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What Does 30,000:1 Magnification Really Mean?

Some Useful Guidelines for Understanding Magnification in Today’s New Digital Microscope Era

One important criterion concerning the performance of an optical microscope is magnification. This report will offer digital microscopy users helpful guidelines to determine the useful range of magnification values.

For more than 150 years, optical microscopy, which uses glass lenses to focus light and produce the phenomenon of magnification, has allowed the observation of microscopic entities not seen by the unaided eye [1]. Today there are many types of optical microscopes, but here the focus will be on two of the most common ones: digital microscopes [2], which have electronic image sensors, but no eyepieces, and microscopes for visual observation [3, 4], which have eyepieces. Additionally, a microscope for visual observation can be equipped with a digital camera, so it can be used in a similar manner as a digital microscope.

Updated June 26, 2018; first published February 06, 2015

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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. Magnification serves a useful purpose only when it is possible to see more details of an object in the image than when observing the object with the unaided eye. At the present time, magnification is well defined when viewing an image of a sample through the eyepieces of a microscope. For this case, rigorous international standards have been documented [5–9]. Many of these standards also apply to digital microscopy, but strict definitions and standards for magnification achieved by a digital microscope, where the image is most often viewed by display on an electronic monitor, have only recently been published [10].

Digital microscopes, as well as microscopes for visual observation equipped with digital cameras, allow the rapid acquisition of high quality images. Often they are used for a variety of technical applications [11, 12], in many different fields and industries.

Magnification in digital microscopy

Basic definition

What exactly is magnification? A basic definition of magnification is the ratio of the size of a specific feature of an object or sample as seen in an image produced by an optical system to the actual size of the feature on the object itself. Thus, lateral magnification, MDIS, can be defined as:

It should be noted that the useful range of perceived visual magnification significantly depends on the maximum resolving power of the microscope system. When the magnification passes beyond the useful range, then no additional details about the sample can be seen. This situation is referred to as empty magnification [13, 14]. Based on the maximum resolving power, also a useful range of viewing distance, i.e. the distance between the digital display and the observer’s eyes, can be defined for practical reasons.

Digital microscopes or microscopes for visual observation with digital camera

When observing the image through the eyepieces of a microscope for visual observation, the total (lateral) magnification is defined as [8]:

where

  • MTOT VIS is the total lateral magnification observed through the eyepiece,
  • MO is the objective lens magnification,
  • q is the total tube factor (zoom and other tube lenses), and
  • ME = eyepiece lens magnification.


For the case of detecting an image of a microscope which is projected onto an electronic sensor, such as that of a digital camera, the magnification for the image formed at the sensor is [8]:

where

  • MTOT PROJ is the (lateral) magnification of the microscope (image projected onto sensor),
  • p is the projection factor from eyepiece to camera, and
  • MPHOT is the magnification of the photographic projection lens from the tube to camera.

The total tube factor, q, is normally between 0.5 : 1 and 25 : 1. The photographic projection lens magnification, MPHOT, is normally between 0.32 : 1 and 1.6 : 1.
For digital microscopes, there are no eyepieces, so an image is projected onto and detected by an electronic sensor of a digital camera, and then displayed onto an electronic monitor for observation. This fact is also true for a microscope for visual observation equipped with a digital camera when the image is observed via the monitor. Thus, the final total magnification for digital microscopy, MDIS, will always depend on the size of the image displayed on the monitor. For this report, a display of the image from the camera sensor to the monitor is assumed to occur in a 1-to-1 pixel correspondence mode, the simplest case scenario. The signal from one pixel of the camera is displayed on one pixel of the monitor. Thus, the ratio of the monitor to camera sensor image size is directly proportional to the actual pixel size of the monitor and sensor (refer to the Appendix below for more details). It can be defined as:

where MDIS is the total lateral display magnification for an image displayed on a monitor and pixel ratio is the "enlargement" of the image due to the signal transmission of the image from the camera to the electronic monitor display.
The pixel size ratio is determined by the ratio of the pixel size of the monitor to that of the camera sensor:

As already mentioned above, a 1-to-1 pixel correspondence mode is assumed for image display from the camera sensor to the monitor. In this display mode, depending on the monitor’s number of pixels, only a portion of the image may visible on the monitor.

