1.

INTRODUCTION

Polarized light under some circumstances is the dominant orientation cue for many insects, both walking and flying. Sensitivity to polarized light is enabled by the linear polarization sensitivity of the dorsal rim area of the compound eye, the location of which is shown on a dragonfly head in figure 1a. Animal polarization compasses were observed behaviourally in ants by Santschi in 1914,¹ although the interpretation was made later by von Fritsch as reported by Thorpe.² Santschi discovered that desert ants of the genera Cataglyphis and MonomoriumSantschi could continue to navigate successfully when the sun was occluded by a cylinder that surrounded them on their homeward path. Von Fritch famously documented polarization as the source of orientation in the honeybee dance.³ What was observed were daytime sun compasses that used the pattern cast in the sky by Rayleigh scattering⁴ as an indirect, distributed measurement of sun position. It was found that even after the sun had set scattered sunlight still provided a direction signal to foraging bees. Subsequently polarization navigation behaviour has been found in spiders,⁵ fish⁶ and other insects.^7–11 Polarization sensitivity in the structures of the dorsal rim area of the compound eye has been found anatomically in more species, such as dragonflies¹² where behaviour is less tractable by behavioural experimentation. Manually operated polarization astrolabes were fitted in passenger airliners operating at high lattitudes prior to the advent of the global positioning system,¹³ to compensate for the overall degradation of magnetic sensors in the Arctic Circle.

Figure 1:

(a) Detail of the head of a dragonfly, Hemianax papuensis, the dorsal rim area along the seam between the left and right eyes of many insects is polarization sensitive. (b) The sky polarization pattern cast by the sun is approximately tangential to the sun at every point. The polarization pattern cast by the moon or sun is used in daylight by certain flying insects and in other species at night¹⁵ and has been convincingly found in night foraging dung beetles.¹⁶

The principle pattern of linear polarization in the sky is depicted in figure 1b. The direction of polarization of light forms a tangential pattern around a light source. Looking directly upwards the pattern is simply orthogonal to the light source except when the source is at zenith, at which time the pattern (and the position of the source) provides no direction information on the horizontal plane. Both angle and degree of polarization vary throughout the day and depend on weather conditions.¹⁴

The principles are fundamental for the passage of light through gas and apply to the night sky for the sun just below the horizon, but still illuminating the sky, for the moon in the night sky and for light pollution on the ground, the latter having emerged after the evolution of most organisms.

The dung beetle Scarabaeus zambesianus, has been shown to use this night sky polarization as a navigation aid by Dacke et. al¹⁶ indicating a usable navigation aid in a particular desert environment at twilight and night.¹⁷ Their convincing demonstration used the fact that Scarabaeus zambesianus roll their ball of food along a pre-determined course away from the location where the food supply was found prior to burying it, presumably in order to avoid competition pressure and the risk of having the ball exhumed by other beetles. It was shown that their ability to plot a straight course could be disrupted by negating the polarization signal or manipulating its direction. This behaviour was discovered in a desert environment which is ideal for polarization navigation given the usually insignificant amount of water in the atmosphere.

The development of navigation systems based on biomimetic processes have opened up some noval navigation possibilities for small unmanned aircraft. Unmanned ground vehicles have demonstrated the effectiveness of polarization compasses in desert environments.¹⁸ Demonstrations have been achieved in which unmanned aircraft flew in daylight, with simple polarization sensors based on photodiodes,¹⁹ including implementations in which a polarization compass was part of the flight control system replacing the magnetic sensor.²⁰ Usable polarization orientation information has been established in daylight conditions using calibrated cameras.²¹ Night sky polarization needs some quantification and understanding to allow the design of effective optics and electronics for biomimetic night time sky polarization navigation. There are challenges in the varying night sky due to the cumulative effect of overcast weather conditions and the contributions of man made light pollution.

The compass is a core aspect of the flight control system of an autonomous aircraft so there is a need to understand any sources of anomalies. This paper looks at the effect of overcast weather conditions and the contributions of man made light pollution to determine if there is viable night sky polarization information for navigation in areas of interest for all manner of commercial and defense operations that could be described as “urban fringe”.

