Chapter 3 – Making Light Work in Biology  71

(3.18)

M

f

f

image

objective

=

In practice, there are likely to be a series of several lens pairs placed between the imaging lens

shown and the detector arranged in effect as telescopes, for example, with focal lengths f1, f2,

f3, f4, …, fn corresponding to lenses placed between the objective lens and the camera detector.

The magnification of such an arrangement is simply the multiplicative combination of the

separate magnifications from each lens pair:

(3.19)

M

f

f

f

f

f

f

n

n

=

⋅

…

⋅

…

−

2

4

1

3

1

,

,

,

,

Such additional lens pairs allow higher magnifications to be obtained without requiring a

single imaging lens with an exceptionally high or low focal length, which would necessitate

either an impractically large microscope or would result in severe optical aberration effects.

A typical standard light microscope can generate effective total magnifications in the range

100–​1000.

3.3.2  DEPTH OF FIELD

The depth of field (df, also known as the “depth of focus”) is a measure of the thickness par­

allel to the optical axis of the microscope over which a sample appears to be in focus. It is

conventionally defined as one quarter of the distance between the intensity minima parallel

to the optic axis above and below the exact focal plane (i.e., where the sample in principle

should be most sharply in focus) of the diffraction image that is produced by a single-​point

source light emitting object in the focal plane. This 3D diffraction image is a convolution of

the point spread function (PSF) of the imaging system with a delta function. On this basis, df

can be approximated as

(3.20)

d

n

NA

d n

M NA

f

m

R

m

L

=

+

λ

2

where

λ is the wavelength of light being detected

nm is the refractive index of the medium between the microscope objective lens or

numerical aperture NA and the glass microscope coverslip/​slide (either air, nm =​ 1, or

for high-​magnification objective lenses, immersion oil, nm =​ 1.515

dR is the smallest length scale feature that can be resolved by the image detector (e.g., the

pixel size of a camera detector) such that the image is projected onto the detector with

a total lateral magnification of ML between it and the sample.

3.3.3  LIGHT CAPTURE FROM THE SAMPLE

The NA of an objective lens is defined nm sin θ, where nm is the refractive index of the imaging

media. The angle θ is the maximum half-​angle subtended ray of light scattered from the

sample, which can be captured by the objective lens. In other words, higher NA lenses can

capture more light from the sample. In air, nm =​ 1 so to increase the NA, further high-​power

objective lenses use immersion oil; a small blob of imaging oil is placed in optical contact

between the glass microscope slide or coverslip and the objective lens, which has the same

high value of refractive index as the glass.