Page 102 - Fundamentals of Light Microscopy and Electronic Imaging

CHAPTER
6

DIFFRACTION
AND SPATIAL RESOLUTION

OVERVIEW

In this chapter we examine the role of diffraction in determining spatial resolution and
image contrast in the light microscope. In the previous chapter we emphasized that
Abbe’s theory of image formation in the light microscope is based on three fundamen-
tal actions: diffraction of light by the specimen, collection of diffracted rays by the
objective, and interference of diffracted and nondiffracted rays in the image plane. The
key element in the microscope’s imaging system is the objective lens, which determines
the precision with which these actions are effected. As an example, examine the remark-
able resolution and contrast in the image of the diatom, Pleurosigma, made with an
apochromatic objective designed by Abbe and introduced by Carl Zeiss over 100 years
ago (Fig. 6-1). To understand how such high-resolution images are obtained, we exam-
ine an important parameter of the objective, the numerical aperture, the angle over
which the objective can collect diffracted rays from the specimen and the key parameter
determining spatial resolution. We also investigate the effect of numerical aperture on
image contrast. In examining the requirements for optimizing resolution and contrast,
we make an unsettling discovery: It is impossible to obtain maximal spatial resolution
and optimal contrast using a single microscope setting. A compromise is required that
forces us to give up some spatial resolution in return for an acceptable level of contrast.

NUMERICAL APERTURE

Implicit in the Overview is an understanding that the objective aperture must capture
some of the diffracted rays from the specimen in order to form an image, and that lenses
that can capture light over a wide angle should give better resolution than an objective
that collects light over a narrower angle. In the light microscope, the angular aperture is
described in terms of the numerical aperture (NA) as

NA n sin ,

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