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Showing posts with label photometry. Show all posts
Showing posts with label photometry. Show all posts

Friday, April 3, 2015

Binning



Binning groups pixels together which has the effect of making the group appear as a bigger single pixel as shown in figure 1 below (Templeton & Beck 2014).  Binning is done to decrease the resolution: 


So by increasing the pixel size while keeping the focal length constant, the resolution goes down.  This might seem backwards, but lower numbers imply higher resolution since less of the sky is "landing" on each pixel creating a sharper image.  The benefit of binning is that you gain better sensitivity so you can do shorter exposures (Templeton & Beck 2014).  The drawback is that you do lose some resolution so you have to be careful not to blend close by stars together if you are trying to do accurate photometry (Templeton & Beck 2014).  Another important thing to remember is that you have to redo all of your calibration frames and test the linearity for each set of bins (Templeton & Beck 2014).  In other words, a dark frame at 1x1 binning is not equivalent to a dark frame at 2x2 binning.

Figure 1.  Examples of binning (Templeton & Beck 2014)

References
Templeton, M. & Beck, S. (2014), The CCD Guide to Photometry Version 1.1, Cambridge, MA


Saturday, November 22, 2014

Swan Song


Figure 1. Henrietta Swan Leavitt (Johnson 2005)

Henrietta Swan Leavitt was born on the Fourth of July in 1868 in Lancaster Massachusetts to George Roswell Leavitt and his wife, also named Henrietta Swan (Johnson 2005). The Leavitts were a family that valued education and scholarship (Johnson 2005). George was an ordained minister and his brother, Erasmus Darwin Leavitt, was the second president of the American Society of Mechanical Engineers and played a key part in the design of the Leavitt pumping engine at the Boston Water Works’ Chestnut Hill station (Johnson 2005). The Leavitts were a middle to upper-middle class family that found themselves living in Cambridge by 1880 (Johnson 2005). Their household was crowded as Henrietta’s siblings included George, Caroline, Mira, Martha, Roswell, and Darwin (Johnson 2005). Unfortunately, Mira and Roswell both passed away at very young ages due to childhood illnesses (Johnson 2005). The Leavitt household also included their Aunt Mary, a servant girl, and right next door was their grandfather (Johnson 2005).

In 1885 the Leavitts moved to Cleveland and later that year Henrietta enrolled at Oberlin College (Johnson 2005). However, she returned to Cambridge in 1888 to study at Radcliffe (Johnson 2005). There she took classes in Latin, Greek, modern languages, mathematics, physics, and astronomy (Johnson 2005). Interestingly, she only got a B in physics but did manage an A- in astronomy (Johnson 2005). Her only C was in German (Johnson 2005). She graduated in 1892 at the age of twenty-four with the equivalent of a bachelor of arts from Harvard for a man (Johnson 2005). In 1893, she volunteered at Harvard observatory (Singh 2004). At the time, the Harvard observatory was engaged in an extensive project to catalog the brightness of every star in the sky (Johnson 2005). In charge of this effort was a young physicist from the Massachusetts Institute of Technology named Edward Charles Pickering (Singh 2004).
Figure 2. Edward Charles Pickering (Johnson 2005).

Pickering was more than happy to put someone like Henrietta to work recording the magnitudes of stars (Nelson 2008). While this type of work is now done by machines, in the nineteenth century women were employed as a cost effective means of measuring, calculating, and recording observations of the photographs taken by the observatory’s telescope (Singh 2004). These human “computers” were paid only twenty-five cents an hour for six days of work per week and afforded a month’s vacation (Nelson 2008). Another one of the women at the observatory described the workroom as a “dark and dingy place, all cluttered up and smelling strong of oil,” in reference to the oil-burning fireplaces (Johnson 2005). Nevertheless, Henrietta managed to excel in her work at the Harvard observatory. Her hearing had gradually declined since birth, so this type of work was suited for her (Singh 2004). While fastidiously examining these photographic plates in her workroom, Henrietta Swan would make an incredible discovery that enabled measurement to distances beyond our galaxy and revolutionized modern astronomy.


