Course 3. Photonics Applications I

Module 1. Diagnostic Biomedical Equipment

    1.1 Optical diagnostic instruments
        1.1.1 Ophthalmoscope
            1.1.1.1 Optical design
                - Direct ophthalmoscopes
                - Indirect ophthalmoscopes
            1.1.1.2 Applications of ophthalmoscopes
                - Examination of fundus
                - Cataract detection
                - Diabetes detection
                - Hypertension detection
        1.1.2 Otoscope
            1.1.2.1 Optical design
            1.1.2.2 Applications of the otoscope
    1.2 Fiber optic instruments
        1.2.1 Design
            1.2.1.1 Monofiberscopes
            1.2.1.2 Multifiberscopes
            1.2.1.3 Leached fiberscopes
            1.2.1.4 Light delivery
        1.2.2 Image formation if fiberscopes
            1.2.2.1 Scanning with fiber bundles
            1.2.2.2 Image transfer
            1.2.2.3 Resolution
        1.2.3.Applications
            1.2.3.1 Gastroscopes
            1.2.3.2 Nasolaryngoscopes
            1.2.3.3 Esophagoscopes
            1.2.3.4 Bronchoscopes
            1.2.3.5 Colonoscopes
            1.2.3.6 Laproscopes
            1.2.3.7 Arthroscopes
    1.3 Thermal imaging systems
        1.3.1 Principles
            1.3.1.1 Peak of thermal emission from human body near 10 mm
            1.3.1.2 Design of thermal imagers working near 10 mm
            1.3.1.3 Can detect temperature differences much less than 1 degree
        1.3.2 Applications
            1.3.2.1 Detection of areas with blood flow blockage or restriction
            1.3.2.2 Tumor detection (hot spots)
    1.4 Tumor detection
        1.4.1 Detection and imaging
            1.4.1.1 Fluorescent imaging
            1.4.1.2 Imaging spectroscopy
        1.4.2 Phototherapy monitoring
            1.4.2.1 Mapping of photosensitizer distribution
            1.4.2.2 Determination of boundaries of damage


Module 2. Therapeutic Biomedical Equipment

    2.1 Interaction of laser radiation with tissue
        2.1.1. Coupling of light into tissue
            2.1.1.1 Reflectivity of tissue vs wavelength
            2.1.1.2 Absorption coefficient of tissue vs wavelength
            2.1.1.3 Multiple scattering
        2.1.2 Effects on tissue
            2.1.2.1 Temperature rise
            2.1.2.2 Photocoagulation
            2.1.2.3 Cutting
    2.2 Equipment
        2.2.1 Lasers used
            2.2.1.1 Excimer
            2.2.1.2 Argon
            2.2.1.3 Dye
            2.2.1.4 Nd:YAG and doubled Nd:YAG
            2.2.1.5 Ho:YAG and Er:YAG
            2.2.1.6 Carbon dioxide
        2.2.2 Beam delivery
            2.2.2.1 Ophthalmoscopic
            2.2.2.2 Articulated arms
            2.2.2.3 Optical fiber
    2.3 Applications in ophthalmology
        2.3.1 Retinal defects
            2.3.1.1 Structure of the eye
            2.3.1.2 Transmission thru front structures of eye vs wavelength
            2.3.1.3 Treatment of retinal detachment
            2.3.1.4 Treatment of retinal tears
        2.3.2 Diabetic retinopathy
            2.3.2.1 Abnormal blood vessels on retina
            2.3.2.2 Treatment with argon laser
        2.3.3 Glaucoma
            2.3.3.1 Elevated pressure in eye, due to obstruction of flow
            2.3.3.2 Laser opens hole to relieve pressure
            2.3.3.3 Treatment with argon and Nd:YAG lasers
        2.3.4 Radial keratotomy
            2.3.4.4 Used to treat myopia
            2.3.4.2 Excimer lasers used
            2.3.4.3 Micro incisions made in cornea
            2.3.4.4 Ablation without heating
        2.3.5 Rupture of cloudy membranes
            2.3.5.1 Cloudy membranes may form after cataract surgery
            2.3.5.2 High power laser produces shock wave
                       which uptures membrane
            2.3.5.3 Treatment with Q-switched Nd:YAG lasers
    2.4 Applications in dermatology
        2.4.1 Removal of pigmented areas
            2.4.1.1 Treatment of vascular lesions
            2.4.1.2 Treatment of pigmented lesions
            2.4.1.3 Removal of tattoos
        2.4.2 Tissue welding
            2.4.1.1 Lasers used
            2.4.1.2 Results
    2.5 Applications in surgery
        2.5.1 Tissue removal basics
            2.5.1.1 Mechanics of tissue removal
            2.5.1.2 Use of Ho:YAG lasers
            2.5.1.3 Reduced blood loss
        2.5.2 Use in urology
            2.5.2.1 Prostatectomy
            2.5.2.2 Prostate resection
            2.5.2.3 Removal of small tumors from urinary bladder
        2.5.3 Use in otolaryngology
            2.5.3.1 Removal of nodes and polyps
            2.5.3.2 Removal of small tumors from mouth, tongue and larynx
        2.5.4 Breakup of kidney stones
            2.5.4.1 Pulsed laser light focused on stone thru fiber optics
            2.5.4.2 Shock wave breaks up stone into small pieces
                       which can pass through urinary tract
    2.6 Treatment of tumors
        2.6.1 Hematoporphyrin derivative (HpD)
            2.6.1.1 HpD injected
            2.6.1.2 HpD preferentially taken up by tumor
        2.6.2 Irradiation
            2.6.2.1 Use dye laser tuned to HpD absorption
            2.6.2.2 Molecules broken up, release free radicals
            2.6.2.3 Free radicals kill tumor cells
    2.7 Role of the technician in medical procedures
        2.7.1 Technician does not perform the treatment on patients
        2.7.2 Technician operates and maintains equipment
        2.7.3 Technician monitors and controls output of lasers


