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Formula 5 First Interspace Linear Diameter
FI LD = 2.44 * Lambda * FR
Where:
- FI LD is the First Interspace Linear Diameter
- 2.44 is a constant
- Lambda is the wavelength of the light
- FR is the Focal Ratio of the telescope.
Example: What is the linear diameter of the Airy Disk to the first interspace in a 5 inch f/8 telescope for light at a wavelength of 550nm.
FI LD = 2.44 * Lambda * FR
FI LD = 2.44 * 550nm * 8
Where 550nm = 0.00055 millimeters
FI LD = 2.44 * 0.00055 * 8
FI LD = .010736 mm
where 1 micron = 0.001 mm
FI LD = 10.7 microns
The linear diameter of the Airy Disk of the first interspace for a 5 inch f/8 telescope for light at 550nm, is 10.7 microns.
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From this we can see that the linear spot size of a star depends only on the f/ratio of the telescope.
| Linear Diameter of the Airy Disk to the First Interspace |
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| Focal Ratio |
in millimeters |
in microns |
| f/2.8 |
0.003757 mm |
3.7 µm |
| f/4 |
0.005368 mm |
5.3 µm |
| f/5.6 |
0.007515 mm |
7.5 µm |
| f/8 |
0.0107 mm |
10.7 µm |
| f/11 |
0.01476 mm |
14.7 µm |
Note that this equation calculates the diameter of the Airy disk to the first interspace. It would seem that the actual diameter of the star in the image will be a little less than this figure. However, the Airy disk is actually made up of all wavelengths of light that the eye, or CMOS sensor is sensitive to. Therefore, this figure actually grows a bit larger for visual, and can grow quite a bit larger in longer wavelengths (past hydrogen-alpha at 656.3nm) that are not filtered out for astrophotography.
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