Mock Physics Registry Review Flashcards

Meaning, Exponent, Prefix, Symbol Pairs

• $10^9$$$10^9$$: Giga (G), 1,000,000,000 (Billion), Pairs with Nano (G&n)

• $10^6$$$10^6$$: Mega (M), 1,000,000 (Million), Pairs with Micro (M & u)

• $10^3$$$10^3$$: Kilo (k), 1,000 (Thousand), Pairs with milli (k & m)

• $10^2$$$10^2$$: Hecto (h), 100 (hundred), Pairs with centi (h & c)

• $10^1$$$10^1$$: Deca (da), 10 (Ten), Pairs with deci (da & d)

• $10^{-1}$$$10^{-1}$$: Deci (d), 0.1 (Tenth), Pairs with Deca (da & d)

• $10^{-2}$$$10^{-2}$$: Centi (с), 0.01 (Hundredth), Pairs with Hecto (h & c)

• $10^{-3}$$$10^{-3}$$: Milli (m), 0.001 (Thousandth), Pairs with Kilo (k & m)

• $10^{-6}$$$10^{-6}$$: Micro (u), 0.000001 (Millionth), Pairs with Mega (M & u)

• $10^{-9}$$$10^{-9}$$: Nano (n), 0.000000001 (Billionth), Pairs with Giga (G&n)

• Mnemonic: King Henry Died by Drinking Chocolate Milk

Acoustic Variables

• Pressure: Pascals (Pa)

• Density: Kg/cm³

• Distance (Particle motion): cm, mm

• Temperature (Sometimes): Celsius

Acoustic Parameters

• Period

• Frequency

• Amplitude

• Power

• Wavelength

• Propagation Speed

• Intensity

Sound Frequencies

• Infrasound: Below 20 Hz

• Audible sound: Between 20 and 20,000 Hz

• Ultrasound: Above 20 kHz

Speed

• Determined by Stiffness and Density

• Less Stiff (Slow)

  • Lung: 500 m/s

  • Fat: 1450 m/s

  • Soft Tissue: 1540 m/s

  • Liver and Blood: 1560 m/s

  • Muscle: 1600 m/s

  • Tendon: 1750 m/s

• More Stiff (Fast)

  • Bone: 3500 m/s

Imaging

• Shallow Imaging:

  • Less listening time

  • Short PRP

  • High PRF

  • Higher Duty Factor

• Deep Imaging:

  • More listening time

  • Long PRP

  • Low PRF

  • Lower Duty Factor

Period and Frequency

• Reciprocals

• Frequency Period

• Frequency Period

Parameters

• Determined by Source

  • Period: No adjustment, Units: s, ms, us, Typical Values: 0.06-0.5 us

  • Frequency: No adjustment, Units: Hz, MHz, Typical Values: 2-15MHz

  • Amplitude: Yes adjustment, Units: Pa, kg/cm³, cm, Typical Values: 1MP-3MP

  • Power: Yes adjustment, Units: Watts, Typical Values: 4-90mW

  • Intensity: Yes adjustment, Units: W/cm², Typical Values: 0.01-300 W/cm²

• Determined by both medium and source

  • Wavelength: No adjustment, Units: mm, distance, Typical Values: 0.1-0.8mm

• Determined by medium

  • Speed: No adjustment, Units: m/s, Typical Values: 1,500-1,600

• Determined by source and medium

  • Spatial Pulse Length

Pulse

• Change with Depth

  • PRP

  • PRF

  • Duty Factor

• Don't change with depth

  • Pulse Duration

Duration

• Pulse Duration

  • Adjustable: No

  • Units: us, time

  • Determined By: Source

  • Typical Value: 0.5-3 us

• PRP

  • Adjustable: Yes

  • Units: msec, time

  • Determined By: Source

  • Typical Value: 0.1-1ms

• PRF

  • Adjustable: Yes

  • Units: Hz, per second

  • Determined By: Source

  • Typical Value: 1-10kHz

• Spatial Pulse Length

  • Adjustable: No

  • Units: mm, distance

  • Determined By: Both

  • Typical Value: 0.1-1mm

• Duty Factor

  • Adjustable: Yes

  • Units: None (percent)

