20171120 — The FOV is limited by this field stop and is defined as the diameter of the circle of light seen when looking into a microscope.

where MDIS is the total magnification (Equation 1) and 250 refers to the standard reference for the viewing distance in mm which is based on the average near point for the human eye.

To further clarify the point, imagine a very large piece of paper having a rectangular hole with the dimensions of the 21.5-inch monitor. One could use the paper to cover the 43-inch monitor and an area of the image equivalent to the 21.5-inch monitor would be revealed. An example is shown in Figure A2 below. If the rectangular hole in the paper is moved around over the 43-inch monitor, then it would be similar to moving around the displayed image on the 21.5-inch monitor with software using a mouse or cursor. Again, the same features measured in the image displayed on either the 43- or 21.5-inch monitor with a 1-to-1 pixel correspondence would have the same dimensions, meaning the total magnification is the same.

The OF for a camera sensor can be determined using the width and height of the sensor divided by the total magnification of the optics producing the image of the sample onto the sensor:

Any helical object like this one has a mirror image that is also helical but with the opposite sense of rotation. The mirror image and the original are not identical. In a sense, every chiral molecule also has such a helicity built into it.

magnification中文

The basis for the camera sensor and display monitor resolution limit is the Nyquist rate or frequency from the sampling theorem for digital signal processing (refer to Figure 2) [16,17]. This theorem assumes that at least 2 pixels are needed to resolve 1 line pair. For this report, as stated above, the best-case scenario of a 1-to-1 correspondence is assumed between the pixels of the sensor and monitor. Therefore, using Equation 4 and converting the monitor pixel size into units of µm, it becomes clear that the resolution limit of the sensor and monitor are identical.

where MDIS is the total lateral magnification (Equation 4) and "system resolution" refers to the microscope resolution limit as discussed above.

Modern camera sensors have pixels sizes in the 1 to 6 µm range, well below 10 µm. When a high sample-to-sensor magnification is used, for example 150x, and there is no binning of the pixels and a 1-to-1 sensor to monitor pixel correspondence, then it follows from Equations 6, 7, and 8 above that the microscope system resolution is determined by the optical resolution limit. The optical resolution limit for the largest numerical aperture, approaching 1.3, and the smallest wavelength of visible light, approximately 400 nm, is 5,400 line pairs/mm. For these same conditions, the resolution limit of a camera sensor with a pixel size below 10 µm easily exceeds this value. For the conditions of this specific case, from Equation 11 above the maximum magnification in the useful range of values is 1,800x.

Object field (OF) is the part of the object which is reproduced in the final image. It is also known as the microscope field of view (FOV). Thus, details of an object can only be observed if they are present in the object field.

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where MTOT PROJ is the magnification from the sample to the sensor (Equation 3), the "sensor bin. mode" refers to the binning mode which is 1 for full frame, 2 for 2 × 2 pixel binning, etc. (refer to Figure 2), and "pixel size" refers to the sensor pixel size in µm; and

What exactly is magnification? A basic definition of magnification is the ratio of the size of a specific feature of an object or sample as seen in an image produced by an optical system to the actual size of the feature on the object itself. Thus, lateral magnification, MDIS, can be defined as:

The resolution limit of the digital microscope system resolution is determined by the smallest of the 3 resolution values above.

Image

Table 3: Pixel size ratios (Equation 5) for UHD or FHD (21.5” only) monitors (Table 2) and sensors used in the Emspira 3 digital microscope, Ivesta 3 stereo microscope with integrated camera, and Flexacam, K3C, and K5C digital cameras (Table 1).

