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Photometric Measurement of Limb Darkening at the October 14, 2023 Annular Eclipse

Description of photometric measurement of limb darkening at the October 14, 2023 Annular Eclipse

Published onMar 07, 2024
Photometric Measurement of Limb Darkening at the October 14, 2023 Annular Eclipse


We demonstrate that a simple spectral sensor can measure the changes in brightness and color that take place during an annular solar eclipse. This color change is due to the Moon blocking the bluer light shining directly from the Sun’s central face while allowing an annulus of limb-darkened light to reach us. This initial experiment was plagued by clouds, and we look forward to repeating this experiment during future eclipses.

1. Introduction

The most striking visual effect of an annular solar eclipse is the ashen color of the sunlight during annularity. With the central part of the photosphere obscured by the Moon, the remaining illumination comes from an annulus on the solar limb from which emitted light reaches the Earth at a lower escape angle. This effect is known as Limb Darkening and is well-known in stellar astronomy. Limb darkening arises because we see deeper, hotter gas layers when we look directly at the center of the disk (rays that travel straight up) and higher, cooler layers when we look at the limb (rays that travel at an angle through the atmosphere) (Moon et al, 2017). Light seen through these cooler layers of incandescent gas will have a lower black body temperature than light emitted from deeper, hotter layers of gas and will thus show a redder coloration to the observer.

black sensor chip with white writing
Figure 1

The optical sensor chip is the small rectangular device in the center. 

The recently released Osram AMS AS7341 chip is a ten- channel spectral sensor on a single microchip (AMS, 2020). A pre-soldered breakout board is available from Adafruit Industries (Figure 1)1. This device measures illumination in eight color channels from 415 to 680 nm (Figure 2). There is also an infrared channel at 910 nm and a clear channel with no filter.

image of wavelengths from purple to red across wavelength spectrum.
Figure 2

Spectral response of the filter channels normalized to the F8 channel. The channel labeled “Flicker” was not used.

This experiment was done to determine if this device can record scientifically valid environmental effects during a solar eclipse.

2. Methods

The photometer was deployed at a site northeast of Torrey, Utah in Bureau of Land Management wilderness, at 38 degrees 22 minutes north, 111 degrees 08 minutes west. The Sun was at 30 degrees elevation at time of maximum eclipse and was 95% occulted at this location.

The sensor chip was mounted in a plastic box 1.5 cm below a circular aperture of 0.47 cm diameter, giving a 17-degree acceptance angle pointed straight up at the zenith. The photometer was placed in the shadow of a nearby rock (Figure 3) to prevent direct exposure to sunlight, which oversaturates the optical sensor. A total of 275 data samples were taken at 30 second intervals over a period of 137 minutes covering the period before, during and after the eclipse. Sky conditions were partly cloudy before and after the eclipse (Figure 4). For the purposes of this study, we assume clouds to effectively be neutral density filters and the scattered light observed from the shadows to have scattered equally in all wavelengths.

device on the ground
Figure 3

Photometer with external power cell deployed in the shadow of a rock

Sun showing through clouds over a mountain
Figure 4

Sky conditions during the eclipse

3. Data Analysis

The eight visual channels of raw data (Figure 5) and the IR channel were normalized to the clear channel (unfiltered) data which reflects the overall illumination during the eclipse (Figure 6). Due to a timer error, the period of annularity was determined by finding the lowest point in the clear photometer channel. Sample 180 was determined to represent the period of maximum eclipse. Many of the samples were affected by the passage of clouds over the site before and after the eclipse, but a period around sample 10 was determined to be well enough behaved to be used as a reference point for the uneclipsed Sun.

Figure 5

Raw data as recorded by the multispectral sensor

graph of data
Figure 6

Normalized data (raw data / clear channel data)

Histograms were plotted for sample 10 representing the uneclipsed sun (Figure 7) and for sample 180 representing the time of maximum eclipse (Figure 8). A computer program was written to fit a black body curve calculated by Planck’s equation2 to the eight visible light data points and to the infrared channel. The intensity of each black body curve was adjusted to match the value of the data point for the 555 nm channel, the adjusted curves are also plotted on Figure 7 and Figure 8.

bar graph of data
Figure 7

Uneclipsed Sun – sample 010.  

5800 Degree Black Body curve normalized to 555 nm channel

bar graph of data
Figure 8

Maximum Eclipse – sample 180.  

4850 Degree Black Body curve normalized to 555 nm channel

The computer program was then extended to fit a black body plot of Planck’s equation to each of the 275 samples by the method of least squares. The results of this fit are plotted at the top of Figure 9.

multiple graphs of data overlaid
Figure 9

Final Results- Normalized data plotted below. Best fit black body temperature  plotted at the top of the graph for each of the 275 samples.

4. Discussion

For the purposes of our analysis, we assume that any color changes we see between the uneclipsed Sun (sample 10) and the annularly eclipsed Sun (sample 180) are due to changes observed Sunlight, and not related to clouds or other scattered light. However, the presence of clouds in the sky did complicate the analysis of the data, the sensor probably would have performed better if it had been mounted under an optical diffuser as recommended by the manufacturer.

5. Conclusion

The best fit color temperature for the uneclipsed sun was determined to be 5800 K, in good agreement with the accepted value of 5777 K (Drilling et al, 2000).

The black body temperature of the solar limb visible through the annular ring of the eclipse was determined to be 4600 to 4750 K as plotted in figure 9. Neckel (2003) obtained a value of 4750 K for the solar limb using data from the McMath-Pierce Solar Telescope of the National Solar Observatory at Kitt Peak. This effect of viewing angle is a powerful tool for measuring different layers of the Sun.

The photometric measurements of black body temperature are in good agreement with other measured and accepted values obtained by other investigators using different instruments. The existence of a low-cost ten-color multi-spectral photometer has implications for solar research and educational work. The reader is invited to submit ideas of how this device might be used at future eclipses.

6. Future Work

The experiment will be repeated at the April 8 total solar eclipse, although the amount of limb-darkened light will be less during the moments just before second contact and just after third contact. This is one experiment that actually works better at an annular eclipse because of the larger annular ring surrounding the eclipsed Sun. It is unknown if the device is sensitive enough to record the color of the solar corona but hopefully, we will find out next April.

For future eclipses, a light diffuser might be installed over the sensor, or the sensor may be used to measure a solar illuminated screen with the sensor facing away from the Sun.

The next annular eclipse will occur on October 2, 2024, in the South Pacific, including Easter Island. Anyone who is traveling there and willing to transport and deploy the photometer is asked to contact the author.

7. Suggestions for Public Outreach

The visual effect is immediately apparent to astronomers who understand limb darkening but may seem strange to observers not familiar with this concept. Outreach efforts should be made to explain this effect before future eclipses so that inexperienced observers may look out for and appreciate the visual effect. An annular eclipse is the ideal event to observe limb darkening because there are fewer visual distractions than are present at a total solar eclipse.


The photometer was transported to Utah and deployed by Bert Pasquale of the NASA Goddard Space Flight Center Astronomy Club.

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