Approximation for the Rayleigh Resolution of a Circular Aperture

• Autores: Carl E. Mungan
• Localización: The Physics Teacher, ISSN 0031-921X, Vol. 47, Nº. 5, 2009, págs. 288-289
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Rayleighs criterion states that a pair of point sources are barely resolved by an optical instrument when the central maximum of the diffraction pattern due to one source coincides with the first minimum of the pattern of the other source. As derived in standard introductory physics textbooks,1the first minimum for a rectangular slit of width ais located at angular position ??sin-1?afor light of wavelength . If the angular separation of the two sources is small, we can use the small-angle approximation sin to conclude that the resolution is min??afor a rectangular aperture. On the other hand, for a circular aperture of diameter D, the limiting angle is shown in optics texts2to be min??1.22?D.The derivation of the numerical prefactor of 1.22 involves finding the zero of a Bessel function and is beyond the reach of introductory physics students. Consequently, elementary texts simply pull that prefactor out of thin air. The purpose of the present paper is to briefly explain why we expect a prefactor larger than unity and to make simple estimates of its value, using only algebra.