Biomedical imaging
MICROSCOPY PART
Resolution = ability to distinguish two points: 1,1mm for human eye
→ microscopes have a better resolution of 200nm
H1 Microscopy basics
1.1 Wave-like properties of light
Light has a wave-like property:
▪ Amplitude
▪ Frequency: number of waves produced each second
▪ Wavelength: distance between two maxima
o A wave is defined by its wavelength → the higher, the
more energy it contains
▪ Speed
▪ Phase
▪ Polarisation
We can only see a fraction of it: 390-770nm
! Light also has a particle-like property
Refraction
= bending of light due to a difference in refractive index of two media
speed of light in vacuum
▪ 𝑅𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥, 𝑛 =
speed in medium
o ⇡ n = low speed in medium | ⇣ n = fast speed in medium
▪ If n1 < n2, the angle of refraction will be smaller than the angle of incidence
Snell’s law describes how light bends (refracts) when it passes from one medium into another with a different optical
density: 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2
- n = the refractive index of the medium
- 𝜃1 = angle of incidence (incoming ray)
- 𝜃2 = angle of refraction (bent ray)
Dispersion
▪ Each λ diffracts differently (at different angles) which creates dispersion
▪ Bigger λ (red) know less deviation from the original path than smaller λ
(blue)
▪ Bigger λ → less sensitive to refraction than smaller λ
Reflection
When the angle of refraction = angle of incidence → light will reflect
Diffraction
= coherent light spreads out when passing a narrow slit (most of the time when
it’s smaller than the wavelength)
▪ Diffraction changes the way light is perceived and displayed
1
, ▪ ⇣ opening = stronger bending of the light waves
▪ Diffraction generates a characteristic pattern that depends on the amount of slits
▪ The middle part is undeviated light that passes straight through the gap
▪ The light surrounding the middle area are deviated
▪ Important formula for diffraction: d ∙ sin θ = mλ
o d = size of slit
o m = maxima
Interference
= phenomenon that takes place when two waves meet and combine → can either increase or decrease the
amplitude of the new wave
Constructive interference: when two waves meet and have an increase in amplitude as a result
Destructive interference: when two waves meet and have a decrease in amplitude as a result
Which interference happens depends on the phase difference of both waves
If the phase difference between both is nπ (with n an even number), the amplitude of the new, combined
wave increases
If the phase difference between both is mπ (with m an odd number), the amplitude of the new, combined
wave decrease
! EXAM: terms can be asked in multiple choice
Diffraction is based on interference
▪ More pronounced diffraction pattern when you have multiple slits
▪ Direct, inverse relationship between the position of the maxima and minima with the distance between the
slits → the closer, the more spread out the maxima and minima will be
1.2 Lens theory
Basic convex lens:
▪ Focal point: for every lens at a certain point
▪ Focal distance (f)
▪ Optical axis
There are 3 rules relating to the light path through this perfect convex lens
2
,Rule 1: parallel rays converge at the focal point
Rule 2: rays from the focal point exit in parallel
Rule 3: rays that pass through the centre of the lens, remain unaffected
Calculating the magnification
Four factors for calculation:
1. Focal distance (f)
2. Size of the object (ℎ0 )
3. Position of the object relative to the lens (𝑑0 )
4. Position of the real image relative to the lens (𝑑𝑖 )
Lens maker equation
f < 0: image is left of the lens
f > 0: image is right of the lens
Magnification
M < 0: object is inverted
M > 0: object is not inverted
d0 = f
Infinity → to focuse the image we need an additional lens → much used in
microscopy so that we can put something in between the two lenses so we can
intervene
! EXAM: need to be able to do the exercises
3
, 1.3 Optical train of compound microscope
Different parts of a microscope
Upright microscope Inverted microscope
The compound microscope is a two-lens magnifier
Light from object B goes through the
objective and creates a magnified, inverted
image B’ (f < do < 2f)
Light from the inverted image B’ goes
through the eyepiece and creates an
inverted virtual image behind the object
Eyepiece: 2nd lens that creates a focused and magnified image on the same
side as the ‘object’ (i.e. the image created by the 1st lens)
Objective: creates a real inverted image of the object that lies on the other
side of the lens
Condenser: focuses the incoming light rays in the focal point
Lightsource: emits the light rays used in the image creation
Concept of conjugated planes
Two planes are said to be conjugate when an object at one plane is sharply imaged onto the other plane by the
optical system → in other words, whatever structure exists in one conjugate plane will also appear in focus at its
partner plane
Image forming path
▪ The object plane (specimen) is conjugated with the intermediate image plane and finally with the retina of the
eye
▪ Similarly, the field stop diaphragm is conjugated with the fixed eyepiece diaphragm and the retina
This ensures that the specimen and the field of view are clearly imaged together
Illuminating path
