Optical Powers
Resolution

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Activity 8 Resolution

Experiment:
Experiment with aperture by taking images with various size masks over the 24-inch telescope. Analyze the results.

Activities:  Resolution refers to how much detail you are able to see in an image.  It is defined as the ability to distinguish two objects from one another.  In these activities you will learn to measure how sharp the image is using a measurement called “full width at half maximum” (FWHM).  You will use the slice tool in HOU-IP; you will adjust the options for plotting the resulting graph of the star's profile. You will compare images taken with different aperture masks and with adaptive optics systems on or off.

Introduction to FWHM Analysis

Activity 8a: Resolution of Ring Nebula Images at three different telescope apertures.

Activity 8b: Resolution of Double Double Star at different telescope apertures.

Activity 8c: Resolution with Adaptive Optics on and off.

Image Sets: 8 Resolution

Introduction: FWHM

Full Width Half Max (FWHM) is a measure astronomers use to analyze the resolution of their images. Under ideal conditions (no atmosphere and perfect telescope optics) all the light from a star should fall into a single pixel.  FWHM measures how much the light is spread out at half the maximum counts for the star.

Introduction: Practice showing and quantifying FWHM with HOU-IP software.

 

  1. Open stars-fwhm.fts

  2.  Draw a short slice line through the center of a star on the image. The Slice Graph will pop up.

  3. Choose Options, Axes Setup.

  4. Adjust the Slice graph X axis. If the slice line is too long the numbers crowd together on the graph.  However one can limit the numbers shown on the X axis under the Options menu, Axes Setup.  Look at the Min and Max values for the X Axis.  Change the values to fit the part of the slice line which includes the star profile.  See example below of Slice graph for stars-fwhm.fts. Notice the X axis starts at 7 instead of 0, with the last value labeled as 19, though the slice extended beyond 19 in the original slice graph. 

  5. Change the tick spacing on the X Axis to 1.

  6. Adjust the Slice graph Y Axis.  Show the half-maximum and the peak line.    Look at the Min and Max values for the Y axis.  If Min is zero, just divide the Max value by two and enter the divided value in the tick spacing box.  If Min is not zero, then first subtract the value of Min from Max and then divide by two to determine the value for Tick spacing. Then look at the Max value for Y.  If the Max is an even number, add one to the value.  (This makes the peak line visible on the graph.)

  7. Quantify FWHM. Count the distance in pixels across the graph at the half maximum point.  This distance is the number you record for FWHM. If you want to change the number to an angular size, multiply the number of pixels times the pixel scale in arcseconds.  See Activity 9 for more information on pixel scale.

Difference between min and max is the same as max in this case.  But sometimes the min value is not zero.  See an example below for M57-2in_n90s.fts image.

Activity 8a – Calculating FWHM with images of the Ring Nebula, M57
Images were taken with the 2 inch, 8 inch, and 24 inch aperture openings on the Univ. of Chicago's 24 inch telescope. 

  1. Using you HOU IP software, open the three images of the ring nebula (m57).

  1. Describe the images.

 

 

  1. Make a horizontal slice through the bright star to the left (east) of the ring nebula attempting to go through the center of the same bright star in each image.  Each slice graph should look slightly different.  Describe/sketch the graphs.





  2. In order to calculate FWHM, you must first adjust the appearance of the graphs to make them easier to read.  Here is an example for the first graph of m57-2in_90s.fts.  Make sure you are working with the window for the 2 inch aperture by clicking on the graph you made for slice.  When a new display of the plot appears, use the mouse to grab the bottom right corner and stretch out the plot to see the numbers better.  Do this for each of the slice you made on each image.

Quantify the slice graph.  These instructions are similar to the ones in the introduction but are worded slightly differently and include adjusting the style to include plot points and adjusting for a non-zero Y Min value.

Choose Options, Style.

  1. Go to Options, Style on the slice graph.
  2. Check plot the points, then click on Circle.

Options, Axes Setup.

  1. Next go back to options, Axes Setup.
  2. Click the box for grids for both the X and Y axes.
  3. Change the tick marks to 1 for the X axis.
  4. For the Y axes, change the value of the tick marks to half the difference between the minimum and the maximum value.
  5. Finally, add 1 to the maximum value if it is an even number.  Click OK.
  6. When the new display of the plot appears, use the mouse to grab the bottom right corner and stretch out the plot to see the numbers better.  You can shorten the display by changing the Y axis to show only the pixels of interest in the Y Axis setup.
  7. Count the pixels at the midpoint.  The FWHM for the graph below would be the number of pixels crossed at half max, or about 5.75 pixels.  (For the Yerkes 24 inch telescope with the Apogee APy7p CCD, each pixel is 0.62 arcseconds.   So, the in arcseconds, the FWHM is 3.65  arcseconds.)
  1. You should now be able to easily count the number of pixels across the graph at half the height of the peak.  This is the measurement of full width at half max (FWHM).  Record your values below. To calculate the FWHM in arcseconds, multiply by the pixel scale.  For the images from the 24 inch telescope taken with the Apogee AP7p CCD, the pixel scale is 0.62 arcseconds per pixel. 
FWHM of star slice on images of M57 for apertures 2, 6, and 24 inches, respectively:
    1. FWHM in pixels ______________  FWHM in arcseconds _______________
    2. FWHM in pixels ______________  FWHM in arcseconds _______________
    3. FWHM in pixels ______________  FWHM in arcseconds _______________
  1. If you are able, print one of your graphs.  Print Screen then open in a Paint program.  From the Paint program you can label your graph and print it.  

