Optics in medicine Flashcards
General classification of electromagnetic waves
- Electromagnetic waves are transverse waves because the electric and magnetic field vectors oscillate perpendicular to the direction of propagation.
- The electrical and magnetic field vectors are in phase and oriented perpendicular to one another. The magnitudes of the fields are relatd by
E=cB
-Electromagnetic waves can vary in wavelength and frequency but they all travel at the speed of c = 3 x 108 m/s in a vacuum.
c = fλ
- Propagation of electromagnetic waves does not require any medium.
- The electromagnetic spectrum refers to the full range of frequency and wavelength of electromagnetic waves.
Radiowaves 109 m – 1mm 10 Hz
Infrared 1mm - 700nm
Visible light 360nm-760nm
Ultraviolet light 400 – 10 nm
X-ray 10nm – 10-2
Gamma ray less than 10-2
- Light of well defined wavelengths is produced by electrons undergoing transitions between energy levels
- Light of a continuous range is produced by the random accelerations of electrons in hot bodies.
- Intensity* of Light: instantaneous power incident on a unit area (Watts/m2)
Given by the Poynting vector S which is defined as the product of E and B
Since E and B flunctuate with time, the average intensity can be defined
The electrical and magnetic field components carry the same amount of energy.
An electromagnetic wave transports linear momentum and exerts radiation pressure (force/area)
Radiation pressure = F/A
Units are N/m2 or J/m3
Planck´s law
Planck’s law describes the electromagnetic radiation emitted by a black body in thermal equilibrium at a definite temperature.
Stefan-Boltzmann and Wien laws
At temperatures above 0 K, matter emits electromagnetic radiation. The amount of energy radiated depends on the temperature of the emitter.
Wein’s Displacement Law
Wein’s displacement law states that the wavelength of maximum emission is inversely proportional to temperature.
-the greater the temperature of the emitter the smaller the wavelength of emitted radiation.
We get Weinís Law by:
taking the first derivative of Planck’s Law setting it equal to zero solving for wavelength
λmax= a/T
where a = Wein’s constant = 2.90 x 10-3 mK
Stefan-Boltzmann law:
The Stefan- Boltzmann law states that the total energy being emitted per unit area per second is proportional to the 4th power of the absolute temperature.
P =power in watts, A is in m2, T in degrees Kelvin,
Stefan-Boltzmann constant (s) = 5.67 10-8 W/m2K4.
Lens equation
Converging lens- are thicker at the center than at the rim.
-cause parallel rays to be focuses at the focal point
Diverging lens- are thicker at the rim than the center.
- cause parallel rays to diverge from a virtual focal point
- Thin lens equation* –relates the object distance, image distance and focal length of the lens.
1/f = 1/a + 1/b
where a= object distance, b = image distance, f= focal distance
Sign convention:
- object distance (a) is positive (real) on the left of the lense and negative (virtual) on the right
- image distance (b) is positive and real behind the lens since rays of light actually converge there, and negative on the left
- focal length (f= r/2) is + for a converging lens and – for a diverging lens
*converging lenses can produce all types of images depending on the object distance, but a diverging lens can only create a virtual, reduced, and erect image.
Magnification –the ratio of the image height to the object height
M = -b/a= y1/y0
Y1=image height, y0= object height
Power of a Lens (D) – optical power
P = 1/f
- Unit is the diopter, defined as the reciprocal of the focal length in meters
- P has the same sign as f, so if f is +, P is + and vice versa
Therefore, a converging lens has a positive power while a diverging lens has a negative power
If several lenses are placed in series, the total optical power for the system is
D(total)=D1+D2-D1*D2d
d=distance between lenses
Followup info:
Lens suffer from
- Chromatic aberration* – different colors have different focal points; thin lenses suffer from chromic aberration; can be fixed with a second diverging lens after the thin one
- Sherical aberration* – a monochromatic beam cannot be brought to the focal point; can be reduced by only dealing with paraxial rays
*Least distance of distinct vision - the closest point that a person can comfortable bring an object to their eye is 25 cm for a normal eye (children can bring it closer, the elderly must hold it further).