Examples of digital microscopy are shown in Figure 1: a digital microscope and stereo microscope with digital camera.

Resolution

For optical instruments in general, resolution is the ability to see fine details in an image. More specifically, resolving power is the ability to distinguish in an image adjacent points or lines of the object which are closely spaced together. Usually these two terms are used synonymously, however resolution is the more practical one. In microscopy, resolution is expressed in line pairs per millimeter. In other words, pairs of black and white lines with equal line thickness and spacing can be distinguished at a given resolution.

High magnification values without sufficient resolution lead to empty magnification, as already mentioned above [13, 14]. Therefore, it is of vital importance to understand the limiting factors for resolution, not just for digital microscopy, but all forms of optical microscopy.

Camera sensor and display monitor pixel number and size

The sensors used in all microscope digital cameras produced by Leica Microsystems have a number of pixels typically between 1,600 × 1,200 and 4,080 × 3,072 and a pixel size between 2 and 6.5 μm (examples in Table 1). High definition (HD) computer monitors or televisions have 1,920 × 1,200 or 1,080 pixels and a pixel size between 0.1 and 0.9 mm (examples in Table 2) [15, 16]. Therefore, the monitor pixels are typically 25 to 450 times bigger than the camera pixels.

Camera

Sensor type

Width (mm)

Height (mm)

Pixel size (mm)

Pixels

Megapixels

DFC450

2/3“

8.7

6.5

3.4

2,560 x 1,920

4.92

MC120 HD / DMS300

1/2.3“

6.1

4.6

3.34

1,824 x 1,368

2.5

MC170 HD / DMS1000

1/2.3“

6.1

4.6

2.35

2,592 x 1,944

5.04

MC190 HD / IC90 E

1/2.3“

6.1 / 6.44

4.6

1.67

3,648 x 2,736

9.98

DMC5400

1”

13.2

8.8

2.4

5,472 x 3,648

19.96

Table 1: Specifications of image sensors used in the DFC450 and MC120/170/190 HD, IC90 E, and DMC5400 digital cameras and the DMS300/1000 digital microscopes supplied by Leica Microsystems.

HD flat display Width (mm) Height (mm) Pixel size (mm) Pixels Megapixels
PC monitor 21.5'' 476 267 0.25 1,920 × 1,080 2.07
PC monitor 24'' 521 324 0.27 1,920 × 1,200 2.3
PC monitor 27'' 597 337 0.31 1,920 × 1,080
2.07
TV 32'' 699 394 0.36
TV 40'' 880 495 0.46
TV 48'' 1,054 593 0.55
TV 55'' 1,211 681 0.63
TV 65'' 1,429 804 0.74
TV 75'' 1,648 927 0.86
TV 79'' 1,734 976 0.45 3,840 × 2,160
8.29
TV 84'' 1,860 1,046 0.48
TV 85'' 1,882 1,058 0.49

Table 2: Examples of HD electronic monitor displays: computer monitors or TVs.

Pixel size ratio

From knowing the typical pixel sizes of the camera sensors (Table 1) and flat screen HD monitors (Table 2), then values for the size ratios can be easily calculated using Equation 5 (Table 3).

Camera type Monitor size (inch)
85” 79” 75” 65” 48” 32” 27” 24” 21.5”
Pixel size ratio
DFC450 144:1 132:1 253:1 218:1 162:1 106:1 91:1 79:1 74:1
MC120 HD / DMS300 147:1 135:1 258:1 222:1 165:1 108:1 93:1 81:1 75:1
MC170 HD / DMS1000 209:1 192:1 366:1 315:1 234:1 153:1 132:1 115:1 106:1
MC190 HD / IC90 E 293:1 270:1 515:1 443:1 329:1 216:1 186:1 162:1 150:1
DMC5400 204:1 188:1 358:1 308:1 229:1 150:1 129:1 113:1 104:1

Table 3: Pixel size ratios (Equation 5) for HD monitors (Table 2) and sensors used in the DMS1000/300 digital microscopes and MC190/170/120 HD, DFC450, IC90 E and DMC5400 digital cameras supplied by Leica Microsystems (Table 1).

