and white target board gave a much better correlation with the theory.

Download Full Size | PPT Slide | PDF

F. Observer Tests

We will shortly mention the observer tests in connection with the 2011 measurements. A more detailed presentation is found in a recent SPIE paper [37]. Different datasets were put together for the observer perception testing. The observer tests were based on videos and still images from the different cameras working both in the passive and active modes. A small computer program was developed that enables the observer to decide what activity or object that the person was associated with. The 6–8 handheld objects were presented beforehand [axe, broom, pole, shovel, board, handgun, rocket-propelled grenade (RPG), rifle] and the observer had to choose between these objects as rapidly as he could but avoiding guessing. The parameters measured for each choice were the correctness (right/wrong) and the time to respond, measured from the point in time when the image or video clip first was visible and to the point when the observer made a choice by pushing a stop button. The observer had to choose among a fixed number of choices excluding a “don’t know” alternative.

A man performing some activities was imaged at 2 and 2.5 km ranges during different slant-path and turbulence levels. Figure 19 showed one example of active/passive imaging for different sensor heights. When evaluating recognition from active imaging the range gate was varied in three ways. In one the gate was long and included both the target and the terrain background. The other two used short gates placed around the target isolating that from the background behind giving a target silhouette. As shown in [37] it was found that using a short gate around the target gave a better recognition performance than silhouette imaging followed by the long-gate imaging including both target and background.

In the test result illustrated in Fig. 29, only one gate position, the one with the gate around the target, was included. Passive images at 1.5 μm were also in the dataset. In total this set involved 34 video clips each about 10 s long. Figure 29 analyzes the result of the subset (28 clips) based on the 2 km daytime data (cf. Fig. 21 for typical image examples). The influence of sensor height for the 2 km path is obvious. The video clips at a sensor height of 1.6 m corresponded to strong turbulence, the height at 5 m to moderate and at 10 m to weak turbulence. In general, a high probability of correct ID corresponded to a shorter response time for the ID decision.

 

Fig. 29. Probability of recognition and median time to response for different activities related to the normal use of the object listed on the x axis. A=active and P=passive imaging. Range 2 km with average sensor heights of 1.6 m (strong turbulence), 5 m (moderate), and 10 m (weak).

Download Full Size | PPT Slide | PDF

There was no distinct difference between active and passive SWIR imaging as seen illustrated in Fig. 29. Remember that passive SWIR imaging needs ambient light and that active imaging mostly is aimed for night vision.

Ten of the activity clips were also collected from the FOI rooftop laboratory during evening time using a target range equal to 2.5 km. The turbulence was weak and the resolution evaluated from a test board indicated a resolution of 20–25 μrad or 5–6 cm at the target. The instrument resolution based on focal length and pixel size was about 3 cm. Except for the activities “video filming” and “putting on gloves” where the probability of recognition was about 0.6–0.7, the activity recognition probability was better than 0.9 for using larger objects like weapons, axes, and shovels.

5. Conclusions

Controlled measurements of active and passive images were performed at an airfield over paths length from 1–2 km. The turbulence was measured with a scintillometer and at three positions along the path using anemometers. One interesting notation is that the difference in these observed turbulence values could vary by a factor of 3 or more along the path as well as between the anemometer and scintillometer readings. During daytime the turbulence level was above or close to saturation over the 0.8 and 2 km horizontal paths. During the evening the turbulence was reduced below saturation even for the horizontal ground path. For elevated sensor positions the image quality measured in angular resolution was often dramatically improved. Even a few meters above ground will substantially improve image quality—an observation that has important tactical implications. We obtained a relative good correspondence relative to a model based on the accepted height dependence (Cn2(h)=Cn2(1)·hα) of turbulence close to ground.

The activity recognition for both passive and active SWIR had a good performance in observer tests with a recognition probability of about 0.9 for weak turbulence, 0.85 for moderate, and 0.6 for strong turbulence when observing a man at 2 km range. Corresponding objects during moderate to strong turbulence were not resolved but the corresponding activities using the objects were. This is in accordance with other investigations [38] including our own [37].

During analysis we used both the MTF derived from the resolution chart as well the edge response from the black and white target. A relatively good correspondence between the measurement methods was obtained. Especially for high turbulence the estimate from the edge response was more relevant due to the angular bar pattern where the largest pattern corresponded to 52.6 μrad, a resolution value greatly exceeded in severe turbulence.

We also tried to characterize the turbulence for elevated paths by measuring the image jitter. The observed jitter fell in the range 13–70 μrad and was in good accordance with the one derived from a theoretical expression using turbulence readings. The method of measuring the jitter by observing the relative motion of two stationary lights was important to eliminate the elevated platform jitter. This technique might have a general interest if one can find two independent glint or other characteristic point-like targets within the sensor field of view. In this way an approximate turbulence level can be estimated, which will speed up turbulence mitigation techniques based on optimization of the image sharpness.

The authors acknowledge the Swedish Armed Forces (FM) and the Swedish Material Administration (FMV) for their support of this research. We also want to thank Kjell Karlsson and Frank Gustafsson FOI for their technical assistance in the trials.

References

1. Modeling of Active Imaging Systems, NATO RTO Technical report, TR-SET-072, Final report of task group 40, June 2009.

2. O. Steinvall, P. Andersson, and M. Elmqvist, “Image quality for range-gated systems during different ranges atmospheric conditions,” Proc. SPIE 6396, 639607 (2006). [CrossRef]  

3. E. Repasi, P. Lutzmann, O. Steinvall, M. Elmqvist, B. Göhler, and G. Anstett, “Advanced short-wavelength infrared range-gated imaging for ground applications in monostatic and bistatic configurations,” Appl. Opt. 48, 5956–5969 (2009). [CrossRef]  

4. D. Bonnier, S. Lelievre, and L. Demers, “On the safe use of long-range laser active imager in the near-infrared for Homeland Security,” Proc. SPIE 6206, 62060A (2006).

5. O. David, R. Schneider, and R. Israeli, “Advance in active night vision for filling the gap in remote sensing,” Proc. SPIE 7482, 748203 (2009).

6. O. Steinvall, M. Elmqvist, K. Karlsson, H. Larsson, and M. Axelsson, “Laser imaging of small surface vessels and people at sea,” Proc. SPIE 7684, 768417 (2010).

7. R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003). [CrossRef]  

8. C. E. Halford, A. L. Robinson, R. G. Driggers, and E. L. Jacobs, “Tilted surfaces in SWIR imagery: speckle simulation and a simple contrast model,” Opt. Eng. 46, 053201 (2007). [CrossRef]  

9. R. L. Espinola, E. L. Jacobs, C. E. Halford, R. Vollmerhausen, and D. H. Tofsted, “Modeling the target acquisition performance of active imaging systems,” Opt. Express 15, 3816–3832 (2007). [CrossRef]  

10. B. Göhler and P. Lutzmann, “An analytical performance model for active imaging systems including slant-path applications,” 4th International Symposium on Optronics in Defence and Security, CD-ROM, Paris, France, 3 –5 February 2010.

