Page 83 - Fundamentals of Light Microscopy and Electronic Imaging

66 DIFFRACTION AND INTERFERENCE IN IMAGE FORMATION

the lens diameter and f is the focal length. In this case, the aperture angle is the angular
diameter of the lens as seen from a point in the image plane at focal length f. The size of
the diffraction disk radius d is given by

d 1.22λ (f/D).

In a microscope, the aperture angle is described by the numerical aperture NA,
which includes the term sin , the half angle over which the objective can collect light
coming from a nearby object. (NA is defined further in Chapter 6.) In the case of a
microscope image, the radius d of the diffraction spot for a self-luminous point of light
in the image plane is described by a related expression:

d 1.22 λ/2NA

In both situations, the size of the spot decreases with decreasing wavelength and
increasing numerical aperture, but always remains a disk of finite diameter. The spot
size produced by a 25 oil immersion objective with NA 1 is about 30 m. Obtain-
ing an image whose resolution is limited by the unit diffraction spot, rather than by scat-
tered light or lens aberrations, is what is meant by the term diffraction limited. We
examine the relationship between diffraction and resolution in Chapter 6.

Demonstration: Viewing the Airy Disk with a Pinhole Aperture

It is easy to observe the Airy disk by examining a point source of light through a
pinhole (Fig. 5-5). This is best done in a darkened room using a bright lamp or
microscope illuminator whose opening is covered with a piece of aluminum foil
containing a pinhole that will serve as a point source of light when viewed at a
distance of several feet. The illuminator’s opening should be completely covered
so that the amount of stray light is minimal. A second piece of foil is prepared
with a minute pinhole, 0.5 mm diameter or less, and is held up to the eye to exam-
ine the point source of light at the lamp. The pinhole–eye lens system (a pinhole
camera) produces a diffraction pattern with a central Airy disk and surrounding
diffraction rings. The same observation can be made outdoors at night examining
distant point sources of light with just the pinhole held over the eye. This simple
diffraction pattern is the basic unit of image formation. If the eye pinhole is made
a little larger, the Airy disk becomes smaller, in accordance with the principle of
angular aperture we have described. Now turn on the room lights and look
through the pinhole at objects in the room, which look dim (not much light
through the pinhole) and blurry (low resolution). The blurry image is caused by
large overlapping diffraction spots of image components on the retina. When the
pinhole is removed and the objects are viewed directly, the image is clearer
because the larger aperture size afforded by the eye’s iris and lens results in
smaller diffraction spots and an increase in resolution and clarity. We begin to
appreciate that an extended image can be viewed as the summation of a myriad of
overlapping diffraction spots.