  • Determined By: Source

  • Typical Value: 0.2-0.5%

Attenuation

• More Attenuation

  • High Frequency

  • Longer Distance

• Less Attenuation

  • Low Frequency

  • Short distance

• Extremely low: Water, Biofluids

• Low: Fat

• Intermediate: Soft tissue, Muscle

• High: Bone and Lung, Air

Decibel

• Meaning

  • 3: 2x

  • 6: 4x

  • 9: 8x

  • 10: 10x

  • 20: 100x

  • 30: 1000x

  • -10: 1/10

  • -9: 1/8

  • -6: 1/4

  • -3: 1/2

Sound

• Organized:

  • Sound back to transducer

  • Specular

• Disorganized:

  • Sound in all directions

  • Rayleigh

  • Diffuse, Backscatter

Scattering

• Low

• Even higher

• Extremely High

Speeds

• Angle of Transmission

  • No refraction, transmission angle= incident angle

  • Speed 2 > Speed 1

    • Transmission angle > incident angle

  • Speed 2 < Speed 1

    • Transmission angle < incident angle

Time of Flight

• Distance

• Depth

  • 13 us = 1cm = 2cm

  • 26us = 2cm = 4cm

  • 39us = 3cm = 6cm

• Use 13 microsecond rule!

Events

• Reflection with normal incidence

  • Requirement: Different impedances required

• Reflection with oblique incidence

  • Can't predict, Too complex!

• Transmission

  • Requirement: Use law of conservation of energy

• Refraction

  • Requirement: Oblique incidence, change in propagation speed

Acoustic

• Component:

  • Active Element

  • PZT

• Matching Layer

• Backing Material

  • Acoustic Insulator

  • Electric Shield

• Thickness:

  • Active element: ½ wavelength

  • Matching Layer: 14 wavelength

Transducer

• Mechanical Transducer
  *Image shape: sector/fan
  *Beam steering: mechanical
  *Beam Focusing: fixed
  *Advantage: best slice thickness
  *Outdated Now

• Linear Phased Array Transducer
  *Crystal #/Shape: 100-300 in a line
  *Image shape: Fan or sector
  *Beam Focusing: Phasing
  *Advantage: small footprint, no moving parts; can fit between ribs, good for cardiac
  *Damaged PZT: erratic steering

• Annular Phased Array
  *Crystals #/Shape: multiple rings with common center
  *Image Shape: fan or sector
  *Beam Steering: mechanical
  *Beam Focusing: multi-focus
  *Advantage: multiple focal zones, Best slice thickness resolution
  *Damaged PZT: horizontal

• Linear Sequential Arrays
  *Crystal #/Shape: 12-250, rectangular PZT side-by-side
  *Image Shape: rectangular, large footprint
  *Beam Steering: small groups fired simultaneously parallel to each other
  *Beam Focusing: electronically
  *Damaged PZT: vertical dropout
  *Used for superficial structures

• Curved, Convex, Curvilinear Array Transducer
  *Crystal #/Shape: 120-250 rectangular side-by-side
  *Image Shape: Blunted Sector
  *Beam Steering: some but not all crystals fired simultaneously
  *Beam Focusing: Electronically
  *Damaged PZT: Vertical drop out
  *Used for imaging large spaces… Abdomen/ OB

• Vector Array
  *Crystals #/Shape: 120-250 rectangular shaped strips
  *Image Shape: trapezoidal, small footprint, fits between ribs
  *Beam Steering: combines linear and phased technology. Some but not crystals fired at one time
  *Combination of linear sequential and linear phased array

Imaging and Non-Imaging Transducer

• Imaging Transducer

  • Short pulse duration and spatial pulse length

  • Uses backing material

  • Reduced sensitivity

  • Wide bandwidth

  • Lower Q-Factor

  • Improved axial resolution

  • Characteristics of High Frequency Pulse Wave Imaging Transducers

    • Thinner PZT crystal

    • PZT with higher speed

• Non-Imaging Transducer

  • Long pulse duration and wavelength

  • No dampening

  • Increased sensitivity

  • Narrow bandwidth

  • High Q-Factor

  • Cannot create image

  • Characteristics of Low Frequency Pulsed Wave Imaging Transducers

    • Thicker PZT crystal

    • PZT with lower speed

  • "Thin fast guy wins the race, slow fat guy doesn't"

