Step EE-1, Detect the star locations in a photograph

It seems easy to locate stars in an astrophotograph: they are the bright dots.

I am recording images of the sky with my Canon EOS 60Da. It has a resolution of 5184 x 3456 pixels (after demosaic) in each of red, green and blue color channels. This is a wonderfully high resolution that exceeds the resolution of the lens and the atmosphere through which it is seeing. A “pinpoint” star is actually around 10 pixels in diameter, more if it is really bright.

And the background is not black. There is light pollution, and when the moon (or eclipsed sun) is near, there is skyglow, and there is always the background noise of the detector. All of these add up and make it more difficult to find the stars, especially if they are dim.

Here is my strategy to detect them, and then to measure their exact sub-pixel positions.

  1. Establish the local average and local variation of the background sky. This tells me what the average light level is, and the amount of random noise.
  2. Set a threshold above that noise level and detect everything that exceeds it. These will include stars and “hot pixels” (detector noise).
  3. Eliminate the isolated single pixels; they are the sensor hot pixels.
  4. For what remains, these are the “cores” of the star images. Expand the neighborhood around each. Take the weighted average of those pixels and find their geometric center. This is the star’s location in the image.

I wrote a Matlab script to do this, and applied it to various test images I have taken of the eclipse field of stars. It yields (subpixel image) coordinates of the stars it identifies. These are used as inputs to the next step.

starRegionsCompositeChannelsStars detected in each of the three color channels (RGB) for the eclipse field. Not all stars are seen in all channels, and noise creates spurious stars in each channel. This exposure is 1 second at ISO 100, the best signal to noise setting on the camera.

 

starRegionsCommonChannelsThe detected stars found in all three color channels. The double star to the left is Regulus (alpha Leo) and its companion.

 

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Measuring star deflections, step by step for the Eddington Experiment.

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From “Measuring Starlight Deflection during the 2017 Eclipse: Repeating the Experiment that made Einstein Famous,” Donald Bruns

Even with high quality equipment, it will be challenging to make measurements of the tiny deflections expected. There are some helpful references available on the web; some are encouraging, others are scary. Here are a few:

Measuring Starlight Deflection during the 2017 Eclipse: Repeating the Experiment that made Einstein Famous:

http://www.skyandtelescope.com/wp-content/uploads/Bruns-SAS2016-paper-v7.pdf
An update from Bruns:
my-do-it-yourself-relativity-test

http://deluxeeclipsetours.com/uncategorized/modern-eddington-experiment

https://eclipse2017.nasa.gov/testing-general-relativity

After reviewing them, is not clear to me whether my equipment and technical abilities will be able to find the small signal in a big noisy field, but I will enjoy the attempt.

Here is my star deflection measurement outline. It comprises distinct image and data processing stages, which I demark by the following labels, and will subsequently refer to:

EE-1.      Detect star locations in the “before” and “during” images. These will be pixel locations relative to the image origin (upper left corner).

EE-2.      Transform the image into a standard orientation where the sun is at the exact center, and two reference stars are at the correct relative angles to it. Do this for both before and during images.

EE-3.      Solve the “rigid point set registration” problem that best aligns the stars between the two images. Do not allow scaling, only translation and rotation.

EE-4.      Measure the radial distance from the (sun’s) center for each of the stars in the field and compare their relative values. They are expected to fall on a 1/R curve and at a value that matches Einstein’s predictions. The differences will be small, a pixel or less.

 

These all sound quite doable, but of course there are details. I will describe some of them for each step in what follows.  If all goes well, perhaps I will end up with a chart like Eddington’s:

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A plan for 2017, but first, an introduction to celestial coordinates

 

RA_Dec

Astrometry is the term used for measuring the positions of the stars. It has a long history, dating from pre-telescope times, and which has introduced units that may seem archaic, but persist to this day (making them seem both arcane and archaic). Because of the Earth’s rotation, just like the sun, stars rise in the east and set in the west. The angular position in the sky depends on how many hours it has been ascending since “star-rise”.   If we pick one point in the sky as a reference, we can count the hours of ascension the star has traveled from that reference point: its “right ascension”. Right ascension (RA) is measured in hours, minutes and seconds, but is easily converted into its sky angle (24 hours equals 360 degrees).

I think of right ascension as the “horizontal” position in the sky (from east to west). The vertical coordinate, declination, is more conventional: it is the north-south angle from the Earth’s equator. These two numbers, right ascension and declination, define a star’s position in the sky.

Before photography, astrometry was conducted by aiming a fixed telescope at a specific declination angle, and the observer would watch the stars drifting through the field of view. When a target star appeared, the observer would mark the time at which it crossed the center of the view. This would be its right ascension, hence the units of time rather than angle.

When photographic emulsions became sensitive enough, the star field could be recorded and then the positions measured from the photographic plate. But because the Earth is rotating, the stars moved during the exposure, blurring their positions. This required that telescopes be equipped with “clock drives” so that they could track the star’s motion across the sky during the length of the exposure. This was the (mechanical, weight-powered) mechanism employed in Eddington’s expedition to track the sun and stars during his exposures, which lasted from 2 to 20 seconds.

As I contemplate the modern reconstruction of this experiment, I have the advantage of telescope mounts with motorized clock drives. I need only to align them with the Earth’s polar axis, and the battery-powered motors will do the rest. I also have the advantage of digital image sensors, but this comes with some tradeoffs as I hope to explain later.