Figure 3. Henrietta Swan Leavitt, at work for the Harvard College Observatory, Cambridge, Massachusetts (Bartusiak 2009)

Henrietta Leavitt’s work is embodied in what is now known as Henrietta’s Law. During the time of her employment at the observatory, one of the great questions in astronomy involved the cloud-like nebulae that shined in the night sky. Were these objects nearby and part of the Milky Way or were they distant galaxies? In particular, Henrietta was studying photographic plates of the Large and Small Magellanic clouds in search of variable stars, carefully plotting the change in magnitudes of certain stars with respect to others and determining the period, or length of time between one bright phase to the next (Johnson 2005). She was a variable star fiend, later writing that she was making “an extraordinary number” of discoveries (Johnson 2005). She published her findings in the Harvard observatory’s bulletin and made an immediate impression on the astronomical community (Johnson 2005). One astronomer noted that he could not keep of with the pace of Henrietta’s new discoveries (Johnson 2005). She eventually discovered and cataloged hundreds of variable stars in the Magellanic Clouds (Johnson 2005).

Figure 4: 1-Inch Cooke Telescope used to take photographs (HARVARDweb)

Miss Leavitt continued to amass new discoveries and report them in the Harvard circular. The sheer volume of her data accumulation would have been impressive enough, but this human computer was able to see something that the professional astronomers had missed. In 1908, one of her reports included a note that simply stated, “The brighter variables have the longer periods” (Leavitt et al. 1908). In her typical humble style, she was simply trying to relay the facts and not over-interpret the data. However, the implications were immediately obvious: because the stars she was observing were all in the Magellanic Clouds, they were all about the same distance from Earth (Mitchell 1976). If the correlation she uncovered was in fact correct, a star’s absolute brightness (luminosity) could be gleaned from determining its period. Then comparing this absolute luminosity with its apparent brightness will yield the distance (Mitchell 1976). Knowing the distance would then be a major piece of the puzzle to solve the great question about nebulae and whether or not they are beyond the Milky Way galaxy. More data was needed to confirm this hypothesis.

Figure 5. The Period-Luminosity relationship observed by Henrietta Leavitt (Mitchell 1976)

Unfortunately, soon after her report was published, she fell ill and returned to stay with her parents who were now in Wisconsin (Bartusiak 2009). Since was gone for so long and because Pickering so valued her work, a box of plates was shipped to her so she could examine them while recovering (Bartusiak 2009). She finally made it back to Harvard in 1910 after a year and half absence, but almost immediately had to leave again when father passed away (Bartusiak 2009). She eventually got back to the observatory and published her latest results in the 1912 Harvard Circular. The report boldly stated, “A remarkable relation between the brightness of these variables and the length of their periods will be noticed” (Leavitt et al. 1912). In other words, brighter stars have longer periods. The stars measured are known as Cepheid variables because the first of its type was found in the constellation Cepheus (Johnson 2005). This new Cepheid yardstick (i.e., Henrietta’s law) could be used to determine the relative distances between stars (Johnson 2005). Now all that was needed was the distance to the closest star in order to calibrate this yardstick.

The technique used to measure the distance to the closest stars is known as parallax (Johnson 2005). This involves measuring the angle to a star at a certain time and then measuring it again precisely six months later when the Earth is on the other side of the Sun (Johnson 2005). Stars that are relatively close will appear to move in relation to the further away background star similar to the way one’s extended thumb appears to move in relation to background objects when one alternately blinks his eyes. Although simple in theory, this technique is difficult to implement in practice due to the enormous distances of the stars and the precision instruments required to detect their motion (Johnson 2005). After several attempts, the American astronomer Henry Norris Russell used parallax to put the distance of the Small Magellanic Cloud at 80,000 light years, a truly mind blowing number at the time (Johnson 2005). Russell wrote to his colleague Ejnar Hertzsprung, “I had not thought of making the very pretty use you make of Miss Leavitt’s discovery about the relation between period and absolute brightness. There is of course a certain element of uncertainty about this, but I think it is a legitimate hypothesis” (Johnson 2005). Thanks to Henrietta Swan Leavitt, astronomy finally had a way to measure beyond the closest stars and determine if there were objects beyond the Milky Way.