Magnificationof image

When observing the image through the eyepieces of a stereo microscope, the total (lateral) magnification is defined as [8]:

The pixel ratio value which corresponds to a total magnification of 30,000:1 with the above magnification of 32x onto the sensor is:

The pixel size of the Flexacam camera sensor is 1.55 μm. Using the pixel ratio value above, 938:1, and a 1-to-1 camera to monitor pixel correspondence, the monitor pixel size must be:

The plane of polarization of the resulting linearly polarized wave thus prepared can be changed (rotated) by applying a phase shift between its two circularly polarized components. With the help of this concept we can explain the phenomenon of optical rotation: We have seen that chiral molecules interact slightly differently with the two circularly polarized components of a linearly polarized light beam. This is true both for absorption and refraction. Left and right circularly polarized light beams also have slightly different refractive indices in a chiral medium. This means that left and right circularly polarized light travel waves at slightly different speeds through the medium. Therefore, this causes a phase shift between the two circularly polarized components, which increases proportionally to the path length that the light travels through the chiral medium. This phase shift manifests itself as a rotation of the plane of polarization of the resultant linearly polarized light beam—optical rotation. In fact this is exactly how the animation of optical rotation at the top of the page was created with the Mathematica software.

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Table 2: Examples of UHD/4k (3,840 x 2,160 pixels), FHD (1,920 x 1,080 pixels), and FHD+ (1,920 x 1,200) electronic monitor displays: computer (PC) monitors or TVs.

Which monitor pixel size would be needed to attain a total lateral display magnification of 30,000:1? An example can be shown using the M205 A microscope with Flexacam c5 digital camera and Equations 3b, 4, and 5. The maximum magnification for the M205 A for an image of the sample projected onto the camera sensor is:

It should be noted that the useful range of perceived visual magnification significantly depends on the maximum resolving power of the microscope system. When the magnification passes beyond the useful range, then no additional details about the sample can be seen. This situation is referred to as empty magnification [13]. Based on the maximum resolving power, also a useful range for the viewing distance, i.e. the distance between the digital display and the observer’s eyes, can be defined for practical reasons.

The two forms of circular polarization of light (left or right) are mirror images of each other. First, let’s see what a circularly polarized light wave looks like. We consider only the electric field component of the electromagnetic wave. Suppose you superimpose (add) two linearly polarized electromagnetic waves with the same amplitude and frequency (wavelength) but where the electric field vector in the one case oscillates, say, in the xz plane and in the other case it oscillates in the yz plane. Suppose the waves propagate in the z direction. If the two waves have a phase shift of exactly one quarter of the wavelength, voila! We obtain a light wave where the resulting electric field vector at any point along the z direction turns around on a circle either clock-wise or anti-clock-wise. This is why we call this light wave circularly polarized. See the animation below on the left. In the case that the two amplitudes are not exactly equal, the electric field vector rotates clock-wise or anti-clock-wise on an ellipse instead and we obtain elliptically polarized light. See the animation below on the right. You can also download interactive versions of these animations by following the Download links. You need the Wolfram Player (free download from the Wolfram research web site)

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It is likely that both height and width of the object field are not necessarily jointly limited by the image sensor or the display. For example, the height can be limited by the display whereas the width can be limited by the sensor. The final OF will depend on the dimensions and aspect ratio of the image sensor and display and the pixel correspondence (1:1, 1:2, 2:1, etc.) between them for image display. In this report, a 1-to-1 sensor pixel to monitor pixel correspondence is assumed.

From knowing the typical pixel sizes of the camera sensors (Table 1) and flat screen UHD monitors (Table 2), then values for the size ratios can be easily calculated using Equation 5 (Table 3).

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The optometer can also take the measurement time into account and integrate the laser power over time, showing directly the resulting energy/laser dose (in J).

High-magnification values without sufficient resolution lead to empty magnification, as already mentioned above [13]. Therefore, it is of vital importance to understand the limiting factors for resolution, not just for digital microscopy, but all forms of optical microscopy.