2.

DATA AND ANALYSIS

The use of cameras to determine sky polarization has been demonstrated by Pust and Shaw²² the investigations of night sky polarization have been done in support of astronomical photography^23,24 as have the effects of urban light pollution on night sky polarization.²⁵ This work provides some data points for the investigation of biomimetic night sky polarization navigation, however, the locations of astronomical observatories is not representative of real world night navigation situations.

For baseline information of the amount of polarized light in the sky a number of photographs were taken from a semi-rural location on a clear night and a night of partially transparent cloud both with a near full moon. These photographs are initial data collection that to inform the methods of investigating the likely polarization characteristics and noise sources in the night sky, particularly when analysed for the orientation of linear polarization.

All photographs were taken with a Nikon D5100 through a polarized filter. The lens used was a Nikon AF-S DX nikkor ED 18-55mm 1:3.5-5.6GII. The polarized filter was from 3Dlens.com product number P50. Transmittance: single (38%) ; Parallel (30.1%); crossed (0.00455%), Color: neutral gray, Polarizer wavelength: 400-700nm

A fitting was made to go over the lens of the camera such that the photograph was taken through the filter. The direction of polarization was selected by manually rotating the filter holder on the lens.

The camera settings used were: Lens set at 35mm and focused at infinity and F4.5. (This gives a field of view of 46 degrees), ASA 2000, Exposure 6 seconds. The images are 4928 pixels by 3264 pixels and stored as JPEG images.

2.1

Calibration of night sky intensity

To gain an estimate of the light intensity of the night sky from the polarization photographs a calibration curve for the camera was obtained by taking photographs of daylight sky with the only difference in camera setting being the exposure time. At the same time as taking the photograph the light intensity was recorded by pointing the sensor of a Lutron LX-1118 calibrated light meter in the same direction as the camera and located next to the camera.

The calibration photographs were taken on an overcast day late in the afternoon facing South South West from under cover. The intensity histogram plot from the GIMP software shows some silhouetted feature information in the lower part of the spectrum with a broad main peak, see figure 2a.

Figure 2:

(a) An example intensity histograms for the calibration photographs or the total light intensity taken in day time (b) Data for 1/500 sec which yields the curve of linear best fit, with origin crossing forced (c) Plot of the measured light intensity from the polarization photographs for some cases of clear night sky and overcast night sky (d) Data for 1/500 sec GIMP mean bulk intensity analysis taken at different times during the day against the Lux value from the Lutron LX-1118 calibrated light meter.

The extracted mean intensity data of these photographs was used to derive calibration curves. The spread of points from the fitted line is from the GIMP software calculating the mean using all the data in the intensity histograms including contribution from silhouetted objects as discussed above. The resulting curve is shown in figure 2b.

This gives an absolute error with these limited figures of less than 30% (including the 2% error of the light meter). This is sufficient to obtain the order of magnitude estimation of the observable night sky light intensity required for defining the required parameters of instrumentation to measure the night sky polarization.

By including that the ratio of Lux to Mean intensity calibration curves is inversely proportional to the ratio of the exposure times the estimation of total mean light intensity of the horizontal polarization photographs is calculated for selected data sets in the table in figure 2d below. The night sky intensities are plotted in figure 2c.

The night sky light intensity for the clear night looking up into open sky being 0.0028 Lux is consistent with listed astronomical values for the night sky given by Patat.²⁶

2.2

Data set

The photographs were taken at a site in the Adelaide Hills, South Australia. The location is approximately lat -34.9 lon 138.8, approximately 3.3km from Lobethal and 2.2km from Woodside with the population of each town approximately 2000. The location is sheltered from direct light from both towns as well as from light from traffic on the main road.

