72

3.3  Light Microscopy: The Basics

The solid angle Ω subtended by this maximum half angle can be shown using simple inte­

gration over a sphere to be

(3.21)

Ω=

−

2π

θ

(1

cos )

Most in vivo studies, that is, those done on living organisms or cells, are likely to be low

magnification ML ~ 100 using a low numerical aperture objective lens of NA ~ 0.3 such as

to encapsulate a large section of tissue on acquired images, giving a df of ~10 μm. Cellular

studies often have a magnification an order of magnitude greater than this with NA values of

up to ~1.5, giving a df of 0.2–​0.4 μm.

Note that the human eye has a maximum numerical aperture of ~0.23 and can accommo­

date typical distances between ~25 cm and infinity. This means that a sample viewed directly

via the eye through a microscope eyepiece unit, as opposed to imaged onto a planar camera

detector, can be observed with a far greater depth of field than Equation 3.20 suggests. This

can be useful in terms of visual inspection of a sample prior to data acquisition from a camera

device.

KEY POINT 3.1

Higher-​magnification objective lenses have higher NA values resulting in a superior

optical resolution, but with a much smaller depth of field than lower magnification

lenses.

3.3.4  PHOTON DETECTION AT THE IMAGE PLANE

The technology of photon detection in light microscopes has improved dramatically over

the past few decades. Light microscopes use either an array of pixel detectors in a high-​

sensitivity camera, or a single detector in the form of a PMT or avalanche photodiode (APD).

A PMT utilizes the photoelectric effect on a primary photocathode metal-​based scintillator

detector to generate a primary electron following absorption of an incident photon of light.

This electrical signal is then amplified through secondary emission of electrons in the device.

The electron multiplier consists of a series of up to 12 anodes (or dynodes) held at incremen­

tally higher voltages, terminated by a final anode. At each anode/​dynode, ~5 new secondary

electrons are generated for each incident electron, indicating a total amplification of ~10⁸.

This is sufficient to generate a sharp current pulse, typically 1 ns, after the arrival of the inci­

dent photon, with a sensitivity of single-​photon detection.

An APD is an alternative technology to a PMT. This uses the photoelectric effect but with

semiconductor photon detection coupled to electron–​hole avalanche multiplication of the

signal. A high reverse voltage is applied to accelerate a primary electron produced following

initial photon absorption in the semiconductor with sufficient energy to generate secondary

electrons following impact with other regions of the semiconductor (similarly, with a highly

energetic electron hole traveling in the opposite direction), ultimately generating an enor­

mous amplification of free electron–​hole pairs. This is analogous to the amplification stage in

a PMT, but here the amplification occurs in the same semiconductor chip. The total multi­

plication of signal is >10³, which is less sensitive than a PMT, however still capable of single-​

photon detection with an advantage of a much smaller footprint, permitting in some cases a

2D array of APDs to be made, similar to pixel-​based camera detectors.

Many light microscopes utilize camera-​based detection over PMT/​APD detection pri­

marily for advantages in sampling speed in not requiring slow mechanically scanning over

the sample. Several standard light microcopy investigations that are not photon limited (e.g.,

bright-​field investigations) use CCD image sensors, with the most sensitive light microscopes

using electron-​multiplying CCD (EMCCD) detection or complementary MOS (CMOS)

technology. A CCD image sensor contains a 2D array composed of individual p-​doped