Another important phenomenon that is only observed for chiral substances is called circular dichroism (CD). In a nutshell, if we record the electronic absorption spectrum (typically in the UV-Vis range) of a chiral substance with circularly polarized light (see explanations below) instead of linearly polarized light, the spectra for one of the enantiomers recorded with left or right circularly polarized light differ slightly. Compare the red and green curves in the image below. (See the next paragraph for some animations of circularly and elliptically polarized waves and further explanations). If we plot the difference between the two absorption spectra we have what is called the CD spectrum shown in the graphics below in blue (here: ‘red minus green’). The CD spectrum (the Δ𝜀 curve) for the other enantiomer would have the opposite sign, i.e. we would obtain the blue curve mirrored at the horizontal axis. Nonchiral substances do not exhibit CD except in the presence of a static magnetic field (Faraday effect).

The graphics below shows an animation of a linear polarized light wave as it passes through an optically active medium (indicated by the rectangular box). The plane of polarization of the light wave rotates proportional to the path length. The box dimension, the amount of rotation, and the amplitudes are not to scale. Optical rotation is measured by polarimetry. The wavelength used in polarimetry experiments is often 589.3 nm (this is the yellow light from a sodium lamp). Optical rotation data are typically given in terms of a path length of 10 cm (1/3 foot).

Due to the diversity of camera sensor dimensions and electronic display monitor sizes, determining magnification and resolution when using digital microscopy can be challenging. With this report, users of digital microscopy can better understand how to evaluate the total magnification and its useful range. In addition, helpful information concerning the object field or field of view is discussed.

The viewing distance is the distance between the observer’s eyes and the displayed image. The useful range for the viewing distance is affected by the system resolution of the microscope and visual resolution angle of the observer [18,19]. The latter is normally 2.3 to 4.6 minutes of arc for typical human eyes. In other words, a human eye is capable of distinguishing details on a monitor which have a separation distance corresponding to an angular difference of more than 2.3 to 4.6 minutes of arc for a specific viewing distance. The useful range for the viewing distance can be expressed as:

Now one must ask the question if this level of magnification, 30,000:1, is simply beyond the useful range, meaning it is empty magnification. How do we determine a useful range of magnification for digital microscopy, where an image is observed from a monitor? First it is important to understand better the microscope system resolution and the viewing distance.

An example (not a real case) can be used to illustrate the answer. From Table 2 there are 2 size monitors, the 21.5 inch (55 cm) FHD and 43 inch (109 cm) UHD, which have identical pixel sizes, 0.25 mm. The 43-inch monitor has 4 times as many pixels (3,840 x 2,160 pixels) as the 21.5-inch monitor (1,920 x 1,080 pixels), twice as many pixels for each dimension. Now imagine using a camera sensor also with 8.29 MP (UHD, 3,840 x 2,160 pixels) to display the same image on both monitors with a 1-to-1 pixel correspondence (signal of 1 sensor pixel, with no binning, is displayed on 1 monitor pixel). The 43-inch monitor would show the full image projected onto the sensor. However, the 21.5-inch monitor, having 4 times fewer pixels than the sensor, would show only 1/4 of the image projected onto the sensor. Still, the total magnification for the image displayed on both monitors would be the same. To prove this fact, Figure A1 below shows the same image from a camera displayed on both the 21.5- and 43-inch monitor. The white double arrow indicates the same features on the sample. The length of the arrow is the same in each image, as the pixel sizes are the same for each monitor and the feature covers the same number of pixels in each image.

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As an example, consider the molecule ‘hexahelicene’. Its chemical formula is shown below on the left (‘hexa’ because of the 6 aromatic rings). The molecule adopts a helical shape as shown in the middle, otherwise the atoms at the ends of the molecule would get too close. There are two possible forms: a left-handed helical form as shown below (M for the ‘Minus’ sense of hecility), and its the mirror image which has a right-handed helical shape (not shown. This molecule is named (P)-hexahelicene, ‘Plus’). Because of its helical shape, the molecule is chiral. It has a very intense CD spectrum shown below on the right. In green is the experiment. The red spectrum is the result of a computation that we performed in 2002 (Ref. [9]) which agrees quite well with the experiment except at the shortest wavelengths where we cut off the computation of additional excitations. (P)-Hexahelicene would have a CD spectrum of the opposite sign.