  • "Toast with a thick beer mug will produce low frequency sound, Toast with thin champagne glass will produce a high frequency sound"

Beam Diameter

• Location

  • At the transducer: Equals transducer diameter

  • At the focus: ½ transducer diameter

  • At 2 near zone lengths: Equal transducer diameter

  • Deeper than 2 near zone lengths: Wider than transducer diameter

Focus

• Small Diameter or Low Frequency X-ducer

  • Shallow Focus

  • More Divergence

• Large Diameter or High Frequency X-ducer

  • Deep Focus

  • Less Divergence

Resolution

• Axial Resolution (LARRD): Front-to-back; parallel

  • Determined By: Pulse length

  • Best With: Shortest pulse, highest frequency, fewest cycle

  • Does it Change?: Same at all depths

  • In Near field best with: Shortest pulse

  • In Far field best with: Shortest pulse

• Lateral Resolution (LATA): Side-to-side; perpendicular

  • Determined By: Beam width

  • Best With: Narrowest beam

  • Changes with depth, best at focus

  • In Near field best with: Smallest diameter crystal

  • In Far field best with: Largest diameter crystal and highest frequency (least divergence)

Type

• External: Lens, Fixed, conventional, or mechanical

• Internal: Curved PZT, Fixed, conventional, or mechanical

• Electronic: Phased array, Adjustable

Effects of Focusing

• Beam diameter in near field and focal zone reduced

• Focal depth is shallower

• Focal zone smaller

• Beam diameter in far zone increases

Beam Steering and Focus

• Electronic

  • Sound

  • Pattern

  • Slope

• Curvature

  • Focus

Characteristics

• Frequency-CW: Frequency of electrical signals from US

• Frequency-PW: Thickness of PZT and speed of sound in PZT

• Focal Length: Diameter of ceramic and frequency of sound

• Beam divergence: Diameter of ceramic and frequency of sound

• Lateral resolution: Beam width

Mode

• A-mode

  • X-axis: Depth

  • Y-axis: Amplitude

  • Z-axis: None

• B-mode

  • X-axis: Depth

  • Y-axis: None

  • Z-axis: Amplitude

• M-mode

  • X-axis: Time

  • Y-axis: Depth

  • Z-axis: Amplitude

Resolution

• Better Axial Resolution

  • Shorter spatial pulse length

  • Shorter pulse duration

  • Higher frequencies (short wavelengths)

  • Fewer cycles per pulse (less ringing)

  • Lower numerical values

Transducer Type

• Mechanical

  • Steering Technique: Mechanical

  • Focusing Technique: Fixed

  • Image Shape: Sector

  • Effect on Image (PZT Defective): Loss of entire image

• Linear Sequential

  • Steering Technique: Electronic

  • Focusing Technique: Electronic

  • Image Shape: Rectangular

  • Effect on Image (PZT Defective): Drop out of image information from top to bottom

