8.2 Resolution and Diffraction Limit
When viewing an object in a microscope, the light coming from the specimen can
be represented as consisting of multiple point sources of light. As the light from
these point sources passes through the various optical elements and aperture dia-
phragms of a microscope, the optical waveforms start to spread out due to scattering
and diffraction effects [ 9 – 11 ]. This spreading results in a small, broadened
diffraction pattern that appears in the image of the point source. Because of the
image broadening, there is a lower limit below which the instrument cannot resolve
the separation of the images of two adjacent point sources to show the real struc-
tural features and details of a specimen. This condition occurs when two source
points in the specimen are separated bya lateral distance that is less than
approximately half the wavelength of the imaging light. This restriction is referred
to as theAbbe criterionor thediffraction limit. Thus, according to the diffraction
limit, the minimal distances (δxmin, δymin) that can be resolved in the lateral
xy-plane are approximated by
ðdxmin;dyminÞk= 2 ð 8 : 5 ÞAnother consequence of the diffraction limit is that it is not possible to focus a
laser beam to a spot with a dimension smaller than aboutλ/2. However, note that
Sect.8.8describes super-resolutionfluorescence microscopic methods that enable
the capture of images with a higher resolution than the diffraction limit.
The broadened image of a point source is called an Airy pattern. The
three-dimensional distribution of light intensity in the Airy pattern is called the
point-spread function(PSF) of the microscope lens. An Airy pattern and the cor-
responding xz distribution of the PSF are illustrated in Fig.8.7. For an ideal,
aberration-free lens, the size of the light distribution is determined only by the
wavelength of the light, the NA of the lens, and diffraction. The point-spread
function shows an oscillatory behavior with a large main central peak and
low-intensity side lobes surrounding the main peak. The central maximum, which is
the region enclosed by thefirst minimum (thefirst side lobe) of the Airy pattern, is
called thezeroth-order maximum Airy disk. This disk contains 84 percent of the
luminous energy and is surrounded by concentric rings of sequentially decreasing
brightness that make up the total intensity distribution. The intensity of thefirst side
lobe is 3 % of the intensity of the main peak. Thefirst side lobe is located at a
distance x 0 =2nλ/(NA)^2 from the center of the pattern.
The termresolutionorresolving poweris used to describe the ability of an
imaging system to distinguish the Airy disks of two point sources that are close
together. The value of the resolution of a microscope is defined in terms of the
numerical aperture. The value of the resolution is not a precise number because the
total NA of different microscope setups depends on the NA values of both the
objective lens and additional lenses in the optical path to the viewer. However,a
higher total NA yields a better resolution. Note thatsmaller values of the resolution
244 8 Microscopy