Digital microscopes, as well as stereo microscopes equipped with digital cameras, allow the rapid acquisition of high-quality images. Often they are used for a variety of technical applications [12], in many different fields and industries.

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The difference in OF between images seen by the eyepieces versus those recorded by the camera sensor, for the same sample, objective, and zoom setting, are shown in Figures 3 and 4 below. For Figure 4, the total magnification of the objective and zoom lens is 1x, but several types of Leica C-mounts with different magnification have been used to install the Leica camera with a sensor size of 2/3’’ onto a M205 A stereo microscope. The red rectangle seen in Figure 4a represents the OF of Figure 4b, an image taken with the 0.32x C-mount. The blue rectangle indicates the OF of Figure 4c, taken with the 0.5x C-mount. The green rectangle shows the OF of Figure 4d, taken with the 0.63x C-mount. Figure 4b shows the problem of vignetting where the edges of the image are darker than the center. To avoid such a problem, normally it is recommended that a 0.32x C-mount is used with a digital camera having a 1/3” (8.5 mm) sensor size, a 0.4x C-mount with a 1/2.3” (11 mm) sensor size, a 0.5x C-mount with a 1/2" (12.7 mm) sensor size, and a 0.63x C-mount with a 2/3” (16.9 mm) sensor size.

For a size ratio, a single image dimension, such as the image width or height, could be used. Working with the width, then the image width on the monitor equals the number of monitor pixels in the image width times the pixel size. For the image width on the sensor, a similar argument applies, therefore:

As already mentioned above, a 1-to-1 pixel correspondence mode is assumed for image display from the camera sensor to the monitor. In this display mode, depending on the monitor’s number of pixels, only a portion of the image may be visible on the monitor.

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When looking through the eyepieces, the OF is a visible circular image of a portion of the sample. The size of the OF (refer to Equation 12) is dependent on the field number (FN) of the eyepiece as well as the magnification of the objective and tube lenses (refer to Figure 3).

These two forms of circularly polarized light interact slightly differently with a chiral molecule, which causes the circular dichroism. A different interaction of the two forms of circularly polarized light with an enantiomer of a chiral molecule also causes the optical rotation, which is explained further below.

© 2005 – 2024 J. Autschbach. The material shown on this web page is in parts based on the results of research funded by grants from the National Science Foundation (NSF, CHE 0447321, 0952253) and educational projects supported by these grants. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

The sensors used in all Leica digital microscope cameras have a number of pixels typically between 3,072 × 2,048 and 5,472 × 3,648 and a pixel size between 1.55 and 2.4 μm (examples in Table 1). Ultrahigh-definition (UHD/4k) computer monitors or televisions have 3,840 x 2,160 pixels and full-high-definition (FHD+ or FHD) ones have 1,920 × 1,200 or 1,080 pixels. Pixel sizes are between 0.1 and 0.5 mm (examples in Table 2) [14,15]. Therefore, the monitor pixels are typically 40 to 325 times bigger than the camera pixels (examples in Table 3).

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For digital microscopes, there are no eyepieces, so an image is projected onto and detected by an electronic sensor of a digital camera, and then displayed onto an electronic monitor for observation. This fact is also true for a stereo microscope equipped with a digital camera when the image is observed via the monitor. Thus, the final total magnification for digital microscopy, MDIS, will always depend on the size of the image displayed on the monitor. For this report, a display of the image from the camera sensor to the monitor is assumed to occur in a 1-to-1 pixel correspondence mode, the simplest case scenario. The signal from one pixel of the camera is displayed on one pixel of the monitor. Thus, the ratio of the monitor to camera sensor image size is directly proportional to the actual pixel size of the monitor and sensor (refer to the Appendix below for more details). It can be defined as:

Magnification meaningin microscope

Identically prepared solutions of the two enantiomers of a chiral molecule rotate the polarization plane in equal but opposite directions. A mixture of equal amounts of the two enantiomers (racemate) or a nonchiral substance does not exhibit this effect. However, the sign of the rotation is not in a simple way related to the chiral structure in the sense that, say, a D configuration would always have a positive or negative optical rotation. Therefore, without additional structural information it is not possible to deduce an unknown absolute configuration of a molecule simply from the sign of the optical rotation. Quantum theoretical calculations are very useful in this case.

