3.1.

Fog Generation Test Facility

The Sandia National Laboratories (SNL) fog chamber, shown in Fig. 1, is $\sim 55\mathrm{m}\times 3\mathrm{m}\times 3\mathrm{m}$ ($L\times W\times H$). The test facility purpose is primarily to test and evaluate optical systems, such as visible cameras, thermal imagers, or laser-based devices, within a stable laboratory environment. The SNL fog chamber has the capability of utilizing differing chemical constituents to seed the fog mixture with environmentally relevant products using 64 two-fluid air-atomizing nozzles. In this proof-of-concept test, the simulated fog was seeded with a $10\mathrm{g}/\mathrm{L}\mathrm{NaCl}$ salt water mixture. NaCl was chosen to closely mimic the primary constituent found in naturally forming sea coastal fog.^23–25 The chamber is separated into three sections, which enable varying fog densities and particulate concentrations. However, for the purposes of test consistency, all sections were run with the same nozzle conditions: an air flow rate of 3 to 4 cubic feet per minute and a liquid flow rate of $115\mathrm{mL}/\min$.

Fig. 1

(a) SNL fog chamber under nominal conditions and (b) SNL fog chamber with simulated coastal fog. Safety LED lights were kept on in these images to demonstrate the scattering nature of the generated fog. However, subsequent tests removed all sources of illumination except for the test source located within the test target chamber.

Particle size distribution is measured in 1-s intervals using a Malvern Spraytec instrument and inhalation cell accessory. The Malvern Spraytec instrument calculates particle size, which is inversely proportional to scattering angle, via indirect measurements of light scatter off particulates onto a detector. Mie theory, which predicts absorption and light scatter intensity of a spherical particle, is the fundamental model that the Malvern software utilizes to determine particle size.^24,26,27 Additionally, the inhalation cell accessory was used as an enclosed measurement zone with a controlled sample flow rate. This is important for particle size accuracy and postmeasurement concentration calculations, which utilizes the Beer–Lambert law and particle diameter to determine volume concentration. Accuracy of the particle size measurements was verified using the wet dispersion cell accessory and NIST traceable standards. Verification was determined by the manufacturer by taking measurements of three different polystyrene latex sphere sizes at 1, 9, and $40\mu \mathrm{m}$. The Malvern instrument correctly predicted test particle size to within $\pm 1\%$ accuracy.

During data collection, the Malvern Spraytec calculates particle size measurements as volume-based results. Restated, each particle size bin consists of a derived percentage of the total volume of all particles in the distribution. These data are then converted to a number-based (i.e., number per cubic centimeter) distribution by²⁴

3.2.

Meteorological Optical Range Calculations

Metrics defining the transparency of the atmosphere are utilized in several domains such as aviation, meteorology, transportation, and shipping. The prominent metric was once termed “visual range” but has since become known as visibility.²⁸ Classically, visibility was a quantity that was determined subjectively by an observer. However, an alternative visibility metric exists today that is quantitatively defined as the distance required to reduce the luminous flux of a collimated beam from a 2700-K color temperature lamp to 5% of its original value. This metric is known as the MOR. For the tests performed in this study, we utilize an MOR measurement to provide quantitative and repeatable measurements of the optical effects of fog on visible imager performance. The concepts of the MOR are founded on the Beer–Lambert law,²⁹ which states that

To calculate MOR, we define the ratio of the measured intensity to the nominal intensity as 5%. Mathematically, we define this as follows:

3.3.

Relative Spatial Frequency Response Area under Curve Methods

Measurement of SFR can be achieved via a number of methods.³¹ We chose to utilize a sinusoidal Siemens star test target as described by the ISO 12233 photography resolution standard. Motivation to utilize the sinusoidal Siemens star test rather than the more common slanted edge measurement is due to the presence of algorithmic edge enhancements applied to captured images from the camera tested. These edge enhancements artificially alter the contrast recorded by the camera at the slanted edge and thus modify the SFR if slanted edge techniques are utilized. Previous work suggests that the sinusoidal Siemens star test is less sensitive to artifacts induced by edge enhancement algorithms.³²

However, the use of a sinusoidal Siemens star target can be complicated due to incorrect determinations of the test target center. Care must be taken to precisely identify the center of the test target either using closed form mathematics for curve fitting of decentered radial sinusoid profiles or increasing the number of radial segments used to fit a sine wave to measured data.³³ In this analysis, we utilized 64 sinusoidal Siemens star segments to mitigate errors due to misidentified target centers.

SFR AUC nominal measurements were taken before fog generation began. All subsequent SFR data were then normalized by the nominal set, and a trapezoidal numerical integration was performed to find the SFR AUC for every 1-s interval during a test. This method of normalization was used to account for imperfections in the imaging system or residual defocus that reduced the absolute SFR of the system at the beginning of a test, enabling direct measurement of the impact of atmospheric conditions on optical performance.

3.4.

Proof of Concept Test Method

A Lumenera Li165 color network surveillance camera was used to evaluate the effects of fog density on reported relative SFR AUC and MOR for different fog levels in the SNL fog chamber facility. The camera was placed in a weatherproof casing and mounted on a tripod at the end of the fog tunnel. An open test target chamber with positive pressure housed an optical test target consisting of sinusoidal Siemens star targets and grayscale patches conforming to the ISO 12233 standard. The test target chamber contained two LED illumination sources oriented toward the test target. These light sources were the only illumination within the testing facility during the duration of a test. The camera was focused by visually maximizing the aliasing of the high-frequency elements of the sinusoidal Siemens star test target before fog was generated. Video was then recorded from the camera for the duration of a test, and frames were averaged together into 1-s intervals to match that of the Malvern Spraytech system. These 1-s interval datasets were then utilized to calculate relative SFR AUC and MOR, as previously described.