- *converging lenses can form real or virtual, smaller or enlarged, erected or reversed images
- *diverging lenses can only form virtual, smaller and erected images
Extinction, Lambert-Beer law
EXTINCTION (absorbance): the absorption of a portion of light’s energy as it passes through a material.
The resulting intensity is given by
*Where d is the thickness of the medium and α is the coefficient of absorption
-The absorption coefficient is a function of wavelength. Therefore, absorption is a selective process and materials absorb only a distinct wavelength or set of wavelengths.
* α is 10-3 m-1 in air, 1m-1 in glass, 106 m-1 in metal. Therefore, intensity decreases to 1/e or 1/2.7 = 36% of its initial value when passed through 103 m of air, 1m of glass, or 10-6 m of metal.
- When light is passed through a solution, its absorption coefficient is proportional to its concentration.
- where є is the molar extinction coefficient. Its value depends on the type of molecules present in solution, the solvent, and the wavelength of incident light.
- The Lambert-Beer Law states that the extinction (absorbance) of a solution is directly proportional to its concentration.
~Also, there is a logarithmic dependence of the intensity of light passing through a solution and the concentration of the sample.
* The Lambert-Beer law is used for determining concentration of a substance by measuring the extinction E.
Scattering of light
Light may be scattered in two ways:
Rayleigh Scattering –occurs when light passes through a dilute gas and interacts with its molecules.
~In order for interaction to occur, the molecules must have a size much smaller than the wavelength of incident light.
-the interaction occurs as the electric field of the incident electromagnetic wave induces an oscillating magnetic moment that emits an electromagnetic wave of the same frequency and wavelength → elastic scattering
~light is scattered into all directions but its intensity is very low
~The ratio of the intensity of scattered light to incident light is
- k is a constant, M is the molar mass, λ is the wavelength of incident light
- this relationship suggests a very strong dependence of scattering intensity on incident wavelength. Violet light (short wavelength) scatters much more intensely than does red light (long wavelength).
- Red light which has a wavelength 2 x that of blue light scatters 16 x less intensely than blue light.
- If the concentration is known, the molar mass can be calculated from this equation
Raman Scattering
- Raman scattering occurs when light interacts with molecules and the resulting spectrum has added spectral lines corresponding to short and long wavelengths of scattered light.
- Two types of energy changes can occur in the scattering molecules upon interaction with light
~the vibrational and rotational energy of the molecules can increase (the photons transfer some of their energy) → the scattered photon has a lower energy
~the vibrational and rotational energy of the molecules can decrease → the scattered photon has a higher energy
*the probability of Raman scattering is very low and the intensity of the spectral lines is very weak (cannot be detected by the naked eye) → can use laser to increase intensity, photodetectors or photographic plates are used to detect radiation.
Dispersion of light
- Dispersion:* separation of white light into its spectral components of different wavelengths due to various velocities of the spectral components and resulting refractive indices.
- Although the speed of light for all wavelengths in a vacuum is the same, light of different wavelengths travels through a medium of refractive index n, with different velocities.
- The speed of light through a medium is a function of its wavelength and the refractive index of a medium is therefore a function of the wavelength of incident light.
- The effect is seen when white light is incident at an angle upon a glass surface where the two sides are nonparallel (prism).
- The nonparallel surfaces act to increase the angular separation between wavelengths.
- Thus each color has its own angle of deviation.
~Red has the longest wavelength, smallest refractive index and thus it is bent at an angle much smaller than that violet light which has a short wavelength and large refractive index.
Refraction and its use in spectroscopy
- Reflection* –the rebounding of light rays at the boundary of a medium. Governed by the law of reflection which states that the angle of incidence is equal to angle of reflection
- Refraction* – the bending of light rays at the boundary of two media.
- This occurs because the speed of light in media is less than that in a vacuum.
- A ray will bend toward the normal when it enters a medium in which its wave velocity is slower.
- The refractive index n is defined as the ratio of the speed of light in a vacuum c to the speed of light in a particular medium v.
. n = c/v
n=refraction index, c= speed of light in a vaccum, v= speed of light in a medium
Snells Law: predicts the bending of light rays as they pass from one media to another.
n1*sinQ1=n2sin*Q2
~If the refractive index of the second medium is greater than that of the first, the light rays will bend toward the normal
~If it is smaller, the light rays will bend away from the normal (angle of refraction will be greater than the angle of incidence)
*The frequency of the wave does NOT change as light passes from one medium to another.
