 When a lens system is irradiated at its aperture with a uniform intensity distribution, a diffraction pattern is formed at the focus. The pattern consists of a bright central spot surrounded by rings of rapidly diminishing intensity. The diameter of the central spot, known as the Airy disc, is approximated by this equation:
S = 2.44lF/#
Where S is the diameter of the central spot, l is the wavelength of the source, and F/# is the ratio of the focal length to the lens aperture. In the absence of any lens imperfection, 84% of the energy is contained within the diameter s and the remainder is distributed in the outer rings. If a difference exists between the longest and shortest optical paths leading to a focus, a change in the size of the central spot as well as a redistribution of energy occurs. For an optical path difference of one quarter of the wave-length (l/4), the size of the central spot is essentially unchanged, but there is a decrease of energy from the central spot to 68%. Traditionally, when this l/4 limit on optical paths (known as the Rayleigh criterion) is not exceeded, the lens system is considered diffraction limited. |
In the case of a lens system irradiated by a laser operating in the fundamental transverse mode (TEMoo), some flexibility is required in assigning a diffraction-limited label to the lens system. The Gaussian distribution which describes the fundamental mode of a laser is given by the formula: where Po is the total output power,l(r) is the intensity at the distance r from beam center and a is the radius where the intensity falls to l/e2 or 13.5% of the central intensity. The accepted beam diameter of the laser is defined as 2a and contains 86.5% of the total beam power.
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