What is the total magnification if you will use the high power objective with has 40x magnification?

Power vs Pixels!

Nowhere is the magnification versus resolution question more prevalent than in digital microscopy. In many cases, these two terms are used interchangeably. However, they are distinct and should not be confused.

Magnification

Each objective lens has a magnification printed on its side. It's easy to understand. A 40x objective makes things appear 40 times larger than they actually are. Comparing objective magnification is relative—a 40x objective makes things twice as big as a 20x objective while a 60x objective makes them six times larger than a 10x objective.

The eyepiece in a typical desktop microscope is 10x. The product of the objective magnification and the eyepiece magnification gives the final magnification of the microscope. So, a 60x objective and a 10x eyepiece gives a total magnification of 600x.

So, what happens when you couple an objective to a 2 or 5 or 8-megapixel camera with no eyepiece? Then, what is the magnification? If you use a 20x objective, is the final image 20 times larger? 200 times larger?

Pixel Mapping

In digital microscopy, we use a term called pixel mapping to answer the question of digital image magnification. In general, a 20x objective maps 0.5 microns (of the specimen on the slide) to a single pixel on the camera. The final magnification is obtained by dividing the display pixel size (in microns) by the pixel mapping.

For a 70" HD TV (1920x1080), the pixel size is about 0.8mm (800 microns). And 800 divided by 0.5 gives a final magnification of 1,600x. For more magnification, you need a larger monitor!

Instead of displaying the image data pixel for pixel, we could display one image pixel on 4 (2x2), 9 (3x3) or 16 (4x4) display pixels and achieve double, triple, or quadruple the apparent magnification. But, that only gives us bigger pixels—not better resolution.

Resolution

Resolution is the objective's ability to resolve really small stuff. In objective terminology, this is the NA (numerical aperture) specification, which, like the magnification, is also printed on the side of the objective. The higher the NA, the more (smaller) stuff can be resolved. In general, higher magnification objectives have higher NA.

In general, for digital scanners, the maximum magnification of an objective is approximately 1000x the objective's NA. So, an objective with a .65NA can achieve approximately 650x in the digital domain. You might assume that we would always want the highest NA objective we could get, but that's not always the case.

Increased NA comes at a price: reduced depth of field and increased cost.

Numerical Aperture and Depth of Field are two sides of the same coin, and they are (more or less) inversely proportional. As NA increases, depth of field decreases, and vice-versa. Matching resolution and depth of field to the subject material is a key factor in choosing the right objective for the job at hand.

Depth of Field

Depth of Field is the distance between the nearest and farthest objects that are in focus without moving the objective. Anyone who regularly uses a desktop microscope knows that a 4x or 10x objective is much easier to focus than a 60x or 100x objective. The reason is because the depth of field of the lower NA objectives is very large (so, more stuff is in focus at the same time). And that means that getting the objective "close" to ideal focus is good enough because a deeper volume of the specimen is in good focus.

High NA objectives have a lower depth of field which means setting the focus is more critical and difficult to achieve. Getting the objective close-enough just doesn't work. Changing the focus only slightly can reveal different features in the specimen. Using an objective with a lower depth of field, objects may look different depending on how "deep" into the specimen you focus.

Striking a Balance

After all of the above detail, you might think it would be best to find a microscope objective with great magnification, high NA, and large depth of field. Such an objective does not exist—at any cost. So, we need to find a happy medium that satisfies as many requirements as possible. We make these kinds of trade-offs with whole slide scanners because of their general purpose nature.

How Does This Affect Whole Slide Scanning?

The best way to answer this question is to present a list of whole slide scanner truths to keep in mind.

• Doubling the objective magnification quadruples the pixel data in the scan area. The reason for this is that the region doubles vertically and horizontally and we need to acquire four times as many images.
• Doubling the magnification quadruples the scan time (more or less). Since you're capturing four times the image data, it will naturally take four times as long to do so.
• Increasing the magnification (or NA) increases the precision (and time) required to focus. So, a scan with a 10x (low NA) objective is likely more than four (4) times faster than a 20x (high NA) objective. This is due to the greater precision required when focusing the higher NA objective. Focus gets even more critical with 40x or 60x objectives.

Conclusion

So, just what does all of this information and detail mean and what can we take away from it?

Choose the objective that matches the depth of field and resolution requirements of the job.