The photographs were taken within a few minutes on Thursday 30 April 2015 at 23:00 and Friday 1 May 2015 at 21:20 being a clear night and overcast night respectively. The sun had set in both cases and using Kstars astronomical software²⁷ the moon had the positions of:

• 30 May 2015 at 23:00 local time Azmith 326° 43′ Elevation 50° 33′

• 1 April 2015 at 21:20 local time Azmith 27° 27′ Elevation 56° 10′

Examples of the photographs are shown in figures 3(a)–(f). While some photographs convey little information, such as looking up into a cloudy night sky, others show stars and silhouettes of foreground objects, see figure 3a and figure 3c. The most striking photographs show the effect of township light pollution in overcast conditions, see figure 7b.

Figure 3:

(a) Facing East with horizontal polarization Thursday 30 April 2015 - Clear night with near full moon. Brightness and contrast adjusted for this display purposes (Gimp seetings +70 +40) so that image structure is visible. (b) Vertical polarization Brightness and contrast adjusted for this display purposes (Gimp seetings +70 +40) so that image structure is visible. (c) Facing East with horizontal polarization Friday 1 May 2015 -Overcast night with near full moon (d) Vertical polarization (e) Facing South West looking over Woodside with horizontal polarization Friday 1 May 2015 - Overcast night with near full moon. (f) Vertical polarization Friday 1 May 2015.

The photographs were analyzed for intensity distribution using GIMP 2.8.14 GNU Image Manipulation Program.²⁸ This analysis allows for the separation of the effect of the three photo sensor colors as well as an aggregate value. Examples of the histogram plots of the intensities for the different polarization are presented.

Figure 4 shows the histograms for a clear night facing East. Figure 5 shows the histograms for an overcast night facing East. Figure 6 shows the histograms for an overcast night facing North North West (towards a town).

Figure 4:

The intensity histograms for the polarization photographs on Thursday 30 April 2015 for a clear night with near full moon facing East for (a) horizontal and (b) vertical polarization filter settings. The upper set of histograms show the results for each of the cameras color channels while the lower set show the histograms for the total light intensity for (c) horizontal and (d) vertical polarization filter settings.

Figure 5:

The intensity histograms for the polarization photographs on Friday 1 May 2015, an overcast night with near full moon facing East (a) horizontal and (b) vertical polarization filter settings. The upper set of histograms show the results for each of the cameras color channels while the lower set show the histograms for the total light intensity for (c) horizontal and (d) vertical polarization filter settings.

Figure 6:

The intensity histograms for the polarization photographs on Friday 1 May 2015, an overcast night with near full moon facing North West looking over a town (a) horizontal and (b) vertical polarization filter settings. The upper set of histograms show the results for each of the cameras color channels while the lower set show the histograms for the total light intensity for (c) horizontal and (d) vertical polarization filter settings.

Figure 7a(a) and 7b(b) shows the images captured in the same direction on both a clear and overcast night.

Figure 7:

(a) Thursday 30 April 2015, a clear night with near full moon facing West (between the towns), horizontal polarizing filter setting. Brightness and contrast adjusted for this display purposes (Gimp seetings +70 +40) so that image structure is visible. (b) Friday 1 May 2015, an overcast night with near full moon facing West, horizontal polarizing filter setting.

2.3

General observations of the intensity analysis

The difference between a clear night, see figure 3a/3b and an overcast night 3c/3c and 3e/3f, is seen to be the increase of different types scattering on the overcast night, mostly by Mie scattering, given that the difference is water vapour in the form of mist.²⁹ The silhouettes of foreground objects show a much brighter night sky on the overcast nights, further demonstrated by the higher means from the intensity histograms for the overcast night.

The data sets looking in the direction of the moon, shown on a clear night in figure 8a, shows a strong polarization signal, indicated by the variation of intensity around the moon when viewed through the horizontally polarizing filter. The mean from the intensity histogram of 62.2 with a Std Dev of 49.7 in the horizontal polarization and a mean from the intensity histogram of 69.6 with a Std Dev of 48.9 in the vertical polarization. The photographs of the moon on the overcast night show a more even exposure in the region of the moon with a mean from the intensity histogram of 41.1 with a Std Dev of 8.9 in the horizontal polarization and a mean from the intensity histogram of 40.9 with a Std Dev of 6.3 in the vertical polarization. Another marked difference is that on the clear night data set there are clear dark bands in the photographs from the cross polarization effect indicating highly polarized light. There is no discernable polarization structure in figure 8b.