Figure 6. A typical report of new variables in the Harvard Circular (Leavitt 1913)

Unfortunately, despite her invaluable contribution, Henrietta continued to toil away in obscurity as a glorified computer. This did not deter her efforts as she continued to not only amass data, but also provide details notes about biases and uncertainties. For example, she wrote about the uncertainty in her measurements, “It is evident that, owing to the small range of the variable and the difficulty of estimating the magnitude of so bright an object, the observations are not sufficiently precise to permit a further correction to the period” (Leavitt et al. 1914). Johnson (2005) wrote, “It was work to take pride in. Ph.D.s have been awarded for less.” Astronomer Harlow Shapley admired Henrietta’s work and used it to calibrate the size of the Milky Way in order to debate the theory of “island universes.” This was the idea that the Milky Way was just one of many galaxies throughout the universe. Of Henrietta, Shapley wrote, “Her discovery of the relation of period to brightness is destined to be one of the most significant results of stellar astronomy” (Johnson 2005). After he assumed leadership of the Harvard observatory following Pickering’s death, Shapley called Henrietta, “one of the most important women ever to touch astronomy.” Tragically, Henrietta would not live long enough to see all the fruits her discovery would be bear as she passed away on December 12, 1921 (Johnson 2005).

As a consequence, it is vitally important that Henrietta Swan Leavitt’s importance to the field of astronomy be recognized. According to Johnson (2005), Henrietta Swan Leavitt’s story has “slipped through the cracks.” Perhaps this is because she never married and died young (Johnson 2005). Another reason could be her solemn Puritanical nature. In her obituary, a colleague wrote:

“Miss Leavitt inherited, in a somewhat chastened form, the stern virtues of her puritan ancestors. She took life seriously. Her sense of duty, justice and loyalty was strong. For light amusements she appeared to care little. She was a devoted member of her intimate family circle, unselfishly considerate in her friendships, steadfastly loyal to her principles, and deeply conscientious and sincere in her attachment to her religion and church.” (Johnson 2005).

Henrietta accomplished her work during a time when astronomy was decidedly dominated by males. Even the scant praise she earned was somewhat hollow as it condescendingly described women as being adept at detailed work, but affirmed that more difficult think matters were best suited for men (Johnson 2005). Despite all of this, she endured unflinchingly and led the way for refining the astronomical yardstick. Unlike some of her colleagues, Henrietta left behind little in the form of personal writings that would give some clue as to her feelings about her status in the field. Instead, she left behind a wealth of data and meticulous notes that enabled other astronomers to unlock the mysteries of the universe. Even to this day, astronomers are still refining her period-luminosity relationship, particularly the influence of metallicity (Garcίa-Varela 2013).

The h-index is a way of quantifying an individual’s research impact. According to Harzing (2007), Henrietta is credited with authorship of thirty-nine articles and has received 319 citations for an average of 8.18 citations per paper giving her an h-index of 4. For comparison, Henry McEwen was an amateur astronomer during the same time period wrote 89 papers, received 1119 citations (12.57 citations per paper), giving him a h-index of 16 (McKim 2005 & Harzing 2007). This may paint Henrietta’s contribution as low until we look at the two Harvard observatory directors whose careers she most powerfully influenced: Pickering’s h-index of 28 and Shapley’s h-index of 30 are incredibly high. It is difficult, if not impossible, to assess Henrietta Swan Leavitt’s importance using traditional metrics. She was not technically an astronomer, but rather a “skilled laborer” at the observatory (Johnson 2005). Consequently, while she did submit her data in the observatory’s bulletin, she rarely submitted in the more prestigious astronomical journals. Nevertheless, she was undoubtedly an astronomer in the purest sense of the word: she took observations and looked for underlying phenomena to predict future astronomical events. She understood that the discovery was the important thing, not the discoverer (Johnson 2005). Everyone interested in astronomy should know not only about the role Cepheid variables on the distance ladder, but also about the remarkable woman who unlocked their secret.