4
MICROSCOPY PART
Resolution = ability to distinguish two points: 1,1mm for human eye
→ microscopes have a better resolution of 200nm
H1 Microscopy basics
1.1 Wave-like properties of light
Light has a wave-like property:
▪ Amplitude
▪ Frequency: number of waves produced each second
▪ Wavelength: distance between two maxima
o A wave is defined by its wavelength → the higher, the
more energy it contains
▪ Speed
▪ Phase
▪ Polarisation
We can only see a fraction of it: 390-770nm
! Light also has a particle-like property
Refraction
= bending of light due to a difference in refractive index of two media
speed of light in vacuum
▪ 𝑅𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥, 𝑛 =
speed in medium
o ⇡ n = low speed in medium | ⇣ n = fast speed in medium
▪ If n1 < n2, the angle of refraction will be smaller than the angle of incidence
Snell’s law describes how light bends (refracts) when it passes from one medium into another with a different optical
density: 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2
- n = the refractive index of the medium
- 𝜃1 = angle of incidence (incoming ray)
- 𝜃2 = angle of refraction (bent ray)
Dispersion
▪ Each λ diffracts differently (at different angles) which creates dispersion
▪ Bigger λ (red) know less deviation from the original path than smaller λ
(blue)
▪ Bigger λ → less sensitive to refraction than smaller λ
Reflection
When the angle of refraction = angle of incidence → light will reflect
Diffraction
= coherent light spreads out when passing a narrow slit (most of the time when
it’s smaller than the wavelength)
▪ Diffraction changes the way light is perceived and displayed
1
, ▪ ⇣ opening = stronger bending of the light waves
▪ Diffraction generates a characteristic pattern that depends on the amount of slits
▪ The middle part is undeviated light that passes straight through the gap
▪ The light surrounding the middle area are deviated
▪ Important formula for diffraction: d ∙ sin θ = mλ
o d = size of slit
o m = maxima
Interference
= phenomenon that takes place when two waves meet and combine → can either increase or decrease the
amplitude of the new wave
Constructive interference: when two waves meet and have an increase in amplitude as a result
Destructive interference: when two waves meet and have a decrease in amplitude as a result
Which interference happens depends on the phase difference of both waves
If the phase difference between both is nπ (with n an even number), the amplitude of the new, combined
wave increases
If the phase difference between both is mπ (with m an odd number), the amplitude of the new, combined
wave decrease
! EXAM: terms can be asked in multiple choice
Diffraction is based on interference
▪ More pronounced diffraction pattern when you have multiple slits
▪ Direct, inverse relationship between the position of the maxima and minima with the distance between the
slits → the closer, the more spread out the maxima and minima will be
1.2 Lens theory
Basic convex lens:
▪ Focal point: for every lens at a certain point
▪ Focal distance (f)
▪ Optical axis
There are 3 rules relating to the light path through this perfect convex lens
2
,Rule 1: parallel rays converge at the focal point
Rule 2: rays from the focal point exit in parallel
Rule 3: rays that pass through the centre of the lens, remain unaffected
Calculating the magnification
Four factors for calculation:
1. Focal distance (f)
2. Size of the object (ℎ0 )
3. Position of the object relative to the lens (𝑑0 )
4. Position of the real image relative to the lens (𝑑𝑖 )
Lens maker equation
f < 0: image is left of the lens
f > 0: image is right of the lens
Magnification
M < 0: object is inverted
M > 0: object is not inverted
d0 = f
Infinity → to focuse the image we need an additional lens → much used in
microscopy so that we can put something in between the two lenses so we can
intervene
! EXAM: need to be able to do the exercises
3
, 1.3 Optical train of compound microscope
Different parts of a microscope
Upright microscope Inverted microscope
The compound microscope is a two-lens magnifier
Light from object B goes through the
objective and creates a magnified, inverted
image B’ (f < do < 2f)
Light from the inverted image B’ goes
through the eyepiece and creates an
inverted virtual image behind the object
Eyepiece: 2nd lens that creates a focused and magnified image on the same
side as the ‘object’ (i.e. the image created by the 1st lens)
Objective: creates a real inverted image of the object that lies on the other
side of the lens
Condenser: focuses the incoming light rays in the focal point
Lightsource: emits the light rays used in the image creation
Concept of conjugated planes
Two planes are said to be conjugate when an object at one plane is sharply imaged onto the other plane by the
optical system → in other words, whatever structure exists in one conjugate plane will also appear in focus at its
partner plane
Image forming path
▪ The object plane (specimen) is conjugated with the intermediate image plane and finally with the retina of the
eye
▪ Similarly, the field stop diaphragm is conjugated with the fixed eyepiece diaphragm and the retina
This ensures that the specimen and the field of view are clearly imaged together
Illuminating path
4
