Lenses, apertures and resolution 16.9.2016

Lenses in TEM vs. optical microscope An electron beam is used to view the sample Electromagnetic lenses made from metal To magnify and focus our image we change the current running through a coil around a soft metallic core, which changes the strength of the resulting magnetic field surrounding the electron beam Light is used to see the sample Glass lenses We physically move the lenses up and down to change the focus and intensity of the image To increase the magnification we have to change lenses

Ray diagram A ray diagram is a diagram that shows how light rays pass through a lens Electrons passing through the middle of the lens are unaffected while all other electron paths are bent when passing through a lens The strength of the lens determines where electrons are focused (stronger lenses have shorter focal lengths) The focal plane is where parallel rays intersect after passing through the lens. The image formed by the lens is rotated by 180°

Principal optical elements Lens plane (the plane where the lens is located) Object plane (the plane containing the viewed object) Image plane (the plane containing the image, which always lies below the lens) Focal plane (the plane in which the parallel rays are brought to a focus) 1 𝑓 = 1 𝑑 0 + 1 𝑑 𝑖 For convex lenses the focal plane lies behind the lens, while for convex lenses the focal plane lies in front of the lens f – distance of focal plane from the lens plane d0 – distance of object plane from lens plane di – distance of image plane from lens plane

Magnification and Focus Magnification in convex lenses can be described as: 𝑀= 𝑑 𝑖 𝑑 0 In a TEM we change the magnification by changing the strength of the lens without actually changing the lens If we make the lens stronger than we shorten the focal length, which means that the magnification becomes smaller Compared to other microscopes, TEM can also gain information from images that are out of focus (overfocused, underfocused) Typically we tend to operate the objective lens at a fixed strength, while moving the object plane closer to the lens thus making d0 smaller and M larger In theory we could achieve unlimited magnification, but unfortunately there are other factors limiting the resolution of the microscope

Electromagnetic LENSES Electromagnetic lenses are constructed from two parts: A cylindrically symmetrical core made from a soft magnetic material (polepiece) with a hole (bore) drilled through it A coil of copper wire surrounding each polepiece When a current is passed through the copper coil a magnetic field is created. The strength of the field controls the electron trajectories Soft refers to the materials magnetic properties and not mechanic. Soft iron is usually used as a material for the core. In most lenses there are two polepieces which can be part of the same piece of iron or two separate pieces. Because of resistive heating of the coil the lenses need to be cooled by a water recirculating system.

Objective lenses A TEM has several lenses (multi-lens system) from which most of them are weak. The strongest lens is the objective lens which forms the images magnified by other lenses. There are several different types of objective lenses: Split polepiece objective lens (A): Can produce a broad electron beam for TEM and a fine beam for AEM and STEM. The lens has also enough space for other instruments (x-ray spectrometer) to reach the sample. The sample can also be tilted and rotated Immersion objective lens (B): Due to its short focal length, this lens is capable of producing very high resolutions. There is not enough space to move the sample or do additional analysis

Objective lenses Snorkel objective lens (C)

Superconducting lenses To overcome the limitation of ferromagnetic polepieces (saturized magnetization) superconducting lenses can be used. Superconductor lenses can generate intense fields which are promising for forming fine probes with high-energy electrons, their aberrations are smaller and they do not require any cooling making the lenses smaller Unfortunately superconductors generate fixed fields and cannot be varied, which means that they are not very flexible. These lenses became popular with the discovery of high-Tc superconductors

Electron path through magnetic fields In a magnetic field, electrons do not travel in a straight line but rather spiral in a helical trajectory The electrons rotate under the influence of the rotationally symmetrical magnetic field This effect causes the sample image to rotate on the display screen as we change the focus or magnification of the electromagnetic lense For electrons with higher energies, we must use stronger lenses to get similar ray paths The optic axis is sometimes referred as the rotation axis. If we wish to deflect the beam or tilt it we need to use an additional electromagnetic field. If we wish to blank the beam we need to apply an electrostatic field.

Apertures and diaphragms Apertures are inserted into the lens in order to limit the collection angle of the lens. This allows us to control the resolution of the image formed by the lens, the depth of field, the depth of focus, the image contrast and many other things The apertures are circular holes in metal disks made from either Pt or Mo Diaphragms come in several forms. They can be either individual disks, or they can be a series of different apertures in a single metal strip Often the diaphragm collects contamination caused by the electron beam. These contaminations are known to cause astigmatism

Lens PROBLEMS Electromagnetic lenses have many imperfections which limit the resolution the microscope but paradoxically help us get a better depth of field and focus. The main defects that electromagnetic lenses experience are: Spherical aberration Chromatic aberration Astigmatism

Spherical aberration This defect occurs when the lens field behaves differently for off-axis rays A point object is imaged as a disk of finite size, which limits our ability to magnify details because they are degraded by the imaging process To correct this aberration we can create a diverging (concave) lens which spreads out the off-axis beams in such a way that they re-converge to a point rather than a disk. The further the electron beam is off axis the stronger the bend

Chromatic aberration This term refers to the frequency, wavelength or energy of the electrons The problem occurs due to the variation of the electron energy that pass through the sample. The objective lens bends electrons with lower energy stronger and thus electrons from a point once again form a blurred disc This aberration gets worse for thicker specimens To correct this aberration by using thinner samples or through energy-filtering In reality electrons aren’t monochromatic

Astigmatism Astigmatism occurs when the electrons sense a non-uniform magnetic field as they spiral around the optic axis. This defect arises because we can’t create perfectly cylindrically symmetrical polepieces This is easily corrected using stigmators, which are small octupoles that introduce a compensating field to balance the inhomogeneities causing astigmatism

Depth of focus and field Small apertures need to be used to minimize their aberrations, which in turn give us a better depth of focus and better depth of field The depth of field refers to the distance along the axis on both sides of the object plane within which we can move the object without detectable loss of focus in the image The depth of focus refers to the distance along the axis on both sides of the image plane within which the image appears focused