# Intro To Microscopy: Understanding Depth Of Field And Depth Of Focus

When it comes to microscopy, there is a lot to get your head around. Two of the most important concepts to understand are the depth of field and depth of focus.

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Many people use these terms interchangeably, but they are different and related principles.

To learn more about these two concepts, including how to calculate them, how they are related to each other, and how they are related to other aspects of microscopy, take a look at the info-packed guide below.

## Depth Of Focus Definition

In microscopy, the depth of focus describes how well the sensor is able to retain the focus of an image as it is changing its position. This is otherwise known as the image space, and it is a rather complicated concept.

It is considered to be complicated because it is affected by a number of different factors.

For instance, it takes into account the tip and tilt of the space between the objective lens sensor plane and the image plane.

Additionally, it is affected by diffraction figures and aberrations that extend beyond the image plane. As such, calculating the depth of focus can be quite tricky.

But, it is possible! Take a look at the section below to find out how.

## Calculating Depth Of Focus

To calculate the depth of focus of a single plan object in space, you can use the equation below:

t=2Nc(v/f)

Where t is the total depth of focus, N is the f-number of the lens, c is the circle of confusion, v is the image distance, and f is the focal length of the lens.

However, in many cases, the depth of focus can be approximated using the equation below:

t=2NC

However, it is important to note that this equation can only be used in situations wherein an image contains minimal magnification. If an image doesn’t contain minimal magnification, this approximation cannot be used.

## Depth Of Field Definition

In the world of microscopy, the depth of field number refers to how far below and above the sample plane the specimen and objective lens can be whilst staying in focus.

The depth of field is largely dependent on the objective lens’ numerical aperture, and is usually very small.

Interestingly, the human eye has one of the best depth of field values when it is compared to all artificial and natural optical instruments.

The depth of field of an optical instrument can be affected by a number of different factors. Take a look at the section below to learn more.

## Factors Affecting Depth Of Field

Understanding the depth of field of a microscope is very important. This is because it directly determines the extent to which you need to move the specimen slide around.

Whilst the numerical aperture of the objective lens is the main thing that can affect the depth of field, there are a few more factors that should be understood and taken into consideration.

### Depth Of Field Formula

First, it is necessary to state the formula for working out the depth of field. Below, we’ve written one formula for calculating the depth of field.

D represents the depth of field, 𝝀 represents the wavelength, n represents the refractive index of the medium between the coverslip and the objective front lens element, and NA is the objective numerical aperture.

The symbol e is the smallest distance that can be resolved by a detector that is placed in the image plane of the microscope objective, whose magnification is M.

D=(λn/NA2) + (n/MNA)e

### Numerical Aperture

The numerical aperture is the size of the area where light passes through an optical component. When you are considering the depth of field of a microscope, the numerical aperture is the size of the objective lens.

The depth of field is inversely proportional to the numerical aperture. This means that if you have a high numerical aperture, you will end up with a low depth of field.

Likewise, if you have a low numerical aperture, you will get a high depth of field.

### Resolution

Generally speaking, the clarity of the magnified image is inversely proportional to the numerical aperture. From this, we can determine that the resolution is directly proportional to the depth of field.

This means that, if there is a low resolution, the depth of field will also be low, but the numerical aperture will be high. Likewise, if the resolution is high, the depth of field will also be high, and the numerical aperture will be low.

### Contrast

The contrast of an image is related to the resolution of the image. In turn, different contrasts and resolutions correspond to different depths of the field. If the image has small specimen details, it will require a larger spatial frequency.

In turn, this will mean a smaller depth of field and vice versa.

### Magnification

Magnification is an especially important factor to consider when you are using a lens with high magnification. For example, oil immersion lenses may have a high depth of focus, but a low depth of field.

In turn, this means that making an error in focusing an image at a higher magnification is more likely.

As such, the depth of field becomes integral when you are viewing objects that have complex shapes or a variety of high and low surface points.

### Working Distance

The working distance is the space between the front lens of the objective and the nearest surface of the coverslip when the specimen is focused. The working distance has an effect on the depth of field.

A small working distance will result in a smaller depth of field, and a long working distance will result in a larger depth of field. As such, we can say that working distance and depth of field are directly proportional.

## Regular Depth Of Field Figures

The formula for depth of field above can look a bit confusing. But, when you get to grips with what each symbol means, it becomes a lot more clear. And, as you get started, you should be aware of some of the average figures of these symbols.

### Wavelength (𝝀)

The wavelength of the light is represented by Lamba 𝝀. Most optical microscopes will use visible light to show the specimen. Visible light can have a wavelength from 400 nanometers to 700 nanometers.

### Refractive Index (n)

The refractive index will depend on the medium. Usually, your medium will either be air or immersion oil. Air and vacuum have a refractive index of 1.00, whereas immersion oil has a refractive index of 1.52.

You may also use water, which has a refractive index of 1.33.

### Numerical Aperture (NA)

It is regular for the numerical aperture of the lens in question to increase with the magnification. On a 10x lens, you can expect a numerical aperture of around 0.25.

On a 20x lens, you can expect a numerical operative of 0.7. With an oil immersion lens, you can expect a numerical aperture of around 1.47.

### Magnification (M)

In this instance, magnification (M) refers to the magnification of the objective lens. This does not tell you anything about the magnification of the ocular lens.

If you have a light microscope, you can expect a magnification of somewhere between 4x and 100x.

This can be a difficult topic to understand. That’s why we’ve included this handy FAQ section. If you still have questions regarding the depth of field and depth of focus, take a look at the information below. You’ll be an expert in no time!

### What Is The Relationship Between The Depth Of Field And Depth Of Focus?

Simply put, a smaller depth of field refers to a small range in which the object will appear in focus. Whereas, a larger depth of field refers to a longer range in which the object will appear in focus.

### Why Does Depth Of Field Decrease As Magnification Increases?

The specimen will look bigger with a high magnification because a small area of the specimen is enlargened to cover the whole field of view of your eye.

Essentially, depth of field can be understood as a measure of the thickness of a plane of focus. Therefore, when the magnification increases, the depth of field decreases.

### Does A 4x Or A 10x Lens Have A Smaller Depth Of Field?

This follows perfectly from the previous question. As we just stated, magnification and the depth of field are inversely proportional. As such, the 10x will have a shorter depth of field, and the 4x will have a larger depth of field.

## Conclusion

Depth of field and depth of focus are complex concepts. But, when it comes to microscopy, understanding them is a necessity. We hope that this article has helped you to understand these concepts so that you can use them confidently in your work.

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