Module 3. Scientific Instruments

    3.1 Laser spectroscopic applications
        3.1.1 Capabilities of laser based spectroscopy
            3.1.1.1 Use of tunable lasers
            3.1.1.2 Spectral range
            3.1.1.3 Resolution compared to conventional spectroscopy
        3.1.2 Absorption spectroscopy
            3.1.2.1 Resonant absorption of light
            3.1.2.2 Useful for molecular structure
        3.1.3 Laser-induced fluorescence
            3.1.3.1 Light emitted from atomic and molecular levels
                       excited by laser light
            3.1.3.2 Useful for analytical spectrochemistry
        3.1.4 Photoionization spectroscopy
            3.1.4.1 Measurement of change in ionization equilibrium
            2.1.4.2 Useful for ultrasensitive detection of gases
        3.1.5 Photoacoustic spectroscopy
            3.1.5.1 Absorbed light transferred to acoustic energy
            3.1.5.2 Useful for analytical spectrochemistry
        3.1.6 Doppler-free spectroscopy
            3.1.6.1 One beam saturates absorption, 2nd beam probes it
            3.1.6.2 Reveals true line width
            3.1.6.3 Extremely high resolution spectroscopy
        3.1.7 Laser induced breakdown spectroscopy
            3.1.7.1 Laser creates hot plasma which emits light
            3.1.7.2 Useful for real time spectrochemistry
        3.1.8 Raman spectroscopy
            3.1.8.1 The Raman effect
            3.1.8.2 Excitation of molecular vibrational frequencies
            3.1.8.3 Useful for trace species identification
        3.1.9 Coherent anti-Stokes Raman spectroscopy
            3.1.9.1 Two lasers coherently excite vibrational frequency
            3.1.9.2 Useful for trace species identification
        3.1.10 Ultraviolet resonance Raman spectroscopy
            3.1.10.1 Raman scattering from electronic state
            3.1.10.2 Reveals structure and dynamics of excited states
    3.2 Chemical diagnostics
        3.2.1 Picosecond photochemistry
            3.2.1.1 One pulse initiates photochemical reaction
            3.2.1.2 Second pulse probes reaction products
            3.2.1.3 Provides very high speed monitoring of dynamics of
                       chemical reaction
            3.2.1.4 Specific example of picosecond photochemistry
        3.2.2 Flash photolysis
            3.2.2.1 Break up molecules with intense light pulse
            3.2.2.2 Second pulse with variable time delay probes the products
            3.2.2.3 Useful for studying kinetics of chemical reactions
        3.2.3 State-to state chemistry
            3.2.3.1 Laser irradiation produces molecules in selected
                       internal quantum states
            3.2.3.2 Can determine reaction rates for producing molecules
                       in specified quantum states
    3.3 Velocity measurements
        3.3.1 Fluid flow
            3.3.1.1 Method of laser Doppler velocimetry
            3.3.1.2 Advantages of laser Doppler velocimetry for probing fluid flow
        3.3.2.Surface velocity
            3.3.2.1 Arrangement using Michelson interferometer
            3.3.2.2 Measurement of Doppler shift of light reflected
                    from surface
            3.3.2.3 Use for analysis of shock waves in solids