*only its wavelength and speed change
*wavelength of light is reduced when traveling through a medium
Total Internal Reflection
- When light passes from a medium with a higher index of refraction to one with a lower index of refraction, it bends away from the normal.
- If the angle of incidence is increased to the critical angle, the refracted ray will be at an angle of 90º to the normal and will emerge parallel to the surface of the boundary.
- Total Internal Reflection occurs when the angle of incidence is greater than the critical angle and the light ray is reflected back into the original material.
* Application of total internal refraction is endoscopy and optic fibers.
* Refraction is applied in spectroscopy to identify different molecules according to how they refract light.
- Using a prism spectroscope, the dispersion of light according to wavelength is studied.
- A diverging beam of white light is emitted from a source and the rays are collimated and made parallel. The rays are dispersed through a prism and passed through an objective lens which forms the corresponding spectrum on an indicator (photographic plate or photomultiplier).
Interference and light reflection
- Evidence for the wave character of light is provided by the interference and diffraction of light.
- Interference is caused by the interaction of light waves which leads to the addition of their amplitudes.
- Interference can be observed in two ways:
- When light passes through a thin layer of medium with refractive index n between two parallel planes and the refractive and reflected waves interact with one another.
- During diffraction in which light deviates from its original path when passing through a narrow slit.
- Interference can only observed with coherent waves –light waves whose phase difference does not change with time. In relation with each other they only differ by a constant phase shift and not in their frequency (wavelength)
- Interference can be constructive or destructive in nature:
- Constructive interference (maximum) - occurs if the path difference is an integer multiple of wavelength
- regions where two light waves interfere constructively appear as bright spots (max light intensity) on the screen
- Destructive inteference (minimum) - appears if the path difference is an odd number of half wavelength
- regions where two light waves interfere destructively appear as dark areas on the screen (min light intensity)
The path difference and phase difference of interfering light waves are related by:
Phase difference:
Wavelength of a light wave changes in a medium with refractive index n according to
New phase speed is:
The phase difference between a wave traveling path d1 in a medium with refractive index n1 and a wave traveling path d2 with a refractive index of n2 equals:
The phase difference is also equal to the difference between optical paths multiplied by
Where according to the Fermet principle, the optical path is equal to the product of refractive index and geometrical path
*When light passes through a thin layer of medium with a refractive index of n between two parallel planes, the interference of refracted and reflected waves takes place.
Difference in optical paths is given by (when n of air =1)
Where d is the thickness of the layer, α is the angle of incidence, λ is the wavelength of applied light.
When light encounters a medium of higher refractive index, the reflected wave undergoes a phase shift equal to π and λ/2 (path change that corresponds to π) must be added to the right side of the equation.
- The interference of the reflected and refracted wave will increase in intensity if
- and will decrease if
- when white light passes through a thin layer, maxima and minima on the screen appear for each wavelength individually (soap bubbles
Refractometry & Polarimetry
- Refraction* – the bending of light rays at the boundary of two media.
- This occurs because the speed of light in media is less than that in a vacuum.
- Dispersion:* separation of white light into its spectral components of different wavelengths due to various velocities of the spectral components and resulting refractive indices.
- Although the speed of light for all wavelengths in a vacuum is the same, light of different wavelengths travels through a medium of refractive index n, with different velocities.
Refractometry:
-Used to determine the refractive index of a substance in order to assess its composition or purity.
* Refraction is applied in spectroscopy to identify different molecules according to how they refract light.
- Using a prism spectroscope, the dispersion of light according to wavelength is studied.
- A diverging beam of white light is emitted from a source and the rays are collimated and made parallel. The rays are dispersed through a prism and passed through an objective lens which forms the corresponding spectrum on an indicator (photographic plate or photomultiplier).
* Also used in determining the refraction of the eye. This gives the degree to which the eye differs from normal which will determine whether or not the patient needs glasses and, if so, how strong they should be.
Polarimetry
- -Unpolarized light* – a beam of natural light in which the electrical field vectors of the waves are oriented randomly in space.