Examples: Digital microscope and stereo microscope with digital camera

For simplicity, only 2 examples of digital microscopy, actually a digital microscope and a stereo microscope equipped with a digital camera, will be discussed in this report. It is assumed that an image is displayed, using a 1-to-1 camera to monitor pixel correspondence, onto a HD monitor with sizes ranging from 21.5'' (diagonal dimension 21.5 inches [54.6 cm]) to 75'' (diagonal dimension 74.5 inches [189 cm]). The 2 examples are the DMS1000 digital microscope and the M205 A stereo microscope having the MC170 HD digital camera installed with a C-mount. Table 4 shows examples of total magnification (refer to Equations 2 and 4) values obtainable with the DMS1000 or M205 A microscope equipped with the MC170 HD camera. For the DMS1000 microscope, the magnification range for the objective lens is 0.32x to 2x and the tube factor (q) including the photographic projection lens has a 8.4 : 1 range. For the M205 A microscope with MC170 HD camera, the magnification range for the objective is 0.5x to 2x, for the zoom 0.78x to 16x, for the eyepieces 10x to 25x, and for the C-mount lens 0.4x to 1x.

DMS1000M205 A/MC170 HD
Monitor size (inch)


EyepieceMonitor size (inch)


21.5''75''10x25x21.5"75"
MDISMTOT VISMDIS
8.4 : 129 : 1min.3.99.7516.5 : 157 : 1min.
420 : 11,450 : 1max320x800x3,400 : 111,700 : 1max.


Table 4: Total magnification data, MTOT VIS and MDIS (Equations 2 and 4), for the DMS1000 digital microscope and the M205 A stereo microscope equipped with the MC170 HD digital camera. The possible range of magnification values, minimum to maximum, for the discussed HD monitor sizes (Table 2) and pixel ratios (Table 3).

30,000 : 1 magnification

Which monitor pixel size would be needed to attain a total lateral display magnification of 30,000 : 1? An example can be shown using the M205 A microscope with MC170 HD digital camera and Equations 3b, 4, and 5. The maximum magnification for the M205 A for an image of the sample projected onto the camera sensor is:

Max. magnification onto sensor  =  2x (objective)  x  16x (zoom)  x  1x (C-mount)  =  32x

The pixel ratio value which corresponds to a total magnification of 30,000 : 1 with the above magnification of 32x onto the sensor is:

The pixel size of the Leica MC170 HD camera sensor is 2.35 μm. Using the pixel ratio value above, 938 : 1, and a 1-to-1 camera to monitor pixel correspondence, the monitor pixel size must be:

Monitor pixel size  =  938 (pixel ratio)  x  0.00235 mm (pixel size sensor)  =  2.2 mm

Therefore, to achieve a total magnification of 30,000 : 1 with the M205 A and MC170 HD camera, the monitor pixel size would have to be 2.2 mm. This pixel size would correspond to a HD monitor diagonal of 4.9 m!

Useful range of magnification for digital microscopy

Now one must ask the question if this level of magnification, 30,000 : 1, is simply beyond the useful range, meaning it is empty magnification. How do we determine a useful range of magnification for digital microscopy, where an image is observed from a monitor? First it is important to understand better the microscope system resolution and the viewing distance.

Microscope system resolution

The system resolution for a digital microscope (or stereo with digital camera) is influenced by 3 main factors:

Optical resolution:

where NA is the numerical aperture and λ is the wavelength of light in nm;

Image sensor (camera sensor) resolution:

where MTOT PROJ is the magnification from the sample to the sensor (Equation 3), the "sensor bin. mode" refers to the binning mode which is 1 for full frame, 2 for 2 × 2 pixel binning, etc. (refer to Figure 2), and "pixel size" refers to the sensor pixel size in µm; and

Image display (monitor) resolution:

where MDIS is the total lateral magnification (Equation 4) and the monitor pixel size is in mm.

The basis for the camera sensor and display monitor resolution limit is the Nyquist rate or frequency from the sampling theorem for digital signal processing (refer to Figure 2) [17]. This theorem assumes that at least 2 pixels are needed to resolve 1 line pair. For this report, as stated above, the best case scenario of a 1-to-1 correspondence is assumed between the pixels of the sensor and monitor. Therefore, using Equation 4 and converting the monitor pixel size into units of µm, it becomes clear that the resolution limit of the sensor and monitor are identical.