• Phased Array

  • Steering Technique: Electronic

  • Focusing Technique: Electronic

  • Image Shape: Sector

  • Effect on Image (PZT Defective): Erratic steering and focusing

• Annular Phased

  • Steering Technique: Mechanical

  • Focusing Technique: Electronic

  • Image Shape: Sector

  • Effect on Image (PZT Defective): Horizontal or side-to-side band of drop out

• Convex

  • Steering Technique: Electronic

  • Focusing Technique: Electronic

  • Image Shape: Blunted sector

• Vector

  • Steering Technique: Electronic

  • Focusing Technique: Electronic

  • Image Shape: Trapezoidal

Contrast

• High Contrast

  • Very different

  • Black and white

  • Cardiac

• Low Contrast

  • Less difference

  • Grayscale

  • Abdomen

• Look at next # for possible of shades, highest shade will be 1 number less

  • 256 128 64 32 16 8 4 2 1

  • number of bits

  • fill in from left to right

Preprocessing vs Postprocessing

• Preprocessing

  • Analog

  • Transducer to Memory

• Postprocessing

  • Digital

  • Memory to Display

Factors Affecting Frame Rate

• Speed of sound in the medium

• Imaging depth

Imaging Depth

• Shallow Imaging

  • Short go-return time

  • Short Ttime

  • Higher frame rate

  • Superior temporal resolution

• Deep Imaging

  • Long go-return time

  • Longer Ttime

  • Lower frame rate

  • Poor temporal resolution

Systems Settings Affecting Frame Rate

• Imaging depth

• Number of pulses per frame

Factor Determining Number of Pulser per Frame

• Number of focal points

• Sector size

• Line density

Focus Imaging

• Single Focus

  • One pulse per scan line

  • Shorter Tframe

  • Higher frame rate

  • Better temporal resolution

  • Poor lateral resolution

• Multi-Focus

  • Many pulses per scan line

  • Longer Tframe

  • Lower frame rate

  • Diminished temporal resolution

  • Improved lateral resolution

Sector Imaging

• Narrow Sector

  • Fewer pulses per frame

  • Shorter Tframe

  • Higher frame rate

  • Superior temporal resolution

• Wide Sector

  • More pulses per frame

  • Longer Tframe

  • Lower frame rate

  • Diminished temporal resolution

Line Density

• Low Line Density

  • Widely spaced lines

  • Fewer pulses per frame

  • Shorter Tframe

  • Higher frame rate

  • Poor spatial resolution

  • Higher temporal resolution

• High Line Density

  • Tightly packed spaced lines

  • More pulses per frame

  • Longer Tframe

  • Lower frame rate

  • Lower temporal resolution

  • Excellent spatial resolution

Frame Rate

• Better: Higher Frame Rate

  • Shallower imaging

  • Single focus

  • Narrow sector

  • Low line density

• Worse: Lower Frame Rate

  • Deeper imaging

  • Multiple focal points ( improved lateral res)

  • Wide sector

  • High line density (improved spatial res)

Receiver Functions

• Amplification: Yes Adjustable,All signals treated equally,Effect on Image: Entire image made lighter or darker

• Compensation: Yes Adjustable, Signals treated differently based on specific depths,Effect on Image: Images will be uniformly bright from top to bottom

• Compression: Yes Adjustable, Signals treated differently depending on their strength, Effect on Image: Changes gray scale mapping

• Demodulation: No Adjustable, Prepares electrical signals to be suitable for display, Effect on Image: None

• Reject: Yes Adjustable, Only weak signals affected; strong signals remain unchanged,Effect on Image: Weak echos appear or are eliminated from image

Image

*Receiver Gain:
*Changes brightness of entire image, Alters signal-to-noise ratio
*Output Power:
*Changes brightness of entire image, Doesn't affect signal-to-noise ratio, Alters patient exposure, Bioeffects concerns, Decrease this first if image is too bright
*Increase this first if image is too dark

Pixel Density

• Low Pixel Density

  • Few pixels per inch

  • Larger pixels

  • Poorly detailed image

  • Lower spatial resolution

• High Pixel Density

  • Many pixels per inch

  • Smaller pixels

  • More detailed image

  • Higher spatial resolution

Pixels

• Image element

• Image detail

• Spatial resolution

Bits

• Computer memory

• Grey shade

• Contrast resolution

• Few Bits per Pixel: Few shades of gray, Degraded contrast resolution

• Many Bits per Pixel: More shades of gray, Improved contrast resolution

Imaging

• Shallow Image

  • Shorter listening

  • Shorter PRP

  • High PRF

  • Improved axial res

• Deep Image

  • More listening

  • Longer PRP

  • Low PRF

  • Higher spatial resolution

Coded Excitation

• Provides

  • Higher signal to noise ratio

  • Improved spatial res

  • Improved contrast res

  • Deeper penetration

Preprocessing and Post Processing

• Preprocessing:

