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 !!
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 !!
