Final answer:
A high signal-to-noise ratio and larger numerical apertures in microscopes, as well as larger apertures in telescopes, are most likely to produce high-quality images by allowing more light and diffraction modes to be captured, which enhances image resolution.
Step-by-step explanation:
A high-quality image is typically associated with a high signal-to-noise ratio (SNR). In optics, such as in microscopy or astronomy, the Numerical Aperture (NA) of a system and the size of telescope apertures are critical. The larger the NA, the greater the ability of the system to bring in light and collect more diffraction modes, which translates into more information for the formation of a clear image, thus enhancing the resolving power of a microscope.
Similarly, for telescopes, a larger aperture allows more light to be collected, which improves the resolution and sharpness of the images produced. Issues with Earth's atmosphere have historically limited the resolution of visible-light and infrared telescopes, but advances in technology have enabled sharper images in line with theoretical expectations.