Module 4. Environmental Measurements

    4.1 Introduction to environmental monitoring
        4.1.1 Needs for environmental measurements
            4.1.1.1 Pollutants present in the atmosphere
            4.1.1.2 Emissions from specific locations
            4.1.1.3 Particulate materials
            4.1.1.4 Global monitoring (like carbon dioxide)
        4.1.2 Advantages of optical technology for atmospheric sensing
            4.1.2.1 Measurements can be made remotely, at large distances
            4.1.2.2 No sample collection
            4.1.2.3 No chemical processing
            4.1.2.4 Usually results can be available immediately
    4.2 Optical radar (LIDAR)
        4.2.1 Approach
            4.2.1.1 High-power, short laser pulse fired into atmosphere
            4.2.1.2 Particulate material causes backscattering
            4.2.1.3 Detector senses backscattered light
            4.2.1.4 Round trip time of light gives range of particulates
            4.2.1.5 Signal strength gives measure of particulate concentration
        4.2.2 Advantages
            4.2.2.1 Single ended
            4.2.2.2 Offers range resolution
        4.2.3 Disadvantage: No identification of gases
    4.3 Raman backscattering
        4.3.1 Approach
            4.3.1.1 Definition of the Raman effect
            4.3.1.2 High-power, short laser pulse fired into atmosphere
            4.3.1.3 Molecules backscatter light at different frequency
            4.3.1.4 Detector senses backscattered light
            4.3.1.5 Frequency shift used to identify molecules
        4.3.2 Advantages
            4.3.2.1 Single ended
            4.3.2.2 Offers range resolution
            4.3.2.3 Detects molecular species
        4.3.3 Disadvantage: Low sensitivity
    4.4 Resonance fluorescence
        4.4.1 Approach
            4.4.1.1 High-power, short laser pulse fired into atmosphere
            4.4.1.2 Molecules fluoresce
            4.4.1.3 Detector senses fluorescence
            4.4.1.4 Wavelength of fluorescence identifies molecules
        4.4.2 Advantages
            4.4.2.1 Single ended
            4.4.2.2 Offers range resolution
            4.4.2.3 Allows identification of molecules
        4.2.3 Disadvantage: Relatively low sensitivity
    4.5 Absorption methods
        4.5.1 Transmission spectroscopy
            4.5.1.1 Conventional spectroscopic measurement
            4.5.1.2 Source on one side of air mass, detector on other
            4.5.1.3 Absorption gives total amount of material
                       between source and detector
            4.5.1.4 Advantages
                - High sensitivity
                - Identification of gases
            4.5.1.5 Disadvantages
                - Double ended
                - No range resolution
        4.5.2 Differential optical absorption spectroscopy (DOAS)
            4.5.2.1 Spectroscopic measurement of differences in maxima
                       and minima of absorption spectrum of gas being probed
            4.5.2.2 Advantages
                - Very high sensitivity
                - Identification of gases
            4.5.2.3 Disadvantages
                - Double ended
                - No range resolution
        4.5.3 Differential absorption laser (DIAL) spectroscopy
            4.5.3.1 Send out pulse, return is from atmospheric backscattering
            4.5.3.2 Tune laser on and off absorption line
            4.5.3.3 Advantages
                - High sensitivity
                - Single-ended
                - Range resolution
                - Identification of gases
            4.5.3.4 Disadvantages: Few, this is the preferred technique for many applications
    4.6 Open path Fourier Transform Infrared spectroscopy (FTIR)
        4.6.1 Approach
            4.6.1.1 Non-laser light source (e.g. sun, xenon lamp)
            4.6.1.2 Michelson interferometer analyzes signal over wide range in infrared
            4.6.1.3 Fourier transform changes signal to intensity vs wavelength
            4.6.1.4 Absorption lines compared to stored library
        4.6.2 Features
            4.6.2.1 Identifies many gases in sample simultaneously
            4.6.2.2 High sensitivity
            4.5.2.3 Works in the presence of interfering gases
    4.7 Applications
        4.7.1 Specific site monitoring
            4.7.1.1 Industrial plants
            4.7.1.2 Smokestacks
            4.7.1.3 Volcanoes
            4.7.1.4 Enforcement of air pollution regulations (EPA)
        4.6.2 Wide area observations
            4.7.2.1 Plane flights over long paths
            4.7.2.2 Monitoring of greenhouse gases
            4.7.2.3 Monitoring of the ozone layer