The part of this experiment that will be challenging is to detect the background stars through the sun’s corona and any residual sky brightness. Eddington had the advantage of relatively bright stars, and a long, deep, period of totality. The stars we have available are at least 5 times dimmer, and totality will be two minutes, not six.

In anticipation, I have made plans to record the stars in the sun’s future gravitational neighborhood during the eclipse, and to compare them to the same field without the sun. There are two challenges. One is the practical ability to detect the starlight above the ambient light background of the sky and corona of the eclipse. The second is the technical ability to compare images taken before and during the eclipse, in order to measure the stellar deflections to subpixel accuracy.

I will outline the technical plan first, assuming that the stars will be successfully recorded on eclipse day. The issue of how to best detect them will follow.

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The “Modern Eddington Experiment”

0*K_tYN4NbxjACv4RGImages credit: New York Times, 10 November 1919 (L); Illustrated London News, 22 November 1919 (R).

 

Notes and comments on reproducing a famous historical event.

Most people today do not know the reference to Sir Arthur Eddington, but he is responsible for making Albert Einstein a household name. In 1919, the English physicist took on an experiment that would test Einstein’s theory of gravity, general relativity, an abstract and mathematically beautiful explanation of space and time that few people at the time fully understood.

The prevailing theory of gravitation was Isaac Newton’s, one that worked to great success in explaining nearly all the motions of the planets. Einstein’s theory was a refinement that would show only tiny differences. But it is important to get this right; modern GPS navigation would not otherwise work.

Both theories predicted that light would be deflected by gravity. The light from a star positioned near the sun’s edge would be bent, like a mirage, to an apparent position slightly shifted from where it would normally be. But Einstein’s theory predicted the deflection to be twice that of Newton’s.

20151128_STC969

It is impossible to see such stars while looking at the sun because, well, it is daytime. Even if you block the direct view of the sun, the scattered skylight washes out all but the very brightest of stars and planets. During a total solar eclipse however, the moon’s shadow makes a hole in the sky and the stars become visible.

Eddington’s experiment then, was to photographically record the nearby stars during the eclipse and measure the apparent deflections from their true positions. He mounted an expedition to a small island off the coast of Africa for the eclipse of May 29, 1919, where he encountered the usual problems that astronomers face: bad weather. It rained in the morning, and clouds obscured the view. They had thinned somewhat by the time of the eclipse, and his team forged ahead and made sixteen exposures on various photographic emulsions on 8”x10” glass plates.

It is fascinating to read the account of obtaining these photographs (as reported in the Philosophical Transactions of the Royal Society of London). Totality for this eclipse was long: six minutes, which allowed the manipulation of the large plates to be placed in position in the telescope, the large refractor from Oxford that had been dismantled, packed and transported. It was stopped down to 8” in order to use the best part of the lens. The clock drive was driven by a weight, and a pit was dug “deep enough to allow a run of 36 minutes without rewinding.”

All but two of the plates failed to show measurable stars, mostly due to the cloud cover. But that was enough. Combined with the results from a sister expedition to Brasil, Eddington’s analysis showed that the observed deflections were best explained by Einstein’s theory. These results were reported later that year, and the world found it fascinating. Einstein, previously known and respected only in a select group of theoretical physicists, became a celebrity.

Eddington made these measurements nearly a hundred years ago. Although he suffered poor weather, he had many things going for him. A long duration eclipse, and a collection of bright stars in the near field of the sun, made it possible using early 20th century technology to make a precision measurement. He recognized this, and at the end of the report wrote: “The unusually favourable conditions of the 1919 eclipse will not recur, and it will be necessary to photograph fainter stars, and these will probably be at greater distance from the sun.”

Well, we are a hundred years on from that groundbreaking experiment. One would think that modern optics and photographic equipment would make this an easy exercise. And indeed, it has become a goal for amateur astronomers. The Astronomical League, an umbrella organization of local amateur astronomy clubs has offered a special observing award to those amateurs that can detect the deflection of starlight during the eclipse of 2017.

But even with the advantages of a century of technological advance, this is a difficult measurement to make. Yes, we don’t have to worry about how long the clock drive will run before we need to reset the weights, and our optics are better, and the photographic emulsions have been replaced by digital sensors, but the measurement still involves finding stellar deflections that are smaller than a pixel!

My exploration into this project has uncovered some interesting details, which I will share in the following blog entries.  They start with a general introduction of celestial coordinates, and an outline of my plan, but then might become somewhat tedious as I devolve into some of the image processing and mathematical details.  Much of it may be of little interest except maybe to other Eddington experimenters, but if you find it useful in some way, or wish to make contributions, feel free to add commentary.

Here are some useful entry points:

Intro to celestial coordinates 

The overall plan to measure star deflections

 

 

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What, me blog? Part deux.

I have made an earlier venture into blogging, but found that I did not have the time, or the compulsive urge, to compose and promulgate the ideas that pass by me in my day-to-day experiences.

But in recent months there has been a renewed desire to share some of the experiences, plans, projects, and opinions I have with anyone who might find them interesting or who might contribute to their evolution into more than just the musings and interests of a curious person.

Spontaneous emission is the process where an atom or molecule, previously activated to a high energy level, returns to its natural state and emits a photon.  The photon and its energy is then returned and released to the universe.

It cannot be predicted when an atom will host such an event; it is spontaneous.  And so are the entries in this blog.  But each entry will be the release of creative energy being delivered to the cyber universe that we all now explore.  I hope you find them of interest.

Torr Oslo

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