The most common telescopes used for astronomy are either refractor telescopes that use multiple lenses to capture light or reflector telescopes that use a mirror to capture light. Both designs have their advantages but they both suffer in degree with Flat Field and / or Coma issues.
You will generally see field curvature problems when you connect a camera sensor to a telescope. For refractors, the reason is the camera sensor is flat relative to the curved lenses in a refractor; light that hits the center of the camera’s sensor is in focus but light that hits away from the optical axis and towards the edges of the camera’s sensor are not in focus. This optical aberration is normally corrected through the use of a Field Flattner. A Field Flattner is an accessory you will need to match your telescope and camera sensor with to reduce and hopefully eliminate this problem.
For reflectors, field curvature is much less of a problem, but this type of telescope suffers from an associated problem called Coma. In the mid 17th century, Sir Issac Newton realized that if he used a concave mirror in a tube, the light would be reflected back to a point on the optical axis of the tube / mirror combination. This point would be called the Prime Focus. If you put something like an eyepiece there, you could view the image reflected from the light rays from the mirror. There was only one problem; your head would get in the way. To solve this problem, Newton put a flat mirror at a 45 degree angle at the Prime Focus point and reflected the light rays at a 90 degree angle out of a hole that he cut out of the side of the tube. This became the Newtonian Reflector that many of us love and enjoy using in the form of a dobsonian telescope or astrograph. This design eliminated the chromatic aberration problem of refractor telescopes. The optical alignment of both the primary concave mirror and the flat secondary mirror is absolutely critical and it has to be checked regularly through a process called collimation. However, the major problem inherent with this design as it uses a parabolic mirror where light from any object, like a star that is not aligned with the optical axis of this telescope. This will result in an aberration - stars near the edges of telescope will have comet like tails in the direction outward from the center of view. This is called coma and the faster the focal ratio is, the worse the aberration will be. This is where a coma corrector is used; again, it’s inserted before the eyepiece or camera and needs to be matched with your telescope and camera specifications.
Both Field Flattners and Coma Correctors are found at your favorite astronomy shop. Both of them can come with the ability to reduce the focal ratio of your telescope, making it a faster device but you'll need to confirm that they are properly matched to your equipment specifications.