# Depth of Field in Microscopy

## How sharp images are formed

In microscopy, depth of field is often seen as an empirical parameter. In practice it is determined by the correlation between numerical aperture, resolution and magnification. For the best possible visual impression, the adjustment facilities of modern microscopes produce an optimum balance between depth of field and resolution – two parameters which in theory are inversely correlated.

## Practical values for visual depth of field

In DIN/ISO standards, the depth of field on the side of the object is defined as the "axial depth of the space on both sides of the object plane within which the object can be moved without detectable loss of sharpness in the image, while the positions of the image plane and the objective are maintained".

However, the standard does not give any clues on how to measure the detection threshold of the deterioration of focus. The author of the first publication on the subject of visibly experienced depth of field was Max Berek, who published the results of his extensive experiments as early as 1927. Berek’s formula gives practical values for visual depth of field and is therefore still used today. In its simplified form, it is as follows:

TVIS = n [λ/(2 × NA²) + 340 μm/(NA × MTOT VIS)]

TVIS:  Visually experienced depth of field
n:  Refractive index of the medium in which the object is situated. If the object is moved, the refractive index of the medium that forms the changing working distance is entered in the equation.
λ:  Wavelength of the light used, for white light, λ = 0.55 μm
NA:  Numerical aperture on the side of the object
MTOT VIS:  Total visual magnification of themicroscope

If in the above equation the total visual magnification is replaced by the relationship of useful magnification (MTOT VIS = 500 to 1,000 x NA), it can be seen that, to a first approximation, the depth of field is inversely proportional to the square of the numerical aperture.

Particularly at low magnifications, the depth of field can be significantly increased by stopping down, i.e. reducing the numerical aperture. This is normally done with the aperture diaphragm or a diaphragm on a conjugated plane. However, the smaller the numerical aperture, the lower the lateral resolution.

It is therefore a matter of finding the optimum balance of resolution and depth of field depending on the structure of the object. With their high-resolution objectives (high NA) and adjustable aperture diaphragms, modern light microscopes enable flexible matching of the optics to the requirements of the particular sample. In the case of stereomicroscopes it is often necessary to make a certain compromise in favor of higher depth of field, as the z dimension of three-dimensional structures frequently demands it.

## Even more depth of field

A sophisticated optical approach of Leica Microsystems that cancels the correlation between resolution and depth of field in stereomicroscopes is FusionOptics™. Here, one of the light paths provides one eye of the observer with an image of high resolution and low depth of field. Via the second light path, the other eye sees an image of the same object with low resolution and high depth of field.

The human brain combines the two separate images into one optimal overall image that features both high resolution and high depth of field.

Another example illustrating the phenomenal capabilities of the human brain is the Greenough stereomicroscope. Here, the object planes of the left and right light paths are at a slight angle to each other. In the overall image, the entire hatched area appears to be sharply focused, although this is not the case in either the left or the right image.

## Depth of field in digital image processing

The Multifocus module of the Leica Application Suite (LAS) was developed to extend the field depth of the automated microscope many times over. The illumination, image brightness and all other camera parameters can be set individually to optimize the quality of the resulting image.

The LAS Multifocus module provides an easy solution to capturing the extended field depth of live images by fully integrated control of the microscope with the motorfocus. The automatic capture of z stacks together with the intelligent image combination algorithms guarantees easy photography and storage of sharply focused images.

Thanks to the automated processing routine, there is hardly any need for user intervention. The settings can be easily altered for working with a wide range of samples. The Multifocus module is useful for applications in materials science, forensic medicine as well as in bio and geo sciences.

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