Abstract

Dappled light is often unnoticed and underappreciated. This paper illustrates and describes dappled light under foliage during a solar eclipse, shows how a bush can create images of the Sun eclipsed by local objects any sunny day, and presents a free application to simulate dancing dappled light using mobile phone video of foliage.

1. Introduction

Images of the Sun cast by naturally occurring apertures in foliage result in a phenomenon called dappled light. Resolved images of the Sun appear under any dense foliage amongst blurry images and foliage shadows, the entirety executing a mesmerizing dance when wind disturbs the foliage.  During an eclipse, a remarkable effect appears - the sharp circular images suddenly become crescent-shaped. Figure 1 shows mobile phone images of dappled light on a horizontal white box under a bush and on a sidewalk under a tree during the 2024 solar eclipse, as observed in Madison, Wisconsin.

Eclipse watchers are usually focused on observing the Sun through eclipse glasses, through filters with their mobile phone cameras, or through the use of paper or aluminum foil-based pinhole cameras.  Few in my experience even notice the natural pinhole eclipse images in their environment nor understand these are an everyday phenomenon, not unique to a solar eclipse. Natural images of the Sun and of other bright light sources described below appear around us every day and night and include images of the Sun locally eclipsed, not eclipsed by the distant Moon.

In what follows, artificial pinhole imaging of a solar eclipse is described, and pinhole imaging concepts are reviewed. An example of a natural image of a local solar eclipse is then presented, and possible experiments the reader might undertake are suggested. Finally, the algorithm and some results of an available simulation of dappled light based on video or still images of real foliage are presented with nods to a possible application,  the limitations of the model, and possible extensions.

2. Pinhole camera imaging

Figure 2 shows mobile phone camera images illustrating artificial pinhole imaging of the Sun during an eclipse. To create the left image, a linear array of pinholes with size decreasing from bottom to top was made in a piece of paper. Pinhole images of the Sun were cast obliquely onto a horizontal surface into the shadow of the handheld mobile phone camera that took the image in the figure. As the pinhole diameter decreases, the Sun’s image may be seen to both sharpen and dim. To create the image on the right, the author’s hand was clenched to create two irregular apertures, one much smaller than the other.  A resolved image of the Sun from the smaller aperture appears as a crescent in the shadow of the hand. The larger irregularly shaped anti-shadow produced by the larger aperture exhibits a penumbra region interior to its edge. That anti-shadow can be understood as a convolution of light from small patches on the light source projected through the aperture.

 Dappled light illustrates that in pinhole imaging, the “pinhole” needs to be neither the size of a pin nor round.  To resolve the Sun on some image plane, an aperture must only have an angular size, as seen from the image plane, that is small compared to the angular size of the Sun, about 0.5 degrees or about 0.01 radians.  A square aperture as large as one meter on a side will begin to resolve the Sun on a screen at distances larger than about 100 m. This distance approaches the scale for the “dappled light” cast by low cumulus clouds.  Resolved images of the Sun and of the local colorful outdoor environment can be observed by eye on surfaces interior to a room a few meters in linear dimension if a window blind contains apertures with dimensions of order one cm.

To detect a pinhole camera image of some bright source projected on some surface by eye or other means, the intensity of the direct light transmitted through the aperture must dominate the intensity of diffuse background light on the image plane. The direct light intensity is proportional to the area of the aperture, and the angular resolution is proportional to the linear dimension of the aperture until it is limited by diffraction. As shown in Figure 2, it is possible to resolve the Sun and see its image with the naked eye on a white surface without enclosing the surface in a black box to reduce stray light, but it is challenging to observe the Sun this way with an aperture with an angular resolution that is a small fraction of the solar diameter, and it is insufficient to pick out a sunspot - the direct light intensity is too small to detect with a daylight-adapted eye and ultimately also too dim to detect above noise level in a background-subtracted digital image. 

3. Local eclipses

If you study dappled light on a windy day, you may begin to appreciate that the apertures arise through the projection of a three-dimensional collection of objects, not simply an overlap of, say, pieces of paper, each containing various apertures. In particular, a distant (on a human scale) object can partially obstruct sunlight before it is imaged by a nearer aperture. The resulting pinhole image can be that of a locally eclipsed Sun.

To observe a local solar eclipse by eye, place yourself in the shadow of branches of a distant tree that is relatively free of foliage and that is partially eclipsing the Sun and use a makeshift pinhole in paper or a natural foliage pinhole to project the partially eclipsed sunlight onto a white surface. As illustrated in Figure 3, you may observe the shadow of the tree trunk or branches within the bright disk of the Sun. (As in the case of observing a solar eclipse by the Moon, do not stare directly at the Sun while performing this experiment.) To make an artificial crescent-shaped local eclipse image, find or create a local object with appropriate angular size and curvature, such as a basketball on a long pole.

4. The Moon and artificial light sources

Any distant extended light source can be used to explore pinhole imaging. The curious or those seeking a challenge might attempt to observe dappled moonlight, light cast by a full or crescent Moon projected through foliage onto a white surface, possibly during a lunar eclipse by Earth or by a local object. As is the case with the Sun during the day, if the Moon is the principal source of stray light at night, the signal-to-noise ratio will be comparable to the ratio when observing a solar eclipse in the daytime, with or without an enclosure, and an image might be observable to the dark-adapted eye. Modern mobile phone camera image processors support  10-30 second exposure times that can be exploited to observe dim, dappled light.  Artificial light sources like streetlights, mobile phone flashlights, or the interior of a house seen through a window from the exterior can also serve when exploring pinhole imaging in the “dark.”

5. Seeing is believing. Modeling is understanding.

To model dappled light in an engaging way, a MATLAB interactive Live Script (Carlsmith, 2024) was written by the author for astronomy and physics students. The code identifies foliage apertures in still or video frame images, convolves with all apertures light from a simulated light source of uniform intensity, circular shape, and variable diameter, and then projects and merges the transmitted light onto a realistic candidate surface. As illustrated in the movie frame in Figure 4, a student can use their own mobile phone video of their favorite foliage and an image of their favorite surface to create a video of dancing dappled light on that surface and then vary the size and shape of the light source to study the dappled light appearance at different angular resolutions over time.

This Live Script and the movie, as well as about 80 or more other Live Scripts for STEM education by the author, are freely available at the MATLAB File Exchange. Those scripts that do not reference certain specialized proprietary codes may be run in the cloud by anyone who opens a free MathWorks account. For each script, the File Exchange landing page introduces the script and lists the dependencies. The download package contains the necessary files, the script, and a PDF of the executed script. The script can be run natively on any laptop with a student or professional license or with a free user’s cloud account in any browser window.

The reader may notice in Figure 4 that after a tree has leafed out, it may be quite challenging to assess the number of leaves it bears. However,  the total aperture area represented by anti-shadows could be a practical proxy for foliage density and be useful in forest management and other applications.

Inspection of the tree images in Figure 4 also reminds one that leaves absorb, transmit, and reflect direct and environmental light in a manner dependent upon species, life stage, and environmental conditions. The model of dappled light described here is highly simplified and not easily generalized, but deep learning models now routinely identify plant species in a wide variety of environmental conditions based on a single image, with results nearly instantaneously available on a mobile phone. Such models likely have already been brought to bear on vegetation monitoring and assessment. Such considerations might excite curious or forward-looking entrepreneurial student when exploring dappled light with their mobile phones, newly aware of connections between solar eclipses and their everyday world.