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Understanding Magnifi cation

Table 4 : Total magnifi cation data, M TOT VIS and M DIS (Equations 2 and 4b), for a digital microscope with 5 MP image sensor (DMS1000) and a stereo microscope (M205 A) equipped with a 5 MP digital camera. The possible range of magnifi cation values, minimum to maximum, for the discussed HD monitor sizes ( Table 2 ) and pixel ratios ( Table 3 ) are shown.

Digital microscope with 5 MP sensor Monitor Size (inch)

21.5” M DIS

8.4× 420×

29× 1,450×

min max

3.9× 320×

T e resolution limit of the digital microscope system resolution is determined by the smallest of the three resolution values above. T e diff raction limit of the light microscope (Equation 6) still governs the ultimate level of detail that can be observed and recorded. T is last point is important: the best resolution of a microscope generally is measured from a recorded image rather than a viewed image; methods for this fall outside the topics of this article [ 16 ]. Useful viewing distance . T e viewing distance is the distance between the observer’s eyes and the displayed image. T e range for a useful viewing distance is aff ected by the system resolution of the microscope and the visual angle of the observer [ 17 , 18 ]. T e minimal angle of resolution depends on the intensity of light emitted or refl ected from the observed object and the contrast between its specifi c features. T e angle ranges, on average, from 2.3 to 4.6 minutes of arc (low to high light intensity and contrast) for human eyes [ 9 , 19 – 21 ]. T is angular range indicates the optimal performance, in terms of visual acuity (resolution) and contrast sensitivity, of the human eye averaged over a large population varying in age from young to old. T us, on average, an eye is capable of distinguishing details on a monitor which have a separation distance corresponding to an angular diff erence of 2.3 to 4.6 minutes of arc (0.038 to 0.077 degrees; 0.669 to 1.338 × 10 -3 radians) for a specifi c viewing distance. To understand how the range for a useful viewing distance is determined, imagine a person observing an image displayed on a monitor which shows the smallest line pair spacing resolvable by the digital microscope system. It follows that the actual line pair spacing on the sample would then be:

minimal line pair spacing observed monitor = MDIS · (minimal resolvable line pair spacing sample)

where M DIS is the total magnification (Equation 4). To determine the minimal angle of resolution for the observer’s eye necessary in order to see two separate lines in the pair, the minimal line spacing observed on the monitor must be divided by the viewing distance:

75” 10× M TOT VIS

9.75× 800×

16.5× 3,400× Eyepiece

Stereo microscope with 5 MP camera Monitor Size (inch)

25× 21.5” M DIS 57× 11,700×

min max

As noted above, the minimum angle of resolution for the eye falls between 6.669 × 10 -4 and 1.338 × 10 -3 radians, so rearranging the equation above for viewing distance (in mm) and setting it equal to the lower and upper values of the angle of resolution, the useful viewing distance range can be expressed as (converted from units of mm to meters):

75”

Again, M DIS is the total lateral magnifi cation (Equation 4),

and the system resolution refers to the light microscope system resolution limit as discussed above (Equations 6–8). For the following calculations, it is assumed that the viewing distance is always within the useful range. Range of useful magnifi cation . To understand how to determine the range of useful magnifi cation for digital microscopy—the lowest and highest magnifi cation values for an image displayed on a monitor where the system resolution limit is clearly observed for optimal and non-optimal illumination—it is fi rst necessary to mention briefl y the “perceived” magnifi cation from visual observation of an image or object. Everyday experience shows that the perceived size of an object depends on the distance from which it is observed. Using geometrical optics and the relationship between angular and lateral magnifi cation, the following can be derived:

(10)

where M DIS is the total magnifi cation (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, that is, the closest point on which the eye can focus [ 22 ]. T e Appendix at the end of this article provides a more detailed derivation of Equation 10.

Finally, the range of useful magnifi cation can be defi ned by combining Equations 9 and 10. From Equation 10, aſt er converting the near point of the eye from units of mm to meters:

T e minimal resolvable line pair spacing on the sample is the inverse of the microscope system resolving power or resolution, thus:

T en, substituting the expression just above for the viewing distance into Equation 9 and dividing all sides by 0.25 and M DIS :

26

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Table 4 : Total magnifi cation data, M TOT VIS and M DIS (Equations 2 and 4b), for a digital microscope with 5 MP image sensor (DMS1000) and a stereo microscope (M205 A) equipped with a 5 MP digital camera. The possible range of magnifi cation values, minimum to maximum, for the discussed HD monitor sizes ( Table 2 ) and pixel ratios ( Table 3 ) are shown.

