Optical Powers
Field of View

Teacher Page - Will it Fit on the Chip?
Activity 9b  Field of View

Standards (see Appendix A):

Unifying Concept:  Evidence, Models and Explanations, Size and Scale; Systems, Order, and Organization.

Objective: 

Students understand that the field of view is dependent upon the size of the chip used to capture the image and the degree to which the image has been magnified by the telescope.  Magnification in a telescope/CCD system is dependent upon the focal length of the telescope.

Overview:   

When you are choosing an object to image one of the things you want to know is how big it is in relationship to your imaging system.   If an object is very small you may want to use a telescope with a longer focal length that produces a larger image. If the object is very small compared with the field of view available from your telescope/CCD system, you are likely to be dissatisfied with the low resolution of the image.  In most cases however, you don’t want to choose an object that is so large it no longer fits on the chip or one that has been magnified beyond the limits of your chip. The ability to calculate and compare the target with the available recording space is an important one in astronomy imaging.

Students build an understanding or field of view by analyzing three sets of images. The first involve changing just the focal length of the telescopes, the second involves changing both the focal lengths and the pixel sizes. The third involves changing just the size of the pixel array. Each of these scenarios affects the field of view.

Among the challenges of this activity is the importance of using the same units of measure in the formulas and being able to convert from one unit to another. References are provided for the telescopes and CCD cameras with the dimensions reported in a variety of units

Background:

A pixel is just one of an array of light capturing surfaces that make up the CCD chip.  The size of the entire chip is defined as its dimensions in pixels and millimeters.  When you are determining how much of the sky will fit on your CCD chip, you need to know how big this surface is as well as how much the sky has been magnified by your telescope. 

In the previous activity, we learned to calculate pixel scale which uses the actual size of the pixel and the focal length of the telescope to determine how much of the sky is imaged by each pixel.  The same method is use to determine field of view except the largest chip dimension is substituted for the pixel size.  Everything else remains the same.

Formulas for Determining Pixel Scale

Pixel Scale = 3438 arc minutes X pixel size / focal length
or
Pixel Scale = 206,265 arc seconds X pixel size / focal length

Steps for calculating field of view:

  1. Access “Image Info” under “Data Tools." Astronomers refer to this information as the 'FITS Header'.
  2. Note the CCD camera used to record the image and the focal length of the telescope. It is usually found under INSTRUME in Image Info.
 
  1. Then look up the number of pixels on each axis of the image.  You find this in Image Info at the top, under NAXIS = 1 for the X axis, and NAXIS = 2 for the Y axis.  CCD Reference is provided.  However, since images are often cropped or binned, you need to check in the Image Info window for each image. 

               
  2. Next multiply the number of pixels for each axis by the pixel size to get the pixel array dimension for the image.

    Pixel Array Dimension = Number of Pixels x Pixel Size

    Because the CCD chip is a grid of pixels, the field of view uses the same formula as the one used to calculated pixel scale only instead of pixel size, you use the measurements for the dimensions of the pixel array.  If the pixel array is rectangular you must calculate the size for each axis.   (If the array is square, your work is easier!)

  3. One variable in the formula is the focal length of the telescope; focal length and pixel array dimensions must be in the same units.  To determine the focal length of the telescopes, check the Image Info of the image file to find the focal length of the specific telescope.  Then go to the reference sheets.  Telescope Specs is a reference sheet on telescopes used to take the images for Optical Powers.  Use this sheet in combination with the data found in Image Info.  Also, the reference page, Microns and More should help with converting units.
           

