Basic Concepts in Light Microscopy

Microscope Illumination

Bright-Field Illumination

In bright field illumination, the specimen is evenly lit by the light source. The specimen appears dark/ pigmented in a light background. This is the standard mode of light microscope illumination. The contrast in the image is resulting from different light absorption qualities of the specimen itself or through the use of stains. Thus, suitable for specimens that naturally absorb visible light or specimens stained with dyes. The contrast is controlled by adjusting the diameter of the condenser diaphragm. The illumination is controlled by adjusting the brightness of the light source (LED lamp) or by adding or removing neutral density filters.

Dark-Field Illumination

In dark field illumination, specimen is illuminated by a condenser with an obstruction centered in light path, to block the central portion of the illumination cone. This is resulted in illumination of the specimen at a very wide angle. Light that does not interact with the specimen passes outside of the collecting angle of the objective lens. Therefore, only the light that reflected or refracted by the specimen enters into the objective lens. The specimen appears bright on a dark background. When using dark field illumination, the NA of the condenser must be larger than that of the objective lens.

Magnification Power

Figure 01: Ray diagram of a compound microscope with two lenses.

Magnification is the ability of a microscope to produce an image of an object at a scale larger (or even smaller) than its actual size. The total magnification of a compound microscope is the product of individual magnifications of its lenses.

Where,

M_net = Total magnification of the microscope

M_o = Magnification of the objective lens

M_e= Magnification of the eyepiece

An image formed by a convex lens is described by the lens equation

where u is the distance of the object from the lens; v is the distance of the image from the lens and f is the focal length.

The magnification (m) is the ratio between the size of the image to the size of the object.

The linear magnification of the objective lens (M_o) can be calculate using the following equation;

Where L_i and L_o are the image and object distances. L_o can be measured. However, we have to calculate L_i.

If we assume that the object is placed very close to the focal point of the objective lens,

If we apply the lens formula to the objective lens of our example;

By rearranging the equation;

Now we can calculate the value for L_i;

If the final image is formed at the infinity, then the image created by the objective lens must be located on the focal point of the eyepiece (F_e). If the distance between the objective and eyepiece lenses (tube length) is L;

L_i= L - F_e

_Therefore,

If we assume L >>> than F_e, then,

The magnification of the eyepiece (M_e) can be determined by calculating the angular magnification of a simple lens. When the final image is formed at the near point, the angular magnification by the eyepiece (M_e), can be calculated using the following equation;

Where,

M_o = Magnification of the objective lens

f_e= Focal length of the eyepiece

D = The least distance of distinct vision (25 cm)

The angular magnification by the eyepiece (M_e) when the final image forms at infinity, can be calculated using the following equation;

The net magnification power of the compound microscope with the image at infinity is;

Specifications of Objectives

Figure 02: Specifications of Objective lenses

Microscope lens manufacturers design various types of objective lenses to be used in different scenarios based on the requirements of the users. To indicate different features and limitations of objective lenses, the manufacturers use codes, numbers and color bands as shown in figure 02. Since objective lenses are very expensive, and the price increases with additional features, the users must purchase the correct objective lenses suitable for their need. Purchasing the wrong objective lenses may result in incorrect images or incompatibility with the microscope, making the objective lens useless. If you are not certain about the objective lenses you need, seek help from an expert before purchasing.

Resolving Power

Resolving power is defined as the smallest distance between two points on a specimen, where the two points are distinguishable as separate entities. At near point (25 cm), the resolving power of human eye is 0.25 mm. Thus, human eye cannot distinguish any two points closer than 0.25 mm.

Figure 03: Central airy disc and concentric interference patterns caused by difraction of light through a circular aperture.

When light from the various points of a specimen passes through the objective lens, the points of the specimen appear in the image in patterns known as airy patterns, not as points. This phenomenon is caused by scattering or diffraction of light as it passes through the small parts and spaces in the specimen and the circular back aperture of the objective lens. Diffraction of light through a circular aperture resulted in a central bright circle, called the airy disc, surrounded by a series of concentric alternative light and dark rings, which correspond, respectively to constructive and destructive interference of the light waves from the point source object (figure 03).

Figure 04: Light interaction and the resulting interference patterns between two adjacent diffraction patterns from two closely located point light sources.

