Understanding Magnifi cation

Figure 3 : Diagram showing direct comparison of an image viewed through eyepieces (white circle) and simultaneously with the sensor (rectangles) of a 5 MP digital camera. The two examples shown are: (a) eyepiece with a fi eld number (FN) of 20 mm and C-mount with 0.4× lens, and (b) eyepiece with 23 mm FN and C-mount with 0.5× lens. Some cameras detect images in a 4:3 aspect ratio (red rectangle) format for data storage and a 16:9 aspect ratio (green rectangle) format for live image output.

range of useful viewing distance. As discussed above, the range of useful magnification is derived based on the average performance of the eye. Whenever a sample is observed with a light microscope, sample features that correspond to the microscope’s resolution limit become resolvable by the eye under optimal illumination conditions at the lower magnification value of the useful range (Equation 11). For non-optimal illumination, then the higher magnification value may be necessary for the eye to resolve the features. Beyond the higher magnification value of the range, no finer details of the sample can be resolved, so it is empty magnification.

The example above for high magnification demonstrated that the best possible resolution attained with a light microscope (objective with a 1.4 numerical aperture and illumination with 400 nm light) is about 5,740 line pairs/ mm. Now, the range of useful magnification for the best resolution case can be calculated using Equation 11:

So the range of useful magnifi cation for this case, where the sensor limits the resolution of the microscope, is about 14× – 28×. In order to resolve features on a sample with a spatial frequency equivalent to 85 line pairs/mm, the total magnifi cation ( M DIS ) of the observed image should fall between 14× and 28×. Beyond 28× it would be empty magnifi cation. To make sure that sample features with a spatial frequency corresponding to the resolution limit of 85 line pairs/mm can be resolved, then the choice of a monitor with appropriate dimensions and pixel size becomes important.

Object Field (Field of View) An object fi eld (OF) is the part of the object that is reproduced

in the fi nal image. It is also known as the microscope fi eld of view (FOV). T us, details of an object can only be observed if they are present within the OF. When looking through the eyepieces, the visible OF is a circular image of a portion of the sample. T e size of the OF (Equation 12) is dependent on the fi eld number (FN) of the eyepiece, as well as the magnifi cation of the objective and tube lenses ( Figure 3 ). In digital microscopy, the OF is rectangular because of the shape of the image sensor that collects the image and the monitor that displays it (see Figure 3 ). It is expressed in width and height given in mm. 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. T e 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 width and height and their physical size (pixel pitch), has to be taken into account.

So the highest useful magnifi cation for a light microscope is about 1,900×–2,000×. Magnifi cation values exceeding 2,000× fall under empty magnifi cation. When below the lower end of the range, 957×, again it means that the average eye can no longer distinguish details on a sample with a spatial frequency equivalent to 5,740 line pairs/mm. However, most samples are not uniform with features of the same exact dimensions and spatial frequency everywhere on the surface. Normally, as magnifi cation is decreased, other larger features with lower spatial frequencies (below the resolution limit) become resolvable. T e example for low magnifi cation above, where the image sensor limits the resolution of the microscope (objective with a 0.05 numerical aperture and sensor with 3 µm pixel size), shows a limit of about 85 line pairs/mm. Now, the range of useful magnifi cation for this low magnifi cation case also can be calculated:


To calculate the OF, the physical size of the active area of the sensor (Equation 13) must be divided by either the magnification of the objective, tube, and camera projection lenses ( M TOT PROJ ) or, for the monitor, by the total lateral display magnification, M DIS . The smaller of these values for each width and height define the digital microscope’s OF. It is likely that both width and height of the OF are not necessarily jointly limited by the image sensor or display. For example, width can be limited by the sensor, whereas the height can be limited by the display. The final OF will depend on the dimensions and aspect ratios of the image sensor and display and the pixel correspondence (1:1, 1:2, 2:1, etc.) between them for image display. In this article, a 1-to-1 sensor pixel to monitor pixel correspondence is assumed (refer to section with Equation 5 above). Eyepiece object fi eld . T e OF for eyepieces can be determined by:

where OF eyepiece is the object fi eld observed through an eyepiece, FN is the eyepiece fi eld number in mm, and M O · q (Equation 2) is the total magnifi cation before the eyepiece due to the objective, zoom, and any tube lenses. • 2018 July

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