    Formulas for Determining Field of View

    Field of View = 3438 arc minutes X pixel array dimension / focal length
    or
    Field of View = 206,265 arc seconds X pixel array dimension / focal length

     

  4. Use the formula above to calculate the angular size of the pixel array  in arcminutes.  Arcminutes is the more practical unit for field of view.  You may also choose to calculate in arcseconds; but this is a better unit for pixel scale.  Refer to Teacher Page 9a Pixel Scale for more information about how this formula is derived. 
Time:  15 minutes for introduction
            50 minutes to complete the activity

Directions:

  1. Having worked through Activity 9a, students should be comfortable with the formula for calculating pixel scale.  Before they begin this activity review this formula and the changes that were made so that it now describes field of view.  The diagram on page 2 of the Student Page should be helpful. Instead of determining the amount of sky captured by one pixel, we are now looking at the entire chip.
  2. You may choose to do the introduction together in class to ensure that students realize that each field of view can have its own advantages and that when comparing two images the magnification and field of view are not always obvious.  Making accurate comparisons between images in not possible without a little calculating.
  3. Distribute the CCD Reference Page. They only number they will need to complete the formula is the chip dimensions in millimeters.  The rest of the information is provided for comparison.  The SBIG-ST9 and Apogee Ap7p are particularly interesting because they 512 x 512 pixels however the Apogee chip is significantly larger because the individual pixels are larger. 
  4. Students should be able to work through the activity on their own.  Watch for common mistakes like not using the same units when doing the field of view calculation or using the wrong dimension. 

CCD Reference

Note:  Images are often cropped or trimmed.  To find out the actual number of pixels in the image array, check the image fits header (Image Info in HOU-IP) under NAXIS = 1 for the X axis, and NAXIS = 2 for the Y axis. 

Apogee AP7p CCD
Pixel Array: 512 x 512 pixels
Array Dimensions: 12.3 mm x 12.3 mm
Pixel Dimensions: 24 micron square

SBIG ST7 CCD
Pixel Array: 765 x 510 Pixels
Array Dimensions: 6.9 mm x 4.6 mm
Pixel Dimensions: 9 micron square
Pixel Binning Options:
   2x2; yielding 18 micron pixels, 382 x 255 array in pixels
   3x3; yielding 27 micron pixels, 255 x 170 array in pixels

SBIG ST8e CCD
Pixel Array: 1530 x 1020 Pixels
Array Dimensions: 13.8 mm x 9.8 mm
Pixel Dimensions: 9 micron square
Pixel Binning Options:
   2x2; yielding 18 micron pixels, 765 x 510 array in pixels
   3x3; yielding 27 micron pixels, 510 x 340 array in pixels

SBIG ST9e CCD
Pixel Array: 512 x 512 Pixels
Array Dimensions: 10.2 mm x 10.2 mm
Pixel Dimensions: 20 micron square

Evaluation/Assessment:

Through this activity students discover:

They should be able to discuss the Conclusions questions with their classmates and come to a consensus in agreement with the above statements. 

After completing this activity students should be able to successfully choose an appropriate object to observe with any telescope / CCD system for which they have the relevant information.  They should also be able to choose the appropriate telescope for an observing project. 

Listed below are Internet sites which describe the angular size of different astronomical targets.  Many books and websites can provide ideas for interesting targets but often do not list their angular sizes.

You might suggest to students to plan an observing project, researching available telescopes such as those used in the HOU Request System .  Please refer to the Reference Page for Telescopes.  Or, students may wish to plan the 'imaginary' purchase of a telescope, CCD camera, etc. to match an proposed observing project.   

Web Resources that Include Angular Size for Astronomical Objects

http://www.ngcic.com/oblstgen.htm

http://www.virtualcolony.com/sac/

Web Resource for Telescope Dealers

http://dmoz.org/Science/Astronomy/Business/Telescopes,_Binoculars_and_Accessories/Dealers/

List of telescope retailer links or type “telescope dealers” into your favorite search engine

Web Resources for Definitions and Measurement Conversions

Astronomical Glossary
http://nedwww.ipac.caltech.edu/level5/Glossary/Glossary_index.html

Discovery School - Metric and English Systems
http://school.discovery.com/homeworkhelp/webmath/metric.html

World Wide Metric
http://www.worldwidemetric.com/metcal.htm

Washington State Metric Conversion Factors
http://www.wsdot.wa.gov/Metrics/factors.htm

Science Made Simple - Metric Conversions
http://www.sciencemadesimple.com/conversions.html