- -Linearly polarized light* – light in which the electrical field vectors are all oriented in the same direction (parallel to eachother) The magnetic field vectors are also aligned.
- -Polarization* is the process of separating linearly polarized light from a beam of natural (white) light.
It can be carried out in 3 ways:
- Reflection & Refraction* –when light is incident on the boundary between two media at Brewster’s angle of incidence, the reflected and refracted angles are perpendicular to each other and their sum = 90º. At this angle of incidence, the reflected and refracted rays are linearly polarized.
- Birefringence* – polarization of natural light using an anisotropic substance
- Isotropic materials* – properties do not depend on direction. (arrangement of atoms is random) Ex: liquids and amorphous substances such as glass
- Anisotropic materials* – properties depend on direction. There is an ordered arrangement of atoms which only transmits electrical fields in a certain direction and absorbs all other incident light. Results in linearly polarized light. (sunglasses)
- absorb ordinary rays
- transmit extraordinary rays bc their electrical field is aligned with the polarization axis
- If two polarizing materials are placed in sequence, the amount of light transmitted through them varies from a minimum to maximum value depending on how they are oriented in respect to one another.
- If the polarization axes are aligned (parallel), all light passing through the first passes through the second as well
- If the polarization axes are perpendicular, no light is able to pass through
Law of Malus – gives the intensity of light transmitted by a polarizer
Where Io gives the intensity at α = 0 (when the polarization axes are parallel and the same amount of light is transmitted through the second polarizer as is transmitted through the first)
-Optically active substances rotate the plane of polarized light.
- The angle of rotation is directly proportional to the concentration of the optically active substance.
- This property is exploited in polarimetry which is used to determine the concentration of optically active compounds.
In polarimetry, a beam of light is emitted from a source, passed through a filter, polarizer, cuvette, analyzer, and finally the intensity of its transmitted light is evaluated.
~when the cuvette is filled with water, max intensity of light is observed between the polarizer and analyzer
~when the cuvette is filled with an optically active substance, the analyzer must be rotated by an angle corresponding to the new angle of plane polarized light in order for max amount of intensity to be observed
The angle of rotation of plane polarized light by an optical substance is given by
Biophysics of vision
The eye functions in detecting light energy and transmitting information about intensity, color, and shape to the brain
- sensitive to wavelengths of 400 – 750nm
- The transparent cornea at the front of the eye bends and focuses incoming light. The rays travel through the pupil whose diameter is controlled by the muscular iris. The iris responds to the intensity of light by adjusting the size of the pupil.
- The light continues on to the lens which focuses the image on the retina. The shape of the lens is controlled by the ciliary muscle.
- Changing the shape of the lens allows the eye to vary its focal length and focus on objects at various distances (accommodation).
- The retina contains photoreceptors called cones and rods.
- Cones* – sense high intensity illumination and color (located in the fovea centralis and some in the periphery)
- Rods* – detect low intensity illumination and are important in night vision (located in the periphery of the retina)
- *we have much more rods than cones*
- Rods and cones transduce light energy into nerve impulses. This process contains a photochemical step which functions in adaptation of the eye to the current light intensity.
- the cones contain three types of pigments each of which absorbs light of a certain band of wavelength.
- The rods contain a red pigment called visual purple or rhodopsin that is bleached by light. It is a conjugated protein bonded to the pigment retinene. Rhodopsin is stable until exposed to light. Light causes it to disscociate into protein and retinene. Under dark conditions, it is reformed with the help of vitamin A.
* Only about 10% of light intensity stimulates the photoreceptors and some wavelengths stimulate the retina more than others.
- Photopic vision* – maximum sensitivity in daylight is 550 nm (yellowish green)
- Scotopic vision* – maximum sensitivity in the dark is shifted toward shorter wavelengths of 505 nm.
- The image formed on the retina is inverted and reduced in size.
- The information obtained by the photoreceptors is transmitted to the brain via the optic nerves.
- Far point* –the furthest distance at which the human eye can focus is infinity
- Near point* –the closest distance that the human eye can comfortably focus on is 25cm.
