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| A Venus Transit Illusion Photoshop Simulation of the Black Drop Effect |
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| I watched the June 8, 2004 transit of Venus from the parking lot of my
daughter's middle school, a location with a good view of the sky near the eastern horizon.
One of the things I looked for, but didn't see, was the so-called black drop effect, a
distortion of the planet's silhouette as it gets close to the edge of the Sun's disk. This
effect had frustrated attempts during previous transits to record the times of second and
third contact with enough precision to be scientifically useful. Prior to June 8, no one
now alive had seen a Venus transit, so there was some uncertainty about the cause of the
black drop effect. Afterward, that situation hadn't changed much, because most people
didn't see the effect this time around. The following Photoshop simulation, suggested by a
discussion on the astronomy newsgroups soon after the transit, seems to support a fairly
simple explanation, however. |
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Photoshop's Gaussian blur is a filter function that replaces each pixel with a weighted sum of the pixel and its neighbors. The weight is a function of pixel distance, one of a family of so-called Gaussian filter functions commonly used in computer graphics. The radius scales the support, or width, of the function, and this sets the size of the pixel neighborhood. The contrast adjustment performs a scale operation on the intensities. In Photoshop,
where i is the intensity in the range [0, 1], a is the average intensity of the image, and c is the contrast setting divided by 100, so that it's in the range [-1, 1). When contrast is increased, intensities less than a get smaller and those greater than a get bigger, and anything that falls off the ends is clamped to 0 or 1. The gamma adjustment raises the pixel intensity to a power, making the mapping from intensity number to pixel brightness non-linear. On the Adjust Levels dialog in Photoshop, where you set the gamma, you can also scale the intensities by setting the black and white points (the first and third numbers). With suitable choices for these numbers, the effect is exactly equivalent to contrast adjustment. Relating this to physical effects, the Gaussian filter simulates a point spread function (PSF), the gamma simulates the non-linear response of a sensor, and the contrast adjustment simulates a sensor with inadequate dynamic range. It appears that the PSF and basic components of sensor response can account for the black drop effect. I'd expect limb darkening to make a contribution too, but I didn't need to simulate it in order to see the effect. On the morning of the transit, I brought both of my telescopes to the middle school. I used the Thousand Oaks glass filter on the Dob and Baader film on the TV85. I'd stayed up late the previous evening making the TV85 filter cell out of posterboard, and it was worth the effort. The TV85 and Baader film produced views with much better detail and contrast. For more about the transit, see NASA's Venus transit website and Fred Espenak's visibility and timing calculations. |
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