 

Activity 8b: The Double Double!

  1. a.  Open double-double.fts.  This is the star, Epsilon Lyrae in Lyra.  It is a popular multiple star system to look at with telescopes for backyard astronomers. 

b.  Open the four images of Epsilon Lyrae, corresponding to the 2, 4, 8 and 24 inch apertures.  In order to adjust the display so you can see the double stars, add 2 zeros to the Max value on the tool bar and click Redraw. 

  1. You might prefer to use the Zoom Box function on either upper or lower object. Be consistent and zoom on the same object in each image. Don’t make the Zoom Box too small.  It needs to be between 50 and 100 pixels across.  You can analyze either the northern or southern set of stars. 

Click on the image and drag on a slant to create a Zoom Box.

 
  1. Compare the images.  What differences do you note for the different telescope apertures?

 

 

 

  1. Make a slice through the center of both stars in each Zoom Box.  It is easier to compare graphs if you keep the length of each slice nearly the same.

                       

  1. Compare and contrast the information available from the Zoom Box to the information available from the slice graph.  What do you notice about the shape of the graphs as compared to the image it was produced from?

 

 

 

  1. What conclusions if any can you draw from comparing the slice graphs?

 

 

  1. Using what you learned in Part I of this activity, calculate the FWHM of each image.
    1.  2 inch
    2.  4 inch
    3.  8 inch
    4. 24 inch
  2. Make a graph of your data.
  3. Create a best fit line through your data.
  4. Compare your results with other groups.

 

  1. A telescope's resolution is limited by the aperture and the wavelength of light.

    In 1835 George Bittle Airy determined that a mathematical relationship exists between telescope aperture and resolution.  The diffraction limit of a telescope is explained on a webpage of the Center for Adaptive Optics: http://cfao.ucolick.org/ao/   Following is an excerpt from the CfAO web page. 

    Under ideal circumstances, the resolution of an optical system is limited by the diffraction of light waves. This so-called "diffraction limit" is generally described by the following angle (in radians) calculated using the light's wavelength and optical system's pupil diameter:

    where the angle is given in radians. Thus, the fully-dilated human eye should be able to separate objects as close as 0.3 arcmin in visible light, and the Keck Telescope (10-m) should be able to resolve objects as close as 0.013 arcsec.

    a.  Describe the resolution of an image (clearness, ability to see detail) as compared to the FWHM plot of any star in the image?

    b.  Assuming the filter and therefore the wavelength remain the same, if you increase D (diameter of the telescope) in the equation above, what happens to the angle of resolution? 

    c.  The smaller the angle of resolution, the more easily it is to 'see' separation between objects. Was this true for your analysis of the Epsilon Lyrae images taken with different diameter apertures?  Provide evidence based on your analysis of the images with FWHM plots.



    A telescope's resolution is also limited by atmospheric 'seeing'.  Notice the image resolution of the double star in Epsilon Lyrae's southern component at varying telescope apertures.

     
    In Earth based telescope systems, starlight travels through our atmosphere before it reaches the telescope.  Our turbulent atmosphere limits the resolution of our telescopes.  The phenomenon is referred to as 'seeing' by astronomers.  Notice how the separation of the stars of the images improves from the 2 inch to the 4 inch to the 6 inch aperture.  However, after 6 inches, the resolution of the image does not change very much.  It can even get worse!

    This is because after a telescope's aperture is about 6 inches, the resolution is more affected by the Earth's atmosphere than by the diameter of the telescope's aperture.

    These effects are due to properties of light and characteristics of our atmosphere.  Astronomers and engineers working on adaptive optics study these effects and design systems to adjust telescope optics in response to changing atmospheric conditions. 

     

Activity 8c: Adaptive Optics ON/OFF

A large part of the success of the Hubble Space Telescope (HST) is due to the fact that it is located in space, orbiting Earth above the turbulent effect of Earth’s atmosphere.  But, space-based telescopes are  are expensive to build and difficult to maintain, and telescope time on HST is limited.  Astronomers are seeking ways to create images with high resolution from Earth based telescopes.  A new technology known as Adaptive Optics (AO) is being developed.  AO systems respond to changes in the atmosphere.  Some systems are designed to make continuous small adjustments to the shape of a telescope’s mirror which cancel out the effects of atmospheric turbulence.

Learn more at the website of the National Science Foundation's Center for Adaptive Optics (CfAO). http://cfao.ucolick.org/ao/.

 

  1. Examine two images that were taken by an astronomer, Rhodri Evans, at Mt. Wilson Observatory.  One image was taken with the AO system on; the other was taken with the AO system off.  With the HOU-IP software, open 1999111964.fts and 1999111965.fts.

 

  1. Which image was taken with the adaptive optics system turned off?  How do you know?  Quantitatively analyze the images with a slice plots, with the options selected to show FWHM.  Record your findings.

 

  1. Adaptive optics allows for image quality that rivals HST on telescopes with much larger apertures.   What advantages would a larger aperture telescope, such as the Keck in Hawaii, with a 10 meter primary mirror, have over the HST in space, with a 2.4 meter mirror?