Back focal plane

After propagation into the back focal plane of tire objective lens, the scattered electron wave can be expressed in tenns of the spatial frequency coordinates k as... 

The schlieren microscope is able to detect refractive index variations to six decimal places. Any small difference in optical path (index difference, film thickness, etc) is very precisely detected by the schlieren microscope, especially in the Dodd modification. It is, in effect, a darkfield method. The specimen is illuminated with light in a portion of the illuminating cone and that direct light is masked in the conjugate back focal plane of the objective (Fig. 3). The only light to pass through this plane is refracted, reflected, or diffracted by the specimen. 

The Bertrand lens, an auxiliary lens that is focused on the objective back focal plane, is inserted with the sample between fully crossed polarizers, and the sample is oriented to show the lowest retardation colors. This will yield interference figures, which immediately reveal whether the sample is uniaxial (hexagonal or tetragonal) or biaxial (orthorhombic, monoclinic, or triclinic). Addition of the compensator and proper orientation of the rotating stage will further reveal whether the sample is optically positive or negative. 

Collectively, the post-specimen lenses serve one of two purposes they magnify either the diffraction pattern from the sample produced at the back focal plane of the objective lens or they magnify the image produced at the image plane of the objective lens. These optical planes are illustrated in the elearon ray diagram in... 

A TEM provides the means to obtain a diffraction pattern from a small specimen area. This diffraction pattern is obtained in diffraction mode, where the post-specimen lenses are set to examine the information in the transmitted signal at the back focal plane of the objective lens. 

There are three primary image modes that are used in conventional TEM work, bright-field microscopy, dark-field microscopy, and high-resolution electron microscopy. In practice, the three image modes differ in the way in which an objective diaphragm is used as a filter in the back focal plane. 

Fig. 2. (a) Ray diagram in the electron microscope under imaging (microscopy) conditions. E electron source C condenser lens S sample O objective lens bfp back focal plane of O I intermediate lens P projector lens, (b) Structural imaging, diffraction and compositional functionalities of TEM. 

Electron diffraction takes place as early as when the incident electrons interact with the specimen. The objective lens acts as a diffractometer to make the electron diffraction pattern observable at its back-focal plane. Electron diffraction is not affected by the CTF of the objective lens so that the resolution limit of the diffraction pattern is much higher than that in the image. T q)ically the EDP contains reflections up to resolution of 1 A or... 

Figure 2.5 Operational principles of a transmission electron microscope. S, specimen OL, objective lens BF, back focal plane Imj, intermediate image IL, intermediate lens Im2, second intermediate image PL, projector lens FIm, final image DP, diffraction pattern.

The limits zmjn and zmax are the values of defocus at which the reflected rays just fill the area of the transducer thus for zmin < z < zmax all the reflected rays that enter the lens fall on the transducer, while for values of defocus outside that range some of the rays miss it altogether. The value z0 is the defocus at which the geometrically reflected rays are focused on the transducer at this point, as indeed at z = 0, ray optics breaks down because it does not allow for diffraction, although it does correctly predict the position of a minimum in V(z) at z0. The approximate expressions are valid when D/n > q, as is usually the case in a high-resolution acoustic microscope. In the approximation for z0, the quantity Ft is the ratio of the separation between the transducer and the back focal plane of the lens D — q/n) to the Fresnel distance for the transducer (na /Ao),... 

Chapter 1 is concerned with the fundamental principles of image formation by a lens. These principles were first formulated by Ernst Abbe in 1873 and are basic to the chapters that follow. According to the Abbe theory, the image of an illuminated object is the result of a twofold diffraction process. First, the Fraunhofer diffraction pattern of the object is formed in the back focal plane of the lens. Second, the light waves travel... 

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