Image

The total tube factor, q, is normally between 0.5x and 25x. The photographic projection lens magnification, MPHOT, is normally between 0.32x and 1.6x.

For the case of detecting an image of a microscope which is projected onto an electronic sensor, such as that of a digital camera, the magnification for the image formed at the sensor is [8]:

Magnification meaningin Physics

For simplicity, only 2 examples of digital microscopy, actually a digital microscope and a stereo microscope equipped with a digital camera, will be discussed in this report. It is assumed that an image is displayed, using a 1-to-1 camera to monitor pixel correspondence, onto a UHD or FHD monitor with sizes ranging from 21.5'' (diagonal dimension 21.5 inches [54.6 cm]) to 75'' (diagonal dimension 74.5 inches [189 cm]). It is also assumed that the cameras display the image with a UHD format. For a FHD monitor (21.5"), then a camera-pixel binning of 2x2 (refer to figure 2) must be used, meaning that the pixel size doubles and pixel size ratio is cut in half. The 2 examples are the Emspira 3 digital microscope and the M205 A stereo microscope having the Flexacam c5 digital camera installed with a C-mount. Table 4 shows examples of total magnification (refer to Equations 2 and 4) values obtainable with the Emspira 3 or M205 A microscope equipped with the Flexacam c5 camera. For the Emspira 3 microscope, the magnification range for the objective lens is 0.32x to 5x and for the zoom 0.75x to 6x (tube factor, q, including the photographic projection lens has an 8:1 range from highest to smallest magnification). For the M205 A microscope with Flexacam c5 camera, the magnification range for the objective is 0.5x to 2x, for the zoom 0.78x to 16x, for the eyepieces 10x to 25x, and for the C-mount lens 0.4x to 1x.

Suppose we investigate optical rotation at a wavelength where the medium absorbs some of the light’s intensity. Because a chiral medium absorbs left and right circularly polarized light differently (the CD effect), the amplitudes of the outgoing two circularly polarized components of the light beam are not equal anymore after they have passed through the absorbing chiral medium. They have a phase shift and a different amplitude. We end up with a situation similar to the one depicted in the animation above of elliptic polarization (caused by the different amplitudes of the linearly polarized components). In other words, the outgoing light beam is not linearly polarized anymore. Instead, it is elliptically polarized. See the animation below. It was created with Mathematica in the same way as the animation at the top of the page, but with one of the circular components being reduced in amplitude as it passes through the optically active medium. The ellipticity of the outgoing light is clearly visible in the electric field vector (orange) at some fixed position.

Interestingly, a monochromatic linearly polarized light beam can be considered as a superposition of two circularly polarized electromagnetic waves that are propagating in the same direction with the same frequency but the opposite sense of rotation. Consider the animation of circularly polarized light above. If we superimpose this wave with a circularly polarized wave of the opposite ‘handedness’ where the blue component is 1/4 wavelength behind (instead of ahead), the two blue components will completely cancel because they are 180 degrees (half a wavelength) out of phase. Thus, we would be left with just a linearly polarized wave.

Definemagnificationin microbiology

Table 1: Specifications of image sensors used in the Flexacam c5 and i5, K3C, and K5C digital cameras, Emspira 3 digital microscope, and Ivesta 3 stereo microscope with integrated camera supplied by Leica Microsystems.

Table 5: Object field (OF) data (Equation 13) for a UHD image (3,840 x 2,160 pixels) from the Emspira 3 digital microscope and M205 A stereo microscope equipped with a Flexacam c5 digital camera showing the range from minimum to maximum values.

