Magnification and resolution relationship goals

Resolution In general as the magnification increases the resolution increases, however, this What is the difference between resolution and magnification?. This article highlights differences in magnification and resolution between the conventional microscopes and the digital pathology systems. Magnification & Resolution. Magnification and Resolution objectives (4X, 10X, 40X and X), the total magnifying power of a typical compound bright-field.

In addition to the number of photons collected and various optical aberrations, the sampling process itself, which is a fundamental feature of digital microscopy, plays a role in determining contrast, and therefore resolution, in the fluorescence confocal microscope.

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As stated previously, the fact that digital confocal images must be not only recorded, but processed and displayed within discrete picture elements introduces imaging variables that may be unfamiliar to microscopists that are new to digital imaging.

Furthermore, the pixelation, or division of an image into finite picture elements, takes place at several stages of the imaging process, and these must interact with each other to transfer image information from the specimen to the final visual image display. The possibility of mismatches among these discrete elements at the various stages is another factor that potentially limits image contrast and resolution. The resolution imposed by the microscope optical system at the specimen level is sometimes described on the basis of the resel, which is the smallest optically resolvable element.

Depending upon the criterion utilized to define a detectable intensity difference between two elements, the size of the resel can correspond to the Rayleigh limit, the Sparrow limit, or another arbitrary definition. The effect of pixelation, or digitization, is initially manifested in the imaging sequence at the optical resolution level, through the sampling of the Airy patterns that correspond to point-like features in the specimen.

Partitioning, or pixelation, also takes place at the display stage of the imaging process, and differences in the use of terminology in the published literature can lead to confusion in discussing the digitization process occurring at various stages throughout the imaging sequence.

The term resel refers specifically to the smallest area of the specimen object that can be distinguished from neighboring areas, without regard to its subsequent detection, processing, or display. In three-dimensional confocal imaging, a volume resolution element is sometimes referred to as a voxel, although there is no reason to restrict the concept of the resel to two dimensions, and the term may be used to describe the minimum spatially-resolved element in two or three dimensions at the specimen, determined by the optics of the microscope system.

Figure 4 illustrates the mechanism by which the process of sampling the intensity of closely spaced Airy patterns reduces image contrast. The Airy pattern is generally assumed to be a smooth continuous function described by an infinite number of samples or data pointsas shown in the typical analog representation of the intensity variation across the pattern. When considered as continuous functions, the Airy patterns exhibit their full intensity variations and produce the maximum theoretical contrast for a given separation distance.

If divided into a finite number of measurement points or areas, by a scanner or digital imaging device, for example, the smooth curves are transformed into a series of intensity values, each of which can be stored in a computer memory location. By sampling at discrete intervals, the possibility is introduced of overlooking the positions that include the minimum and maximum of the function. Each pixel averages, or summarizes, the intensity response of the optical system within a specified area.

Since the Airy function zero crossings occur at points, not areas, a pixel value cannot be zero for any finite pixel size. Similarly, the measured maximum value of the intensity peaks is reduced by the area averaging, and the combined effect of increasing the minimum and decreasing the maximum is to reduce the contrast.

Consequently, the cut-off distance is increased and the resolution decreased for any contrast criterion by the pixelation process. Furthermore, if pixel size relative to the resel size is too large, ambiguity is introduced in the positions of the minima and maxima of the intensity response in the image plane. The severity of the effect of partitioning the intensity into pixels depends directly upon the size of the pixel with respect to the Airy disk diameter, which in turn is related to the resel size imposed by the system optics at the wavelength of the image-forming light.

It is unavoidable that any resolution inherent in the optical system, which is not sufficiently sampled by the detector, is lost. The effect of pixelization is minimized as more pixels are utilized to describe the intensity variations. Several detector designs acquire pixelated data as an intrinsic property of the detector CCD cameras, for examplewhile others require a continuous analog signal to be digitized by an analog-to-digital converter or similar digitizer, following detection.

The line scan of confocal laser scanning systems utilizing a single detection channel operate in this manner.

