Airy Disk - Obscured Airy Pattern

Obscured Airy Pattern

Similar equations can also be derived for the obscured Airy diffraction pattern which is the diffraction pattern from an annular aperture or beam, i.e. a uniform circular aperture (beam) obscured by a circular block at the center. This situation is relevant to many common reflector telescope designs that incorporate a secondary mirror, including Newtonian telescopes and Schmidt–Cassegrain telescopes.

where is the annular aperture obscuration ratio, or the ratio of the diameter of the obscuring disk and the diameter of the aperture (beam)., and x is defined as above: where is the radial distance in the focal plane from the optical axis, is the wavelength and is the f-number of the system. The fractional encircled energy (the fraction of the total energy contained within a circle of radius centered at the optical axis in the focal plane) is then given by:

E(R) = \frac{1}{ (1 - \epsilon ^2) } \left( 1 - J_0^2(x) - J_1^2(x) + \epsilon ^2 \left - 4 \epsilon \int_0^x \frac {J_1(t) J_1(\epsilon t)}{t}\,dt \right)

For the formulas reduce to the unobscured versions above.

Read more about this topic:  Airy Disk

Famous quotes containing the words obscured, airy and/or pattern:

    “The fatal metaphor of progress, which means leaving things behind us, has utterly obscured the real idea of growth, which means leaving things inside us.”
    —Gilbert Keith Chesterton (1874–1936)

    “But this rough magic
    I here abjure, and when I have required
    Some heavenly music—which even now I do—
    To work mine end upon their senses that
    This airy charm is for, I’ll break my staff,
    Bury it certain fathoms in the earth,
    And deeper than did ever plummet sound
    I’ll drown my book.”
    —William Shakespeare (1564–1616)

    “The kind of relatedness to the world may be noble or trivial, but even being related to the basest kind of pattern is immensely preferable to being alone.”
    —Erich Fromm (1900–1980)