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Understanding Magnifi cation


Sensor object fi eld . T e OF for a camera sensor can be determined using the width and height of the sensor divided by the total magnifi cation of the optics producing the image of the sample projected onto the sensor:


instruments, such as scanning electron microscopes, transmission electron microscopes, and scanning probe microscopes. While the concepts would remain the same, the equations for calculating specifi c values of magnifi cation would need modifi cation.


Conclusion


where w and h are the width and height of the OF observed by a sensor, M TOT PROJ is the total magnifi cation from sample to sensor (Equation 3b), and the sensor pixel size is in µm. Figures 3 and 4 show the diff erence in OF between images seen by the eyepieces versus those recorded by the camera sensor, for the same sample, objective lens, and zoom setting. For Figure 4 , the total magnifi cation of the objective and zoom lens was 1×, but several types of C-mounts with diff erent magnifi cation were used to install the 5 MP camera on the stereo microscope. T e red rectangle seen in Figure 4a represents the OF of Figure 4b , an image taken with the 0.32× C-mount. T e blue rectangle indicates the OF of Figure 4c , taken with the 0.5× C-mount. T e green rectangle shows the OF of Figure 4d , taken with the 0.63× C-mount. Figure 4b shows the problem of vignetting where the edges of the image are darker than the center. Vignetting almost always occurs with stereo or compound microscopes having a C-mount with too low a magnifi cation. In that case, the image projected onto the camera sensor is smaller than the sensor size resulting in dark edges. To avoid such a problem, normally it is recommended that a 0.32× C-mount is used with a digital camera having a 4.8 × 3.6 mm sensor size, a 0.4× C-mount with a 6.1 × 4.6 mm sensor size, a 0.5× C-mount with a 8.0 × 6.4 mm sensor size, and a 0.63× C-mount with a 8.8 × 6.6 mm sensor size. T e OF of the camera sensor can be calculated ( w


× h ) using Equation 13a and 13b above. T e range of values for the OF seen with a digital microscope and stereo microscope equipped with a digital camera are shown in Table 5 .


Discussion


In planning a set of experiments, it is useful to know the lowest magnifi cation for which the object fi eld does not exhibit vignetting, as well as the useful range of magnifi cation to avoid introducing empty magnifi cation. While these issues have been described for the cases of relatively low-magnifi cation digital microscopes and stereo microscopes, typically used for inspection during manufacturing, the same concepts can be applied to other types of light microscopes, such as compound or higher-performance digital microscopes. Indeed, the issues of magnifi cation range and magnifi cation values related to various monitor sizes are quite general and they are relevant to other


2018 July • www.microscopy-today.com


Digital microscopes use electronic image sensors (camera sensors) to replace eyepieces. Microscopes for direct visual perception, such as stereo and compound microscopes, have eyepieces and can be equipped with digital cameras. Digital microscopy allows rapid acquisition of high-quality images. It is oſt en used for fast and easy documentation, quality control (QC), failure analysis, and research and development in a variety of fi elds. Because of the diversity of camera sensor dimensions and electronic display monitor sizes, determining magnifi - cation and magnifi cation range when using digital microscopy can be challenging. With this article, users of digital microscopy can better understand how to evaluate the total magnifi cation and its useful range for a particular microscope. T e useful range of magnifi cation is dependent upon the resolution of the optical instrument and average performance of the human eye with respect to visual acuity (angular resolution) and contrast sensitivity for optimal and non-optimal illumination conditions.


Acknowledgments


We would like to thank our colleagues Reto Züst and Harald Schnitzler of Leica Microsystems, Heerbrugg, Switzerland, for useful discussion and clarifi cation about the many concepts and defi nitions concerning magnifi cation and resolution described in the microscopy standards.


Figure 4 : Images of a Siemens star taken with a stereo microscope (M205 A) having a total objective and zoom lens magnifi cation (M O · q) of 1×. The fi rst black line circle has a 10 mm diameter and the second a 20 mm diameter. (a) Image photographed through a 10× eyepiece with 23 mm fi eld number (FN). Images (b–d) recorded using a digital camera installed with a C-mount (M PHOT ): (b) 0.32× M PHOT and 27.2 × 20.3 mm OF; (c) 0.5× M PHOT and 17.4 × 13 mm OF; and (d) 0.63× M PHOT and 13.8 × 10.3 mm OF. The red rectangle in 4a represents the OF of 4b (0.32× C-mount), the blue the OF of 4c (0.5× C-mount), and the green the OF of 4d (0.63× C-mount).


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