biophysics theory

types of radiations

radiation can be classified in 2 ways:

1. type of energy transferred

   • propagation as a result of kinetic energy → requires a medium

     • particle radiation (electrons, protons, positrons, neutrons + ions)

     • mechanical radiation (sound waves, ultrasound, seismic waves)

   • propagation as a result of an electromagnetic field → doesn’t require a medium

     • electric + magnetic forces act on surrounding particles that have electromagnetic properties (transverse waves)

2. how the energy interacts with matter

   • ionising radiation → high frequency radiation that transfers energy to electrons bound to atoms + liberates them

     • non-ionising radiation → frequencies lower than UV + don’t have enough energy to ionise matter (radio, microwave, infrared)

dependence of irradiance on distance from the source

irradiance → radiant energy that arrives + radiates onto an object from a source

• sphere → irradiance is inversely proportional to the squared distance from the source (E = 1/r²)

• cylinder → irradiance is inversely proportional to the distance from the source (E = 1/r)

• planar surface → irradiance doens’t change

  • these laws are only valid if we assume that energy doesn’t disappear in the medium between the source + target

fundamentals of geometric optics

• light ray → an extremely thin parallel beam of light

• if light passes through a slit much larger than its wavelength → the spreading of the wave front can be simplified into a single light ray

• if light passes through a slit comparable or smaller than its wavelength → wave properties must be taken into account

• principle of reversibility → direction of energy propagation may be reversed

  • in optically denser media, the speed of propagation is reduced

radiometric quantities

quantities that are related to electromagnetic radiation

• radiant energy (Q) → energy carrier from any electromagnetic field (J)

• radiant flux/power (P) → the amount of energy emitted over time (J/s = W)

• radiant exitance/emittance (M) → radiant energy emitted from a source per unit area + direction is neglected (W/m²)

• radiant intensity (I/J) → the amount of power propagating through unit area aka. “photon density” (W/m²)

• irradiance (E/J) → the radiant energy that arrives + radiates onto an object from a source (W/m²)

• radiance (L) → radiant power emitted from an extended unit solid angle + per unit projected source area [W/(steradian•m²)]

• attenuation (J) → the amount of energy lost between the source + the object

attenuation law

• attenuation → gradual loss of flux intensity through a medium

  • absorption of energy as it propagates through the medium

  • scattering of photons

• attenuation law → exponential relationship between intensity of the perpendicularly incident radiation (J₀) + intensity of the parallel beam that passes through the absorbent (J)

• attenuation coefficient (µ) → constant that describes the fraction of attenuated incident radiation per unit thickness of the absorbent

  • depends on type + density of absorbent

  • depends on radiation energy

fermat’s principle

path of travelling light from 1 point to another is not decided by the shortest distance, but by the shortest time (this is what causes refraction)

law of refraction

• refraction → change in direction of a wave passing from 1 medium to another or from a gradual change in the medium

• snell’s law → the relationship between the path taken by a ray of light in crossing the boundary or surface of separation between 2 contacting substances + the refractive index of each

• incident ray, normal of incidence + refracted ray are all on one plane

law of reflection

• reflection → the change in direction of a wavefront at an interface between 2 different media so that the wavefront returns into the medium from which it originated

• laws of reflection:

  • incident ray, normal of incidence + reflected ray are all on one plane

  • angle of incidence = angle of reflection

total internal reflection + its applications

• total internal reflection → happen when the angle of incidence is much greater than the critical angle

• endoscopy → a long, thin, flexible tube that has a light source + a video camera at 1 end allows a physician to examine the GI tract

  • outer coating → cladding plastic + metal

    • less these than core → total internal reflection of light rays travelling inside happens

  • inside → core filled with optical fibres

    • light rays must hit the walls of the fibre at a minimum of 82º

image formation on a curved surface

1. an object is placed at point A on the optical axis

2. incident ray travels on the optical axis + through the interface without deviation

3. another incident ray travels from point A at an angle, meets the interface + refracts

4. 2 incident rays meet at point B + image is formed there (point B is the focal point)

principal light rays

• parallel rays → parallel to the optical axis + pass through the real focal point

• focal rays → drawn through the front focal point + are parallel to the optical axis

• central ray → drawn through the centre of the lens + is undeflected

lens combinations