11. B. Göhler and P. Lutzmann, “Range accuracy of a gated-viewing system as a function of the number of averaged images,” Proc. SPIE 8542, 854205 (2012). [CrossRef]  

12. B. Göhler and P. Lutzmann, “Range accuracy of a gated-viewing system compared to a 3-D Flash LADA Runder different turbulence conditions,” Proc. SPIE 7835, 783504 (2010). [CrossRef]  

13. C. J. Carrano, “Progress in horizontal and slant-path imaging using speckle imaging,” Proc. SPIE 5001, 56–64 (2003). [CrossRef]  

14. D. Dayton, S. Browne, J. Gonglewski, S. Sandven, J. Gallegos, and M. Shilko, “Long-range laser illuminated imaging: analysis and experimental demonstrations,” Opt. Eng. 40, 1001–1009 (2001). [CrossRef]  

15. D. C. Dayton, J. D. Gonglewski, J. B. Martin, M. A. Kovacs, J. C. Cardani, F. Maia, T. Aflalo, and M. L. Shilko, “Prediction and performance measures of atmospheric disturbances on an airborne imaging platform,” Proc. SPIE 5237, 117 (2004). [CrossRef]  

16. R. R. Beland, “Propagation through atmospheric optical turbulence” in The Infrared and Electro-Optical Systems Handbook, J. S. Accetta and D. L. Shumaker, eds., Vol. 2 (SPIE, 1993).

17. M. C. Roggemann and B. M. Welsh, Imaging Through Turbulence (CRC Press, 1996).

18. O. Korotkova and L. C. Andrews, “Speckle propagation through atmospheric turbulence: effects of partial coherence of the target,” Proc. SPIE 4723, 73–84 (2002). [CrossRef]  

19. J. W. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53, 1688–1700 (1965). [CrossRef]  

20. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, Optical Engineering, 1998).

21. V. A. Banakh and V. L. Mironov, LIDAR in a Turbulent Atmosphere (Artech House, 1987).

22. R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).

23. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Optical Engineering, 2001).

24. D. H. Tofsted and S. G. O’Brien, “Simulation of atmospheric turbulence image distortion and scintillation effects impacting short wave infrared (SWIR) active imaging systems,” Proc. SPIE 5431, 160–171 (2004).

25. E. Jacobs and R. L. Espinola, “Beam scintillation effects on identification performance with active imaging systems,” Proc. SPIE 5987, 598703 (2005).

26. D. H. Tofsted, “Analytic improvements to the atmospheric turbulence optical transfer function,” Proc. SPIE 5075, 281–292 (2003).

27. D. Edouart, P. Churouxa, and P. H. Flamant, “Burst illumination imaging lidar: intensity correlation function in the image plane,” Proc. SPIE 4723, 189–197 (2002).

28. O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path 1.5 μm range gated imaging close to ground,” Proc. SPIE 8037, 803703 (2011). [CrossRef]  

29. O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path range gated imaging of static and moving targets,” Proc. SPIE 8379, 83790W (2012). [CrossRef]  

30. K. O. S. Gustafsson, M. Henriksson, and L. Sjöqvist, “Wall induced turbulence distortions of optical measurements,” Proc. SPIE 74820, 74820E (2009). [CrossRef]  

31. R. J. Hill, “Spectra of fluctuation in refractivity temperature, humidity, and the temperature-humidity cospectrum in the inertial and dissipation ranges,” Radio Sci. 13, 953–961 (1978). [CrossRef]  

32. G. Potvin, D. Dion, J. L. Forand, C. Zeisse, P. Frederickson, and K. Davidson, “Scintillation in the coastal atmospheric surface layer,” in 14th Symposium on Boundary Layer and Turbulence (American Meteorological Society, 2000), pp. 534–537.

33. L. Sjöqvist, L. Allard, O. Gustafsson, M. Henriksson, and M. Pettersson, “Turbulence effects in a horizontal propagation path close to ground: implications for optics detection,” Proc. SPIE 8187, 81870M (2011). [CrossRef]  

34. M. Henriksson and L. Sjöqvist, “Time-correlated single-photon counting laser radar in turbulence,” Proc. SPIE 8187, 81870N (2011). [CrossRef]  

35. Obzerv images model ARGC-750, http://www.obzerv.com/night-vision-cameras/products/land-systems/argc-750/.

36. N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998).

37. O. Steinvall, M. Elmqvist, and T. Chevalier, “Identification of handheld objects and human activities in active and passive imaging,” Proc. SPIE 8542, 854206 (2012). [CrossRef]  

38. J. D. O’Connor, B. L. O’Kane, C. K. Royal, K. L. Ayscue, D. E. Bonzo, and B. M. Nystrom, “Recognition of human activities using handheld thermal systems,” Proc. SPIE 3394, 51–61 (1998). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. Modeling of Active Imaging Systems, NATO RTO Technical report, TR-SET-072, Final report of task group 40, June 2009.
  2. O. Steinvall, P. Andersson, and M. Elmqvist, “Image quality for range-gated systems during different ranges atmospheric conditions,” Proc. SPIE 6396, 639607 (2006).
    [Crossref]
  3. E. Repasi, P. Lutzmann, O. Steinvall, M. Elmqvist, B. Göhler, and G. Anstett, “Advanced short-wavelength infrared range-gated imaging for ground applications in monostatic and bistatic configurations,” Appl. Opt. 48, 5956–5969 (2009).
    [Crossref]
  4. D. Bonnier, S. Lelievre, and L. Demers, “On the safe use of long-range laser active imager in the near-infrared for Homeland Security,” Proc. SPIE 6206, 62060A (2006).
  5. O. David, R. Schneider, and R. Israeli, “Advance in active night vision for filling the gap in remote sensing,” Proc. SPIE 7482, 748203 (2009).
  6. O. Steinvall, M. Elmqvist, K. Karlsson, H. Larsson, and M. Axelsson, “Laser imaging of small surface vessels and people at sea,” Proc. SPIE 7684, 768417 (2010).
  7. R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
    [Crossref]
  8. C. E. Halford, A. L. Robinson, R. G. Driggers, and E. L. Jacobs, “Tilted surfaces in SWIR imagery: speckle simulation and a simple contrast model,” Opt. Eng. 46, 053201 (2007).
    [Crossref]
  9. R. L. Espinola, E. L. Jacobs, C. E. Halford, R. Vollmerhausen, and D. H. Tofsted, “Modeling the target acquisition performance of active imaging systems,” Opt. Express 15, 3816–3832 (2007).
    [Crossref]
  10. B. Göhler and P. Lutzmann, “An analytical performance model for active imaging systems including slant-path applications,” 4th International Symposium on Optronics in Defence and Security, CD-ROM, Paris, France, 3–5 February2010.
  11. B. Göhler and P. Lutzmann, “Range accuracy of a gated-viewing system as a function of the number of averaged images,” Proc. SPIE 8542, 854205 (2012).
    [Crossref]
  12. B. Göhler and P. Lutzmann, “Range accuracy of a gated-viewing system compared to a 3-D Flash LADA Runder different turbulence conditions,” Proc. SPIE 7835, 783504 (2010).
    [Crossref]
  13. C. J. Carrano, “Progress in horizontal and slant-path imaging using speckle imaging,” Proc. SPIE 5001, 56–64 (2003).
    [Crossref]
  14. D. Dayton, S. Browne, J. Gonglewski, S. Sandven, J. Gallegos, and M. Shilko, “Long-range laser illuminated imaging: analysis and experimental demonstrations,” Opt. Eng. 40, 1001–1009 (2001).
    [Crossref]
  15. D. C. Dayton, J. D. Gonglewski, J. B. Martin, M. A. Kovacs, J. C. Cardani, F. Maia, T. Aflalo, and M. L. Shilko, “Prediction and performance measures of atmospheric disturbances on an airborne imaging platform,” Proc. SPIE 5237, 117 (2004).
    [Crossref]
  16. R. R. Beland, “Propagation through atmospheric optical turbulence” in The Infrared and Electro-Optical Systems Handbook, J. S. Accetta and D. L. Shumaker, eds., Vol. 2 (SPIE, 1993).
  17. M. C. Roggemann and B. M. Welsh, Imaging Through Turbulence (CRC Press, 1996).
  18. O. Korotkova and L. C. Andrews, “Speckle propagation through atmospheric turbulence: effects of partial coherence of the target,” Proc. SPIE 4723, 73–84 (2002).
    [Crossref]
  19. J. W. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53, 1688–1700 (1965).
    [Crossref]
  20. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, Optical Engineering, 1998).
  21. V. A. Banakh and V. L. Mironov, LIDAR in a Turbulent Atmosphere (Artech House, 1987).
  22. R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
  23. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Optical Engineering, 2001).
  24. D. H. Tofsted and S. G. O’Brien, “Simulation of atmospheric turbulence image distortion and scintillation effects impacting short wave infrared (SWIR) active imaging systems,” Proc. SPIE 5431, 160–171 (2004).
  25. E. Jacobs and R. L. Espinola, “Beam scintillation effects on identification performance with active imaging systems,” Proc. SPIE 5987, 598703 (2005).
  26. D. H. Tofsted, “Analytic improvements to the atmospheric turbulence optical transfer function,” Proc. SPIE 5075, 281–292 (2003).
  27. D. Edouart, P. Churouxa, and P. H. Flamant, “Burst illumination imaging lidar: intensity correlation function in the image plane,” Proc. SPIE 4723, 189–197 (2002).
  28. O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path 1.5 μm range gated imaging close to ground,” Proc. SPIE 8037, 803703 (2011).
    [Crossref]
  29. O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path range gated imaging of static and moving targets,” Proc. SPIE 8379, 83790W (2012).
    [Crossref]
  30. K. O. S. Gustafsson, M. Henriksson, and L. Sjöqvist, “Wall induced turbulence distortions of optical measurements,” Proc. SPIE 74820, 74820E (2009).
    [Crossref]
  31. R. J. Hill, “Spectra of fluctuation in refractivity temperature, humidity, and the temperature-humidity cospectrum in the inertial and dissipation ranges,” Radio Sci. 13, 953–961 (1978).
    [Crossref]
  32. G. Potvin, D. Dion, J. L. Forand, C. Zeisse, P. Frederickson, and K. Davidson, “Scintillation in the coastal atmospheric surface layer,” in 14th Symposium on Boundary Layer and Turbulence (American Meteorological Society, 2000), pp. 534–537.
  33. L. Sjöqvist, L. Allard, O. Gustafsson, M. Henriksson, and M. Pettersson, “Turbulence effects in a horizontal propagation path close to ground: implications for optics detection,” Proc. SPIE 8187, 81870M (2011).
    [Crossref]
  34. M. Henriksson and L. Sjöqvist, “Time-correlated single-photon counting laser radar in turbulence,” Proc. SPIE 8187, 81870N (2011).
    [Crossref]
  35. Obzerv images model ARGC-750, http://www.obzerv.com/night-vision-cameras/products/land-systems/argc-750/ .
  36. N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998).
  37. O. Steinvall, M. Elmqvist, and T. Chevalier, “Identification of handheld objects and human activities in active and passive imaging,” Proc. SPIE 8542, 854206 (2012).
    [Crossref]
  38. J. D. O’Connor, B. L. O’Kane, C. K. Royal, K. L. Ayscue, D. E. Bonzo, and B. M. Nystrom, “Recognition of human activities using handheld thermal systems,” Proc. SPIE 3394, 51–61 (1998).
    [Crossref]