Figure 8:

(a) Thursday 30 April 2015, a clear night with near full moon facing the moon with horizontal polarization. (b) Friday 1 May 2015 - Overcast night with near full moon facing North North East looking at the Moon with horizontal polarization.

The most notable difference between the clear and overcast nights is that the scattered light from nearby towns becomes observable. The effect is strong when looking West, between the towns and looking directly towards a town. The Mie scattered light is still dominant when looking in the direction between the two towns, shown in figure 6. When looking at the the RGB intensity histograms it is noticeable that there is more red light on the overcast night than on a clear night, see figure 6a/6b.

The derived sky polarization in this analysis uses the bulk intensity parameters from the photographs for consistency. There has been no attempt to minimize the effect of silhouetted objects by either using reduced fields of view (done by selecting a region without any silhouettes) or by using the higher mean value peak in the intensity histograms to obtain the mean sky intensity.

2.4

Observations of the derived sky polarization H/V ratio

Photos from near the horizon were processed for the ratio of horizontal to vertical (H/V) polarization intensity for blue in figure 9a and red in figure 9b. The direction of observation (East, North, North North West and South) is the important consideration, given the presence of population centres to the West and North West. The azimuthal separation between the West and North North West measurements eliminates that possibility that the orientation of the planar polarization is 45° in both directions. There are two data sets representing the clear night and the overcast night.

Figure 9:

(a) Ratio of H to V polarization in the Blue response of the camera for clear and overcast conditions (b) Friday 1 May 2015 - Overcast night with near full moon facing North North East looking at the Moon with horizontal polarization.

There is enough sky polarization information as a function of direction for use as a navigation aid. Blue contains the highest ratio between horizontal and vertical polarization and in the direction of population centres the ratio approaches 1.0 on both clear and overcast nights. The data set looking north and West included scattered light from nearby towns and this appears to be enough to disrupt the usefulness of the sky polarization as a navigation aid in these areas, particularly when looking directly over the town. The presence of a polarization pattern offset by superposition of light scattered from the town is expected, however large offsets and small contrast between channels would challenge the instrument and make it prone to biases and alignment errors. The effect may well be much less when gazing directly upwards.

3.

DISCUSSION

We have shown that under the right circumstances the moonlit night sky may provide an accurate heading reference. Artificial light acts as a contaminant to this signal and may result in errors in navigation. Condition of the atmosphere, including mist dramatically reduces the polarization signal. Despite reduced contrast it was also probable that a residual polarization signal still exists if the moon can be seen.

The ecological implications of this work are clear. The navigation performance of night flying insects is likely to be severely disrupted near cities. This would be most marked in migratory night flying insects where an entire population could be adversely affected by an aritificial light source.

A study of the practical performance of a night polarization compass in a UAV may have the dual effect of demonstrating a new compass modality and also of explaining the diversion of night flying organisms near towns.

4.

CONCLUSION

From the analysis above some conclusions can be drawn. There is enough light to obtain information of a night sky intensity when the moon is present, from which polarization orientation can be derived. The signal will be adversely affected by overcast conditions and stray light from the ground and the shorter visible wavelengths are a better choice than the longer. Further it is likely that the directions measured by a polarization compass will be distorted by stray light, indicating that a device gazing directly upwards is the best option for minimising the distortion.

We have shown that a viable polarization pattern exists in the moonlit night sky that can be resolved using off the shelf optical equipment. Even in the midst of significant light pollution a measurable signal was available. It remains to be seen how much light pollution affects navigation accuracy, which could be tested on an autonomous aircraft travelling over a distance containing terrestrial light sources or via a structured series of ground measurements.

More data needs to be collected to resolve the orientation of polarization across the entire sky and across a wider range of weather conditions and phases of the moon for a better understanding of the limitations of an insect-like night sky polarization navigation. Currently we are much better able to define the parameters required for a workable night sky polarization navigation system for small autonomous aircraft.