the beam at the sample position to be independently controlled and also ensure that the beams remain near the low-aberration centers of every lens in the lens stacks. the stigmators compensate for slight imperfections and aberrations that cause astigmatism—a lens having a different focal strength in different directions. typically a tem consists of three stages of lensing. the stages are the condenser lenses, the objective lenses, and the projector lenses. the condenser lenses are responsible for primary beam formation, while the objective lenses focus the beam that comes through the sample itself (in stem scanning mode, there are also objective lenses above the sample to make the incident electron beam convergent). the projector lenses are used to expand the beam onto the phosphor screen or other imaging device, such as film. the magnification of the tem is due to the ratio of the distances between the specimen and the objective lens' image plane. tem optical configurations differ significantly with implementation, with manufacturers using custom lens configurations, such as in spherical aberration corrected instruments, or tems using energy filtering to correct electron chromatic aberration. reciprocity the optical reciprocity theorem, or principle of helmholtz reciprocity, generally holds true for elastically scattered electrons, as is often the case under standard tem operating conditions. the theorem states that the wave amplitude at some point b as a result of electron point source a would be the same as the amplitude at a due to an equivalent point source placed at b. simply stated, the wave function for electrons focused through any series of optical components that includes only scalar (i.e. not magnetic) fields will be exactly equivalent if the electron source and observation point are reversed. r reciprocity is used to understand scanning transmission electron microscopy (stem) in the familiar context of tem, and to obtain and interpret images using stem. display and detectors the key factors when considering electron detection include detective quantum efficiency (dqe), point spread function (psf), modulation transfer function (mtf), pixel size and array size, noise, data readout speed, and radiation hardness. imaging systems in a tem consist of a phosphor screen, which may be made of fine (10–100 μm) particulate zinc sulfide, for direct observation by the operator, and an image recording system such as photographic film, doped yag screen coupled ccds, or other digital detector. typically these devices can be removed or inserted into the beam path as required. (photograph film is no longer used.) the first report of using a charge-coupled device (ccd) detector for tem was in 1982, but the technology didn't find widespread use until the late 1990s/early 2000s. monolithic active-pixel sensors (mapss) were also used in tem. cmos detectors, which are faster and more resistant to radiation damage than ccds, have been used for tem since 2005. in the early 2010s, further development of cmos technology allowed for the detection of single electron counts ("counting mode"). these direct electron detectors are available from gatan, fei, quantum detectors and direct electron. components the electron source of the tem is at the top, where the lensing system (4,7 and 8) focuses the beam on the specimen and then projects it onto the viewing screen (10). the beam control is on the right (13 and 14) a tem is composed of several components, which include a vacuum system in which the electrons travel, an electron emission source for generation of the electron stream, a series of electromagnetic lenses, as well as electrostatic plates. the latter two allow the operator to guide and manipulate the beam as required. also required is a device to allow the insertion into, motion within, and removal of specimens from the beam path. imaging devices are subsequently used to create an image from the electrons that exit the system. vacuum system to increase the mean free path of the electron gas interaction, a standard tem is evacuated to low pressures, typically on the order of 10−4 pa. the need for this is twofold: first the allowance for the voltage difference between the cathode and the ground without generating an arc, and secondly to reduce the collision frequency of electrons with gas atoms to negligible levels—this effect is characterized by the mean free path. tem components such as specimen holders and film cartridges must be routinely inserted or replaced requiring a system with the ability to re-evacuate on a regular basis. as such, tems are equipped with multiple pumping systems and airlocks and are not permanently vacuum sealed. the vacuum system for evacuating a tem to an operating pressure level consists of several stages. initially, a low or roughing vacuum is achieved with either a rotary vane pump or diaphragm pumps setting a sufficiently low pressure to allow the operation of a turbo-molecular or diffusion pump establishing high vacuum level necessary for operations. to allow for the low vacuum pump to not require continuous operation, while continually operating the turbo-molecular pumps, the vacuum side of a low-pressure pump may be connected to chambers which accommodate the exhaust gases from the turbo-molecular pump. sections of the tem may be isolated by the use of pressure-limiting apertures to allow for different vacuum levels in specific areas such as a higher vacuum of 10−4 to 10−7 pa or higher in the electron gun in high-resolution or field-emission tems. high-voltage tems require ultra-high vacuums on the range of 10−7 to 10−9 pa to prevent the generation of an electrical arc, particularly at the tem cathode. as such for higher voltage tems a third vacuum system may operate, with the gun isolated from the main chamber either by gate valves or a differential pumping aperture – a small hole that prevents the diffusion of gas molecules into the higher vacuum gun area faster than they can be pumped out. for these very low pressures, either an ion pump or a getter material is used. poor vacuum in a tem can cause several problems ranging from the deposition of gas inside the tem onto the specimen while viewed in a process known as electron beam induced deposition