# Optical Microscopy

## The Abbe diffraction limit

Observation of sub-wavelength structures with microscopes is difficult because of the Abbe diffraction limit. Ernst Abbe found in 1873 that light with wavelength λ,travelling in a medium with refractive index n and converging to a spot with angle φ will make a spot with radius

$d=\frac{0.61 \lambda}{n sin \phi}$

The denominator nsinφ is called the numerical aperture (NA) and can reach about 1.4 in modern optics, hence the Abbe limit is roughly d=λ/2. With green light around 500nm the Abbe limit is 250nm which is large compared to most nanostructures or biological cells with sizes on the order of 1μm and their internal organelles being much smaller. To increase the resolution, shorter wavelengths can be used such as UV and X-ray microscopes. These techniques offer splendid resolution but are expensive, suffer from lack of contrast in biological samples, and also tend to damage the sample.

## The optical microscope

Sketch of an optical microscope

### Bright Field

The light is sent to the sample in the same directions as you are looking - most things will look bright unless they absorb the light.

### Dark Field

Light is sent towards the sample at an angle to your viewing direction and you only see light that is scattered. This makes most images appear dark and only edges and curved surfaces will light up.

# Laser Scanning Confocal Microscopy (LSCM)

Confocal laser scanning microscopy is a technique that allows a much better resolution from optical microscopes and three dimensional imaging. A review can be found in Paddock, Biotechniques 1999

Using a high NA objective also gives a very shallow depth of focus and hence the image will be blurred by structures above or below the focus point in a classical microscope. A way to circumvent this problem is the confocal microscope, or even better the Laser Scanning Confocal Microscope (LSCM). Using a laser as the light source gives better control of the illumintaion, especially when using fluorescent markers in the sample. The theoretical resolution using a 1.4 NA objective can reach 140nm laterally and 230nm vertically [1] while the resolution quoted in ref [2] is 0.5×0.5×1μm. The image in the LSCM is made by scanning the sample in 2D or 3D and recordning the signal for each point in space on a PC which then generates the image.

# X-ray microscopy

X-ray microscopy uses X-rays to image with much shorter wavelength than optical light, and hence can provide much higher spatial resolution and use different contrast mechanisms. X-ray microscopy allows the characterization of materials with submicron resolution approaching the 10's of nanometers. X-ray microscopes can use both laboratory x-ray sources and synchrotron radiation from electron accelerators. X-ray microscopes using synchrotron radiation provide the greatest sensitivity and power, but are unfortunately rather large and expensive. X-ray microscopy is usually divided into two overlapping ranges, referred to as soft x-ray microscopy (100eV - 2keV) and hard x-ray microscopy (1keV-40keV). All x-rays penetrate materials, more for higher energy x-rays. Hence, soft x-ray microscopy provides the best contrast for small samples. Hard x-rays do have the ability to pass nearly unhindered through objects like your body, and hence also give rather poor contrast in many of the biological samples you would like to observe with the x-ray microscope. Nevertheless, hard x-ray microscopy allows imaging by phase contrast, or using scanning probe x-ray microscopy, by using detection of fluorescent or scattered x-rays. Despite its limitations, X-ray microscopy is a powerful technique and in some cases can provide characterization of materials or samples that cannot be done by any other means.