The diameter of the central maximum of the airy disc determines the resolving power of the lens system. For two closely associated points to be distinguishable as separate entities, their airy discs must be sufficiently separated from each other. In the case of figure 04A, the two points are resolved as the airy discs are not overlapped. The two points of the figure 04B are considered as just resolved, as their airy discs are partially overlapped. However, the two points still appear as a single point. In the case of figure 04C, the two points are unresolved as the two points are too close to each other, thus the airy discs overlaps, forming as single disc forming a 'circle of confusion'.

Microscope Resolution

The resolving power of a microscope depends on the NA of the objective lens and condenser and the wavelength of the light source. Objective lenses with higher NA will results in high resolving power. More details can be seen on the micrographs taken with the higher NA (figure 05). The resolution and magnification of a lens system are independent from each other. When images are magnified beyond the limit of the microscope, no increase in resolving power would be achieved. Increase of magnification without additional resolution in details is know as 'empty magnification'.

Where,

d= the resolving power in micrometers

λ = the wavelength of the light source

NA_obj= the numerical aperture of the objective lens

NA_cond= the numerical aperture of the condenser

Figure 05: Two micrographs of the same vascular bundle. The image on the left was taken using an objective with NA=0.30 and the image on the right was taken using an objective with NA=0.75.

Numerical Aperture (NA)

The numerical aperture (NA) or the light gathering power of an objective lens is mainly determined by the diameter of the cone of light collected by the front lens element. NA determines the resolution and the brightness of the image. Higher the NA, higher the resolution and brightness. The angle of the light cone is referred to as the angular aperture. This angle is described by the edges of the front element of the objective lens and the object point at the focal plane. In the above figure, angular apertures of the objectives are 2ϴ. The NA values in the above example increase in the following order; A<B<C, However, the working distances of the objectives decrease as the NA increases.

NA of an objective lens can be calculated using the following equation;

NA = n sin ϴ

Where

NA= Numerical aperture

n = Refractive index of the medium between the specimen and the objective lens

ϴ = Maximum angle of the light cone (half of the angular aperture)

The theoretical maximum NA value for a dry objective lens is 1.0 (where, n = 1 (air) and ϴ = 90°). If NA values >1.0 is required, the refractive index of the medium between the specimen and the objective lens must be increased. This can be achieved by using immersion oil with a refractive index greater than 1.0, and an appropriate objective lens.

Immersion media

The immersion media used in light microscopy are non volatile, optically clear, liquids with no color. They refractive indices similar to that of glass. The type of immersion medium to be used with the immersion objective lens is marked on the objective lens either in letters or color codes (Figure 02). The common immersion media used in microscopy are Water (n: 1.333), Glycerol (n: 1.475) , Canada Balsam (n: 1.547), Permount (n: 1.525), Wintergreen oil (n: 1.535), etc.,.

Immersion media and NA

The highest numerical aperture for dry objective lens is 1.0. Thus, filling the gap between the specimen and the objective lens with an immersion medium could increase the NA >1.0. However, it is mandatory to use appropriate immersion lenses along with the immersion media. If you attempted to use immersion media with a dry objective lens, it could damage the objective lens and will result in distorted images.

Figure 04: The Effect of immersion oil on the NA of the objective lens

When an immersion oil is absent, and air is present between the specimen and the objective lens, light rays with large incident angles can get refracted (ray B) or reflected (ray C) away from the collecting angle of the lens, thus reducing the NA. However, when immersion oil is added, the objective lens can collect the rays (B and C) that would otherwise be lost.

Working Distance (WD)

The distance between the front lens element of the objective and the surface of the slide at which the sharpest image is obtained. WD is inversely proportional to the NA. Therefore, the WD decreases in the following order (A) High power> (B) Low power> (C) Scanning >Oil immersion. However, there are special high power objectives with long working distances (e.g. 13 mm).

Depth of Field

A lens or lens system, has a defined focal plane which gives the sharpest image. The image becomes blurred extending away from the focal plane. However, there is a region below (-ΔZ) and above (+ΔZ) the focal plane where object remained nearly focused without a detectable loss of sharpness, which is called the depth of field (DOF). The total visual depth of field of a given lens is 2ΔZ.

Depth of field of two lenses with different numerical apertures. +Z and -Z the acceptable focus above and below the object plane, respectively. Objective (A) has a wide DOF and objective (B) has a shallow DOP.

The total visual DOF can be calculated using the Pluta (1988) formula.

Where,

n = the refractive index of the medium

NA = numerical aperture of the objective

λ = The wavelength of the light source

M_m = the total magnification of the microscope

The DOF has a strong inversely proportional relationship with the NA of the lens system. Therefore, lenses with large Na values have a shallow DOF and lenses with small NA have a wide DOF.

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