2012 (3)

B. Göhler and P. Lutzmann, “Range accuracy of a gated-viewing system as a function of the number of averaged images,” Proc. SPIE 8542, 854205 (2012).
[Crossref]

O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path range gated imaging of static and moving targets,” Proc. SPIE 8379, 83790W (2012).
[Crossref]

O. Steinvall, M. Elmqvist, and T. Chevalier, “Identification of handheld objects and human activities in active and passive imaging,” Proc. SPIE 8542, 854206 (2012).
[Crossref]

2011 (3)

L. Sjöqvist, L. Allard, O. Gustafsson, M. Henriksson, and M. Pettersson, “Turbulence effects in a horizontal propagation path close to ground: implications for optics detection,” Proc. SPIE 8187, 81870M (2011).
[Crossref]

M. Henriksson and L. Sjöqvist, “Time-correlated single-photon counting laser radar in turbulence,” Proc. SPIE 8187, 81870N (2011).
[Crossref]

O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path 1.5 μm range gated imaging close to ground,” Proc. SPIE 8037, 803703 (2011).
[Crossref]

2010 (2)

B. Göhler and P. Lutzmann, “Range accuracy of a gated-viewing system compared to a 3-D Flash LADA Runder different turbulence conditions,” Proc. SPIE 7835, 783504 (2010).
[Crossref]

O. Steinvall, M. Elmqvist, K. Karlsson, H. Larsson, and M. Axelsson, “Laser imaging of small surface vessels and people at sea,” Proc. SPIE 7684, 768417 (2010).

2009 (3)

E. Repasi, P. Lutzmann, O. Steinvall, M. Elmqvist, B. Göhler, and G. Anstett, “Advanced short-wavelength infrared range-gated imaging for ground applications in monostatic and bistatic configurations,” Appl. Opt. 48, 5956–5969 (2009).
[Crossref]

O. David, R. Schneider, and R. Israeli, “Advance in active night vision for filling the gap in remote sensing,” Proc. SPIE 7482, 748203 (2009).

K. O. S. Gustafsson, M. Henriksson, and L. Sjöqvist, “Wall induced turbulence distortions of optical measurements,” Proc. SPIE 74820, 74820E (2009).
[Crossref]

2007 (2)

C. E. Halford, A. L. Robinson, R. G. Driggers, and E. L. Jacobs, “Tilted surfaces in SWIR imagery: speckle simulation and a simple contrast model,” Opt. Eng. 46, 053201 (2007).
[Crossref]

R. L. Espinola, E. L. Jacobs, C. E. Halford, R. Vollmerhausen, and D. H. Tofsted, “Modeling the target acquisition performance of active imaging systems,” Opt. Express 15, 3816–3832 (2007).
[Crossref]

2006 (2)

O. Steinvall, P. Andersson, and M. Elmqvist, “Image quality for range-gated systems during different ranges atmospheric conditions,” Proc. SPIE 6396, 639607 (2006).
[Crossref]

D. Bonnier, S. Lelievre, and L. Demers, “On the safe use of long-range laser active imager in the near-infrared for Homeland Security,” Proc. SPIE 6206, 62060A (2006).

2005 (1)

E. Jacobs and R. L. Espinola, “Beam scintillation effects on identification performance with active imaging systems,” Proc. SPIE 5987, 598703 (2005).

2004 (2)

D. C. Dayton, J. D. Gonglewski, J. B. Martin, M. A. Kovacs, J. C. Cardani, F. Maia, T. Aflalo, and M. L. Shilko, “Prediction and performance measures of atmospheric disturbances on an airborne imaging platform,” Proc. SPIE 5237, 117 (2004).
[Crossref]

D. H. Tofsted and S. G. O’Brien, “Simulation of atmospheric turbulence image distortion and scintillation effects impacting short wave infrared (SWIR) active imaging systems,” Proc. SPIE 5431, 160–171 (2004).

2003 (3)

C. J. Carrano, “Progress in horizontal and slant-path imaging using speckle imaging,” Proc. SPIE 5001, 56–64 (2003).
[Crossref]

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
[Crossref]

D. H. Tofsted, “Analytic improvements to the atmospheric turbulence optical transfer function,” Proc. SPIE 5075, 281–292 (2003).

2002 (2)

D. Edouart, P. Churouxa, and P. H. Flamant, “Burst illumination imaging lidar: intensity correlation function in the image plane,” Proc. SPIE 4723, 189–197 (2002).