References

Bartusiak, M. 2009, Natural History, 118, 14-17
Burleigh, R. 2013, Look Up!, (New York: Simon & Schuster)
Garcίa-Varela et al. 2013, MNRAS, 431, 2278-2284
HARVARDweb: http://dasch.rc.fas.harvard.edu/telescopes.php accessed 29 August 2014
Harzing, A. W. 2007, http://www.harzing.com/pop.htm
Johnson, G. 2005, Miss Leavitt’s Stars, (New York: W.W. Norton & Co.)
Leavitt, H. et al. 1908, Annals of Harvard College Observatory, 60, 87-108
Leavitt, H. et al. 1912, Harvard College Observatory Circular, 173, 1-3
Leavitt, H. et al. 1913, Harvard College Observatory Circular, 179, 1-4
Leavitt, H. et al. 1914, Harvard College Observatory Circular, 186, 1-4
McKim, R. 2005, JBAA, 115, 13
Mitchell, H. 1976, The Physics Teacher, 14, 162-167
Nelson, S. 2008, Nature, 455, 36-37
Singh, S. 2004, New Scientist, 184, 54-55

Tuesday, November 11, 2014

Linearity testing

Figure 1.  CCD bucket analogy (Howell 2006)

Each pixel of a CCD sensor is like a bucket, but instead of collecting rain water, these buckets collect electrons that are generated by the incoming photons.  Just like a bucket can only hold a finite volume of water, a pixel can only collect a finite number of electrons before it "overflows."  When the bucket overflows, the measurement of  the electrons is no longer linear.  What does that mean?  Consider in the water example, a certain number of rain drops will produce a certain change in volume of the amount of water in the bucket.   This relationship holds up to the point where the bucket overflows and the incoming rain drops cannot be measured because all of the space has been taken up.  The same is true for pixels in the CCD sensor:  There is a linear response between the amount of incoming photons and the measured number of electrons per pixel up to a certain point where the relationship breaks down and the pixel "overflows" or "blooms" (see Figure 2 below).

Figure 2.  Example of blooming (AOweb)

Some types of CCD sensors have what is called an Anti-Blooming Gate (ABG) to try to minimize the effects of blooming.  However, since photometry is concerned with precise counting of the number of photons, it is better, but not absolutely necessary, to have a Non Anti Blooming Gate (NABG) to get an unadulterated measurement.  The manufacturer's CCD specifications will include the Full Well Depth of the sensor, or the expected number of electrons that can be collected before the pixels bloom.  In either case (ABG or NABG), it is best practice to actually test the camera to find out where the pixels saturate and if there is any non-linear behavior before the point of saturation.  This will enable better photometry since the "overflow" point is well established and can be avoided.

In practice, most photometry software packages do not actually output electrons, but instead use Analog to Digital Units (ADU).  ADU is simply a numerical representation of the voltage created by the electrons that accumulated in the pixel.  The ADU can be converted to electrons by multiplying by the CCD's gain, another specification given by the manufacturer.  In the case of TECMO, the SBIG ST-8XE (NABG) has a specified Full Well Depth of 100,000 electrons and a gain of 2.5 electrons per ADU.  Therefore, the pixels should bloom at approximately 100,000/2.5 = 40,000 ADU.  To test this, the telescope and CCD were pointed at a diffuse, uniform light source.  For TECMO, white sheets of paper were used to diffuse the light coming from a light bulb.  A good starting place is when a 10 second exposure yields an average ADU measurement of about 10,000.  In this example, the "brightness" was reduced by adding more sheets of paper over the telescope's aperture.  After this, the exposure time was doubled and the ADU measurement was taken again.  What was expected?  Since the exposure time was doubled, the amount of light reaching the pixels was doubled, so the initial ADU value should double as well to around 20,000.  Now another 10 seconds is added so that the exposure is 30 seconds and the ADU measurement should roughly triple.  Keep adding 10 seconds until this relationship breaks down and the ADU measurement no longer goes up because the pixels have "overflowed".  The figure below shows the results of the TECMO linearity test of its SBIG ST-8XE.

