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Understanding Magnifi cation


Table 2 : Examples of high defi nition displays including both computer monitors and TVs.


HD Flat Display (inches)


PC monitor 21.5” PC monitor 24” PC monitor 27” TV 32” TV 40” TV 48” TV 55” TV 65” TV 75” TV 79” TV 84” TV 85”


Display width (mm)


476 521 597 699 880


1,054 1,211 1,429 1,648 1,734 1,860 1,882


Display height (mm)


267 324 337 394 495 593 681 804 927 976


1,046 1,058


Resolution . For optical instruments in general, resolution or resolving power is the ability to see fi ne details in an image. More specifi cally, resolving power is the ability to distinguish in an image adjacent points or lines of the object that are closely spaced. Sometimes the terms magnifi cation and resolution are used synonymously, but this is incorrect. Only resolution determines the limit of the smallest object that can be resolved. Magnifi cation denotes the size of the resolved object. In light microscopy, resolution is typically expressed in line pairs per millimeter observed when lines of various separations are used as the object. In other words, at a given level of resolution pairs of black and white lines with equal line thickness and spacing can be distinguished. High magnifi cation without suffi cient resolution leads to empty magnifi cation, as mentioned above [ 10 ]. T erefore, it is of vital importance to understand the limiting factors for resolution, not just for digital light microscopy, but for all forms of microscopy.


Image Sensor and Display Monitor Combinations Pixel number and size . Image sensors used in most microscope digital cameras have a number of pixels typically between 1,600 × 1,200 and 5,472 × 3,648 and a pixel size between 1.5 µm and 6 µm (see examples in Table 1 ). High-defi nition (HD) electronic displays, including computer monitors and televisions, typically have minimum pixel numbers of 1,200, 1,080, or 2,160 pixels and pixel sizes between 0.12 and 0.9 mm (see Table 2 ) [ 12 , 13 ]. T erefore, monitor pixels are typically 20 to 600 times larger than camera pixels.


Pixel size ratio . Knowing pixel sizes of image sensors


( Table 1 ) and fl at-screen HD monitors ( Table 2 ), values for pixel size ratios can be calculated using Equation 5 (see Table 3 ).


Digital Microscopes and Stereo Microscopes with Digital Cameras Total magnifi cation . For simplicity, only two examples of digital microscopy are described here: a digital microscope and a stereo microscope equipped with a digital camera installed with a C-mount. It is assumed that in each case an image is displayed, using a 1-to-1 camera-to-monitor pixel correspondence, onto an HD monitor where sizes range


2018 July • www.microscopy-today.com


Pixel Size (mm)


0.25 0.27 0.31 0.36 0.46 0.55 0.63 0.74 0.86 0.45 0.48 0.49


Pixels


1,920 × 1,080 1,920 × 1,200


Megapixels 2.07 2.3


1,920 × 1,080


2.07


3,840 × 2,160


8.29


from 21.5” (diagonal dimension 21.5 inches [54.6 cm]) to 75” (diagonal dimension 74.5 inches [189 cm]). Both microscopes use a 5 MP image sensor. Table 4 shows examples of total magnifi cation values (expressed as image size divided by object size) obtainable with the digital microscope or stereo microscope with digital camera.


For the digital microscope, the magnification range for the objective lens is 0.32× to 2×, and the tube factor (q) including the photographic projection lens has a maximum to minimum magnification range of 8:1 (ratio of max to min tube factor magnification). For the stereo microscope with camera, the magnification range for the objective is 0.5× to 2×, for the zoom from 0.78× to 16×, for the eyepieces 10× to 25×, and for the C-mount lens from 0.4× to 1×. Using Equations 2 and 4b, example calculations for the minimum and maximum magnification values ( M TOT VIS and M DIS in table 4) achievable with the stereo microscope having a 5 MP camera sensor can be shown. The stereo microscope has a min and max objective magnification of M O = 0.5× or 2×, a min and max zoom factor of q = 0.78× or 16×, a min and max C-mount magnification of M PHOT = 0.4× or 1×, and a min and max eyepiece magnification of M E = 10× or 25×. Then the minimum and maximum total magnification ( M TOT VIS ) seen via the eyepieces would be:


Minimum: MTOT VIS = 0.5× · 0.78× · 10× = 3.9× Maximum: MTOT VIS = 2× · 16× · 25× = 800×.


Also, the total display magnifi cation ( M DIS ) seen via an image displayed on a 21.5” or 75” monitor (table 2) with a pixel size ratio of 106:1 and 366:1 (table 3) would be:


Minimum: MDIS = 0.5× · 0.78× · 0.4× · 106 = 16.5×. Maximum: MDIS = 2× · 16× · 1× · 366 ≈ 11,700×.


Magnifi cations on large monitors . Question: Which monitor size and pixel size would be needed to attain a total lateral display magnifi cation of 30,000:1? An example can be shown using the stereo microscope with 5 MP camera mentioned above and Equations 3b, 4b, and 5. T e maximum


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