to more severe cathode damages caused by electrical discharge. the use of a cold trap to adsorb sublimated gases in the vicinity of the specimen largely eliminates vacuum problems that are caused by specimen sublimation. specimen stage tem sample support mesh "grid", with ultramicrotomy sections tem specimen stage designs include airlocks to allow for insertion of the specimen holder into the vacuum with minimal loss of vacuum in other areas of the microscope. the specimen holders hold a standard size of sample grid or self-supporting specimen. standard tem grid sizes are 3.05 mm diameter, with a thickness and mesh size ranging from a few to 100 μm. the sample is placed onto the meshed area having a diameter of approximately 2.5 mm. usual grid materials are copper, molybdenum, gold or platinum. this grid is placed into the sample holder, which is paired with the specimen stage. a wide variety of designs of stages and holders exist, depending upon the type of experiment being performed. in addition to 3.05 mm grids, 2.3 mm grids are sometimes, if rarely, used. these grids were particularly used in the mineral sciences where a large degree of tilt can be required and where specimen material may be extremely rare. electron transparent specimens have a thickness usually less than 100 nm, but this value depends on the accelerating voltage. once inserted into a tem, the sample has to be manipulated to locate the region of interest to the beam, such as in single grain diffraction, in a specific orientation. to accommodate this, the tem stage allows movement of the sample in the xy plane, z height adjustment, and commonly a single tilt direction parallel to the axis of side entry holders. sample rotation may be available on specialized diffraction holders and stages. some modern tems provide the ability for two orthogonal tilt angles of movement with specialized holder designs called double-tilt sample holders. some stage designs, such as top-entry or vertical insertion stages once common for high resolution tem studies, may simply only have x-y translation available. the design criteria of tem stages are complex, owing to the simultaneous requirements of mechanical and electron-optical constraints and specialized models are available for different methods. a tem stage is required to have the ability to hold a specimen and be manipulated to bring the region of interest into the path of the electron beam. as the tem can operate over a wide range of magnifications, the stage must simultaneously be highly resistant to mechanical drift, with drift requirements as low as a few nm/minute while being able to move several μm/minute, with repositioning accuracy on the order of nanometers. earlier designs of tem accomplished this with a complex set of mechanical downgearing devices, allowing the operator to finely control the motion of the stage by several rotating rods. modern devices may use electrical stage designs, using screw gearing in concert with stepper motors, providing the operator with a computer-based stage input, such as a joystick or trackball. two main designs for stages in a tem exist, the side-entry and top entry version. each design must accommodate the matching holder to allow for specimen insertion without either damaging delicate tem optics or allowing gas into tem systems under vacuum. a diagram of a single axis tilt sample holder for insertion into a tem goniometer. tilting of the holder is achieved by rotation of the entire goniometer the most common is the side entry holder, where the specimen is placed near the tip of a long metal (brass or stainless steel) rod, with the specimen placed flat in a small bore. along the rod are several polymer vacuum rings to allow for the formation of a vacuum seal of sufficient quality, when inserted into the stage. the stage is thus designed to accommodate the rod, placing the sample either in between or near the objective lens, dependent upon the objective design. when inserted into the stage, the side entry holder has its tip contained within the tem vacuum, and the base is presented to atmosphere, the airlock formed by the vacuum rings. insertion procedures for side-entry tem holders typically involve the rotation of the sample to trigger micro switches that initiate evacuation of the airlock before the sample is inserted into the tem column. the second design is the top-entry holder consists of a cartridge that is several cm long with a bore drilled down the cartridge axis. the specimen is loaded into the bore, possibly using a small screw ring to hold the sample in place. this cartridge is inserted into an airlock with the bore perpendicular to the tem optic axis. when sealed, the airlock is manipulated to push the cartridge such that the cartridge falls into place, where the bore hole becomes aligned with the beam axis, such that the beam travels down the cartridge bore and into the specimen. such designs are typically unable to be tilted without blocking the beam path or interfering with the objective lens. electron gun cross sectional diagram of an electron gun assembly, illustrating electron extraction the electron gun is formed from several components: the filament, a biasing circuit, a wehnelt cap, and an extraction anode. by connecting the filament to the negative component power supply, electrons can be "pumped" from the electron gun to the anode plate and the tem column, thus completing the circuit. the gun is designed to create a beam of electrons exiting from the assembly at some given angle, known as the gun divergence semi-angle, α. by constructing the wehnelt cylinder such that it has a higher negative charge than the filament itself, electrons that exit the filament in a diverging manner are, under proper operation, forced into a converging pattern the minimum size of which is the gun crossover diameter. the thermionic emission current density, j, can be related to the work function of the emitting material via richardson's law j = a t 2 exp ⁡ ( − φ k t ) , \exp \left(\right),} where a is the richardson's constant, φ is the work function and t is the temperature of the material. this equation shows that in order to achieve sufficient current density it is necessary to heat the emitter, taking care not