Problem – When planning an observing session, we want to predict if the image of the object observed will fit on the CCD chip!
The amount of the sky imaged is called field of view or FOV for short. You will learn to calculate field of view. You will discover how an image is affected by changing pixel size, pixel array of the CCD, and focal length of the telescope.
There are three sets of images to investigate. Look up information in the Image Info for each image to determine the pixel size, pixel array of the CCD, and focal length of the telescope. Describe, then analyze, what happens to the image in each system scenario. Calculate the field of view for each image.
Make yourself a FOV Data Analysis Chart or use the one provided. For each image you should record: Pixel Array Dimensions; Focal Length Dimensions; and Field of View. The dimensions should be in the same unit so they cancel out in the calculation.
Open your HOU-IP software. Locate and open the first three images.
Write a sentence comparing the fields of view for these images of the Moon. Unless you are quite familiar with the features of the Moon, it is not possible to say for sure if the fields of view are the same for Moon 2 and Moon 3. What can you do to compare the fields of view for these two images? Think of a situation when you might prefer the field of view of Moon 1 over that of Moon 2.
Calculating Field of View:
Remember our light funnel and light bucket analogies: Light is collected and focused onto the CCD chip by the telescope as if it were a funnel for light. The light is then collected in the pixels of the CCD chip before being sent on to the computer to be interpreted. Because we imagine the sky to be a large sphere surrounding Earth, the amount of sky contributing light to each pixel is measured as an angle. As we learned in the last activity, we can quantify the amount of sky captured by each pixel (pixel scale) by combining the focal length of the telescope and the size of the pixel in a mathematical formula.
Formula for Determining Pixel Scale
Pixel Scale = 206,265 arcseconds X pixel size / focal length
When you are choosing targets for your telescope/CCD system you need to know how big your target is in comparison with the total surface of your system. Objects that are too large for your system will not fit and objects that are too small will not resolve well. Ideally you want to pick targets that have an angular size similar to the angular size captured by your system, the field of view.
The dimensions of the chip are rarely given in the in the Image Info for each image. However, you will find the size of the pixel array. This is listed on the lines "NAXIS1 = " and "NAXIS2 = " for the X and Y axes of the image, respectively. Since many images might be trimmed or cropped, this is the best source of information.
Multiply the number of pixels in one axis by the size of the pixels. If the chip is not square, do the same for the other axis. For the purpose of the equation you must keep all your units the same. Usually the pixel size is given in microns. Remember a micron is a micro-meter, or a millionth of a meter. So to change microns to meters, divide by 1,000,000. To change microns to centimeters, divide by 10,000. To change microns to millimeters, divide by 1,000.
Pixel Array Dimension = Number of Pixels x Pixel Size
The CCD is a grid of pixels. So, the field of view formula requires the dimension of the pixel array. If the pixel array is rectangular you must calculate for each axis. (If the array is square, your work is easier!) We use arcminutes in the formula instead of arcseconds because usually the CCD chip has many pixels. (An arcminute is 60 arcseconds.)
Formulas for Determining Field of View
Field of View = 3438 arcminutes X pixel array dimension / focal length
Calculate the field of view for each of the Moon images. Enter all your calculations on your FOV Data Analysis Chart. It is helpful to record your work. Remember the information you need is located in “Image Info” under “Data Tools”. You might have to scroll down to find the relevant information.
The following screen shot shows you some of the information you will find in Data Tools, Image Info. It is also called the .fts header. This text information is transferred with the image. NAXIS1 and NAXIS2 tell you the number of pixels in the X and Y dimensions of the image. (The CCD chip is larger than this, but this image was trimmed to 500 by 500 pixels.) After INSTRUME you will see the size of the pixels in microns.
Look up the size of the pixel array for each image and the size each pixel.
How is the field of view different for the different images. What variable do you think is responsible for the difference in the field of view between the Moon images?
Open the next two images in this set.Calculate the field of view for each of these images. Enter your calculations in on the FOV Data Analysis Chart.
Each of these images was taken with the same pixel arrays but the resulting images look very different. What accounts for this difference?
Propose a situation when either of the field of views of this galaxy might be preferred by astronomers.
Open the last two images in this set. Calculate and record the field of view for each image and record in the FOV Data Analysis Chart.
Which factor is responsible for the difference in the field of view for each of the images?
What do you notice about the magnification of the images? Adjust one of the images to match the min/max settings of the other.
Choose two stars that you can identify on both images and make a slice line between them. What are the distances between the two stars on each image? What does the result of this measuring test confirm? When might this use of the slice tool come in handy?
Field of view is affected by______________________________________________.
Increasing the size of the CCD chip ___________________________ the field of view.
Increasing the magnification _________________________________ the field of view.
Increasing focal length _______________________________________ magnification.
Increasing focal length _____________________________________ the field of view.
Larger pixels result in __________________________ field of view and chip dimension.
If your field of view is too small, what part(s) of the telescope/CCD system could you change?