Module 5. Industrial Measurements

    5.1 Distance measurements
        5.1.1 Principles used in distance measurement
            5.1.1.1 Michelson interferometer based measurements
            5.1.1.2 Laser Doppler displacement method
            5.1.1.3 Beam modulation telemetry
            5.1.1.4 Comparison of the capabilities of these methods
        5.1.2 Use of Michelson interferometer
            5.1.2.1 Methods to reduce effects of atmospheric turbulence
            5.1.2.2 Machine tool control
            5.1.2.3 Adaptation to measure straightness
            5.1.2.4 Adaptation to measure flatness
        5.1.3 Uses of laser Doppler displacement
            5.1.3.1 Machine tool control
            5.1.3.2 Adaptation to measure straightness
            5.1.3.3 Adaptation to measure flatness
        5.1.4 Uses of beam modulation telemetry
            5.1.4.1 Surveying
            5.1.4.2 Mapping
    5.2 Measurement of profile and surface position
        5.2.1 Methods used for profile and surface position
            5.2.1.1 Triangulation method
            5.2.1.2 Two-spot systems
            5.2.1.3 Interferometric systems
            5.2.1.4 Comparison of these methods
        5.2.2 Uses of triangulation methods
            5.2.2.1 Prototype contour determination
            5.2.2.2 Machine tool wear
        5.2.3 Uses of Two-spot systems
            5.2.3.1 Displacement of a surface
            5.2.3.2 Thickness of a sheet
        5.2.4 Uses of interferometric methods
            5.2.4.1 Surface profiles
            5.2.4.2 Thickness measurements
    5.3 Diffraction-based measurements
        5.3.1 Principles
            5.3.1.1 Diffraction pattern formed by small aperture or
                       small object in the beam
            5.3.1.2 Spacing in pattern depends on object dimension
            5.3.1.3 Very high resolution
            5.3.1.4 Limited to measurement of small dimensions
        5.3.2 Uses
            5.3.2.1 Wire diameter
            5.3.2.2 Gaps in recording heads
    5.4 Strain and vibration measurements
        5.4.1 Strain
            5.4.1.1 Speckle pattern formed on surface of object
            5.4.1.2 Speckle pattern moves as object is strained
        5.4.2 Vibration
            5.4.2.1 Split a beam in two, add modulation on one beam
            5.4.2.2 One beam reflected from vibrating surface
            5.4.2.2 Beat note detected at detector when beams are recombined
    5.5 Applications in construction industry
        5.5.1 Plane of light systems
            5.5.1.1 Rotating pentaprism forms a plane of light
            5.5.1.2 Objects aligned in that plane
            5.5.1.3 Used for applications like ceiling tile installation
        5.5.2 Straight line projection
            5.5.2.1 Laser projects a visible straight line
            5.5.2.2 Objects are aligned to that line
            5.5.2.3 Centering detectors frequently used
            5.5.2.4 Used for aligning sewer pipe
        5.5.3 Heavy equipment control
            5.5.3.1 Scanning laser projects a plane of light
            5.5.3.2 Photodetector array on the equipment
            5.5.3.3 Keeps the equipment at the right level
    5.6 Measurement of angular rotation rate
        5.6.1 Principles of the ring laser gyro
            5.6.1.1 Two counterrotating beams of light in a triangular structure
            5.6.1.2 If no rotation, beams are at same frequency
            5.6.1.3 If rotation is present, there is a frequency shift
                       proportional to the rotation rate
        5.6.2 Use for navigation
            5.6.2.1 The rotation rate may be integrated to form the basis of
                       a navigation system
            5.6.2.2 The ring laser offers advantages compared to
                        conventional rotating gyros
                - Lowered cost for comparable performance
                - No gimbal mounts required
                - No high speed moving parts
            5.6.2.3 The ring laser gyro forms the basis of the navigation
                       system for many planes in the airline industry