The distance of the near point increases with age (presbyopia or old-sightedness)
Photopic vision is the scientific term for human colour vision under normal lighting conditions during the day. In the range above 3.4 cd/m2 human eye uses three types of cones to sense light in three respective bands of colour. The pigments of the cones have maximum absorption values at wavelengths of about 445 nm (blue), 535 nm (green), . 575 nm (red).Their sensitivity ranges overlap to provide continuous (but not linear) vision throughout the visual spectrum. The maximum efficacy is 683 lumens/W at a wavelength of 550 nm (yellow).
Eye defects
- Emmetropia* - The condition of the normal eye when parallel rays converge exactly on the retina and vision is perfect.
- There is no need for the aid of glasses or contact lenses to help with focusing on objects in the distance.
- Ametropia – any deviation from normal resulting from the eye’s inadequate refractive ability. Includes nearsightedness, farsightedness, and astigmatism.
Farsightedness (hyperopia) occurs when light entering the eye focuses behind the retina, instead of directly on it.
- This is caused by an eye that is shorter than the normal eye.
- Farsighted people have trouble seeing up close, but may have difficulty seeing far away as well.
- Corrected with a converging lens.
Nearsightedness (myopia) occurs when light entering the eye focuses in front of the retina instead of directly on it.
This is caused by an eye that is longer than the normal eye.
- Nearsighted people typically see well up close, but have difficulty seeing far away.
- Corrected with a diverging lens.
Presbyopia - is caused by an age-related process. These age-related changes occur within the proteins of the lens making the lens harder and less elastic with age. Age-related changes also take place in the muscle fibres surrounding the lens. With less elasticity, the eye has difficulty focusing on near objects. (Focal length increases with age)
-Corrected with converging lens
Absorption spectral analysis
When light is passed through solution some of its energy is absorbed. This quality can be exploited in absorption photometry to measure concentrations of solutions according to the following law:
-The Lambert-Beer Law states that the extinction (absorbance) of a solution is directly proportional to its concentration.
Also, there is a logarithmic dependence of the intensity of light passing through a solution and the concentration of the sample.
Absorption spectroscopy is employed as an analytical chemistry tool to determine the presence of a particular substance in a sample and, in many cases, to quantify the amount of the substance present.
Optical properties of colloids
Colloidal particles are macromolecules or micelles that move in solution as individual particles.
Scattering of light that passes through a solution containing colloidal particles is called the Tyndal phenomenon.
Since intensity of scattered light depends on particle size, measurement of the intensity of scattered light can be applied for the estimation of concentration in monodispersed colloidal system.
Some solutions may non exhibit the Tyndal effect because the solute particles are too small to scatter light.
Principle of laser
LASER: Light amplification by stimulated emission of radiation
-A laser is a device that produces a very narrow, intense, monochromatic, coherent light beam
Principles behind laser function:
- Electrons can only exist in defined energy states and transition from a higher to lower energy state is accompanied by the release of a quantum of radiation with frequency
- If an electron spontaneously falls to a lower energy state due to interaction with an electromagnetic field, the atom will emit a noncoherent electromagnetic wave. (called induced transitions)
- induced radiation is of the same frequency, polarization, and direction of the radiation that induced the emission
The Boltzmann law describes the distribution of energy levels under normal conditions
*The number of atoms in the excited state is dependent on temperature.
*At normal conditions, only a small portion of atoms are in the excited state.
How a laser works:
-Lasers are able to produce intense coherent light by a process called inversion.
~During inversion, there are more atoms in the excited state than the ground state.
- This is accomplished by exciting atoms into a higher energy level and allowing them to fall into a metastable state for a relatively long period of time (for 10-3 s). Thus many atoms enter and collect in this semi-excited state producing inversion. (occurs in the ruby crystal of a ruby laser)
- When light with energy equal to the difference between the metastable and ground state passes through the crystal, all atoms simultaneously transit into the ground state emitting in a pulse of intense coherent light. Its wavelength is equal to the wavelength of the incident radiation.
- The intensity of the pulse is inversely proportional to its duration
I = F/A
P = E/t (unit is Watts)
*Lasers are used in medicine in the destruction of small sized tissues, in coagulation of tissues, and healing of ulcers.
