Page 105 - Fundamentals of Light Microscopy and Electronic Imaging

88 DIFFRACTION AND SPATIAL RESOLUTION

These equations describe the Rayleigh criterion for the resolution of two closely
spaced diffraction spots in the image plane. By this criterion, two adjacent object points
are defined as being resolved when the central diffraction spot (Airy disk) of one point
coincides with the first diffraction minimum of the other point in the image plane
(Fig. 6-3). The condition of being resolved assumes that the image is projected on the
retina or detector with adequate magnification. Recording the real intermediate image on
film or viewing the image in the microscope with a typical 10 eyepiece is usually ade-
quate, but detectors for electronic imaging require special consideration (discussed in
Chapters 12, 13, and 14). The Rayleigh resolution limit pertains to two luminous points in
a dark field or to objects illuminated by incoherent light. For a condenser and objective
with NA 1.3 and using monochromatic light at 546 nm under conditions of oil immer-
sion, the limit of spatial resolution d 0.61λ/NA 0.26 m. Numerical apertures are
engraved on the lens cap of the condenser and the barrel of the objective lens.
An image of an extended object consists of a pattern of overlapping diffraction
spots, the location of every point x,y in the object corresponding to the center of a dif-
fraction spot x,y in the image. Imagine for a moment a specimen consisting of a
crowded field of submicroscopic particles (point objects). For a given objective magni-

a

b

c

(a) (b) (c)
Figure 6-3
Rayleigh criterion for spatial resolution. (a) Profile of a single diffraction pattern: The bright
Airy disk and 1st- and 2nd-order diffraction rings are visible. (b) Profile of two disks
separated at the Rayleigh limit such that the maximum of a disk overlaps the first minimum
of the other disk: The points are now just barely resolved. (c) Profile of two disks at a
separation distance such that the maximum of each disk overlaps the second minimum of
the other disk: The points are clearly resolved.