O. Korotkova and L. C. Andrews, “Speckle propagation through atmospheric turbulence: effects of partial coherence of the target,” Proc. SPIE 4723, 73–84 (2002).
[Crossref]

2001 (1)

D. Dayton, S. Browne, J. Gonglewski, S. Sandven, J. Gallegos, and M. Shilko, “Long-range laser illuminated imaging: analysis and experimental demonstrations,” Opt. Eng. 40, 1001–1009 (2001).
[Crossref]

1998 (1)

J. D. O’Connor, B. L. O’Kane, C. K. Royal, K. L. Ayscue, D. E. Bonzo, and B. M. Nystrom, “Recognition of human activities using handheld thermal systems,” Proc. SPIE 3394, 51–61 (1998).
[Crossref]

1978 (1)

R. J. Hill, “Spectra of fluctuation in refractivity temperature, humidity, and the temperature-humidity cospectrum in the inertial and dissipation ranges,” Radio Sci. 13, 953–961 (1978).
[Crossref]

1975 (1)

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).

1965 (1)

J. W. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53, 1688–1700 (1965).
[Crossref]

Aflalo, T.

D. C. Dayton, J. D. Gonglewski, J. B. Martin, M. A. Kovacs, J. C. Cardani, F. Maia, T. Aflalo, and M. L. Shilko, “Prediction and performance measures of atmospheric disturbances on an airborne imaging platform,” Proc. SPIE 5237, 117 (2004).
[Crossref]

Allard, L.

L. Sjöqvist, L. Allard, O. Gustafsson, M. Henriksson, and M. Pettersson, “Turbulence effects in a horizontal propagation path close to ground: implications for optics detection,” Proc. SPIE 8187, 81870M (2011).
[Crossref]

Andersson, P.

O. Steinvall, P. Andersson, and M. Elmqvist, “Image quality for range-gated systems during different ranges atmospheric conditions,” Proc. SPIE 6396, 639607 (2006).
[Crossref]

Andrews, L. C.

O. Korotkova and L. C. Andrews, “Speckle propagation through atmospheric turbulence: effects of partial coherence of the target,” Proc. SPIE 4723, 73–84 (2002).
[Crossref]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, Optical Engineering, 1998).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Optical Engineering, 2001).

Anstett, G.

Axelsson, M.

O. Steinvall, M. Elmqvist, K. Karlsson, H. Larsson, and M. Axelsson, “Laser imaging of small surface vessels and people at sea,” Proc. SPIE 7684, 768417 (2010).

Ayscue, K. L.

J. D. O’Connor, B. L. O’Kane, C. K. Royal, K. L. Ayscue, D. E. Bonzo, and B. M. Nystrom, “Recognition of human activities using handheld thermal systems,” Proc. SPIE 3394, 51–61 (1998).
[Crossref]

Banakh, V. A.

V. A. Banakh and V. L. Mironov, LIDAR in a Turbulent Atmosphere (Artech House, 1987).

Barnard, K. J.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
[Crossref]

Beland, R. R.

R. R. Beland, “Propagation through atmospheric optical turbulence” in The Infrared and Electro-Optical Systems Handbook, J. S. Accetta and D. L. Shumaker, eds., Vol. 2 (SPIE, 1993).

Bonnier, D.

D. Bonnier, S. Lelievre, and L. Demers, “On the safe use of long-range laser active imager in the near-infrared for Homeland Security,” Proc. SPIE 6206, 62060A (2006).

Bonzo, D. E.

J. D. O’Connor, B. L. O’Kane, C. K. Royal, K. L. Ayscue, D. E. Bonzo, and B. M. Nystrom, “Recognition of human activities using handheld thermal systems,” Proc. SPIE 3394, 51–61 (1998).
[Crossref]

Browne, S.

D. Dayton, S. Browne, J. Gonglewski, S. Sandven, J. Gallegos, and M. Shilko, “Long-range laser illuminated imaging: analysis and experimental demonstrations,” Opt. Eng. 40, 1001–1009 (2001).
[Crossref]

Cardani, J. C.

D. C. Dayton, J. D. Gonglewski, J. B. Martin, M. A. Kovacs, J. C. Cardani, F. Maia, T. Aflalo, and M. L. Shilko, “Prediction and performance measures of atmospheric disturbances on an airborne imaging platform,” Proc. SPIE 5237, 117 (2004).
[Crossref]

Carrano, C. J.

C. J. Carrano, “Progress in horizontal and slant-path imaging using speckle imaging,” Proc. SPIE 5001, 56–64 (2003).
[Crossref]

Chevalier, T.

O. Steinvall, M. Elmqvist, and T. Chevalier, “Identification of handheld objects and human activities in active and passive imaging,” Proc. SPIE 8542, 854206 (2012).
[Crossref]

O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path range gated imaging of static and moving targets,” Proc. SPIE 8379, 83790W (2012).
[Crossref]

O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path 1.5 μm range gated imaging close to ground,” Proc. SPIE 8037, 803703 (2011).
[Crossref]

Churouxa, P.

D. Edouart, P. Churouxa, and P. H. Flamant, “Burst illumination imaging lidar: intensity correlation function in the image plane,” Proc. SPIE 4723, 189–197 (2002).

David, O.

O. David, R. Schneider, and R. Israeli, “Advance in active night vision for filling the gap in remote sensing,” Proc. SPIE 7482, 748203 (2009).

Davidson, K.

G. Potvin, D. Dion, J. L. Forand, C. Zeisse, P. Frederickson, and K. Davidson, “Scintillation in the coastal atmospheric surface layer,” in 14th Symposium on Boundary Layer and Turbulence (American Meteorological Society, 2000), pp. 534–537.

Dayton, D.

D. Dayton, S. Browne, J. Gonglewski, S. Sandven, J. Gallegos, and M. Shilko, “Long-range laser illuminated imaging: analysis and experimental demonstrations,” Opt. Eng. 40, 1001–1009 (2001).
[Crossref]

Dayton, D. C.

D. C. Dayton, J. D. Gonglewski, J. B. Martin, M. A. Kovacs, J. C. Cardani, F. Maia, T. Aflalo, and M. L. Shilko, “Prediction and performance measures of atmospheric disturbances on an airborne imaging platform,” Proc. SPIE 5237, 117 (2004).
[Crossref]

Demers, L.

D. Bonnier, S. Lelievre, and L. Demers, “On the safe use of long-range laser active imager in the near-infrared for Homeland Security,” Proc. SPIE 6206, 62060A (2006).

Devitt, N.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
[Crossref]

Dion, D.

G. Potvin, D. Dion, J. L. Forand, C. Zeisse, P. Frederickson, and K. Davidson, “Scintillation in the coastal atmospheric surface layer,” in 14th Symposium on Boundary Layer and Turbulence (American Meteorological Society, 2000), pp. 534–537.

Driggers, R. G.

C. E. Halford, A. L. Robinson, R. G. Driggers, and E. L. Jacobs, “Tilted surfaces in SWIR imagery: speckle simulation and a simple contrast model,” Opt. Eng. 46, 053201 (2007).
[Crossref]

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
[Crossref]

Edouart, D.

D. Edouart, P. Churouxa, and P. H. Flamant, “Burst illumination imaging lidar: intensity correlation function in the image plane,” Proc. SPIE 4723, 189–197 (2002).

Elmqvist, M.

O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path range gated imaging of static and moving targets,” Proc. SPIE 8379, 83790W (2012).
[Crossref]

O. Steinvall, M. Elmqvist, and T. Chevalier, “Identification of handheld objects and human activities in active and passive imaging,” Proc. SPIE 8542, 854206 (2012).
[Crossref]

O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path 1.5 μm range gated imaging close to ground,” Proc. SPIE 8037, 803703 (2011).
[Crossref]

O. Steinvall, M. Elmqvist, K. Karlsson, H. Larsson, and M. Axelsson, “Laser imaging of small surface vessels and people at sea,” Proc. SPIE 7684, 768417 (2010).