Module 6. Manufacturing Inspection

    6.1 Introduction to inspection
        6.1.1 Advantages
            6.1.1.1 Non-contact
            6.1.1.2 Non-destructive
            6.1.1.3 Easily automated
        6.1.2 Lasers used
            6.1.2.1 Helium-neon-most early applications
            6.1.2.2 Visible diode-now becoming widely used
    6.2 Product dimension
        6.2.1 Beam obscuration method
            6.2.1.1 Laser beam scanned across object
            6.2.1.2 Time beam is blocked proportional to object dimension
        6.2.2 Dimensional comparison method
            6.2.2.1 Measure position of each surface
            6.2.2.2 Difference is dimension
            6.3.2.3 Methods
                - Triangulation
                - Two-spot method
                - Interferometric methods
        6.2.3 Diffraction method
            6.2.3.1 Useful for small diameters or small apertures
            6.2.3.2 Angular spacing of diffraction orders inversely
                       proportional to dimension
            6.2.6.3 Insensitive to vibration or exact positioning of object in beam
    6.3 Defect detection
        6.3.1 Product dimension measurement
            6.3.1.1 Beam scanned across object
            6.3.1.2 Change in dimension shows defect
        6.3.2 Transmitted light method
            5.3.2.1 Useful for sheet products, webs, paper, etc.
            5.3.2.2 Beam scanned across moving sheet
            5.3.2.3 Change in transmission shows holes, tears, edge defects
        6.3.3 Holographic methods discussed in Module 3-8
    6.4 Particle size distribution
        6.4.1 Particles larger than laser wavelength
            6.4.1.1 Scattering angle increases as particle diameter decreases
            6.4.1.2 Beam scattered from particles, collected and
                       focused onto detector array
            6.4.1.3 Signal distribution analyzed to give particle size distribution
        6.4.2 Particle size same or smaller than wavelength
            6.4.2.1 Complicated scattering function
            6.4.2.2 Use multiple laser beams and multiple detector arrays
            6.4.2.3 Typical example of instrumentation
        6.4.3 Commercial particle size instrumentation
            6.4.3.1 Variety of approaches
            6.4.3.2 Covers range from 0.04 to 2000 micrometers
    6.5 Surface finish
        6.5.1 Scattering method
            6.5.1.1 Beam spread into line and scanned over surface
            6.5.1.2 Increase in scattered light shows defects
        6.5.2 Spatial filter method
            6.5.2.1 Surface illuminated at grazing angle
            6.5.2.2 Specularly reflected light focused on spatial filter
            6.5.2.3 Use imaging detector
            6.5.2.4 Defects show up as bright spots on dark field
     6.6 Cylindrical form
        6.6.1 Grazing incidence interferometer
            6.6.1.1 Definition
            6.6.1.2 Use of diffractive optics
        6.6.2 Capabilities
            6.6.2.1 Roundness
            6.6.2.2 Cylindricity