Digital microscope with 5 MP sensor Monitor Size (inch)

21.5” M DIS

8.4× 420×

29× 1,450×

min max

3.9× 320×

T e resolution limit of the digital microscope system resolution is determined by the smallest of the three resolution values above. T e diff raction limit of the light microscope (Equation 6) still governs the ultimate level of detail that can be observed and recorded. T is last point is important: the best resolution of a microscope generally is measured from a recorded image rather than a viewed image; methods for this fall outside the topics of this article [ 16 ]. Useful viewing distance . T e viewing distance is the distance between the observer’s eyes and the displayed image. T e range for a useful viewing distance is aff ected by the system resolution of the microscope and the visual angle of the observer [ 17 , 18 ]. T e minimal angle of resolution depends on the intensity of light emitted or refl ected from the observed object and the contrast between its specifi c features. T e angle ranges, on average, from 2.3 to 4.6 minutes of arc (low to high light intensity and contrast) for human eyes [ 9 , 19 – 21 ]. T is angular range indicates the optimal performance, in terms of visual acuity (resolution) and contrast sensitivity, of the human eye averaged over a large population varying in age from young to old. T us, on average, an eye is capable of distinguishing details on a monitor which have a separation distance corresponding to an angular diff erence of 2.3 to 4.6 minutes of arc (0.038 to 0.077 degrees; 0.669 to 1.338 × 10 -3 radians) for a specifi c viewing distance. To understand how the range for a useful viewing distance is determined, imagine a person observing an image displayed on a monitor which shows the smallest line pair spacing resolvable by the digital microscope system. It follows that the actual line pair spacing on the sample would then be:

minimal line pair spacing observed monitor = MDIS · (minimal resolvable line pair spacing sample)

where M DIS is the total magnification (Equation 4). To determine the minimal angle of resolution for the observer’s eye necessary in order to see two separate lines in the pair, the minimal line spacing observed on the monitor must be divided by the viewing distance:

75” 10× M TOT VIS

9.75× 800×

16.5× 3,400× Eyepiece

Stereo microscope with 5 MP camera Monitor Size (inch)

25× 21.5” M DIS 57× 11,700×

min max

As noted above, the minimum angle of resolution for the eye falls between 6.669 × 10 -4 and 1.338 × 10 -3 radians, so rearranging the equation above for viewing distance (in mm) and setting it equal to the lower and upper values of the angle of resolution, the useful viewing distance range can be expressed as (converted from units of mm to meters):

75”

Again, M DIS is the total lateral magnifi cation (Equation 4),

and the system resolution refers to the light microscope system resolution limit as discussed above (Equations 6–8). For the following calculations, it is assumed that the viewing distance is always within the useful range. Range of useful magnifi cation . To understand how to determine the range of useful magnifi cation for digital microscopy—the lowest and highest magnifi cation values for an image displayed on a monitor where the system resolution limit is clearly observed for optimal and non-optimal illumination—it is fi rst necessary to mention briefl y the “perceived” magnifi cation from visual observation of an image or object. Everyday experience shows that the perceived size of an object depends on the distance from which it is observed. Using geometrical optics and the relationship between angular and lateral magnifi cation, the following can be derived:

(10)

where M DIS is the total magnifi cation (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, that is, the closest point on which the eye can focus [ 22 ]. T e Appendix at the end of this article provides a more detailed derivation of Equation 10.

Finally, the range of useful magnifi cation can be defi ned by combining Equations 9 and 10. From Equation 10, aſt er converting the near point of the eye from units of mm to meters:

T e minimal resolvable line pair spacing on the sample is the inverse of the microscope system resolving power or resolution, thus:

T en, substituting the expression just above for the viewing distance into Equation 9 and dividing all sides by 0.25 and M DIS :

26

www.microscopy-today.com • 2018 July

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