TEM theory Basic optics, image formation and key elements

Workshop series of Chinese 3DEM community Get acquainted with Cryo-Electron Microscopy: First Chinese Workshop for Structural Biologists TEM theory Basic optics, image formation and key elements Jianlin Lei May 31, 2015

Electron-specimen interactions

General Structure of EM Power Supply Electron Optics Cooling system Vacuum system Control system

Electron Optics Consists of: Illumination system Imaging system Recording system Elements: Electron gun Lenses Stigmators Deflection coils Apertures Holder and stage Recording media

Cross-sectional view of a typical TEM

Holder Holder: Hold a standard size of grid upon which the sample is placed or a standard size of self-supporting specimen. Gatan 626 Gatan/Oxford CT3500

Stage/Goniometer Stage/Goniometer: Bring the region of interest into the path of the electron beam. Top entry Side entry

Elements in Illumination and Imaging Systems Gun Lenses Stigmators Deflection coils Apertures Illumination System Gun C1 C2 C3 Mini-condenser Condenser Gun Beam C1 C2 C3 Imaging System Objective Diffraction Intermediate Projector Objective Diffraction Image Objective Selected-area

System status

Elements in Electron Optics Gun Lenses Stigmators Deflection coils Apertures Holder and stage Recording media

Electron Source W LaB 6 FEG

Some features of electron sources

Electromagnetic spectrum Electron wavelengths () 0.037 Å at 100kV, 0.0349 Å at 120kV, 0.025 Å at 200 kv, 0.01969 Å at 300 kv compare with wavelength of light: 4000 7600 Å or X-rays: 1.5 Å for Cu K 1 Å synchrotron radiation diffraction limit for resolution of any optical system: D = /2

Elements in Electron Optics Gun Lenses Stigmators Deflection coils Apertures Holder and stage Recording media

Electromagnetic lenses Condenser (C1, C2, C3) Mini-Condenser Objective Diffraction Intermediate Projector (P1, P2)

Focal length of Electromagnetic lens f 2 K( U /( IN ) ) f = focal length, K = lens constant, U = voltage, I = current, N is the number of turns in the magnet coil. electromagnetic lens: can change focal length by changing current glass lens: change focus by moving specimen up and down change magnification by switching lenses

Condenser lens C1 Function: Determines the demagnification (size reduction) of the electron source onto the specimen and thus the spot size. How to adjust: change spotsize Spotsize index: 1-11 (FEI) Microprobe vs nanoprobe mode

Condenser lens C2 (C2/C3) Function: Determine how strongly the beam is focused onto the specimen and the convergence angle of the beam. How to adjust: Intensity knob Tecnai series (C2): Intensity Titan series (C2/C3): Illuminated area C2 lens has weak excitation and long focal length, why?

Parallel beam operation in a TEM C1, C2 control the beam size on the specimen. Using C2 to refocus the beam before C3 results in a more coherent beam. Front focal plane of C3 C3 (A) using just the C1 and an underfocused C2 lens. (B) using the C1 and C2 lenses to image the source at the front focal plane of C3.

Objective lens Function: Image formation Image focus in HM / Diffraction focus in LAD How to adjust: Focus knob

Conventional objective lens Objective lens design Riecke-Ruska design of symmetrical condenser-objective lens

Mini-condenser lens Function: produce a wide field of view and coherent illumination on the specimen in Microprobe mode. TWIN-lens design (A) Microprobe mode (B) Nanoprobe mode

Types of objective lens JEOL: URP, HRP, HTP, CRP, HCP FEI: Bio-TWIN, TWIN, C-TWIN, S-TWIN, X-TWIN, U-TWIN

Tecnai F20 with different obj. lens types

Magnetic lenses like Glass lenses are governed by Newton s lens equation http://members.shaw.ca/quadibloc/science/opt05.htm a b and M b v f M ; M ; M a u u f l f f

How to set defocus? Defocus = u real u ideal <0, underfocus =0, in-focus >0, overfocus Underfocus is preferred for HREM/Cryo-EM Two methods to set an underfocus value: Reduce objective lens current (Turn focus knob counterclockwise) Reduce z-height f 2 K( U /( IN ) )

Lorentz lens For magnetic structure of the specimen

Diffraction lens Function: Diffraction focus in D / Image focus in LM How to adjust: Focus knob

Intermediate lens Function: Intermediate (Magnification, Imaging <-> Diffraction) How to adjust: Imaging Diffraction; Magnification knob

Imaging vs Diffraction

Optical modes Imaging: LM, HM (M, SA, Mh) Diffraction: LAD, D Imaging Diffraction LM LM LAD HM M D SA Mh

Projection lenses (P1, P2) Function: Magnification How to adjust: Magnification knob

