1.

Introduction

Research and development of countermeasures for degraded visual environments (DVEs) commonly focuses on technologic solutions to transient ambient conditions. This approach typically views “degraded visuals” as an intrinsic characteristic of the environment, separated from the human operator. When examining human factors in DVEs, it may be helpful to reframe the situation as one in which the operator’s “visual environment” has been degraded. Everything which occurs prior to transduction of photons into neural signals by the photoreceptors contributes to an operator’s “visual environment,” but much of this is not captured in the technology-centric DVE mitigation framework.

Aviation may be one of the fields most broadly interested in DVE, due to safety and performance implications. With the common approach, the “E” portion of DVE is typically everything outside of the cockpit, including changes in lighting, fog, sand, smoke, and dust, which contribute to the “DV” portion. The pilot’s visual environment not only includes the outside world, but the windshield, any obstructions to the windshield, the interior of the cockpit, any worn filters (such as sunglasses), the pilot’s refractive elements (i.e., corrective eyewear, the cornea, and the crystalline lens), the aqueous and vitreous humors (including any debris present), and the macular pigment (MP).

The MP is composed of carotenoids (specifically lutein, zeaxanthin, and mesozeaxanthin¹) derived from dietary sources and deposited in multiple layers through the macula, the part of the retina that supports central vision. The MP is in the optical path between the vitreous humor and the photoreceptors and serves as a filter, attenuating shorter wavelengths in the visible spectrum while allowing longer wavelengths to pass through. Although this has many potential implications for DVE (such as reducing glare disability), of particular interest to the modeling effort described in this paper is the filtering of the short-wave components of light scattered in the atmosphere when viewing distant objects.

When viewing distant objects through the atmosphere, light is scattered by the molecules and particles in the viewing path. Smaller particles tend to cause Rayleigh scattering,² which is strongly wavelength dependent (with shorter wavelengths scattering more than longer wavelengths), and larger particles tend to cause Mie scattering,³ which is largely wavelength independent. As a result, the scattered light between a viewer and a distant object is somewhere between strongly shortwave predominant (such as at high elevations with clear skies) and spectrally flat (such as in extreme fog) depending on local atmospheric conditions. This short-wave scattering, combined with the short-wave filtration of MP, is of particular relevance to the model presented here.

Wooten and Hammond⁴ proposed that MP would improve contrast for objects at long ranges by removing some of the scattered shortwave light (referred to as “airlight”) intruding between the observer and target, and the shortwave component of the background while largely preserving the wavelengths of the target. The rationale they presented for their model is reasonable, but due to technological constraints at the time of their work, the model incorporated simplifying assumptions to reduce computational complexity, assumptions that may have important implications for their conclusions. Examining this situation is of more than theoretical interest as the optical density of the macular pigment (MPOD) in the normal human eye can vary widely between individuals. Moreover, a growing robust literature shows that the MPOD in humans can be substantially affected by diet and dietary supplementation. Thus, the model provides one way to evaluate the impact that differences in MPOD between and within individuals may have on an important aspect of visual performance in DVE. The present paper documents an elaborated, refined, and updated version of the Wooten and Hammond⁴ model. The results reported here extend an earlier report of our instantiation of the model that demonstrated the feasibility of using the model to estimate the impact of MPOD changes on human performance in DVE under photopic conditions. Refinements in the modeling allowed greater resolution in characterizing the effects of MPOD on photopic vision and improvements made it possible to characterize MPOD’s effects under scotopic conditions, which to our knowledge has not previously been reported.

2.

Methods

The model specifically evaluates the effects of MPOD on Weber contrast (WC). WC is the standard measurement of contrast between an object and its background when the ratio of the angular area of the background to the angular area of the object is high. The model incorporates the impact of distance, luminance, and spectra on WC. As the distance between an object and an observer increases, shorter wavelengths of light will be lost to a greater degree than longer wavelengths due to wavelength-dependent Rayleigh scattering.^5,6 This is captured in the exponential term of equation 1 (below). Additionally, as the distance of a viewed object increases, more light (which also exhibits the same wavelength-dependent scattering) is present in the air of the viewing path. This intruded light is identified as the target airlight luminance. The Wooten and Hammond⁴ model treats the horizon sky luminance as the background luminance for calculating the contrast of an object against an open sky. The addition of a term incorporating atmospheric scattering produces the airlight luminance equation. The model presented here treats the background luminance as an extreme-distance case of the airlight luminance. In the presented results, the difference between these two is negligible, as the exponent term approaches values extreme enough to drive the multiplier toward 1. In other applications if the atmospheric scatter constant is sufficiently small (e.g., due to extreme fog) then this multiplier may not be 1 in which case the effective background distance may have a significant impact. For this reason, it is incorporated into the model for future use, but does not currently meaningfully contribute to the results.