The sensor clearly saturates at just over 60,000 ADU.  However, after fitting a straight line to the data, there also appears to be some non-linear behavior before the point of saturation.  It is not entirely clear from this data exactly where the linearity ends, but a reasonable estimate is about 50,000 ADU.  This is a "deeper" full well depth than reported by the CCD manufacturer (SBIG).  However, it is probably best that their estimate is conservative.  In fact, it is smart to use the more conservative number to calculate exposure times for the targets of interest.  For example, if the goal was to expose a target until it reaches half of its full well depth (a typical practice in photometry), it would be wise to use 40,000/2 = 20,000 ADU.  When in the business of counting photons, it is always safer to err on the side of under-exposure in order to maintain the all important linear relationship between the incoming light and measured electrons.


References

1. AOweb:  http://astronomyonline.org/astrophotography/ccd.asp, accessed 11 November 2014
2. Howell, S. B. 2006, Handbook of CCD Astronomy, Cambridge University Press, UK

Saturday, November 8, 2014

Image calibration

Image calibration is simply the removal of the anomalies from the camera sensor and imperfections in the optical pathway.  When taking astronomical pictures, this helps make the image "pretty."  When doing photometry, it is essential in order to get accurate scientific data on the number of photons collected.  One of the priorities of TECMO is to generate solid calibration frames in order to increase the quality of its photometric observations.

Below is a raw picture of a star field.  Mouseover the image to see the effects of calibration:



There are 3 basic types of calibration that must be performed to achieve the intended results:

1.  Bias frame
2.  Dark frame
3.  Flat field

*   Light images are the raw images that will be taken of the astronomical objects.  These are the images that will be calibrated.

These are sometimes collectively referred to as BDF calibration.  Let's start with bias frames.  These are zero-length exposures used to uncover the small errors that cause a pixel to start at a value higher than 0 (Covington 2007).  These errors can be caused by the noise from the electronics in the set-up, including the CCD camera and interference from the computer.  Bias frames should be taken at the same temperature as the light images will be taken and with the telescope's cap on.  To create a Master Bias frame, take around 100 images and then average them together using image processing software.  The Master Bias should be replaced any time the temperature of the light frames changes or a component of the set up (i.e., computer) changes.

Master Bias.  Here is the Master Bias at 0 degrees Celsius for TECMO:



Next is dark frames.  Dark frames account for the thermal noise in the CCD chip.  This noise manifests as "hot pixels" in the image. Dark frames are also taken with the telescope cap on and at the same (or nearly the same) temperature as the light images will be taken.  It is also better to take these images in the dark to prevent any unwanted light from leaking in.  Unlike the bias frames, dark frames should be taken at the same exposure time (or longer) as the light images.  Take 30 or more dark frames and then average them to generate a Master Dark.

Master Dark.  Here is the Master Dark at 0 degrees Celsius, 60 second exposure for TECMO.  The white dots are hot pixels.  For an ideal chip that had no thermal noise, the image would be totally black:



Flat fields are the hardest calibration component to complete.  The idea is to compensate for the variations of light intensity and dust specks in the optical path (Howell 2006).  Therefore, to create a flat field, an image is take of a uniform light source so that the pixel-to-pixel variations will be recorded.  Then when a light image is taken, it can be divided by the values of this calibration image to "flatten" it.  However, the difficulty lies in finding a uniform light source.  TECMO's method is to take exposures at twilight with a white tshirt stretched across the front of the telescope aperture.  Flats must be taken for every filter that will used for light images.  Take around 20 images for each filter, average, and subtract the Master Dark to create the Master Flat.  The Master Flat should ideally be updated weekly to account for dust build up in the system.

Master flat.  Here is the Master Flat for TECMO's V filter at 0 degrees Celsius, 5 second exposure. Notice the 2 dust "doughnuts" and the dark vignetting around the edges:



Final Product:  Below is a raw image of a star field with the variable EM Cyg.  Mouseover the image to see the result of full BDF calibration.  You will notice the removal of many tiny "hot" pixels as well as the "flattening" of the dark vignetting around the edges revealing some stars that were previously hidden in the noise.


References

1. Covington, M. A. 2007, Digital SLR Astrophotography, Cambridge University Press, UK
2. Howell, S. B. 2006, Handbook of CCD Astronomy, Cambridge University Press, UK