Function of electromagnetic lenses Condenser (Beam focus) Objective (Image focus in HM / Diffraction focus in LAD) Diffraction (Diffraction focus in D / Image focus in LM) Intermediate (Magnification, Imaging <-> Diffraction) Projector (Magnification)

Elements in Electron Optics Gun Lenses Stigmators Deflection coils Apertures Holder and stage Recording media

Astigmatism Astigmatism occurs when a lens does not have perfect cylindrical symmetry. This may be by design, or due to manufacturing error. ra f A

Function of stigmators Condenser stigmator: Make the focused beam circular. Objective stigmator: Correct astigmatism in the HM (MI, SA, Mh) image. Correct astigmatism in the low-angle diffraction (LAD) pattern. Diffraction stigmator: Correct astigmatism in the LM image. Correct astigmatism in the diffraction (D) pattern.

Correction of astigmatism Condenser Objective Diffraction Before correction After correction

Elements in Electron Optics Gun Lenses Stigmators Deflection coils Apertures Holder and stage Recording media

Deflector coils A deflection coil is a set of coils on either side of the electron beam. The beam can be deflected into any direction by a suitable combination of x and y. Double deflection coils: The deflection coils are always mounted in sets of two above another. Double deflection coils are capable of two completely independent actions, a tilt and a shift.

Pivot points Tilt and shift actions by double deflection coils should be decoupled.

Type of Deflector coils Gun coils (Gun tilt / shift) Beam coils (Beam shift / tilt) Image coils (Image shift / Diffraction shift)

Elements in Electron Optics Gun Lenses Stigmators Deflection coils Apertures Holder and stage Recording media

Location of apertures C1 aperture Below C1 lens C2 aperture Below C2 lens Objective aperture: Back-focal plane of obj. lens SA aperture: Image plane of obj. lens

Function of apertures C1 aperture (Normally don t touch) Limit beam illuminated area C2 aperture Limit beam illuminated area Objective aperture Contrast forming (HM) Area selection (LM) SA aperture (Normally don t touch for phase contrast imaging) Contrast forming (LM) Area selection (HM) Only C2 and objective aperture can be adjusted on T12.

Summary: role of some elements changed with EM modes Objective lens: Image focus in HM / Diffraction focus in LAD Diffraction lens: Diffraction focus in D / Image focus in LM Objective stigmator: Correct astigmatism in the HM (MI, SA, Mh) image. Correct astigmatism in the low-angle diffraction (LAD) pattern. Diffraction stigmator: Correct astigmatism in the LM image. Correct astigmatism in the diffraction (D) pattern. Contrast aperture HM: Objective aperture LM: SA aperture Diffraction aperture HM: SA aperture LM: Objective aperture

Recording media Film Imaging plate CCD (Charge coupled device) Pseudo-CMOS based detector Direct electron detector

Imaging vs Diffraction

Modes of Operation of a TEM Diffraction Selected Area Electron Diffraction (SAED) Convergent-Beam Electron Diffraction (CBED) Imaging Mass-thickness contrast Diffraction contrast a) Bright-Field (BF) b) Dark-Field (DF) Phase contrast (HREM)

Electron diffraction Diffraction pattern locates at the back focal plane of the objective lens. Bragg angles are small. The diameter of the Ewald sphere is very large compared to the size of the unit cell in the reciprocal lattice. Lenses are able to focus the diffraction pattern and to change the camera length, which is equivalent to moving the film in an x-ray experiment.

Bragg s law 2d sin

Ewald Sphere 薄片样品使得倒易点变成倒易杆 和倒易矢相比, 电子波长非常短导致波矢很大, 因此倒易球半径非常大

SAED

Spot patterns Spot patterns corresponding to single-crystal diffraction

Ring patterns Ring patterns corresponding to powder diffraction from multiple crystals with a variable orientation

Diffraction with parallel illumination and conical illumination Parallel Beam Convergent beam

SAED vs CBED

CBED Pattern CBED diffraction pattern from [111] Si obtained at low (main pattern) and high (inset) camera-lengths.

Image contrasts in TEM Mass-thickness contrast Scattering is dependent upon Z / Eo (Rutherford cross section) and the mean free path (specimen thickness). Diffraction contrast (BF, DF) Crystals and ordered materials diffract electrons at different angles. Phase Contrast (HREM) Constructive / destructive interference from the transmitted electrons gives rise to contrast. Z-contrast - scattering angle is highly dependent upon Z image electrons scattered at high angles

Mass-thickness contrast

Modes of Operation of a TEM Diffraction Selected Area Electron Diffraction (SAED) Convergent-Beam Electron Diffraction (CBED) Imaging Mass-thickness contrast Diffraction contrast a) Bright-Field (BF) b) Dark-Field (DF) Phase contrast (HREM) *Diffraction related