  • Relationship between magnification and resolution in digital pathology systems
  • Magnification & Resolution
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The relationship of the pixel size to the diameter of the Airy disk determines the number of pixels that are required to sample two adjacent Airy disks to achieve a certain contrast. The challenge in digital microscopy is to manage the relationship among optical resolution, sampling interval in the spatial domain, and the pixel dimensions of the display device in order to maximize the capture and display of true specimen information, while minimizing visual artifacts that may be introduced by interactions among the various sampling partitioning stages.

An additional factor of practical interest in determining the contrast and resolution of captured images is the intensity resolution, which governs the brightness value that is assigned to each image pixel.

By analogy to the resel, the size of which is determined by the optical characteristics of the system, the minimum detectable difference in intensity that can be resolved depends upon electronic properties of the detector, in particular its signal-to-noise ratio.

When transferred to the image-output stage, each pixel's brightness is described by a gray level, and the accuracy with which the brightness is represented depends upon the relationship between the number of gray levels utilized and the smallest detectable intensity difference measured by the detector. When stored by the computer, each pixel corresponding to a spatial location in the image has an associated intensity value ranging from 0 to for 8-bit storage gray levels. In confocal microscopy, the use of more than gray levels is seldom justified by the detection resolution, although there may be some value in discriminating more intensity levels for certain data processing algorithms.

It is important to recognize that pixelation at the image display stage is not unique to digital imaging. Some form of "granularity" is inherent in every type of image presentation, and manipulations of the size and organization of the grains are utilized to represent the required range of gray levels.

Photographic film has silver grains of various sizes, television displays are arrays of discrete horizontal lines, each of which displays intensity variations based on electronic bandwidth, and half-tone printing techniques group black and white dots into pixels of various sizes to simulate continuous tonal variations. Video monitors are able to vary the intensity of each displayed dot and achieve some tonal variation even while utilizing one dot per pixel.

However, in order to represent a sufficient number of gray levels to produce the visual effect of continuous-tone images, or to display color variations, a number of dots must be assigned to represent each pixel.

Difference Between Magnification and Resolution

Film-based photographic methods assign multiple silver grains to each image resel in order to provide an adequate range of intensities necessary to give the appearance of continuous tonal variation. In all of these methods, as more fundamental dots or image elements are grouped to achieve greater tonal range, the appearance of the image becomes more "grainy", with the effect of reducing apparent resolution.

The inverse relationship between pixel size and the ability to display greater gray-scale range must be considered and balanced according to the imaging requirements. The fact that all digital confocal microscopy images are acquired, processed, and displayed in the realm of discrete partitions, or pixels, as opposed to being treated as a continuous representation of the specimen data is not a problem of fundamental significance, but rather is a practical matter of imaging technique.

As long as the microscope is operated in accordance with applicable sampling theory, which governs the sampling interval in space or time that is required to reproduce features of interest with sufficient contrast, there is no significant limitation.

The sampling criterion most commonly relied upon is based on the well known Nyquist Theorem, which specifies the sampling interval required to faithfully reconstruct a pure sine wave as a function of its frequency.

The problem in practice is that use of the zoom magnification control on typical confocal microscopes can easily be misused in a manner that violates the Nyquist criterion. The application of Nyquist sampling theory is usually explained by considering the specimen features in the domain of spatial frequency rather than object size.

In effect, the number of objects per spatial unit the frequency is the inverse of object size and emphasizes the importance of the spacing between specimen features in image formation. Use of the spatial frequency domain is consistent with the practice of evaluating performance of optical systems on the basis of their ability to maintain contrast and visibility when transferring image information of different frequencies.

All optical systems degrade contrast in the imaging process, and this effect is more severe for higher spatial frequencies small spacing than for lower frequencies larger spacing. The contrast transfer function CTF of an optical system is constructed by plotting the measured contrast in an image of test patterns consisting of periodic arrays having alternating dark and light bars at a range of frequencies, or spacing intervals.

