Spatial Resolution in Digital Imaging
In terms of digital images, spatial resolution refers to the number of pixels utilized in construction of the image. Images having higher spatial resolution are composed with a greater number of pixels than those of lower spatial resolution.
This interactive tutorial explores variations in digital image spatial resolution, and how these values affect the final appearance of the image. The tutorial initializes with a randomly selected specimen imaged in the microscope appearing in the left-hand window entitledOptical Image. Adjacent to the Optical Image window is a Spatial Resolution window that displays the captured image at varying resolutions that are adjustable with the Pixel Dimensions slider. To operate the tutorial, select an image from the Choose A Specimenpull-down menu, and vary the pixel dimensions (and spatial resolution) with the Pixel Dimensions slider. The number of pixels utilized in the horizontal and vertical axes of the image are presented directly beneath the slider, as is the total number of pixels employed in the entire image composition.
The spatial resolution of a digital image is related to the spatial density of the image andoptical resolution of the microscope used to capture the image. The number of pixels contained in a digital image and the distance between each pixel is known as the sampling interval, which is a function of the accuracy of the digitizing device. The optical resolution is a measure of the microscope's ability to resolve the details present in the original specimen, and is related to the quality of the optics, sensor, and electronics in addition to the spatial density (the number of pixels in the digital image). In situations where the optical resolution of the microscope is superior to the spatial density, then the spatial resolution of the resulting digital image is limited only by the spatial density.
All details contained in a digital image, ranging from very coarse to extremely fine, are composed of brightness transitions that cycle between various levels of light and dark. The cycle rate between brightness transitions is known as the spatial frequency of the image, with higher rates corresponding to higher spatial frequencies. Varying levels of brightness in specimens observed through the microscope are common, with the background usually consisting of a uniform intensity and the specimen exhibiting a spectrum of brightness levels. In areas where the intensity is relatively constant (such as the background), the spatial frequency varies only slightly across the viewfield. Alternatively, many specimen details often exhibit extremes of light and dark with a wide gamut of intensities in between.
The numerical value of each pixel in the digital image represents the intensity of the optical image averaged over the sampling interval. Thus, background intensity will consist of a relatively uniform mixture of pixels, while the specimen will often contain pixels with values ranging from very dark to very light. The ability of a digital camera system to accurately capture all of these details is dependent upon the sampling interval. Features seen in the microscope that are smaller than the digital sampling interval (have a high spatial frequency) will not be represented accurately in the digital image. The Nyquist criterion requires a sampling interval equal to twice the highest specimen spatial frequency to accurately preserve the spatial resolution in the resulting digital image. An equivalent measure isShannon's sampling theorem, which states that the digitizing device must utilize a sampling interval that is no greater than one-half the size of the smallest resolvable feature of the optical image. Therefore, to capture the smallest degree of detail present in a specimen, sampling must occur at a rate fast enough so that a minimum of two samples are collected for each feature, guaranteeing that both light and dark portions of the spatial period are gathered by the imaging device.
If sampling of the specimen occurs at a rate slower than required by either the Nyquist criterion or Shannon theorem, details with high spatial frequency will not be accurately represented in the final digital image. In the optical microscope, the Abbe limit of resolution for optical images is 0.22 micrometers, meaning that a digitizer must be capable of sampling at intervals that correspond in the specimen space to 0.11 micrometers or less. A digitizer that samples the specimen at 512 points per horizontal scan line would produce a maximum horizontal field of view of about 56 micrometers (512 x 0.11 micrometers). If too few pixels are utilized to acquire the sample, then all of the spatial details comprising the specimen will not be present in the final image. Conversely, if too many pixels are gathered by the imaging device (often as a result of excessive optical magnification), no additional spatial information is afforded, and the image is said to have been oversampled. The extra pixels do not theoretically contribute to the spatial resolution, but can often help improve the accuracy of feature measurements taken from a digital image. To ensure adequate sampling for high-resolution imaging, an interval of 2.5 to 3 samples for the smallest resolvable feature is suggested.
A majority of digital cameras coupled to modern microscopes have a fixed maximum sampling interval, which cannot be adjusted to match the specimen's spatial frequency. It is important to choose a camera and digitizer combination that can meet the minimum spatial resolution requirements of the microscope magnification and specimen features. If the sampling interval exceeds that necessary for a particular specimen, the resulting digital image will contain more data than is needed, but no spatial information will be lost.
In the tutorial, as the Pixel Dimensions slider is moved to the right, the spatial frequency of the digital image is linearly reduced. The spatial frequencies utilized range from 175 x 175 pixels (30,625 total pixels) down to 6 x 6 pixels (36 total pixels) to provide a wide latitude of possible resolutions within the frequency domain. As the slider is moved to the right (reducing the number of pixels in the digital image), specimen details are sampled at increasingly lower spatial frequencies and image detail is lost. At the lowest spatial frequencies, pixel blocking occurs (often referred to as pixelation) and masks most of the image features.
Kenneth R. Spring - Scientific Consultants, Lusby, Maryland 20657.
Brian O. Flynn, John C. Long, and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.
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