Table 1

Terms for equations.

For all calculations, $\lambda$ (Table 1) was 1-nm bins ranging from 400 to 700 nm, for a total of 301 wavelengths. $T_{\lambda ,\mathrm{mod}}$ for each wavelength was calculated for 101 possible optical densities (0.00 to 1.00 in increments of 0.01). The ${\lambda }^{-v}$ term for each wavelength was calculated for each of 401 possible atmospheric scatter coefficients (0.00 to 4.00 in increments of 0.01). For any combination of $V,E,a$, and $T_{\lambda ,\mathrm{avg}}$, this represents $\sim 12.19$ million calculations each for target, airlight, and background luminance prior to distance being incorporated. Target luminance, target airlight luminance, and background luminance were calculated for each wavelength for every combination of viewing distance, MPOD, and atmospheric scatter coefficient. In the previous presentation of this approach, the integral approximation was performed using the trapezoidal method. Due to the small width of the $\lambda$ bins and their quantity, this step was replaced by taking the bins as an array along with an equivalent length array of ones and calculating the dot product (i.e., “scalar product”). This significantly reduced run-time, and in cursory testing was not found to significantly alter luminance calculations.

Tested spectra included that of an ideal black body (i.e., a target with no reflectance whatsoever), olive drab green nylon webbing, and yellow nylon webbing. These two nylon samples were chosen because they were among the few synthetic materials with spectra available from the USGS (U.S. Geological Survey), which appear with multiple pigments but identical base materials and are potentially found in a military environment. The D65 standard illuminant was used for the $E_{\lambda }$ term and the luminosity functions used were the 2006 CIE (International Commission on Illumination) Photopic data and the 1951 CIE Scotopic data. Due to the a lack of other suitable values to assume, the $T_{\lambda ,\mathrm{avg}}$ term used corresponded to a zero MPOD observer. It is worth noting that this brings the associated denominator term for all wavelengths to 1 by assuming no filtration from the MP occurs. The $T_{\lambda ,\mathrm{mod}}$ term was calculated by multiplying the normalized absorption spectra for MP by the absorption corresponding to each modeled MPOD, then converting from absorption to transmittance (Fig. 1).

Fig. 1

Reflectance spectra of OD green and yellow nylon webbing samples.

For each spectra, contrasts were calculated for 100 ranges (500 m to 50 km in 500 m increments) and MPOD values of 0.00, 0.10, 0.25, 0.50, and 1.00 were chosen to illustrate a wide range of densities. Additionally, the atmospheric scattering coefficient for all presented results is 2.00, which represents the midpoint between extreme fog ($\sim 0.00$) and pure Rayleigh scattering ($\sim 4.00$) as well as being a reasonable real-world value.⁴ The model was built in Python v3.6.4 and heavily used the NumPy (v1.14.0) and Pandas (v0.22.0) libraries. Percentage improvement (which in some circumstances was negative) relative to a 0.00 MPOD observer was calculated and plotted in R v3.4.3 from the output files generated by the modeling Python code.

Mathematically, the method used here was equivalent to that previously presented by O’Brien et al.⁹ in a photopic-only examination, but the previous presentation relied upon a serial approach using loops to perform calculations for each wavelength while the current version uses NumPy matrix operations to substantially enhance computational efficiency. This enhancement enabled calculations to be performed for a large range of modeled observer MPODs (0.00 to 1.00 in increments of 0.01) and atmospheric scatter constants (0.00 to 4.00 in increments of 0.01), with results being subset and stored to file for conditions of interest. The present approach was taken as a step toward developing the method for future use as an interactive tool or application.

3.

Results

The modeled effects of the filtration of MP on WC varied substantially between different target spectra as well as between the photopic and scotopic luminosity functions. In all cases, contrast was negative for all values, which is to be expected for reflective targets, and approaches 0 as distance increases, which is to be expected as more of the target’s luminance is scattered and more airlight intrudes into the line of sight (Table 2).

Table 2

WC for blackbody target.

The results of the present modeling effort address only the calculation of the contrast of the reflective target and do not include estimates of visual sensitivity. Previous literature¹⁰ has shown that sensitivity for positive contrast targets (i.e., targets with a luminance higher than the background) can be increased with increased MPOD. It may be noted further that the visual system’s sensitivity to contrast may be impacted by nonoptical effects of the MP as discussed by others, for example, Zimmer and Hammond.¹¹

When viewing curves of percent WC change (with increases in contrast treated as positive values) versus a 0.00 MPOD, two distinct phenomena appear.