• If you're looking at insects and most plant biology, a 10x or 20x objective is probably the right choice.
• If you're looking at detail inside a white blood cell, you most likely require a 60x objective.
• If you're looking at pathology, you may find that a 40x objective works well. But, a 20x objective may be just fine for many applications (the scans are certainly faster).

In any case, we are here to help. Just drop us an email or phone call to discuss your whole slide scanner requirements.

Updated December 08, 2020

By Karen G Blaettler

Microscopes magnify the tiniest inhabitants of this world. From the minute details of cells to the delicate cilia of paramecium to the intricate workings of Daphnia, microscopes reveal many miniscule secrets. Calculating total magnification uses simple observation and basic multiplication.

Microscopes use lenses to magnify objects. A simple microscope uses only one lens; a magnifying glass could be called a simple microscope. The magnification of a simple microscope doesn't need any calculation because the single lens is usually labeled. A hand-lens, for example, might be labeled with 10x, meaning the lens magnifies the object to look ten times larger than the actual size.

Compound microscopes use two or more lenses to magnify the specimen. The standard school microscope combines two lenses, the ocular and one objective lens, to magnify the object. The ocular or eyepiece is found at the top of the body tube. The objective lens points down toward the object to be magnified. Most microscopes have three or four objective lenses mounted on a rotating nosepiece. Rotating the nosepiece lets the viewer change the magnification. Different objective lenses provide different magnification options.

Finding the magnification of each lens requires examining the casing of each lens. On the side of the casing is a series of numbers that includes a number followed by x, as 10x. This 10x shows that the lens magnifies an object to appear ten times larger than reality. Depending on the manufacturer, this magnification number may appear at the beginning or at the end of the number sequence. To calculate total magnification, find the magnification of both the eyepiece and the objective lenses. The common ocular magnifies ten times, marked as 10x. The standard objective lenses magnify 4x, 10x and 40x. If the microscope has a fourth objective lens, the magnification will most likely be 100x.

Once the magnification of each individual lens is known, calculating total magnification is simple math. Multiply the magnification of the lenses together. For example, if the eyepiece magnification is 10x and the objective lens in use has a magnification of 4x, the total magnification is:

10\times 4 = 40

The total magnification of 40 means that the object appears forty times larger than the actual object. If the viewer changes to the 10x objective lens, the total magnification will be the ocular's 10x magnification multiplied by the new objective lens's 10x magnification, calculated as:

10\times 10 = 100

Note that calculating magnification in telescopes uses a different equation than calculating magnifiction in microscopes. For telescopes, one magnification calculation uses the focal lengths of the telescope and the eyepiece. That calculation is:

\text{magnification}=\frac{\text{focal length of telescope}}{\text{focal length of eyepiece}}

Like the microscope, these numbers usually can be found on the telescope.

A microscope's total magnification is a combination of the eyepieces and the objective lens. For example, a biological microscope with 10x eyepieces and a 40x objective has 400x magnification. There are however, a few limits to the amount of total magnification that can be reached before empty magnification comes into play. Empty magnification occurs when the image continues to be enlarged, but no additional detail is resolved. This is often the case when higher magnification eyepieces are used. In order to avoid empty magnification, there are a few simple steps that are helpful to follow.

Eyepiece and Objective Combinations for Optimal Magnification

When selecting a combination of eyepieces and objective lenses for the optimal magnification, without ending up with "empty magnification" it is important to consider the numerical aperature (NA) of the objective. The numerical aperture of a microscope objective defines the objective's resolution. Each microscope objective has a minimum and maximum magnification necessary for the details in an image to be resolved. A simple formula for the minimum value is (500 x NA). And for the maximum magnification (1000 x NA). Magnifications higher than this value will result in empty magnification, or an image that has a poor resolution. The table below shows some typical NA values with their corresponding objective and provides a range of useful magnification combinations. The blank boxes in the table would provide empty magnification and should be avoided. For example, pairing 20x eyepieces with a 100x objective would not provide good resolution and would result in empty magnification. To determine this, we took 1.25NA x 1000 = 1250 magnification maximum. However, the combination of the 100x objective x 20x eyepieces = 2000, which is above the maximum magnification.

Range of Useful Magnification based on NA of Objectives

If you have any questions about your microscope's magnification, contact Microscope World.