E. Repasi, P. Lutzmann, O. Steinvall, M. Elmqvist, B. Göhler, and G. Anstett, “Advanced short-wavelength infrared range-gated imaging for ground applications in monostatic and bistatic configurations,” Appl. Opt. 48, 5956–5969 (2009).
[Crossref]

O. Steinvall, P. Andersson, and M. Elmqvist, “Image quality for range-gated systems during different ranges atmospheric conditions,” Proc. SPIE 6396, 639607 (2006).
[Crossref]

Espinola, R. L.

R. L. Espinola, E. L. Jacobs, C. E. Halford, R. Vollmerhausen, and D. H. Tofsted, “Modeling the target acquisition performance of active imaging systems,” Opt. Express 15, 3816–3832 (2007).
[Crossref]

E. Jacobs and R. L. Espinola, “Beam scintillation effects on identification performance with active imaging systems,” Proc. SPIE 5987, 598703 (2005).

Fante, R. L.

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).

Flamant, P. H.

D. Edouart, P. Churouxa, and P. H. Flamant, “Burst illumination imaging lidar: intensity correlation function in the image plane,” Proc. SPIE 4723, 189–197 (2002).

Forand, J. L.

G. Potvin, D. Dion, J. L. Forand, C. Zeisse, P. Frederickson, and K. Davidson, “Scintillation in the coastal atmospheric surface layer,” in 14th Symposium on Boundary Layer and Turbulence (American Meteorological Society, 2000), pp. 534–537.

Frederickson, P.

G. Potvin, D. Dion, J. L. Forand, C. Zeisse, P. Frederickson, and K. Davidson, “Scintillation in the coastal atmospheric surface layer,” in 14th Symposium on Boundary Layer and Turbulence (American Meteorological Society, 2000), pp. 534–537.

Gallegos, J.

D. Dayton, S. Browne, J. Gonglewski, S. Sandven, J. Gallegos, and M. Shilko, “Long-range laser illuminated imaging: analysis and experimental demonstrations,” Opt. Eng. 40, 1001–1009 (2001).
[Crossref]

Göhler, B.

B. Göhler and P. Lutzmann, “Range accuracy of a gated-viewing system as a function of the number of averaged images,” Proc. SPIE 8542, 854205 (2012).
[Crossref]

B. Göhler and P. Lutzmann, “Range accuracy of a gated-viewing system compared to a 3-D Flash LADA Runder different turbulence conditions,” Proc. SPIE 7835, 783504 (2010).
[Crossref]

E. Repasi, P. Lutzmann, O. Steinvall, M. Elmqvist, B. Göhler, and G. Anstett, “Advanced short-wavelength infrared range-gated imaging for ground applications in monostatic and bistatic configurations,” Appl. Opt. 48, 5956–5969 (2009).
[Crossref]

B. Göhler and P. Lutzmann, “An analytical performance model for active imaging systems including slant-path applications,” 4th International Symposium on Optronics in Defence and Security, CD-ROM, Paris, France, 3–5 February2010.

Gonglewski, J.

D. Dayton, S. Browne, J. Gonglewski, S. Sandven, J. Gallegos, and M. Shilko, “Long-range laser illuminated imaging: analysis and experimental demonstrations,” Opt. Eng. 40, 1001–1009 (2001).
[Crossref]

Gonglewski, J. D.

D. C. Dayton, J. D. Gonglewski, J. B. Martin, M. A. Kovacs, J. C. Cardani, F. Maia, T. Aflalo, and M. L. Shilko, “Prediction and performance measures of atmospheric disturbances on an airborne imaging platform,” Proc. SPIE 5237, 117 (2004).
[Crossref]

Goodman, J. W.

J. W. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53, 1688–1700 (1965).
[Crossref]

Gustafsson, K. O. S.

K. O. S. Gustafsson, M. Henriksson, and L. Sjöqvist, “Wall induced turbulence distortions of optical measurements,” Proc. SPIE 74820, 74820E (2009).
[Crossref]

Gustafsson, O.

O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path range gated imaging of static and moving targets,” Proc. SPIE 8379, 83790W (2012).
[Crossref]

L. Sjöqvist, L. Allard, O. Gustafsson, M. Henriksson, and M. Pettersson, “Turbulence effects in a horizontal propagation path close to ground: implications for optics detection,” Proc. SPIE 8187, 81870M (2011).
[Crossref]

O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path 1.5 μm range gated imaging close to ground,” Proc. SPIE 8037, 803703 (2011).
[Crossref]

Halford, C.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
[Crossref]

Halford, C. E.

C. E. Halford, A. L. Robinson, R. G. Driggers, and E. L. Jacobs, “Tilted surfaces in SWIR imagery: speckle simulation and a simple contrast model,” Opt. Eng. 46, 053201 (2007).
[Crossref]

R. L. Espinola, E. L. Jacobs, C. E. Halford, R. Vollmerhausen, and D. H. Tofsted, “Modeling the target acquisition performance of active imaging systems,” Opt. Express 15, 3816–3832 (2007).
[Crossref]

Henriksson, M.

L. Sjöqvist, L. Allard, O. Gustafsson, M. Henriksson, and M. Pettersson, “Turbulence effects in a horizontal propagation path close to ground: implications for optics detection,” Proc. SPIE 8187, 81870M (2011).
[Crossref]

M. Henriksson and L. Sjöqvist, “Time-correlated single-photon counting laser radar in turbulence,” Proc. SPIE 8187, 81870N (2011).
[Crossref]

K. O. S. Gustafsson, M. Henriksson, and L. Sjöqvist, “Wall induced turbulence distortions of optical measurements,” Proc. SPIE 74820, 74820E (2009).
[Crossref]

Hill, R. J.

R. J. Hill, “Spectra of fluctuation in refractivity temperature, humidity, and the temperature-humidity cospectrum in the inertial and dissipation ranges,” Radio Sci. 13, 953–961 (1978).
[Crossref]

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Optical Engineering, 2001).

Israeli, R.

O. David, R. Schneider, and R. Israeli, “Advance in active night vision for filling the gap in remote sensing,” Proc. SPIE 7482, 748203 (2009).

Jacobs, E.

E. Jacobs and R. L. Espinola, “Beam scintillation effects on identification performance with active imaging systems,” Proc. SPIE 5987, 598703 (2005).

Jacobs, E. L.

R. L. Espinola, E. L. Jacobs, C. E. Halford, R. Vollmerhausen, and D. H. Tofsted, “Modeling the target acquisition performance of active imaging systems,” Opt. Express 15, 3816–3832 (2007).
[Crossref]

C. E. Halford, A. L. Robinson, R. G. Driggers, and E. L. Jacobs, “Tilted surfaces in SWIR imagery: speckle simulation and a simple contrast model,” Opt. Eng. 46, 053201 (2007).
[Crossref]

Karlsson, K.

O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path range gated imaging of static and moving targets,” Proc. SPIE 8379, 83790W (2012).
[Crossref]

O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path 1.5 μm range gated imaging close to ground,” Proc. SPIE 8037, 803703 (2011).
[Crossref]

O. Steinvall, M. Elmqvist, K. Karlsson, H. Larsson, and M. Axelsson, “Laser imaging of small surface vessels and people at sea,” Proc. SPIE 7684, 768417 (2010).

Kopeika, N. S.

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998).

Korotkova, O.

