How do digital detectors work?


Here we will engage in the use of virtual detectors to learn how the apparent brightness of stars is actually measured and what the limitations of those measurements are. The term apparent brightness means the amount of energy in that a detector receives on the earth from a distant star. This is also known as the energy flux or just flux. Flux measures the amount of energy that is incident upon one square centimeter of detector area per second. To help better understand this concept we will make use of the CCD simulator JAVA applet. A snapshot of the applet interface is shown below:


The features of this applet are:

  1. Exposure time slider: In this example the exposure time was 80 seconds. The green box is placed around the star and the red box is placed on the image background (anywhere).

  2. Clicking the measure button will allow a "measurement" to be made. Each time you adjust the exposure time you then need to click on measure to re-run the simulator.

  3. A green and a red box. The size of each box is specified by typing a number in the Sample Size window. In this case, the box size is 20x20 pixels (which is what we will be using). Note  to  make an initial  box,   place the cursor on the gray background and use the left mouse button to draw a square. Then change the size of the square to 20x20

  4. The red and green readout boxes show the total number of "counts" (think of these as photons) in the respective red and green boxes. In this example the green box is placed over a star, and the red box is placed over the "background".

  5. To move the green box to another star, grab it with the mouse button by putting the pointer INSIDE the box.

    In this example, the mean count in the green box is 2260, those counts include the background counts since the star sits on the background level of the detector which is determined by the brightness of the night sky at the time of the observation. In this case, that background level has a mean count of 1999 for this 80 second exposure. To obtain the true brightness of the star, therefore, you have to subtract out the background. This can be easily seen as follows:

    Red Box: = counts in background
    Green Box: = counts in background + counts in star
    Green - Red: (counts in background + counts in star) - (counts in background) = counts in star.

  6. So the actual brightness of the star is then 2260 - 1999 = 261 counts.


Now we will apply this procedure to 5 different cases below. In all five cases, the detector is "imaging" the same field of stars so in each case there are 8 stars on the detector (the same 8 stars that are shown above). But not all cases will detect all 8 stars or even Star A. All detectors will record star B. You should think about what aspects of the various virtual observations are precluding detection of the fainter stars as you can also learn, increasing the exposure time still won't cause star A to be detected in most cases. We will go through the detector cases one by one and focus our attention on measuring star 6 for each detector case.

Each one of the 5 cases below represents a different combination of observing conditions. The goal here is to see what kind of observing conditions adversely affect our ability to detect faint stars. Note that the first case (Case 1), which is the best and simulates data taken with the Hubble Space Telescope, shows 8 distinct stars. None of the other cases will show all 8 stars and you should try to think about what combination of detector + observing conditions which is simulated precludes the detection of the fainter stars.


Observations with the Hubble have two primary advantages over those from the ground:

  • Because you're not observing through the aberration effects of the atmosphere, the image size on the detector is smaller. Most of the light from a star is in just one pixel and not spread out over many pixels. Therefore, pay attention to how big the star images are in the following cases.

  • The background is darker: For a given exposure time, less counts will appear in the red (background box). Clearly in the case where the background is zero, it is not necessary to subtract out the background to measure the true brightness of the star.


So go ahead and run the following 5 simulations and measure the brightness of star 6. Pay attention to issues of image size and background level. For instance, some of these simulations may represent observations taking during significant moonlight. Others may represent cases where atmospheric smearing is particularly large. The point of this exercise is to show that your ability to detect and accurately measure the flux/apparent brightness of Star 6 depends upon your observing conditions and the quality of your detector.


Case 1 (80 seconds exposure)

Case 2 (20 seconds exposure)

Case 3 (20 seconds exposure)

Case 4 (20 seconds exposure)

Case 5 (20 seconds exposure)


Flux and Color 



We have just one through measuring one attribute of a star, as viewed from the earth.When you observe a star, whether with your naked eye or a modern digital detector, there are really only two attributes that you can measure for that star:

 

 Image Courtesy of NASA   

  1. Its apparent brightness. This is basically the amount of energy that the star deposits on a detector, whether its your eyeball or some pixel in a CCD detector. The reason you shouldn't look directly at the sun is not because the sun is "too bright" but rather the amount of energy received by your eye is very harmful to it.

  2. Its apparent color. Even with your naked eye you can see that some stars are blue while others are red. Some of this color diversity is seen in the image to the left.

  3. We will later learn that blue stars are hot (and usually young), with relatively short lifetimes and red stars are cool (usually old) and have long lifetimes. For now, however, all we care about is that stars do come in different colors and we can detect those colors differences quite easily (which will be shown in another simulation).