Summary Bio-Imaging

Bio-Imaging and Image informatics
INTRO
. Positron emission tomography (PET)  high Energy Ɣ-rays  1-2 mm Spatial reso
. Magnetic resonance imaging (MRI)  radiowaves  25-100 μm SR
. Computed tomography (CT scans)  X-rays  50-200 μm SR
. Ultrasound  high-freq sound  50-500 μm SR
. Optical Fluo Microscopy  visible, infrared light  < 1 mm SR

CHAP_3 : Concept of optics and light
. Dual nature light  p° sometimes acts like a wave(Huygens, Young)/particle(Newton)
 Particle: Photoelectric effect -> light eject electrons (only certain wavelengths, indep of Intensity)
 Wave: Young -> light between 2 // slits -> light waves interfere -> dark and light bands = diffract°




. 4 main laws optics: 1) straight propagation light. 2) independency light beams. 3) Reflect° 4) Refract°
c
. Refraction: refraction index (medium) = n= = ratio speed light (vacuum) - speed light (medium)
v
 Free space: n = 1 ; Air : n = 1.0003 ; Water : n = 1.33 ; Glass : 1.66 ; Greater n = lower speed light
 Greater/lower n = lower/greater speed of light = light ray bent toward/away the normal (nr>ni)
 Snell’s law :  Angles measured with respect to surface normal

. Specific cases (higher->smaller) :
 θi = 0°  no diffraction
 θi = θcrit  bend 90° away normal (travel btween 2 interfaces)
 θi > θcrit  total reflection

. Thin lens = ideal lens  converging/+ or diverging/- (fct° of curvature)
 Focal points F => // beams focused on F (+) ; projection of // beams focused on F (-)
 Beam pasing by center lens not diffracted ; beam passing by F becomes // to axis after lens
 F_dist depend on concavity  the more concave, the shorter F_dist
 Plane wave fronts  converging spherical wave fronts (+) / diverging spherical wave fronts(-)
=> light slower in lens medium than air => thicker parts retard light.
1 1 1
 Lens formula: + = => where p = dist_obj/lens ; q = dist_im/lens ; f = focal dist (all>0)
p q f
siz e ℑ q
 Magnification M = =
siz e obj p
 Lens system = more than 1 => im from 1st lens = obj second lens ; Mtot = Mlens1 . Mlens2 (µscope)
 Real image  im other side lens, inverted (obj after F)
Virtual image  im same side obj, not invert, bigger (obj btween F and lens)




. 2 syst of lenses in microscope = objective + eyepiece (Mtot = Mobj.Mep)

,  Objective : infinity corrected => // beam after objective => tube lense => intermediate real im
 Eyepiece (ep) : im from objective put btween F_ep and ep => big virtu im >>> obj
. Light = electromagnetic wave (2 components = E + B => amplitude = intensity, wavelength, freq, ..)
 . c= λ . ν : where c = speed light ; λ = wavelength ; ν = frequency
 E( r ,t)=E 0 . cos ¿
2 2 πc
where k = . û where 𝒖̂ = unit vector (direct° propagat°) ; ¿
λ λ
 Diffration = wave spread out after going through small holes/corners (opening±= λ ).
= deviat° geometrical optics due to obstruct° of wave front of light by obstacle/opening
 Princip of superposit° : Yres = Y1 + Y2 (constructive/destructive interferences, period important!!)
 Huygens’ wavelets (no physical basis) : Every pt on a known wave front can be treated as a pt
source of wavelets (= small spherical waves “bubbling” out of the pt) which spread out in all
direct° with a wave speed characteristic of medium. The developing wave front @ any t is the
envelope of these advancing spherical wavelets.

. Young’s double-slit interference experiment :
 Light from both slits is coherent => fixed phase relationship btween waves from both sources.
 Light from both slits same wavelength
λ
 The nth bright frange on screen is @ angle : θn = n . (n = 0,1,2,3,..)
d
 Position of bright/dark fringes : y(B)= m(sλ/a); and y(D)= (m+1/2)(sλ/a)

. Diffraction-Limited Optics => lens diameter D = large circular aperture => focused spot not a point !
 Diffract° pattern = Airy pattern = bright disk @ center (airy disk) + dark and bright rings around
 Caused by diffraction or scattering of light through specimen + circular aperture objective.
. Resolution of a microscope = dist up to which 2 small obj seen as separate entities
 smallest resolvable dist btween 2 pts cannot be smaller than half the wavelength of imaging light
 (Abbe) => Resolution ↑ if d ↓ = NA ↑ = λ ↓ (Attent° ROS)(Approx : d=200nm)

 Alpha = half-angle of the maximum cone of light that can enter/exit obj lens ; n = refraction index

. Other resolution’s criteria based on dist where :
λ
 Rayleigh => max of one Airy pattern intercepts with 1st min of other Airy pattern => d = 0.61
NA
 Full width half max => Both Airy pattern intensity profiles intercept @ points corresponding to 1⁄2
λ
of the maximum intensity @ the center of Airy disk : d = 0.51
NA
λ
 Sparrow => no dip in the intensity of image : d = 0.47
NA
1.22 λ
. Most general expression for resolut° limit => d = NA + N a
obj cd
 consider NA from lenses of condenser (condense light on speci)/objective (receive light speci)

CHAP 4 : Concept of microscope
. 4 major blocks : Lens+mirrors / objectives / light sources / Detectors
1) Mirrors : reflecting light from the lamp to eye/camera => compactness microscope
Lenses : Condenser lens => illumination cone on specimen => objective lens

2) Objectives : Primary image formation => central rôle for quality :
 Compensate for cover glass thickness variat° ; Increase effective working distance ;
Project a diffraction-limited image at a fixed plane (= intermediate image plane)
 Today : infinity corrected objectives => // beam after objective => allow to choose tube length !!