O. Korotkova and L. C. Andrews, “Speckle propagation through atmospheric turbulence: effects of partial coherence of the target,” Proc. SPIE 4723, 73–84 (2002).
[Crossref]

Kovacs, M. A.

D. C. Dayton, J. D. Gonglewski, J. B. Martin, M. A. Kovacs, J. C. Cardani, F. Maia, T. Aflalo, and M. L. Shilko, “Prediction and performance measures of atmospheric disturbances on an airborne imaging platform,” Proc. SPIE 5237, 117 (2004).
[Crossref]

Larsson, H.

O. Steinvall, M. Elmqvist, K. Karlsson, H. Larsson, and M. Axelsson, “Laser imaging of small surface vessels and people at sea,” Proc. SPIE 7684, 768417 (2010).

Lelievre, S.

D. Bonnier, S. Lelievre, and L. Demers, “On the safe use of long-range laser active imager in the near-infrared for Homeland Security,” Proc. SPIE 6206, 62060A (2006).

Lutzmann, P.

B. Göhler and P. Lutzmann, “Range accuracy of a gated-viewing system as a function of the number of averaged images,” Proc. SPIE 8542, 854205 (2012).
[Crossref]

B. Göhler and P. Lutzmann, “Range accuracy of a gated-viewing system compared to a 3-D Flash LADA Runder different turbulence conditions,” Proc. SPIE 7835, 783504 (2010).
[Crossref]

E. Repasi, P. Lutzmann, O. Steinvall, M. Elmqvist, B. Göhler, and G. Anstett, “Advanced short-wavelength infrared range-gated imaging for ground applications in monostatic and bistatic configurations,” Appl. Opt. 48, 5956–5969 (2009).
[Crossref]

B. Göhler and P. Lutzmann, “An analytical performance model for active imaging systems including slant-path applications,” 4th International Symposium on Optronics in Defence and Security, CD-ROM, Paris, France, 3–5 February2010.

Maia, F.

D. C. Dayton, J. D. Gonglewski, J. B. Martin, M. A. Kovacs, J. C. Cardani, F. Maia, T. Aflalo, and M. L. Shilko, “Prediction and performance measures of atmospheric disturbances on an airborne imaging platform,” Proc. SPIE 5237, 117 (2004).
[Crossref]

Martin, J. B.

D. C. Dayton, J. D. Gonglewski, J. B. Martin, M. A. Kovacs, J. C. Cardani, F. Maia, T. Aflalo, and M. L. Shilko, “Prediction and performance measures of atmospheric disturbances on an airborne imaging platform,” Proc. SPIE 5237, 117 (2004).
[Crossref]

Mironov, V. L.

V. A. Banakh and V. L. Mironov, LIDAR in a Turbulent Atmosphere (Artech House, 1987).

Nystrom, B. M.

J. D. O’Connor, B. L. O’Kane, C. K. Royal, K. L. Ayscue, D. E. Bonzo, and B. M. Nystrom, “Recognition of human activities using handheld thermal systems,” Proc. SPIE 3394, 51–61 (1998).
[Crossref]

O’Brien, S. G.

D. H. Tofsted and S. G. O’Brien, “Simulation of atmospheric turbulence image distortion and scintillation effects impacting short wave infrared (SWIR) active imaging systems,” Proc. SPIE 5431, 160–171 (2004).

O’Connor, J. D.

J. D. O’Connor, B. L. O’Kane, C. K. Royal, K. L. Ayscue, D. E. Bonzo, and B. M. Nystrom, “Recognition of human activities using handheld thermal systems,” Proc. SPIE 3394, 51–61 (1998).
[Crossref]

O’Kane, B. L.

J. D. O’Connor, B. L. O’Kane, C. K. Royal, K. L. Ayscue, D. E. Bonzo, and B. M. Nystrom, “Recognition of human activities using handheld thermal systems,” Proc. SPIE 3394, 51–61 (1998).
[Crossref]

Pettersson, M.

L. Sjöqvist, L. Allard, O. Gustafsson, M. Henriksson, and M. Pettersson, “Turbulence effects in a horizontal propagation path close to ground: implications for optics detection,” Proc. SPIE 8187, 81870M (2011).
[Crossref]

Phillips, R. L.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Optical Engineering, 2001).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, Optical Engineering, 1998).

Potvin, G.

G. Potvin, D. Dion, J. L. Forand, C. Zeisse, P. Frederickson, and K. Davidson, “Scintillation in the coastal atmospheric surface layer,” in 14th Symposium on Boundary Layer and Turbulence (American Meteorological Society, 2000), pp. 534–537.

Repasi, E.

Robinson, A. L.

C. E. Halford, A. L. Robinson, R. G. Driggers, and E. L. Jacobs, “Tilted surfaces in SWIR imagery: speckle simulation and a simple contrast model,” Opt. Eng. 46, 053201 (2007).
[Crossref]

Roggemann, M. C.

M. C. Roggemann and B. M. Welsh, Imaging Through Turbulence (CRC Press, 1996).

Royal, C. K.

J. D. O’Connor, B. L. O’Kane, C. K. Royal, K. L. Ayscue, D. E. Bonzo, and B. M. Nystrom, “Recognition of human activities using handheld thermal systems,” Proc. SPIE 3394, 51–61 (1998).
[Crossref]

Sandven, S.

D. Dayton, S. Browne, J. Gonglewski, S. Sandven, J. Gallegos, and M. Shilko, “Long-range laser illuminated imaging: analysis and experimental demonstrations,” Opt. Eng. 40, 1001–1009 (2001).
[Crossref]

Schneider, R.

O. David, R. Schneider, and R. Israeli, “Advance in active night vision for filling the gap in remote sensing,” Proc. SPIE 7482, 748203 (2009).

Shilko, M.

D. Dayton, S. Browne, J. Gonglewski, S. Sandven, J. Gallegos, and M. Shilko, “Long-range laser illuminated imaging: analysis and experimental demonstrations,” Opt. Eng. 40, 1001–1009 (2001).
[Crossref]

Shilko, M. L.

D. C. Dayton, J. D. Gonglewski, J. B. Martin, M. A. Kovacs, J. C. Cardani, F. Maia, T. Aflalo, and M. L. Shilko, “Prediction and performance measures of atmospheric disturbances on an airborne imaging platform,” Proc. SPIE 5237, 117 (2004).
[Crossref]

Sjöqvist, L.

L. Sjöqvist, L. Allard, O. Gustafsson, M. Henriksson, and M. Pettersson, “Turbulence effects in a horizontal propagation path close to ground: implications for optics detection,” Proc. SPIE 8187, 81870M (2011).
[Crossref]

M. Henriksson and L. Sjöqvist, “Time-correlated single-photon counting laser radar in turbulence,” Proc. SPIE 8187, 81870N (2011).
[Crossref]

K. O. S. Gustafsson, M. Henriksson, and L. Sjöqvist, “Wall induced turbulence distortions of optical measurements,” Proc. SPIE 74820, 74820E (2009).
[Crossref]

Steinvall, O.

O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path range gated imaging of static and moving targets,” Proc. SPIE 8379, 83790W (2012).
[Crossref]

O. Steinvall, M. Elmqvist, and T. Chevalier, “Identification of handheld objects and human activities in active and passive imaging,” Proc. SPIE 8542, 854206 (2012).
[Crossref]

O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path 1.5 μm range gated imaging close to ground,” Proc. SPIE 8037, 803703 (2011).
[Crossref]

O. Steinvall, M. Elmqvist, K. Karlsson, H. Larsson, and M. Axelsson, “Laser imaging of small surface vessels and people at sea,” Proc. SPIE 7684, 768417 (2010).

