Optical Powers
Pixel Scale

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Activity 9a Calculating Pixel Scale

Problem – Given pixel size and focal length of a telescope / CCD system, calculate the pixel scale in terms of angle of sky.   

Review:

In the activity F-Box Explorations, you moved a screen toward and away from a lens so until the image of the letter F came into focus.  You did this experimenting using three different lenses each having a different focal length.  The focal length is a very important factor in the pixel scale of a CCD camera, so let’s review:

Define focal length.

 

Make a sketch that describes angular size.

 

 

As focal length increases magnification _______________.

As focal length increases field of view ________________.

As magnification increases, field of view ______________.

 Investigate:

  1. Open your HOU – IP software.  Locate and open the images listed below.

  

  1. Each one of these images is of the moon.  Each is different.  Briefly describe what you observe by simply looking at each image. Record you observations in the data chart.

  2. Under Data Tools you will find a command for Image Info.  Click on this command.

                          

  1. The Image Info. Box gives you a lot of information.  Use this box to locate the size of the pixels on the CCD chip used to take the image and the focal length of the telescope. In the example below the type of camera used was an ST7 which has 9 micron pixels.  Remember, 9 microns is 0.009 cm.  That is small!  The focal length of the telescope is 128 cm. 

  1. For each one of the images, record the focal length and pixel size on your chart. Don’t forget to put everything in the same units.  Centimeters are the best choice.  Refer to the following information to determine the size of the pixels in centimeters for the camera used to take each image.

Apogee AP7p: Pixel Size: 24 microns = 0.000024 m = 0.0024 cm = 0.024 mm

SBIG ST7 and ST8e: Pixel Size: 9 microns = 0.000009 m = 0.0009 cm = 0.009 mm
    2x2 binning yields pixel size of 18 microns = 0.000018 m = 0.0018 cm = 0.018 mm
    3x3 binning yields pixel size of 27 microns = 0.000027 m = 0.0027 cm = 0.027 mm

SBIG ST9e: Pixel Size: 20 microns = 0.000020 m = 0.0020 cm = 0.020 mm

  1. What do you notice about focal lengths of the telescope(s) used to take these images?  


  2. What did you observe about the field of view of the images?


  3. Image 128_moon723 has an obviously larger field of view and lower magnification than the other two images but unless you are very familiar with moon features and craters, it is difficult to make the same comparison for the other two images.  This is where knowing the pixel scale is important. 
Pixel Scale is a measure of the amount of sky that fits on a pixel.  Remember that size in the sky is measured using angles.  We use the same angle measurements for pixel scale.  The amount of sky falling on each pixel will depend on how big the pixel is (pixel size) and how much the object was magnified before it got to the pixel. Since the focal length of the telescope determines magnification, we will use the measure of focal length and the pixel size together to determine the pixel scale.
  1. Use this formula to calculate the pixel scale for each of the images in this lesson.  Record you answer on the chart.

Pixel scale = 206,265 arcseconds x pixel size / focal length

 

  1. What can you now say about image 128_9rains.724 and 128_9tycho.724?  Can you think of a way that you might be able to confirm this conclusion using images taken with these two systems?

 

 

  1. Write a sentence or two that relates the pixel scale with your other observations of the images.

   

 

  1. Predict what the moon would look like if you take the Apogee camera used to capture the image 128_24moon723 and put it on a telescope with a much longer focal length.  What would happen to the pixel scale?

 


   Bigger Challenge -  Compare the pixel scale of other moon images.

There are many images in the HOU Image Archive.  You can search the archive by going to http://sunra.lbl.gov/telescope/ From there:

When the moon images in the archive pop up, you can click on the thumbnail of the image on the right to view a larger version of the image along with some of the important information about that image.  If you click “View Header – here” you will see similar information as you found under “Image Info.” 

Search the header information for “foc length” or “focallen,” and the pixel size.  You may need to look at the entry for pixel width and height to find the dimensions of the pixel.