The first step is to determine your images scale in arc-seconds per pixel. If you take the pixel size in arc-seconds and multiply by the number of pixels, that gives you the field of view the camera sees. You should also consider the field-of-view of your system.
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It may be advantageous to lean towards a higher number, so that on those rare nights of excellent seeing you can take full advantage of the conditions. In practice, you want an absolute minimum of 2 pixels across the FWHM 2.5 to 3 is an excellent match, and up to 4-5 will produce good results. Spreading the same light among more pixels increases noise because each pixel has its own noise contribution. Increasing beyond this point does not increase the image detail however, it does spread the light out and can reduce the signal-to-noise ratio. In practice pixels are square and the star images are round, so 2.5 to 2.8 pixels is generally considered optimal. Unless you are doing profile-fitting photometry, where you need to measure the shape of the PSF accurately, it is usually sufficient to use 2 pixels across the FWHM of the star. This Nyquist Sampling Criteria has been mathematically proven to record all the information present in the image. In order to perfectly replicate an image, you need to sample at least 2X the highest spatial frequency in the image. Pixel Size (arc-seconds) = 206 * Pixel Size (microns) / focal length (mm)Ī camera with 9 micron pixels attached to a telescope with a 2000 mm focal length will result in 0.9 arc-seconds per pixel. How large a spot this produces on the sensor depends on the focal length of the instrument, not the focal ratio.
Such a site will typically have seeing on the order of 2.5 to 3.5 arc-seconds, depending on the weather conditions. At most non-alpine locations seeing disks of 2 arc-seconds are only seen on the most exceptional nights. If you are at a premier observing site, such as the summit of Mauna Kea, the long-exposure seeing disk can be less than 1 arc-second. When atmospheric seeing is taken into account, the spot size is often much larger. Clearly this requires a small pixel to sample adequately. (1/2 NA should be used instead of f/ratio when focusing closer than infinity.)Īt a typical green wavelength of 0.550 microns, an f/5 system will produce a spot 3.4 microns in diameter. Spot size (um) = 1.22 * wavelength (um) * f/ratio Assuming the optics are working to their full potential, the spot size is determined as follows: Tip/tilt guiders such as the SBIG AO-X can improve resolution by removing seeing-related image wander large telescopes (above 1 meter diameter) can use advanced adaptive optics systems with wavefront sensors and “rubber mirrors” to tighten the images.įor small telescopes, and in laboratory settings, the optics dominate. For very small optics this just makes the star images wander about for larger optics you will get multiple cells within the light path, resulting in the star image breaking up and moving in multiple directions at once. The atmospheric bubbling of warm and cool cells affects the path of light through the atmosphere in a random fashion, causing starlight to wander rapidly. Since cool air is denser it also has a higher refractive index. The atmosphere is comprised of cells of warmer and cooler air, which are constantly circulating due to convection. In a laboratory setting you may have to resort to specialized test equipment or work with theoretical numbers.Īstronomers have a difficulty, though, which is called “seeing”. It is straightforward to evaluate the resolution performance of an astronomical telescope. Stars are so remote, compared to their diameter, that they appear as perfect pointlike sources. In general, larger diameter optics provide more resolution, while shorter f/ratio optics produce smaller spot size.Īstronomers have it easy because they have a universe of perfect point-spread functions all around them.
One of the most straightforward is to determine its response to a perfect point source – the resulting image of a perfect point is called a “point-spread function” or PSF. There are a variety of ways to characterize the resolution capability of optics. The key parameter is the physical size of the pixels, which may range from less than 1 micrometer (micron) across for a cell phone camera, to as much as 25 microns for large specialty scientific imagers. On dedicated science instruments such as telescopes and microscopes you are much more limited by the optics, and you need to pick your camera to suit your optics. In conventional photography your lenses are highly adaptable, with adjustable f/ratio and often zoom capability (adjustable focal length). In order to get the best results from your equipment, it is important to match the resolution of your camera to the resolution of your optics.
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