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■A certain telescope has a 10' x 10' field of view that is re- corded using a CCD chip having 2048 x 2048 pixels. What angle on the sky corresponds to 1 pixel? What would be the di- ameter of a typical seeing disk (1" radius), in pixels?

■A certain telescope has a 10' x 10' field of view that is re- corded using a CCD chip having 2048 x 2048 pixels. What angle on the sky corresponds to 1 pixel? What would be the di- ameter of a typical seeing disk (1" radius), in pixels?

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## Recording Telescopic Observations: Pixel and Field of View Correlations A certain telescope has a \(10' \times 10'\) field of view that is recorded using a CCD chip having \(2048 \times 2048\) pixels. ### Problem Statement: 1. What angle on the sky corresponds to 1 pixel? 2. What would be the diameter of a typical seeing disk (1" radius), in pixels? ### Explanation and Solution: 1. **Calculating the Angular Size per Pixel:** The field of view (FOV) of the telescope is \(10' \times 10'\), which is equal to 600 arcseconds \(\times\) 600 arcseconds (since \(1' = 60''\)). The CCD chip has \(2048 \times 2048\) pixels. To find the angular size corresponding to 1 pixel, we divide the total angular size by the number of pixels: \[ \text{Angle per pixel} = \frac{\text{Total angular size}}{\text{Number of pixels}} = \frac{600''}{2048 \, \text{pixels}} \approx 0.293'' \, \text{per pixel}. \] 2. **Calculating the Diameter of a Seeing Disk in Pixels:** A typical seeing disk has a diameter of 2" (since the radius is 1"). Using the angle per pixel calculated above: \[ \text{Seeing disk diameter in pixels} = \frac{\text{Seeing disk diameter in arcseconds}}{\text{Angle per pixel}} = \frac{2''}{0.293'' \, \text{per pixel}} \approx 6.83 \, \text{pixels}. \] ### Summary: - The angle on the sky that corresponds to 1 pixel is approximately \(0.293''\). - The diameter of a typical seeing disk (1" radius), in pixels, is approximately \(6.83\) pixels. This kind of calculation is crucial for astronomers and astrophysicists when calibrating their instruments and ensuring they capture celestial events with the desired resolution.
Transcribed Image Text:## Recording Telescopic Observations: Pixel and Field of View Correlations A certain telescope has a \(10' \times 10'\) field of view that is recorded using a CCD chip having \(2048 \times 2048\) pixels. ### Problem Statement: 1. What angle on the sky corresponds to 1 pixel? 2. What would be the diameter of a typical seeing disk (1" radius), in pixels? ### Explanation and Solution: 1. **Calculating the Angular Size per Pixel:** The field of view (FOV) of the telescope is \(10' \times 10'\), which is equal to 600 arcseconds \(\times\) 600 arcseconds (since \(1' = 60''\)). The CCD chip has \(2048 \times 2048\) pixels. To find the angular size corresponding to 1 pixel, we divide the total angular size by the number of pixels: \[ \text{Angle per pixel} = \frac{\text{Total angular size}}{\text{Number of pixels}} = \frac{600''}{2048 \, \text{pixels}} \approx 0.293'' \, \text{per pixel}. \] 2. **Calculating the Diameter of a Seeing Disk in Pixels:** A typical seeing disk has a diameter of 2" (since the radius is 1"). Using the angle per pixel calculated above: \[ \text{Seeing disk diameter in pixels} = \frac{\text{Seeing disk diameter in arcseconds}}{\text{Angle per pixel}} = \frac{2''}{0.293'' \, \text{per pixel}} \approx 6.83 \, \text{pixels}. \] ### Summary: - The angle on the sky that corresponds to 1 pixel is approximately \(0.293''\). - The diameter of a typical seeing disk (1" radius), in pixels, is approximately \(6.83\) pixels. This kind of calculation is crucial for astronomers and astrophysicists when calibrating their instruments and ensuring they capture celestial events with the desired resolution.
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