Physical Principles for Enhancing Resolution

1. Rayleigh Criterion and Angular Resolution:

   1. Due to the wave nature of light, a point source imaged through an Optical System does not form a perfect point image but rather a diffraction pattern called an Airy disk. The Rayleigh criterion defines the condition for resolving two adjacent point sources: they are just resolvable when the center of one source's Airy disk coincides with the first dark ring of the other's Airy disk. At this point, the angular separation (angular resolution) θ between the sources satisfies the formula

      

      where λ is the wavelength of light and D is the aperture diameter of the optical system (i.e., the mirror's diameter).

   2. From this formula, it's evident that for a given observation wavelength λ, a larger mirror diameter D results in a smaller angular resolution θ. This means closer celestial objects can be distinguished, thereby improving the resolution of astronomical observations. For example, in the same observation band, a large-aperture mirror can improve angular resolution several-fold compared to a small-aperture mirror. Stars too close together to be resolved with a small telescope become clearly separable with a large-aperture mirror.

2. Spatial Frequency and Information Transfer:

   1. From the perspective of spatial frequency, the optical imaging process can be seen as the transfer of an object's spatial frequency information. High-frequency information corresponds to fine details, while low-frequency information corresponds to the overall outline. A large-aperture mirror, with its wider aperture, collects light rays from a greater range of angles. This enables it to transfer higher spatial frequency information, meaning finer details of celestial objects can be rendered, thus enhancing resolution. For instance, when observing galactic structures, large-aperture mirrors can capture subtle details of spiral arms and star-forming regions within galaxies, whereas small-aperture mirrors might only reveal the galaxy's basic outline.

Physical Principles for Enhancing Light-Gathering Power

1. Relationship Between Light Flux and Aperture:

   1. Light-gathering power is typically measured by light flux. According to optical principles, the light flux Φ collected by a telescope is proportional to the area A of its primary mirror, and the mirror area A is proportional to the square of its diameter

      

      (where D is the mirror diameter). This shows that a larger diameter D means a larger mirror area, collecting more light flux. For example, doubling the mirror diameter quadruples its area and the collected light flux. This allows large-aperture mirrors to observe fainter celestial objects because even extremely dim light, when collected and concentrated by the large mirror, can produce a detectable signal on the detector.

2. Signal Strength and Noise Suppression:

   1. Greater light flux not only enables the observation of fainter objects but also significantly improves signal strength and suppresses noise. In astronomical observations, detectors are affected by various types of noise, such as thermal noise and shot noise. Signal strength is proportional to the number of photons collected. A large-aperture mirror collects more photons, thereby increasing the signal strength. According to the statistical relationship between signal and noise, when signal strength increases, the relative impact of noise on the signal decreases, meaning the signal-to-noise ratio (SNR) improves. This allows for clearer extraction of an object's characteristic information during data processing, further enhancing the ability to observe fine details. For example, when observing distant galaxies, the larger number of photons collected by a large-aperture mirror results in clearer spectral features, enabling more accurate measurements of properties like redshift and chemical composition.

In summary, large-aperture mirrors enhance resolution by increasing the diameter to reduce the angular resolution according to the Rayleigh criterion and by utilizing a larger aperture to transfer higher spatial frequency information. Simultaneously, they enhance light-gathering power by increasing the mirror area to collect more light flux and by improving the signal-to-noise ratio. This provides unprecedented observational capabilities for astronomy, driving the continuous advancement of the field.