First, for all tested spectra, there is a “cross-over” distance where MPOD shows no impact on luminance contrast. For distances short of the crossover distance, the MP filters enough of the target luminance to cause a net decrease in contrast. After this distance, the MP reduces enough of both the background luminance and the airlight luminance to offset the filtering of the target luminance and thereby create a net increase in contrast (Tables 3 and 4).

Table 3

WC For OD green nylon webbing target.

Table 4

WC for yellow nylon webbing target.

Second, the distance at which this cross-over point occurs varies dramatically between different target reflectance spectra and also changes substantially between photopic and scotopic vision. For an ideal blackbody (where there is no target reflectance, a situation in which increasing distance has no impact on target luminance), the cross-over point is at 0 m (Fig. 2). For the olive drab nylon webbing spectra tested, the photopic cross-over point is between 0.5 and 1.0 km, but the scotopic cross-over point is between 1.0 and 1.5 km (Fig. 3). With the yellow nylon webbing spectra tested, the photopic cross-over point is between 15.5 and 16 km, but the scotopic cross-over point is between 28.5 and 29 km (Fig. 4).

Fig. 2

WC changes for black body target (relative to MP 0.00 observer).

Fig. 3

WC changes for OD green nylon webbing target (relative to MP 0.00 observer).

Fig. 4

WC changes for yellow nylon webbing target (relative to MP 0.00 observer).

4.

Discussion

The model results suggest that the impact of MP on luminance WC differs between photopic and scotopic vision. For all tested spectra, any contrast enhancement or reduction due to MPOD was of greater magnitude under scotopic conditions than photopic conditions. Considering that the spectral absorption of the MP (Fig. 5) has more overlap with the scotopic sensitivity than with the photopic sensitivity curve (Fig. 6), this is to be expected. Although the original presentation of this model by Wooten and Hammond⁴ suggested only improvements in luminance WC from MP, the present model shows that decreases occur under certain circumstances, and that they are likely nontrivial.

Fig. 5

Spectra of MP and D65 illuminant.

Fig. 6

Photopic and scotopic sensitivity curves.

Before attempting to use this model to estimate human visual performance, several limitations must be taken into consideration. MP is selectively concentrated in the central fovea,¹² which has maximal cone density and minimal rod density,¹³ reducing the impact of MP on scotopic vision. However, there are typically significant levels of MP at the retinal eccentricities where rod density first exceeds cone density.¹⁴ Additionally, some subjects exhibit atypical spatial distributions of MP¹⁵ and the distribution of MP tends to widen with age,¹⁶ both of which could change the influence of MP on scotopic vision. As true scotopic viewing conditions are rare in outdoor environments, interpolating a mesopic model from the photopic and scotopic models is likely to be more useful in predicting visual performance. It may also be useful to treat photopic sensitivity as sensitivity for each cone type, rather than as a monolithic photopic sensitivity curve, to allow for color contrast to be determined in addition to luminance contrast. Incorporating the nonlinear topography of both the photoreceptor mosaic and the distribution of MP into the presented model would both multiplicatively increase the computational requirements well beyond the equipment currently available to the authors, but down-selection of currently captured variables into constants would permit this for future use.

The current iteration of this modeling effort produces an abundance of data. Modeling 101 MP densities for each of 401 atmospheric scatter constants means that 40501 WC values are calculated for each specified combination of distance, luminosity function, illuminant spectrum, and target spectrum. The overhead required to produce these calculations precludes the model from use on most current computing systems prior to some sort of subsetting as tabular data or a database. Nonetheless, these output data may have applications in predicting the visibility of targets in aviation and military environments. Because the luminance WC changes with distance toward an asymptote of 0, it may be practical to calculate values for a small number of ranges and fit to the data an exponential decay function or other smooth curve.

Future developments to the model could address mesopic vision, most likely by taking both a photopic and scotopic luminosity function and creating a combined sensitivity curve based on complementary weights as current CIE standards recommend.¹⁷ If filter spectra other than that of MP are substituted, this model may have utility in designing specialized eyewear for aerial or ground observers of aircraft or unmanned aerial vehicles (UAVs). With some streamlining, this code may eventually be useful in optimizing paint and other material selection for UAVs and aircraft to maximize or minimize visual detection at different distances or under different atmospheric conditions. It should also be possible to run the model in parallel with the sensitivity data for the separate cone classes to aid in the prediction of chromatic contrast. Additionally, this model serves as a potential starting point in creating a detection probability model for observers viewing distant objects, which would need to incorporate the visual angle of the target as well as overall luminance and other factors.¹⁸