Digital microscopes use electronic image sensors (camera sensors) to replace eyepieces. Stereo microscopes have eyepieces and can be equipped with digital cameras. Digital microscopy allows rapid acquisition of high-quality images. It is often used for fast and easy documentation, quality control (QC), failure analysis, and research and development (R&D) in a variety of fields.

Table 4: Total magnification data, MTOT VIS and MDIS (Equations 2 and 4), for the Emspira 3 digital microscope and the M205 A stereo microscope equipped with a Flexacam c5 digital camera. The possible range of magnification values, minimum to maximum, for the discussed UHD or FHD monitor sizes (Table 2) and pixel ratios (Table 3, N.B.: 2x2 camera-pixel binning required for the 21.5” FHD monitor, refer to figure 2).

However, the question arises: If 2 monitors have the same pixel size but different dimensions, will the total magnification be the same if the same image from a camera sensor is displayed on either one with a 1-to-1 pixel correspondence (i.e., no binning)?

Chiral molecules are molecules that do not have a plane of symmetry, an inversion center, or so-called improper rotation symmetry axes. For example, the water molecule has a plane of symmetry but sugar molecules don’t. See this page for an illustration of various types of molecular chirality. As a consequence, chiral molecules such as sugars, amino acids, and most other bio-molecules, come in two forms (enantiomers) that are mirror images of each other and that are not the same. The concept of chirality is not restricted to molecules; one can also speak of chiral objects in general terms. The term ‘chiral’ means ‘handedness’ and refers to the fact that our hands are mirror images of each other [when you press a hand flat against a mirror it looks the same as if you press your hands flat together] but a hand and its mirror image are not identical and you cannot superimpose them. Chiral objects always come in pairs, conceptually. Back to molecules: Two enantiomers have the same chemical reactivity, the same mass, volume, and so on. One can distinguish them most easily in two ways: First, enantiomers react differently with other chiral molecules. Second, chiral molecules are said to be optically active.

For optical instruments in general, resolution is the ability to see fine details in an image. More specifically, resolving power is the ability to distinguish in an image adjacent points or lines of the object which are closely spaced together. Usually these two terms are used synonymously, however resolution is the more practical one. In microscopy, resolution is expressed in line pairs per millimeter. In other words, pairs of black and white lines with equal line thickness and spacing can be distinguished at a given resolution.

To understand how to determine the useful range of magnification for digital microscopy, i.e. the observation of a magnified image on a display monitor, it is first necessary to mention briefly the perceived magnification from visual observation of an image or object. Using geometrical optics, the following can be derived:

Because the elliptic polarization results from the different absorption coefficients at that wavelength (or frequency), the amount of ellipticity is directly related to the circular dichroism. The difference is that the CD is obtained by considering the absorption of left and right circularly polarized light individually and then taking the difference. Ellipticity can be understood as being the result of doing the experiment with both light polarizations simultaneously (by starting out with linearly polarized light).

What is themeaningof resolution

Therefore, to achieve a total magnification of 30,000:1 with the M205 A and Flexacam camera, the monitor pixel size would have to be 1.5 mm. This pixel size would correspond to a UHD or FHD monitor diagonal of 6.6 m or 3.3 m!

Image

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Magnifymeaning

For this discussion of digital microscopy, it is assumed that the image on the monitor is always observed within the useful viewing distance range described above. Whenever the perceived magnification value exceeds the useful magnification range, i.e. 1,800x, then no further details about the sample can be resolved.

