Page 82 - Fundamentals of Light Microscopy and Electronic Imaging

THE DIFFRACTION IMAGE OF A POINT SOURCE OF LIGHT 65

When highly magnified, the pattern is observed to consist of a central spot or diffraction
disk surrounded by a series of diffraction rings. In the nomenclature of diffraction, the
bright central spot is called the 0th-order diffraction spot, and the rings are called the 1st-,
2nd-, 3rd-, etc.-order diffraction rings (see Fig. 5-4). When the objective is focused prop-
erly, the intensity of light at the minima between the rings is 0. As we will see, no lens-based
imaging system can eliminate the rings or reduce the spot to a point. The central diffraction
spot, which contains 84% of the light from the point source, is also called the Airy disk,
after Sir George Airy (1801–92), who described some of its important properties.
The Airy disk pattern is due to diffraction, whose effect may be described as a dis-
turbance to the electric field of the wavefront in the aperture of the lens—the conse-
quence of passing an extended electromagnetic wavefront through a small aperture. The
disturbance continues to alter the amplitude profile of the wavefront as the front con-
verges to a focus in the image plane. Diffraction (the disturbance) constantly perturbs
the incident wavefront, and since no one has invented a lens design to remove it, we
must accept its alteration of points comprising the image. The size of the central disk in
the Airy pattern is related to the wavelength λ and the aperture angle of the lens. For a
telescope or camera lens receiving an incident planar wavefront from an infinitely dis-
tant source such as a star, the aperture angle is given as the focal ratio f/D, where D is

I

(a)

–2.23π –1.22π 1.22π 2.23π
π dsin φ
λ
(b)

Figure 5-4
The diffraction pattern of a point source of light. (a) Diffraction pattern showing central
diffraction disk surrounded by diffraction rings. (b) Intensity profile a diffraction spot. The
central spot and surrounding rings are evident. The separation distance between the center
of the spot and the first minimum depends on the angular aperture of the lens.