Diffraction contrast vs phase contrast Objective aperture

Diffraction contrast BF DF P.B. Hirsch, et al., Electron microscopy of thin crystals, 1993

DF

BF SAED DF

Application of Phase Contrast HREM Cryo-EM

HREM

Cryo-EM image

Phase shift of wave behind object, where Phase shift of wave behind object with thickness t: t 0 2 ( k k 1 1 2meV 2me( V C( r)) 2 2 k0 ( ) is wave vector in vacuum, k ( ) 2 2 is wave vector in the object. V is acceleration voltage, and C(r) 0 ) dz (a) is the 3D Coulomb potential distribution within the object. (a) Can be written as, where ( x, y) ( x, y) C( r) dz V t 0 is projection of potential distribution Wavelength change C 1 C 0 Iso-phase lines

Weak phase object approximation Pure phase object: Transmission function: )), ( ), ( exp( ), ( y x u y x i y x q )), ( exp( ), ( y x i y x q... ), ( 2 1 ), ( 1 2 2 y x y x i Weak phase object approximation: ), ( 1 ), ( y x i y x q

Observed contrast Transmission function: q( x, y) 1i ( x, y) After the object: Q( u, v) ( u, v) i( u, v) Apply CTF A( u, v)exp( i ( u, v)) : ( u, v) i( u, v) A( u, v)cos ( u, v) ( u, v) A( u, v)sin ( u, v) ( x) f ( x) ( x) f (0), and A(0,0) 1, (0,0) 0, [Note because ( u, v ) A( u, v )exp( i( u, v )) ( u, v )] Exit wave function: ( x, y) 1i ( x, y) ( A( u, v)cos( ( u, v))) ( x, y) ( A( u, v)sin( ( u, v))) Observed contrast: c( x, y) ( x, y) *( x, y) 1 2 ( x, y) ( A( u, v)sin( ( u, v))) 2 2 2 ( ( x, y) ( A( u, v)sin( ( u, v)))) ( ( x, y) ( A( u, v)cos( ( u, v)))) 2 ( x, y) ( A( u, v)sin( ( u, v))) Corresponding power spectrum: C( u, v) 2 ( u, v) A( u, v)sin( ( u, v)) 2

Wave aberration function χ(μ,ν) Because astigmatism can be corrected, ) )]( sin 2( 2 [ ) ( 2 ), ( 2 2 0 4 4 3 v u z z v u C v u a s Contributions: Spherical aberration Defocus Astigmatism ) ( ) ( 2 ), ( 2 2 4 4 3 v u z v u C v u s 2 4 3 2 k z k C s 2 2 2 where, v u k

Envelope function A( u, v) R( u, v) E( u, v) Aperture function: 1 R( u, v) 0 for 0 elsewhere 2 2, where ( u v ), 0 is the angle 1 2 corresponding to the radius of the objective aperture Compound envelope function: E( u, v ) E ( u, v ) E ( u, v ) e i E e ( u, v ) : envelope function due to energy spread E i ( u, v ) : envelope function due to partially coherent illumination

E e ( u, v ) : envelope function due to energy spread Due to chromatic aberration, E e 1 2 2 2 2 ( u, v) exp[ c ( u v 2 1 2 2 2 4 exp[ c k ] 2 where c C c ( E) E 2 2 ) 2 ] ( V ) V 2 ( I) I 2

E i ( u, v ) :envelopefunction due topartially coherent illumination Spatial coherence (lateral coherence, transverse coherence) Due to finite source size, 2 E ( u, v) exp[ a i E 2 1 k0 for a Gaussian source distribution F( k0) exp( ) 2 2 a 2 c 3 ( C k for a top hat distribution s 3 zk) F 2 ] 1 ) a 0 3 3 J1[2a c( Cs k zk)] u, v) 2 3 [2a ( C k zk)] i ( 3 c s envelope function due to partially coherent illumination for k c a c a c 2 0 c ( k 0 c elsewhere, with J 1 denoting the first-order Bessel function. (Notethat 3 C s k 3 zk is the gradient of the wave aberration function)

Point resolution vs Information limit Point resolution: 1.7 Å Information limit: 0.8 Å

q( x, y) exp( i ( x, y)) Amplitude contrast => C( u, v) 2 ( u, v) A( u, v)sin( ( u, v)) q( x, y) exp( i ( x, y) u( x, y)) => C( u, v) 2 ( u, v) A( u, v)[sin( ( u, v)) Q( u, v)cos( ( u, v))] It is assumed U( u, v) Q( u, v) ( u, v) (1) the same for all atoms in the specimen; (2) constant within the small spatial frequency range of practical interest in most cryo-em applications C s = 2 mm; Q = 0.15; Δz = -0.9 μm (solid line) Δz = -1.5 μm (dotted line) (a) Zeros shifts toward higher radii (b) CTF starts off with a nonzero term