The resolution limit of the digital microscope system resolution is determined by the smallest of the 3 resolution values above.

Useful range for viewing distance

The viewing distance is the distance between the observer’s eyes and the displayed image. The useful range for the viewing distance is affected by the system resolution of the microscope and visual resolution angle of the observer [18]. The latter is normally 2.3 to 4.6 minutes of arc for typical human eyes. In other words, a human eye is capable of distinguishing details on a monitor which have a separation distance corresponding to an angular difference of more than 2.3 to 4.6 minutes of arc for a specific viewing distance. The useful range for the viewing distance can be expressed as:

where MDIS is the total lateral magnification (Equation 4) and "system resolution" refers to the microscope resolution limit as discussed above.

For the discussion here, it is assumed that the viewing distance is always within the useful range.

Useful range of magnification

To understand how to determine the useful range of magnification for digital microscopy, i.e. the observation of a magnified image on a display monitor, it is first necessary to mention briefly the perceived magnification from visual observation of an image or object. Using geometrical optics, the following can be derived:

where MDIS is the total magnification (Equation 1) and 250 refers to the standard reference for the viewing distance in mm which is based on the average near point for the human eye.

Now, finally the useful range of magnification can be defined by combining Equations 9 and 10:

Thus, the useful range of magnification is between 1/6 and 1/3 of the microscope system resolution.

High magnification

Modern camera sensors have pixels sizes in the 1–6 µm range, well below 10 µm. When a high sample-to-sensor magnification is used, for example 150 : 1, and there is no binning of the pixels and a 1-to-1 sensor to monitor pixel correspondence, then it follows from Equations 6, 7, and 8 above that the microscope system resolution is determined by the optical resolution limit. The optical resolution limit for the largest numerical aperture, approaching 1.3, and the smallest wavelength of visible light, approximately 400 nm, is 5,400 line pairs/mm. For these same conditions, the resolution limit of a camera sensor with a pixel size below 10 µm easily exceeds this value. For the conditions of this specific case, from Equation 11 above the maximum magnification in the useful range of values is 1,800x.

Low magnification

At low magnification from the sample to camera sensor, 1x or even less, numerical apertures are typically below 0.03. The resolution limit of camera sensors with pixels sizes larger than 2 µm will start to be inferior to the optical resolution at such low magnification. Therefore, at low magnification, 1x or less, the sensor or monitor resolution limit will likely be the dominating factor concerning the resolution of the microscope system.

Empty magnification

For this discussion of digital microscopy, it is assumed that the image on the monitor is always observed within the useful viewing distance range described above. Whenever the perceived magnification value exceeds the useful magnification range, i.e. 1,800x, then no further details about the sample can be resolved.

Object field (field of view)

Object field (OF) is the part of the object which is reproduced in the final image. It is also known as the microscope field of view (FOV). Thus, details of an object can only be observed if they are present in the object field.

When looking through the eyepieces, the OF is a visible circular image of a portion of the sample. The size of the OF (refer to Equation 12) is dependent on the field number (FN) of the eyepiece, as well as, the magnification of the objective and tube lenses (refer to Figure 3).

The object field in digital microscopy is of rectangular shape due to the nature of the image sensor which receives the image and the monitor which displays it (refer to Figure 3). It is expressed in width and height given in millimeters. For digital microscopy, care has to be taken that the image created by the optical system is large enough to cover the whole image sensor. In this case, the OF can be limited either by the image sensor or the display. In either case the physical size of the active area, given by the number of active pixels in height and width and their physical size (pixel pitch), has to be taken into account.

To calculate the OF, the physical size of the active area of the sensor (refer to Equation 13) has to be divided by the magnification of the objective, tube, and camera projection lenses (MTOT PROJ) or for the monitor by the total lateral display magnification, MDIS. The smaller of these values for each height and width define the OF of the digital microscope.