E. Repasi, P. Lutzmann, O. Steinvall, M. Elmqvist, B. Göhler, and G. Anstett, “Advanced short-wavelength infrared range-gated imaging for ground applications in monostatic and bistatic configurations,” Appl. Opt. 48, 5956–5969 (2009).
[Crossref]

O. Steinvall, P. Andersson, and M. Elmqvist, “Image quality for range-gated systems during different ranges atmospheric conditions,” Proc. SPIE 6396, 639607 (2006).
[Crossref]

Tofsted, D. H.

R. L. Espinola, E. L. Jacobs, C. E. Halford, R. Vollmerhausen, and D. H. Tofsted, “Modeling the target acquisition performance of active imaging systems,” Opt. Express 15, 3816–3832 (2007).
[Crossref]

D. H. Tofsted and S. G. O’Brien, “Simulation of atmospheric turbulence image distortion and scintillation effects impacting short wave infrared (SWIR) active imaging systems,” Proc. SPIE 5431, 160–171 (2004).

D. H. Tofsted, “Analytic improvements to the atmospheric turbulence optical transfer function,” Proc. SPIE 5075, 281–292 (2003).

Vollmerhausen, R.

Vollmerhausen, R. H.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
[Crossref]

Welsh, B. M.

M. C. Roggemann and B. M. Welsh, Imaging Through Turbulence (CRC Press, 1996).

Zeisse, C.

G. Potvin, D. Dion, J. L. Forand, C. Zeisse, P. Frederickson, and K. Davidson, “Scintillation in the coastal atmospheric surface layer,” in 14th Symposium on Boundary Layer and Turbulence (American Meteorological Society, 2000), pp. 534–537.

Appl. Opt. (1)

Opt. Eng. (3)

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
[Crossref]

C. E. Halford, A. L. Robinson, R. G. Driggers, and E. L. Jacobs, “Tilted surfaces in SWIR imagery: speckle simulation and a simple contrast model,” Opt. Eng. 46, 053201 (2007).
[Crossref]

D. Dayton, S. Browne, J. Gonglewski, S. Sandven, J. Gallegos, and M. Shilko, “Long-range laser illuminated imaging: analysis and experimental demonstrations,” Opt. Eng. 40, 1001–1009 (2001).
[Crossref]

Opt. Express (1)

Proc. IEEE (2)

J. W. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53, 1688–1700 (1965).
[Crossref]

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).

Proc. SPIE (20)

L. Sjöqvist, L. Allard, O. Gustafsson, M. Henriksson, and M. Pettersson, “Turbulence effects in a horizontal propagation path close to ground: implications for optics detection,” Proc. SPIE 8187, 81870M (2011).
[Crossref]

M. Henriksson and L. Sjöqvist, “Time-correlated single-photon counting laser radar in turbulence,” Proc. SPIE 8187, 81870N (2011).
[Crossref]

D. H. Tofsted and S. G. O’Brien, “Simulation of atmospheric turbulence image distortion and scintillation effects impacting short wave infrared (SWIR) active imaging systems,” Proc. SPIE 5431, 160–171 (2004).

E. Jacobs and R. L. Espinola, “Beam scintillation effects on identification performance with active imaging systems,” Proc. SPIE 5987, 598703 (2005).

D. H. Tofsted, “Analytic improvements to the atmospheric turbulence optical transfer function,” Proc. SPIE 5075, 281–292 (2003).

D. Edouart, P. Churouxa, and P. H. Flamant, “Burst illumination imaging lidar: intensity correlation function in the image plane,” Proc. SPIE 4723, 189–197 (2002).

O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path 1.5 μm range gated imaging close to ground,” Proc. SPIE 8037, 803703 (2011).
[Crossref]

O. Steinvall, M. Elmqvist, K. Karlsson, O. Gustafsson, and T. Chevalier, “Slant path range gated imaging of static and moving targets,” Proc. SPIE 8379, 83790W (2012).
[Crossref]

K. O. S. Gustafsson, M. Henriksson, and L. Sjöqvist, “Wall induced turbulence distortions of optical measurements,” Proc. SPIE 74820, 74820E (2009).
[Crossref]

D. Bonnier, S. Lelievre, and L. Demers, “On the safe use of long-range laser active imager in the near-infrared for Homeland Security,” Proc. SPIE 6206, 62060A (2006).

O. David, R. Schneider, and R. Israeli, “Advance in active night vision for filling the gap in remote sensing,” Proc. SPIE 7482, 748203 (2009).

O. Steinvall, M. Elmqvist, K. Karlsson, H. Larsson, and M. Axelsson, “Laser imaging of small surface vessels and people at sea,” Proc. SPIE 7684, 768417 (2010).

D. C. Dayton, J. D. Gonglewski, J. B. Martin, M. A. Kovacs, J. C. Cardani, F. Maia, T. Aflalo, and M. L. Shilko, “Prediction and performance measures of atmospheric disturbances on an airborne imaging platform,” Proc. SPIE 5237, 117 (2004).
[Crossref]

O. Steinvall, P. Andersson, and M. Elmqvist, “Image quality for range-gated systems during different ranges atmospheric conditions,” Proc. SPIE 6396, 639607 (2006).
[Crossref]

B. Göhler and P. Lutzmann, “Range accuracy of a gated-viewing system as a function of the number of averaged images,” Proc. SPIE 8542, 854205 (2012).
[Crossref]

B. Göhler and P. Lutzmann, “Range accuracy of a gated-viewing system compared to a 3-D Flash LADA Runder different turbulence conditions,” Proc. SPIE 7835, 783504 (2010).
[Crossref]

C. J. Carrano, “Progress in horizontal and slant-path imaging using speckle imaging,” Proc. SPIE 5001, 56–64 (2003).
[Crossref]

O. Steinvall, M. Elmqvist, and T. Chevalier, “Identification of handheld objects and human activities in active and passive imaging,” Proc. SPIE 8542, 854206 (2012).
[Crossref]

J. D. O’Connor, B. L. O’Kane, C. K. Royal, K. L. Ayscue, D. E. Bonzo, and B. M. Nystrom, “Recognition of human activities using handheld thermal systems,” Proc. SPIE 3394, 51–61 (1998).
[Crossref]

O. Korotkova and L. C. Andrews, “Speckle propagation through atmospheric turbulence: effects of partial coherence of the target,” Proc. SPIE 4723, 73–84 (2002).
[Crossref]

Radio Sci. (1)

R. J. Hill, “Spectra of fluctuation in refractivity temperature, humidity, and the temperature-humidity cospectrum in the inertial and dissipation ranges,” Radio Sci. 13, 953–961 (1978).
[Crossref]

Other (10)

G. Potvin, D. Dion, J. L. Forand, C. Zeisse, P. Frederickson, and K. Davidson, “Scintillation in the coastal atmospheric surface layer,” in 14th Symposium on Boundary Layer and Turbulence (American Meteorological Society, 2000), pp. 534–537.

Obzerv images model ARGC-750, http://www.obzerv.com/night-vision-cameras/products/land-systems/argc-750/ .

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Optical Engineering, 2001).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, Optical Engineering, 1998).

V. A. Banakh and V. L. Mironov, LIDAR in a Turbulent Atmosphere (Artech House, 1987).

Modeling of Active Imaging Systems, NATO RTO Technical report, TR-SET-072, Final report of task group 40, June 2009.

R. R. Beland, “Propagation through atmospheric optical turbulence” in The Infrared and Electro-Optical Systems Handbook, J. S. Accetta and D. L. Shumaker, eds., Vol. 2 (SPIE, 1993).

