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7 Light in Biology and Medicine
There are several important properties which characterize lens systems: (1)
Field of view; (2) Magnification; (3) Quality of images (i.e. degree of distortion,
resolution, and aberrations). The field of view is the largest angle formed by the
light from any point on an object to the lens system which can be seen in the image.
The linear magnification is the ratio of the image size to the object size. The angular
magnification is the angle formed by the size of the whole image perpendicular to
the optical axis divided by the distance from the last lens to the image. The quality
of an image is determined by its resolution (number of distinguishable points across
the image compared to the number across the object), by a measure of how well an
image matches an object by a single overall scaling factor, and how well colors are
brought to a single focus.
7.29.2 A Simple Microscope
With a ‘magnifying glass’, i.e. a single lens microscope, magnification is limited
because as the lens’ angular magnification (θ ≡ arctan (o/p)) increases, the
distance from the object being viewed and the lens decreases (the image is virtual
and, for comfortable viewing, the lens is positioned so that the image distance is
large, which means p ≈ f , so θ ≈ arctan (o/f )). As the lens has a finite width, say
2w, we must have p > w. This limits the angular magnification to arctan (o/w).
The first microscope, made by van Leeuwenhoek in about 1670, had only one small
glass-ball lens. The smallest ball had a magnification of 275×. The field of view was
strongly limited, due to spherical aberration of the image. Still, van Leeuwenhoek
must have been enchanted by what he saw for the first time in the small world.
Modern visible-light microscopes have many lenses, and can magnify up to 1000×
with resolution down to about 200 nm.
A good microscope is constructed to produce a magnified image with (1) low
distortion, (2) high resolution, (3) an adequate field of view, and (4) sufficient light
and contrast to differentiate small structures. Having two or more lenses gives the
instrument the name ‘compound microscope’. Refinement and expense comes in
making lenses which focus both blue and red the same way (reducing chromatic
aberration) and in making high magnification with little distortion.
Dyes and fluorescent tags (markers) supplement the microscope methods in the
biology lab for making the invisible visible. Fluorescent organic molecules can be
used as tags in order to follow the location and timing of particular intercellular
reactions.
From the Rayleigh limit Eq. (7.13), one can show that the smallest distance that
can be resolved by a microscope is given by d = 0.61λ/(n tan θ i ), where n is the
index of refraction of the object material and θ i is the angle formed by the image
to the objective lens. The depth of focus (i.e. the depth into the object material that
will still be in focus) is given by δz = λ/(4n sin
2 (θ i /2).
7 Light in Biology and Medicine
There are several important properties which characterize lens systems: (1)
Field of view; (2) Magnification; (3) Quality of images (i.e. degree of distortion,
resolution, and aberrations). The field of view is the largest angle formed by the
light from any point on an object to the lens system which can be seen in the image.
The linear magnification is the ratio of the image size to the object size. The angular
magnification is the angle formed by the size of the whole image perpendicular to
the optical axis divided by the distance from the last lens to the image. The quality
of an image is determined by its resolution (number of distinguishable points across
the image compared to the number across the object), by a measure of how well an
image matches an object by a single overall scaling factor, and how well colors are
brought to a single focus.
7.29.2 A Simple Microscope
With a ‘magnifying glass’, i.e. a single lens microscope, magnification is limited
because as the lens’ angular magnification (θ ≡ arctan (o/p)) increases, the
distance from the object being viewed and the lens decreases (the image is virtual
and, for comfortable viewing, the lens is positioned so that the image distance is
large, which means p ≈ f , so θ ≈ arctan (o/f )). As the lens has a finite width, say
2w, we must have p > w. This limits the angular magnification to arctan (o/w).
The first microscope, made by van Leeuwenhoek in about 1670, had only one small
glass-ball lens. The smallest ball had a magnification of 275×. The field of view was
strongly limited, due to spherical aberration of the image. Still, van Leeuwenhoek
must have been enchanted by what he saw for the first time in the small world.
Modern visible-light microscopes have many lenses, and can magnify up to 1000×
with resolution down to about 200 nm.
A good microscope is constructed to produce a magnified image with (1) low
distortion, (2) high resolution, (3) an adequate field of view, and (4) sufficient light
and contrast to differentiate small structures. Having two or more lenses gives the
instrument the name ‘compound microscope’. Refinement and expense comes in
making lenses which focus both blue and red the same way (reducing chromatic
aberration) and in making high magnification with little distortion.
Dyes and fluorescent tags (markers) supplement the microscope methods in the
biology lab for making the invisible visible. Fluorescent organic molecules can be
used as tags in order to follow the location and timing of particular intercellular
reactions.
From the Rayleigh limit Eq. (7.13), one can show that the smallest distance that
can be resolved by a microscope is given by d = 0.61λ/(n tan θ i ), where n is the
index of refraction of the object material and θ i is the angle formed by the image
to the objective lens. The depth of focus (i.e. the depth into the object material that
will still be in focus) is given by δz = λ/(4n sin
2 (θ i /2).