It is likely that both height and width of the object field are not necessarily jointly limited by the image sensor or the display. For example, the height can be limited by the display whereas the width can be limited by the sensor. The final OF will depend on the dimensions and aspect ratio of the image sensor and display and the pixel correspondence (1 : 1, 1 : 2, 2 : 1, etc.) between them for image display. In this report, a 1-to-1 sensor pixel to monitor pixel correspondence is assumed.

The OF for eyepieces can be determined by:

where

  • OFeyepiece is the object field observed through an eyepiece,
  • FN is the eyepiece field number, and
  • MO × q (from Equation 2) is the total magnification before the eyepiece due to the objective, zoom, and any other tube lens before the eyepieces.

The OF for a camera sensor can be determined using the width and height of the sensor divided by the total magnification of the optics producing the image of the sample onto the sensor:

where

  • w is the width of the OF observed by a sensor,
  • h is the height of the OF observed by a sensor,
  • MTOT PROJ is the total magnification from sample to sensor (Equation 3b), and
  • the pixel size is in μm.

The difference in OF between images seen by the eyepieces versus those recorded by the camera chip, for the same sample, objective, and zoom setting, are shown in Figures 3 and 4 below. For Figure 4, the total magnification of the objective and zoom lens is 1x, but several types of Leica C-mounts with different magnification have been used to install the camera, a DFC450 with a chip size of 2/3'' onto a M205 A stereo microscope. The red rectangle seen in Figure 4a represents the OF of Figure 4b, an image taken with the 0.32x C-mount. The blue rectangle indicates the OF of Figure 4c, taken with the 0.5x C-mount. The green rectangle shows the OF of Figure 4d, taken with the 0.63x C-mount. Figure 4b shows the problem of vignetting where the edges of the image are darker than the center. To avoid such a problem, normally it is recommended that a 0.32x C-mount is used with a digital camera having a 1/3'' (8.45 mm) chip size, a 0.4x C-mount with a 1/2.3'' (11 mm) chip size, a 0.5x C-mount with a 1/2'' (12.7 mm) chip size, and a 0.63x C-mount with a 2/3'' (16.9 mm) chip size.

The object field (OF) of the camera sensor can be calculated using Equation 13 above. The range of values of the OF for the DMS1000 digital microscope and M205 A stereo microscope equipped with a MD170 HD camera are shown in Table 5. Again, the magnification range for the DMS1000 is: objective 0.32x to 2x and the tube factor (q) including the photographic projection lens has a 8.4 : 1 ratio, and for the M205 A with MC170 HD camera: objective 0.5x to 2x, zoom 0.78x to 16x, and C-mount 0.4x to 1x.

DMS1000

OF sensor

MTOT PROJ w (mm) h (mm)
0.08 : 1 77 58.1 max. OF
3.96 : 1 1.5 1.2 min. OF

M205 A/MC170 HD

OF sensor

MTOT PROJ w (mm) h (mm)
0.16 : 1 39.1 29.5 max. OF
32 : 1 0.19 0.14 min. OF

Table 5: Object field (OF) data (Equation 13) for an image from the DMS1000 digital microscope and M205 A stereo microscope equipped with a MC170 HD digital camera showing the range from minimum to maximum values.

Summary and conclusions

Digital microscopes use electronic image sensors (camera sensors) to replace eyepieces. Microscopes for visual perception, such as stereo microscopes, have eyepieces and can be equipped with digital cameras. Digital microscopy allows rapid acquisition of high quality images. It is often used for fast and easy documentation, quality control (QC), failure analysis, and research and development (R&D) in a variety of fields.

Due to the diversity of camera sensor dimensions and electronic display monitor sizes, determining magnification and resolution when using digital microscopy can be challenging. With this report users of digital microscopy can better understand how to evaluate the total magnification and its useful range. In addition, helpful information concerning the object field or field of view is discussed.