Figure 5 illustrates a hypothetical CTF for an optical system, and includes curves for the system response to a test target having black and white bars percent contrastand to a target made up of gray and white bars yielding only 30 percent contrast. Examination of the contrast transfer curves of Figure 5 clearly illustrates the interdependence of resolution and contrast, and the problem of some common assumptions that are made, which treat resolution as a constant of instrument performance.

Resolution is a somewhat arbitrary variable that is meaningful only when considered within the framework of other related factors. When defined as the highest spatial frequency that produces a certain contrast, it is easily assumed that any features having frequencies within the stated resolution limit are equally visible, when in fact specimen features that are originally of high contrast will be more clearly visible than those of lower contrast at every frequency up to the contrast cut-off frequency.

The curves Figure 5 illustrate that specimen features initially having only percent contrast due to staining characteristics or other factors, would not maintain the Rayleigh-specified percent contrast level at spatial frequencies anywhere near the theoretical limit, which assumes equal contrast at all frequencies up to the resolution limit.

The contrast of small features that are slightly within the resolution limit produce contrast much lower than that of larger features after each has been degraded by the transfer function of the imaging system. The visibility of specimen features in the microscope image depends upon the contrast of the features with respect to their surroundings, the performance of the optical system as reflected in the contrast transfer function, signal-to-noise statistics, and the manner in which the signal is sampled for digitization.

Nyquist found that in order to faithfully reconstruct a pure sine wave, it must be sampled at least twice during each cycle of the wave, or at two-times the temporal frequency. The frequencies of interest in imaging are of a spatial nature, but the Nyquist theorem is equally applicable to this type of data. The minimum sampling frequency employed in microscopy imaging applications is usually 2. The value of 2.

Low-pass filtration that is applied to the sampled data before the image is reconstructed is analogous to the "filtration" done by the eye and brain to smooth pixelated data such as half-tone images, or to moving farther away from a display such as a large screen television in order to eliminate visible scan lines.

Low-pass filtration performs removal of sampling artifacts that are extraneous to the data, and helps to make the image appear continuous. An ideal filter would permit sampling at 2-times the highest frequency, but since no such devices exist, experience has led to the generalization that sampling at 2. In practical operation of the microscope, there is often some uncertainty in estimating the highest frequency that should be of concern in the specimen.

In the bottom two pictures however, the picture on the left maintains the fine detail, while the one on the right does not. This means we have reached the resolution limit in the image on the right. This takes a bit of work and patience, although Jackson is a trooper. Jackson sacrifices for Science!

Confocal Microscopy - Resolution and Contrast in Confocal Microscopy

Since these ridges are apparent in the images in the left column and not apparent in those on the right, this means that the images in the left column have a resolution limit smaller than 0. You may recall that in the most zoomed-out picture again that handsome face!

In this specific case, resolution is not that important as we are not looking closely enough to see the details. While bigger is often better, magnification can be meaningless if the necessary resolution is lacking as Jackson once again demonstrates.

Magnified with resolution left is much better unless you are into abstract art. So, resolution is the ability of a system to define detail, and this becomes increasingly important the more you magnify something. What if you magnify something A LOT? What are the limits to resolution?

How to Push the Limits? There is a fundamental maximum resolution for a system that is determined by a process known as diffraction.

When light enters a lens, it diffracts, spreading out and making a spot in an object into a slightly larger disk in the image. Therefore, nanoscientists turn to electrons. Resolution can be expressed in arcsec or seconds.

Magnification, on the other hand, is the degree which an object is made bigger by using optical instruments such as a telescope or a microscope. They bend light to enlarge an image up to the point when the magnification becomes indistinguishable. But while high magnification would usually signify high resolution, oftentimes the larger an image becomes, the lesser its resolution because as the image is doubled in size, so is its area. This is due to the irregularity and abnormality in the design of lenses used in optical instruments.

When two objects that are held apart and at a distance from the viewer are magnified many times, they will have edges that become blurry, and it becomes impossible to see two separate objects. To achieve a high magnification and resolution at the same time, a combination of ocular and objective lenses are used with numerical aperture or light range angles that are different.