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Understanding Magnifi cation


of the microscope system. As an example, a digital microscope using a 1.6× objective ( M O = 1.6×) with a numerical aperture of 0.05 ( NA = 0.05), a total tube factor of 1× ( q = 1×), a 0.32× photographic projection lens ( M PHOT = 0.32×), a camera sensor with a 3 µm pixel size and binning mode of 1 × 1, a monitor pixel size of 0.3 mm (pixel ratio of 100:1), a 1-to-1 pixel correspondence between the sensor and monitor, and white light (mixture of all visible light wavelengths [400–700 nm] with an average in the green at λ = 550 nm) illumination, then from Equations 6, 7, and 8:


T is example shows that, at such low magnifi cation, the resolution limit of camera sensors with pixels sizes larger than 2 μm (and monitors with pixel sizes larger than 0.2 mm) will start to be inferior to the light resolution. T erefore, at low magnifi cation, approximately 1× or less, the sensor or monitor will likely be the limiting factor for the microscope system resolution.


Figure 2 : (a) Examples of pixel binning modes for image sensors: no binning (full frame, 1 × 1), double binning (2 × 2), triple binning (3 × 3), and quadruple binning (4 × 4). (b) Image sensor detection of black/white line pairs, used to measure the resolution limit of a microscope, requires a minimum of two pixels (red squares) per line pair (Nyquist rate). However, better image results are obtained if three or more pixels per line pair are used.


Now, by taking the reciprocal of the inequality, remembering to interchange the greater than and lesser than signs, the range of useful magnifi cation is determined:


High magnifi cation . When the magnifi cation from sample to camera sensor is high, generally 50× or greater, then light diff raction is the limiting resolution factor of the microscope system. Again, to illustrate it with an example, a digital microscope using a 160× objective ( M O = 160×) with a numerical aperture of 1.4 ( NA = 1.4), a total tube factor of one ( q = 1×), a 1× photographic projection lens ( M PHOT = 1×), a camera sensor with a 6 µm pixel size and binning mode of 1 × 1, a monitor pixel size of 0.3 mm (pixel ratio of 50:1), a 1-to-1 pixel correspondence between the sensor and monitor, and green light (λ = 550 nm) illumination, then from Equations 6, 7, and 8:


T us, the range of useful magnifi cation is between 1/6 and 1/3 of the microscope system resolution.


What does it mean exactly, the range of useful magnifi - cation? It means the optimal magnifi cation range when observing an object via a microscope (or an optical instrument that can magnify) where the fi nest resolvable features can be seen. Remember that range is based on the average performance of the human eye with respect to visual acuity (resolution) and contrast sensitivity along with the optical system’s resolution limit, as mentioned above. A signifi cant number of individuals will have eyes who perform above or below this average. Low magnifi cation . When the magnifi cation from sample to camera sensor is low, generally 1× or even less, then the camera sensor or monitor are the limiting resolution factors


2018 July • www.microscopy-today.com


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Here at high sample-to-sensor magnifi cation, the system resolution of a microscope using a modern camera sensor with a pixel size in the 1–6 μm range (and a monitor pixels size below 0.6 mm) is limited by the light resolution.


For a best-case scenario, the greatest light resolution possible with the smallest wavelength of visible light, 400 nm, and a very high numerical aperture, 1.4, is approximately 5,740 line pairs/mm. From the example above, it is clearly seen that the resolution limit of a camera sensor with a pixel size below 6 μm easily exceeds this value.


For this description of digital microscopy, it is assumed that the image on the monitor is always observed within the


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