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Understanding Magnifi cation

microscope’s resolving power, the practical level of observable detail also depends on the distance between the display of the image and the observer’s eyes.

Microscopes with Digital Sensors Magnifi cation in conventional light microscopes . When observing the image through the eyepieces of a microscope for visual observation, the total magnifi cation is defi ned as [ 5 , 6 ]:

where M TOT VIS is the total lateral magnifi cation observed through the eyepiece, M O is the objective lens magnifi cation, q is the total tube factor (zoom and other tube lenses), and M E is the eyepiece lens magnifi cation. As an example, a microscope with a 40× objective ( M O = 40×), total tube factor of 1× ( q = 1×), and 10× eyepieces ( M E = 10×), then the total magnifi cation ( M TOT VIS ) seen via the eyepieces would be: M TOT VIS = 40× · 1× · 10× = 400×. Magnifi cation at the digital sensor . For the case of a microscope image that is projected onto an electronic sensor, such as that of a digital camera, the magnifi cation for the image formed at the sensor is [ 5 , 6 ]:

“enlargement” of the image from the sensor to the electronic monitor display. As an example, if a microscope has a 20× objective ( M O = 20×), total tube factor of one ( q = 1), a 0.5× photographic projection lens ( M PHOT = 0.5×), and a sensor and monitor with an image size ratio of 100:1, then the total display magnifi cation ( M DIS ) seen via the image displayed on the monitor would be: M DIS = 20× · 1× · 0.5× · 100 = 1,000×. For an image size ratio, just one dimension could be used, such as the image width. T e size of the image width on the monitor equals the number of monitor pixels in the image width times the pixel size. T e same type of argument applies for the image width on the sensor:

T e ratio of the monitor to sensor pixel size can be defi ned as the pixel size ratio:

When the number of monitor and sensor pixels are the same (a 1-to-1 pixel correspondence), then:

where M TOT PROJ is the (lateral) magnifi cation of the microscope (image projected onto the sensor), p is the projection factor from eyepiece to camera, and M PHOT is the magnifi cation of the photographic projection lens from tube to camera. Standard values for the total tube factor, q , fall between 0.5:1 and 25:1 [ 1 ]. Standard values for the photographic projection lens magnifi - cation, M PHOT , fall between 0.32:1 and 1.6:1 [ 1 ]. Digital microscopes . For digital microscopes, there are no eyepieces, so an image is projected onto and detected by the electronic sensor and displayed on an electronic monitor for observation. T e same is also true for a microscope for visual observation equipped with a digital camera when the image is observed via a monitor. T us, the fi nal total magnifi cation for digital microscopy, M DIS (Equation 1), will always depend on the size of the image on the monitor versus the size on the sensor and can be defi ned as:

where M DIS is the total lateral display magnifi cation for an image displayed on a monitor, and the image size ratio is the

As just stated, the pixel size ratio is the ratio of the pixel size of the monitor to that of the sensor:

For Equation 5, it is assumed that the number of pixels across the image on both the sensor and the monitor occur in a 1-to-1 pixel correspondence mode, that is, one monitor pixel displays the signal from a corresponding single sensor pixel, the simplest case scenario. In this display mode, only a portion of the image may be visible on the monitor, depending on the actual total number of pixels across the image, the fi nal magnifi - cation, and the diff erence in the number of pixels between the camera sensor and monitor [11]. Figure 1 shows two examples of modern light microscopes: (a) a conventional stereo microscope with eyepieces, a digital camera, and two sizes of display monitor, and (b) a direct digital microscope with 2 sizes of display monitor, but without eyepieces.

Table 1 : Specifi cations of image sensors used in digital cameras and microscopes supplied by Leica Microsystems. Image sensor megapixels

Pixels a 2.5

5.04 9.98

19.96

1,824 × 1,368 2,592 × 1,944 3,648 × 2,736 5,472 × 3,648

Sensor physical size (diagonal; mm) b

7.64 7.64 7.91

15.86

Sensor width (mm)

6.1 6.1

6.44 13.2

Sensor height (mm)

4.6 4.6 4.6 8.8

Sensor pixel size (µm)

3.34 2.35 1.67 2.4

a By convention the sensor width is given fi rst. b Sensor sizes are sometimes still given in arcane terms that originated in the vacuum tube era, e.g., 1/2.3” means a sensor 6.1 × 4.6 mm. Even then a 1/2.3” sensor from different manufacturers may have slightly different dimensions.

22 www.microscopy-today.com • 2018 July

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