M. C. Roggemann and B. M. Welsh, Imaging Through Turbulence (CRC Press, 1996).

B. Göhler and P. Lutzmann, “An analytical performance model for active imaging systems including slant-path applications,” 4th International Symposium on Optronics in Defence and Security, CD-ROM, Paris, France, 3–5 February2010.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (29)

Fig. 1.
Fig. 1. Improvement in angular resolution versus sensor height for observing a ground target at 1.9 km range for different values of the parameter α.
Fig. 2.
Fig. 2. Experimental arrangement with the 1.5 μm laser sensor in the cage and the elevated platform.
Fig. 3.
Fig. 3. Edge and resolution charts. At 1920 m range the bar separation for the three largest bar groups corresponds to 26.3, 37.9, and 52.6 μrad, respectively. The ratio of length to width of all black bars is 15 and the linear scale factor between each bar group is 2. The size of the resolution test panel was 1.3×2.2m and the edge chart was about 2 m in square.
Fig. 4.
Fig. 4. Drawing of the air field and the position of the experimental setup at the second day in the September 2010 campaign.
Fig. 5.
Fig. 5. Cn2 as function of time measured using three different ultrasonic anemometer along the runway, 7 September 2010.
Fig. 6.
Fig. 6. Comparison between measured Cn2 along the runway measured with the scintillometer (crosses) and measured with two ultrasonic anemometers halfway down the runway. Measurement performed 7 September 2010.
Fig. 7.
Fig. 7. Two active imaging systems. Left, the Intevac tube with a F=1260mm telescope and a Saab laser range finder at 1.5 μm, and right, the Obzerve system (white box).
Fig. 8.
Fig. 8. Person holding different objects to be identified statically and in conjunction with associated activities.
Fig. 9.
Fig. 9. Example of Cn2 data registered using ultrasound anemometers at position A, AB=B2, and B during 14 June 2011.
Fig. 10.
Fig. 10. Series of images for a low turbulence situation and a horizontal 1.9 km path at 2.1 m above ground. Left: a passive image of the whole FOV and next close-up images of the 2.2*1.3m bar pattern target, partly occluded by grass at the bottom. The angular resolution in the passive and active images are about equal and the improvement of active image averaging is mainly seen as an intensity smoothing. Time 14:54:11 on 7 September 2010. Mean turbulence from anemometers Cn2=1014m2/3.
Fig. 11.
Fig. 11. Above the passive image of the scene and the bar target at about 16:42:30 on 7 September 2011 and below examples of single active frames from increasing heights between the time 16:44:24 to 17:11:47. At the higher elevations of the sensor there is a clear improvement in angular resolution, from about 50 μrad at 2.1 m to better than 18 μrad at 12.2 m.
Fig. 12.
Fig. 12. Left: measured turbulence from the anemometer data, 7 September 2010. El. refers to the elevated anemometer (=sensor height) and Gr. to the mean value of the two ground-based anemometers. S1–S4 refer to different time series of measurements (S1: 14:49–15:11, S2: 15:49–16:19, S3: 16:42–17:12, S4: 17:24–17:46). Right: the resolution evaluated from the bar patterns for the corresponding time series.
Fig. 13.
Fig. 13. Relation between angular jitter measured from the relative movement of two car lights and the angular resolution for single active images.
Fig. 14.
Fig. 14. Measured turbulence from the anemometer data, 8 September 2010. El. refers to the elevated anemometer (=sensor height) and Gr. to the mean value of the two ground-based anemometers. S1–S4 refer to different time series of measurements (S1: 11:29–11:37, S2: 11:47–12:10, S3: 13:21–13:32, S4: 14:06–14:16). Note that the turbulence varies rather irregular with height on this day in opposite of the situation during 7 September 2010.
Fig. 15.
Fig. 15. Angular resolution for different heights and three frames averaged. Left, active and right, passive operation.
Fig. 16.
Fig. 16. Man at 876 m range with a toy weapon. The turbulence level around 1.5×1013m2/3. Note that the 1.5 μm images in the lower row seem to be somewhat less blurry than those from the visible-NIR region.
Fig. 17.
Fig. 17. Images (three frame stabilized average) of active 1.5 μm (above) and passive SWIR images (below) of the resolution chart at 1.92 km range for the sensor heights of 1.6, 5.15, 7.65, 10.35, and 13.15 m, respectively (left to right). Focal length 1260 mm. Collection time period 3:52–4:11 PM, 14 June 2011.
Fig. 18.
Fig. 18. Same as in Fig. 17 but at a later time (7:04–7:23 PM, 14 June 2011) when the ground turbulence measured by the scintillometer was between 47×1014m2/3.
Fig. 19.
Fig. 19. Man with an RPG weapon in different positions at a range of 2 km. The active (above) and passive images were collected with different sensor heights (1.6, 5.15, 7.65, and 10.35 m). The measurements were collected between 6:07 and 6:33 PM 14 June 2011.
Fig. 20.
Fig. 20. (Left two): a man with a shovel imaged at 1.5 μm and (right two) at 0.8 μm. Face reflection is very low at 1.5 μm. Both pair of images show the advantage of silhouette detection for visualizing the shovel. Range 850 m.
Fig. 21.
Fig. 21. Above: the Obzerv system showing images at 2442 m of a man holding a weapon. Below: the same for the 1.5 μm system. Both sensors had a nominal angular resolution about 16 μrad. The sensors were placed 13 m above ground.
Fig. 22.
Fig. 22. Two pairs of passive (left) and active images at 1.5 μm from the targets boards at 1130 m range. The smaller size white target board to the left was placed 10 m in front of the black and white target. Left, the sensor at 1.6 m above ground and right, the sensor at 7.65 m height. The ground value of the turbulence was between 13×1013m2/3.
Fig. 23.
Fig. 23. Estimated angular resolution for single active images using the resolution chart versus edge response from the black and white board. The relatively large spread in data is probably due to the speckle noise.
Fig. 24.
Fig. 24. Left diagram shows the good correspondence between the estimated image jitter from the relative motion of the two lights versus the theoretical values obtained from Eq. (5) using turbulence values from the scintillometer and the three anemometers. The R2 of the linear fits ranged between 0.62–0.92. Right shows calculated image jitter values for different turbulence values from the scintillometer and the anemometers. The anemometer positions A, AB, and B correspond approximately the positions A, B2, and B in Fig. 4.
Fig. 25.
Fig. 25. Height variation of the horizontal (left) and vertical (right) image jitter. Note the increase in image jitter for the height of 10.35 m. The inserted circles reflect the jitter magnitude in an xy diagram.
Fig. 26.
Fig. 26. Measured angular resolution for three frame stabilized active images versus measured image jitter.
Fig. 27.
Fig. 27. Left: Measured angular resolution for three frame stabilized active images versus sensor height [black squares] versus theoretical values based on the conventional choice of α=4/3 (daytime) or α=2/3 (night time). Right: During the evening the choice of α=2/3 gave a good correspondence with the measured and theoretical angular resolution.
Fig. 28.
Fig. 28. Measured angular resolution for three frame stabilized active images versus sensor height [black squares] versus theoretical values based on the conventional choice of α=4/3 (daytime) or α=2/3 (night time). The resolution was measured from the edge response of the black and white target board gave a much better correlation with the theory.
Fig. 29.
Fig. 29. Probability of recognition and median time to response for different activities related to the normal use of the object listed on the x axis. A=active and P=passive imaging. Range 2 km with average sensor heights of 1.6 m (strong turbulence), 5 m (moderate), and 10 m (weak).

Equations (6)

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

Cn2(h)=Cn2(1)·hα,
ρsp=1.22λFD,
Csp=1M.
r0=2.1·[1.46k20LCn2(z)(1z/L)5/3dz]3/5,
σα2.9Cn2LD1/3,
MTF=exp[3.44·(λf/r0)5/3],

Metrics