Module 7. Advanced Holographic Techniques

This module builds on and expands Module 1-7
    7.1 The holographic process
        7.1.1 The recording process
            7.1.1.1 Interference of object and reference beam
            7.1.1.2 I(x,y) = R02 + S02 + 2RS cos (ax - F)
            7.1.1.3 The pattern recorded in the recording medium
            7.1.1.4 Preserves all the information in the light beam, including phase
            7.1.1.5 Development of the film: the D logE curve
            7.1.1.6 Resulting pattern of transmission of the developed medium
        7.1.2 The reconstructing process
            7.1.2.1 Reilluminate the hologram with the reference beam
            7.1.2.2 Transmitted light is product of film transmission and
                        reference beam intensity
            7.1.2.3 This contains a term identical in form with light from
                       the original object- the virtual image
            7.1.2.4 The amplitude and phase of the original light are both preserved
            7.1.2.5 The image is three-dimensional
            7.1.2.6 Another term represents a real image
            7.1.2.6 It also has both phase and amplitude preserved
            7.1.2.7 It may be projected on a screen
    7.2 Holographic recording materials
        7.2.1 Photographic film
            7.2.1.2 Types available
            7.2.1.2 Exposure energy vs wavelength
            7.2.1.3 Resolution
        7.2.2 Bleached photographic film
            7.2.2.1 The bleaching process
            7.2.2.2 Results of the bleaching process
            7.2.2.3 Exposure energy vs wavelength
            7.2.2.4 Resolution
        7.2.3 Dichromated gelatin
            7.2.3.1 Nature of dichromated gelatin
            7.2.3.2 Processing of dichromated gelatin
            7.2.3.3 Exposure energy vs wavelength
            7.2.3.4 Resolution
        7.2.4 Photopolymers
            7.2.4.1 Nature of photopolymers
            7.2.4.2 Processing of photopolymers
            7.2.4.3 Exposure energy vs wavelength
            7.2.4.4 Resolution
        7.2.5 Thermoplastics
            7.2.5.1 An erasable reusable medium
            7.2.5.2 Nature of thermoplastics
            7.2.5.3 Processing of thermoplastics
            7.2.5.4 Exposure energy vs wavelength
            7.2.5.5 Resolution
    7.3 Efficiencies of holograms
        7.3.1 Definition of efficiency
        7.3.2 Maximum theoretical efficiency and maximum achieved efficiency
        7.3.1 Absorption holograms
        7.3.2 Phase holograms
    7.4 Advanced techniques
        7.4.2 Rainbow holograms
            7.4.2.1 Method for recording rainbow holograms
            7.4.2.2 Produces sharp bright images when hologram
                       is illuminated by white light
            7.4.2.3 Image can be viewed in different colors at different angles
        7.4.3 Holographic stereograms
            7.4.3.1 Formation of the hologram
            7.4.3.2 Hologram rolled into a cylinder and illuminated with white light
            7.4.3.3 Subject motion observed as the observer moves
    


Module 8. Holographic Nondestructive Testing

    8.1 Principles of holographic nondestructive testing (HNDT)
        8.1.1 Hologram stores a wavefront
            8.1.1.1 The wavefront represents an image of some object
            8.1.1.2 The wavefront is released by illumination with the reference beam
        8.1.2 The released wavefront interferes with another wavefront
            8.1.2.1 Other wavefront may come from original object
            8.1.2.2 Interference fringes show where object has changes
            8.1.2.3 Method has great sensitivity, of the order of the wavelength of light
    8.2 Types of HNDT
        8.2.1 Real time HNDT
            8.2.1.1 Make hologram, develop it and reposition it
            8.2.1.2 Reconstruct the hologram
            8.2.1.3 Two images (one from hologram and one from object) interfere
            8.2.1.4 Allows viewing of changes in object as they occur
            8.2.1.5 In situ developing avoids repositioning problems
        8.2.2 Double exposure HNDT
            8.2.2.1 Make hologram
            8.2.2.2 Allow object to change
            8.2.2.3 Make another hologram with same recording medium
            8.2.2.4 Develop hologram and reconstruct
            8.2.2.5 Light from the two stored images interferes, allowing
                       determination of the change in the object
        8.2.3 Time average HNDT
            8.2.3.1 Applicable to vibrating surfaces
            8.2.3.2 Vibrating surface spends most time near positions
                        where motion reverses
            8.2.3.3 Make hologram while surface is vibrating
            8.2.3.3 One obtains interference between the images of the
                        vibrating surface in its extreme positions
        8.2.4 Comparison of these methods
            8.2.4.1 Real line HNDT yields most complete information
            8.2.4.2 Double exposure HNDT easier and simpler to do
            8.2.4.3 Time average is the only one useful for vibration
    8.3 Applications of HNDT
        8.3.1 Strain analysis
            8.3.1.1 Allows determination of how a body has changed
                       in response to a stress
            8.3.1.2 One gets one fringe for a change of one-half wavelength
            8.3.1.3 Fringe patterns may be difficult to interpret
        8.3.2 Defect detection
            8.3.2.1 Fringes crowd closer together where there is a defect
            8.3.2.2 May be relatively easy to interpret
        8.3.3 Vibration analysis
            8.3.3.1 Fringes give measure of departure of surface from its static position
            8.3.3.2 Useful for determination of vibrations of musical instruments
        8.3.4 Heat flow analysis
            8.3.4.1 Fringes crowd close together in areas where there is a heat buildup
            8.3.4.2 Useful for analysis of thermal stress in circuit boards

Next course