# Light microscopy

## Resolution

${\displaystyle R=1.22*{\gamma \over {NA_{obj}+NA_{cond}}}}$.[1]
Where:

• ${\displaystyle R}$ = resolving distance; smaller better.
• ${\displaystyle NA_{obj}}$ = numerical aperture of the objective; typically 0.25 - 1.4, >1.0 is oil immersion, it is usu. inscribed on the lens itself.
• ${\displaystyle NA_{cond}}$ = numerical aperture of the condenser.
• ${\displaystyle \gamma }$ = wave length of light.

It follows from the above equation that, closure of the condenser diaphragm results in a loss of resolution, i.e. R is larger.[1]

Stated differently:[2][3]

• Opening the condenser --> increases resolution & brightness -- but -- decreases depth of field (DOF) & contrast.
• Closing the condenser --> increases DOF & contrast -- but -- decreases resolution & brightness.

### Numerical aperture

NA = numerical aperture.

General formula for NA:[4]
${\displaystyle NA=n*sin(theta)}$.

Where:

• n = index of refraction, n = 1.0 for air.
• theta = half-angle of the max. cone of light

### NA and f-number

N = f/D.

Where:

• N = f-number, e.g. f 1.2, f 1.4, f 11.
• Smaller N = larger opening.
• f = focal length.
• D = diameter of entrance pupil.

At infinity:
${\displaystyle N=1/(2*NA_{i})}$.
${\displaystyle f/D=1/(2*NA_{i})}$.
${\displaystyle 2*NA_{i}=D/f}$.

#### Numerical aperture

If one substitutes the above into the equation at the top:
${\displaystyle R=1.22*{\gamma \over (D/2*f)}}$.

Notes:

• Larger 'D' is better.
• Larger NA = better.

## Lenses

• Most lens = 'achromats' -- only correct green.
• 'Apochromatic' lenses - correct all colours; very expensive.

## Condenser

• Condenser -- large flattened lens beneath the specimen.
• Iris diaphragm.
• Condenser diaphragm --> incr. contrast for resolution ---- large dia. good resol. bad contrast?
• Field aperature diaphragm --> optical illumination.

## Depth of field

• Abbreviated DOF.
• DOF depends on the aperature (small is better).

Relation to other parameters:[3]

• Inverse relationship with resolution and brightness.
• Related to contrast.
• High magnification --> smaller depth of field.

### Formula

${\displaystyle DOF={\lambda _{o}n \over NA^{2}}+{n \over M\cdot NA}e}$.[5]

Where:

• ${\displaystyle \lambda _{o}}$ = illuminating light wavelength.
• n = refractive index of the medium, 1.0 for air.
• NA = numerical aperature (objective).
• M = magnification.
• e = resolution.

### Increasing the DOF

• DOF can be increased by focus stacking.

Software:

Image:

## Köhler illumination

### Procedure

1. Any specimen on stage.
2. Focus.
3. Adjust field aperture (bottom) - to obscure periphery of field of view (FOV).
4. Raise or lower condenser until field aperture diaphragm clearly focused.
5. +/-Center 'field aperture diaphragm - using condenser centering screws.

## Resolution

• Usual light microscopes are limited to about 0.2 micrometres.
• Coming is "Super-resolution microscopy" - using high speed CCDs (charge-coupled devices).[6]