Figure 2(a) shows a diagram of the test setup, whereas Figs. 2(b)–2(d) show images of the test target captured by the camera with increasingly dense fog.

Fig. 2

(a) Diagram of the SNL fog chamber and test configuration used in this study and (b)–(d) images captured by the Li165 camera with increasing fog density.

Nominal measurements were recorded from the camera for the duration of 1 min prior to fog generation. The camera was allowed to continue recording during the course of fog generation while concurrent particle number measurements were collected by the Malvern Spraytec instrument. Fog generation continued until fog density was so great that the test target became visually obscured. At this point, fog generation was stopped and natural dissipation of fog particles occurred.

This test procedure was repeated three times for test targets located at 10, 20, and 30 feet from the camera.

4.1.

Test One

Test one placed the optical test target $\sim 10$ feet from the camera. Fog generation proceeded for $\sim 20\min$, until test target visibility was almost completely reduced, whereupon fog generation was halted. Fog dissipation began to reduce the total number of particles in the chamber.

Figure 3(a) shows the recorded values of relative SFR AUC, Fig. 3(b) shows MOR, and Fig. 3(c) shows the total number of particles in the atmosphere as measured by the Malvern Spraytec instrument. All values are a function of time, discretized into 1-s averages as described in the test methodology section.

Fig. 3

(a) Relative SFR AUC, (b) MOR, and (c) total number of particles in the atmosphere during test one. All data are plotted versus time in seconds. This test located the optical test target 10 feet from the camera.

Relative SFR AUC quickly decreased with the initial generation of fog particles, until a minimum value was reached within the 665- to 1340-s period. Once fog generation was stopped, relative SFR AUC rapidly increased for $\sim 300\mathrm{s}$, followed by a slower increase in relative SFR AUC for the remainder of the test.

Similarly, MOR rapidly decreased until a minimum value of $\sim 17$ feet was achieved between 500 and 1375 s. After fog generation was stopped, MOR began a uniform and nearly linear increase for the remainder of the test.

The total number of particles increased during fog generation. The average particle size distribution with a volume-based concentration was bimodal with peaks at 4.6 and $34\mu \mathrm{m}$. However, when converted to a number-based distribution, the peak particle size was $1.4\mu \mathrm{m}$. This indicates that, while large particles are present in the chamber, the majority of particles were small (i.e., $<10\mu \mathrm{m}$). Once fog generation stopped, particles naturally fell out of the atmosphere due to gravitational settling and evaporation affects which, reduced the total number of particles over time. During fall out, the larger particles fall out of air faster than the smaller particles, resulting in a nonlinear decay in the number of particles present within the chamber.

4.2.

Test Two

Test two increased the distance to the optical test target, placing the target $\sim 20$ feet from the camera. Figures 4(a)–4(c) show test results. Due to the increased atmospheric column, a lower fog density was capable of reducing the measured MOR to its minimum point. Fog generation proceeded for $\sim 260\mathrm{s}$. After fog generation halted, a decay in the total number of particles occurred for the duration of the test, similar to that shown in Fig. 3(c).

Fig. 4

(a) Relative SFR AUC, (b) MOR, and (c) total number of particles in the atmosphere during test two. All data are plotted versus time in seconds. This test located the optical test target 20 feet from the camera.

A similar rapid recovery of relative SFR AUC began at $\sim 450\mathrm{s}$, followed by a period of slower recovery starting at 870 s. This test produced elevated relative SFR AUC measurements within time periods of MOR measurements less than the test distance. This spurious increased SFR AUC occurs due to the sinusoidal Siemens star algorithm. This algorithm takes best-fit amplitude and divides by signal DC offset to retrieve a contrast metric at a specific spatial frequency.³¹ The fog environment scatters spatial information and thus causes best-fit amplitude to decrease rapidly to a near-constant noise value. However, it is still possible for DC offset to change after the sinusoidal best-fit amplitude has reached this near-constant noise value. As fog density increases, and thus DC offset of sinusoidal signals from the imager decreases, a spurious increase in relative SFR AUC occurs.

MOR quickly decreased to values smaller than 20 feet. This would imply that less than 5% of the original intensity was being measured by the imager during the thickest fog. After fog generation was halted, MOR recovered similar to Fig. 3(b).

4.3.

Test Three

Test three placed the optical test target $\sim 30$ feet from the camera. Similar behavior to both test one and test two was shown, with a lower particle density needed to reduce MOR due to comparatively larger optical path length. Test results are shown in Fig. 5. MOR rapidly declined to less than the test target distance and increased near-linearly after fog generation was halted. The spurious relative SFR AUC region increased in value during times when MOR was extremely low, but it showed a similar relative SFR AUC recovery after fog generation stopped, followed by a period of slower relative SFR AUC recovery for the duration of the test.

Fig. 5

(a) Relative SFR AUC, (b) MOR, and (c) total number of particles in the atmosphere during test three. All data are plotted versus time in seconds. This test located the optical test target 30 feet from the camera.

4.4.

Discussion

Results obtained in tests one through three show generally similar behavior for the number of particles versus time. A lower fog density was needed to reduce system performance as the target distance increased, and particulate decay after fog generation was halted proceeded in a similar manner for each test. MOR measurements across each test showed a similar rapid decay as fog generation began, followed by a nearly linear increase in MOR after fog generation was halted. However, relative SFR AUC exhibited unexpected behavior; each test demonstrated a period of rapid relative SFR AUC recovery, followed by a slower recovery of relative SFR AUC. We hypothesize that the relative SFR AUC metric is more susceptible to the presence of large particulates; large particulates more rapidly fall out of the atmosphere due to gravitational settling when fog generation is suspended, causing the initial rapid recovery of relative SFR AUC.