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The following table (Table 1) provides a list resolution ( r) and numerical aperture ( NA) values by objective magnification and correction. Other factors, such as low specimen contrast and improper illumination may serve to lower resolution and, more often than not, the real-world maximum value of r (about 0.25 µm using a mid-spectrum wavelength of 550 nanometers) and a numerical aperture of 1.35 to 1.40 are not realized in practice. In some instances, such as confocal and fluorescence microscopy, the resolution may actually exceed the limits placed by any one of these three equations. These equations are based upon a number of factors (including a variety of theoretical calculations made by optical physicists) to account for the behavior of objectives and condensers, and should not be considered an absolute value of any one general physical law. Notice that equation (1) and (2) differ by the multiplication factor, which is 0.5 for equation (1) and 0.61 for equation (2). An optical system with the ability to produce images with angular resolution as good as the instrument’s theoretical limit is said to be diffraction limited.Where r is resolution (the smallest resolvable distance between two objects), NA is a general term for the microscope numerical aperture, λ is the imaging wavelength, NA(obj) equals the objective numerical aperture, and NA(cond) is the condenser numerical aperture. However, there is a fundamental maximum to the resolution of any optical system that is due to diffraction (a wave nature of light). The resolution of an optical imaging system (e.g., a microscope, telescope, or camera) can be limited by factors such as imperfections in the lenses or misalignment. In optical imaging, there is a fundamental limit to the resolution of any optical system that is due to diffraction. Limits of Resolution and Circular Aperatures The deflection of the tip is then measured using a laser spot that is reflected from the surface of the cantilever. The mechanical probe feels the surface with a cantilever with a sharp tip.

Atomic Force Microscopy: The AFM is a scanning probe type of microscopy with very high resolution and is one of the foremost tools for imaging at the nanoscale.The electron beam of the microscope interacts with the electrons in the sample and produces signals that can be detected and have information about the topography and composition. Scanning Electron Microscopes: Referred to as SEM, these microscopes look at the surface of objects by scanning them with a fine electron beam.This interaction forms an image that is magnified and focused onto an imaging device. A beam of electrons is transmitted through an ultra thin specimen, interacting with the specimen as it passes through. Transmission Electron Microscope: The TEM passes electrons through the sample, and allows people to see objects that are normally not seen by the naked eye.With the bright field technique the object is illuminated from below to increase the contrast in the image seen by viewers. These techniques include “dark field” and “bright field.” With the dark field technique the light is scattered by the object and the image appears to the observer on a dark background. There are many illumination techniques to generate improved contrast. In optical microscopes, the better the contrast between the image and the surface it is being viewed on, the better the resolution will be to the viewer.This acts like polarized sunglasses by organizing random x-ray beams into a stack of neatly arranged waves parallel to the plane of the detector. To ensure that the incident beam is continuous, XRD machines are equipped with a Soller slit.

In this method, the detector collects data at a single fixed angle at a time. It is much more efficient than continuous scans. The step scan method is the more popular method. Pulses of energy are plotted with respect to diffraction angle. In continuous scans, the detector moves in circular motions around the object, while a beam of x-ray is constantly shot at the detector. These XRD machines record images in two ways, either continuous scans or step scanning. Now the XRD machines are equipped with semiconductor detectors. Film used to be used to record the data, but that was inconvenient because it had to be replaced often. Diffraction patterns are recorded over an extended period of time, so it is very important that the beam intensity remains constant. The XRD machine uses copper metal as the element for the x-ray source. Where m is total magnification, m o is objective lens magnification, m e is ocular lens magnification.