References

  1. Rühl H: The Optical Microscope – Some Basics (May 2012).
  2. Goeggel D, Schué A: Trends in Microscopy: How Much "Digital" Do You Really Need? (September 2012).
  3. Goeggel D: Factors to Consider When Selecting a Stereo Microscope (January 2012).
  4. Goeggel D, Schué A, and Kiper D: FusionOptics – Combines high resolution and depth of field for ideal 3D optical Images (April 2008).
  5. ISO 8039:2012: Microscopes – Values, tolerances and symbols for magnification. International Organization for Standardization (2012).
  6. ISO 8578:2012: Microscopes – Marking of objectives and eyepieces. International Organization for Standardization (2012).
  7. ISO 9345-1 and -2:2012: Microscopes – Imaging distances related to mechanical reference planes – Parts 1 and 2. International Organization for Standardization (2012).
  8. ISO 10934-1 and -2:2002: Optics and optical instruments – Vocabulary for microscopy – Parts 1 and 2. International Organization for Standardization (2002).
  9. ISO 19012-1 and -2:2013: Microscopes – Designation of microscope objectives – Parts 1 and 2. International Organization for Standardization (2013).
  10. ISO 18221: 2016 Standard Microscopes - Microscopes with digital imaging displays - Information provided to the user regarding imaging performance, International Organization for Standardization (2013)
  11. Schlaffer G: Digital Microscopy: A Collection of Application Videos (October 2012).
  12. DeRose J, Schlaffer G: Are Your Digital Microscope Measurements Accurate and Reliable? (September 2014).
  13. Schué A: Beware of "Empty" Magnification (May 2008).
  14. Schmid U: Digital Cameras Beware of Pixel Mania (May 2009).
  15. Wikipedia: Computer display standard.
  16. Wikipedia: Display resolution.
  17. Wikipedia: Nyquist–Shannon sampling theorem.
  18. Wikipedia: Optimum HDTV viewing distance.

Appendix

Detailed explanation for Equation 4

The basis for the definition of the total lateral display magnification, MDIS, indicated by Equation 4, is the "enlargement" of the image size displayed on the monitor in comparison to the image size projected onto the camera sensor. Thus, the ratio of the image size on the monitor to that on the sensor determines the total magnification:

For a size ratio, a single image dimension, such as the image width or height, could be used. Working with the width, then the image width on the monitor equals the number of monitor pixels in the image width times the pixel size. For the image width on the sensor, a similar argument applies, therefore:

The ratio of the monitor to sensor pixel size has been defined in Equation 5 as the pixel size ratio:

When the number of monitor and sensor pixels are the same (a 1-to-1 pixel correspondence), then:

MDIS = MTOT PROJ x Pixel size ratio

which is, of course, Equation 4 above.

However, the question arises: If 2 monitors have the same pixel size but different dimensions, will the total magnification be the same if the same image from a camera sensor is displayed on either one with a 1-to-1 pixel correspondence?

An example (not a real case) can be used to illustrate the answer. From Table 2 there are 2 size TVs, the 40 inch (102 cm) and 79 inch (201 cm), which have nearly identical pixel sizes, 0.46 mm versus 0.45 mm. The 79 inch TV has 4 times as many pixels (3,840 x 2,160 pixels) as the 40 inch TV (1,920 x 1,080 pixels), twice as many pixels for each dimension. Now imagine using a camera sensor also with 8.29 MP (3,840 x 2,160 pixels) to display the same image on both TVs with a 1-to-1 pixel correspondence (signal of 1 sensor pixel is displayed on 1 monitor pixel). The 79 inch TV would show the full image projected onto the sensor. However, the 40 inch TV, having 4 times fewer pixels than the sensor, would show only 1/4 of the image projected onto the sensor. Still, the total magnification for the image displayed on both TVs would be the same. To prove this fact, Figure A1 below shows the same image from a camera displayed on both the 40 and 79 inch TV. The white double arrow indicates the same features on the sample. The length of the arrow is the same in each image, as the pixel sizes are the same for each TV and the feature covers the same number of pixels in each image.

To further clarify the point, imagine a very large piece of paper having a rectangular hole with the dimensions of the 40 inch TV. One could use the paper to cover the 79 inch TV and an area of the image equivalent to the 40 inch TV would be revealed. An example is shown in Figure A2 below. If the rectangular hole in the paper is moved around over the 79 inch TV, then it would be similar to moving around the displayed image on the 40 inch TV with software using a mouse or cursor. Again, the same features measured in the image displayed on either the 79 or 40 inch TV with a 1-to-1 pixel correspondence would have the same dimensions, meaning the total magnification is the same.