The basis for the definition of the total lateral display magnification, MDIS, indicated by Equation 4, is the "enlargement" of the image size displayed on the monitor in comparison to the image size projected onto the camera sensor. Thus, the ratio of the image size on the monitor to that on the sensor determines the total magnification:

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The object field (OF) of the camera sensor can be calculated using Equation 13 above. A UHD image with a 16:9 aspect ratio (3,840 x 2,160 pixels) is assumed. The range of values of the OF for the Emspira 3 digital microscope and M205 A stereo microscope equipped with a Flexacam c5 camera are shown in Table 5. Again, the magnification range for the Emspira 3 is: objective 0.32x to 5x and zoom 0.75x to 6x (the tube factor including the photographic projection lens has a 8:1 ratio from highest to smallest magnification) and for the M205 A with a Flexacam c5 camera: objective 0.5x to 2x, zoom 0.78x to 16x, and C-mount 0.4x to 1x.

The object field in digital microscopy is of rectangular shape due to the nature of the image sensor which receives the image and the monitor which displays it (refer to Figure 3). It is expressed in width and height given in millimeters. 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. In this case, the 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 height and width and their physical size (pixel pitch), has to be taken into account.  To calculate the OF, the physical size of the active area of the sensor (refer to Equation 13) has to be divided by the magnification of the objective, tube, and camera projection lenses (MTOT PROJ) or for the monitor by the total lateral display magnification, MDIS. The smaller of these values for each height and width define the OF of the digital microscope.

where MDIS is the total lateral display magnification for an image displayed on a monitor and the pixel size ratio is the "enlargement" of the image due to the signal transmission of the image from the camera to the electronic monitor display. The pixel size ratio is determined by the ratio of the pixel size of the monitor to that of the camera sensor:

One important criterion concerning optical microscope performance is magnification. This article offers helpful guidelines for digital microscopy, so users can determine the useful range of magnification values. For more than 150 years, optical microscopy has allowed the observation of microscopic entities not seen by the unaided eye [1]. Today there are many types, but here the focus will be on digital microscopes [2] with electronic image sensors, but no eyepieces, and stereo microscopes [3,4] with eyepieces. Additionally, a stereo microscope can be equipped with a digital camera.

Magnification is the ability of a microscope to produce an image of an object at a scale larger (or even smaller) than its actual size. Magnification serves a useful purpose only when it is possible to see more details of an object in the image than when observing the object with the unaided eye. At the present time, magnification is well defined when viewing an image of a sample through the eyepieces of a microscope. For this case, rigorous international standards have been documented [5-10]. Many of these standards also apply to digital microscopy, but strict definitions and standards for magnification achieved by a digital microscope, where the image is most often viewed by display on an electronic monitor, have only recently been published [11].

In both animations the electric field vector (orange) at a fixed position z in space (here at 12 π) is shown in addition to the wave itself as it propagates. The circular and elliptic polarizations are clearly visible. In blue and red we have the two individual linearly polarized light beams and in green their superposition. Because the ‘green wave’ has the shape of a helix it can be considered chiral in some sense, because there is a left-handed and a right-handed helix which are mirror images of each other. In the animations above, the blue wave is one quarter of a wavelength ahead of the red one. If it were behind instead, we would obtain circularly or elliptically polarized light with the opposite helicity.

At low magnification from the sample to camera sensor, 1x or even less, numerical apertures are typically below 0.03. The resolution limit of camera sensors with pixels sizes larger than 2 µm will start to be inferior to the optical resolution at such low magnification. Therefore, at low magnification, 1x or less, the sensor or monitor resolution limit will likely be the dominating factor concerning the resolution of the microscope system.

Two phenomena play an important role in the context of natural optical activity, that is to say, optical activity that occurs without applying magnetic fields and such. One of them is optical rotation. Optical rotation means the the plane of polarization of a linearly polarized light beam rotates as it passes through an optically active medium such as a solution of chiral molecules. The rotation angle is proportional to the path length through the medium, and in case of a solution it is also proportional to the concentration of the chiral substance.

The fact that the absorption spectra of a chiral substance measured with left and right circularly polarized light differ somewhat can be rationalized by the fact that circularly polarized light is ‘chiral’ in itself. Why is that? Helical objects are chiral. Look at the pictures below (in case you are curious, this is a bike stand; I forgot where I took the photo):