  • Time gain compensation

  • Log compression

  • Wire magnification

  • Persistence

  • Spatial compounding

  • Edge enhancement

  • Fill-in interpolation

  • Write Magnification

    • Acquires new data

    • Preprocessing

    • Identical pixel size

    • More pixels than in the original ROI

    • Improved spatial resolution

    • May improve temporal resolution

• Post Processing:

  • Any change after freeze

  • Black/white inversion

  • Read magnification

  • Contrast variation

  • 3-D rendering

  • B-color

  • Read Magnification

    • Uses old data

    • Postprocessing

    • Larger pixel size

    • Same number of pixels in original ROI

    • Unchanged spatial resolution

    • Unchanged temporal resolution

Type of Medium

• Paper Media

  • Examples: Charts from pen writers

  • Advantages: Portable, Doesn't require device to read

  • Disadvantages: Bulky, hard to store, Difficult to display dynamic images

• Magnetic Media

  • Examples: Computer devices, Computer memory, Magnetic tape, Video Tape

  • Advantages: Able to store large amounts of info efficiently

  • Disadvantages: Can be erased by strong magnetic fields, Bulky, difficult to store and retrieve

• Chemically Mediated

  • Examples: Photographs, Flat films, Multiformat camera film

  • Advantages: Able to store and play dynamic images, Can record color, High resolution, Accepted in the medical community

  • Disadvantages: Requires chemical processing

• Photographs

• Optical Media

  • Examples: Laser disc, Compact disc

  • Advantages: Store huge amount of data, Inexpensive, Not erased by exposure to magnetic fields, Can produce color images

  • Disadvantages: Artifacts can arise from dirt or chemical contamination, Requires a display system, No standardized format for image display and storage

Mechancial Index

• Lower MI

  • Small pressure variation

  • Higher frequency

• Higher MI

  • Large pressure variation

  • Lower frequency

Shade

• Fewer Shades

  • Few choices

  • Black and white (bistable)

  • Narrow dynamic range

  • High contrast

• More Shades

  • Many choices

  • Gray scale

  • Wide dynamic range

  • Low contrast

Harmonics

• Tissue Harmonics

  • Created during transmission

  • Occurs as sound propagates through tissue

  • Results from nonlinear behavior of transmitted beam

  • Weaker harmonic signal

• Contrast Harmonics

  • Created during reflection off microbubbles

  • Occurs only when contrast agents are present with MIs greater than .1

  • Results from nonlinear behavior of microbubbles

  • Stronger harmonic signal

Beam Former

• Functions of the Beam Former

  • Generating voltages that drive the transducer

  • Determining PRP, PRF, coding, frequency, and intensity

  • Steering, focusing, and apodization of the beam

  • Amplifying the returning echo voltages

  • Compensation for attenuation

  • Digitizing the echo voltage system

  • Directing, focusing, apodizing the reception beam

Signal Processer and Image Processor

• Function of the Signal Processor

  • Bandpass filtering

  • Amplitude detection

  • Compression (dynamic range reduction)

• Function of the Image Processor

  • Scan conversion

  • Preprocessing

  • Spatial compounding

  • 3-D acquisition

  • Storing image frames

  • Cine loop

  • Post processing

  • Gray scale

  • Color scale

  • D-to-A conversion

Stenosis

• In a stenosis

  • Normal laminar flow pre- stenosis

  • Max velocity, lowest pressure

  • Post Stenotic

Aliasing

• Less Aliasing
  *Slower blood velocity
  *Lower frequency x-ducer
  *Shallow gate (high PRF)

• More Aliasing
  *Faster blood velocity
  *Higher frequency x-ducer
  *Deep gate (low PRF)

• Strategy (Increase nyquist limit)
  *Adjust scale
  *New, shallower view (sample gate)
  *O baseline shift
  *CW Doppler

• Method
  *Decrease Doppler shift
  *Lower frequency transducer
  *Aliasing remains, visually appealing

CW and Pulsed Doppler

• CW Doppler:
  *Never aliases, but range ambiguity
  *Range ambiguity
  *Unlimited maximum velocity
  *No aliasing

• Pulsed Doppler:
  *Range resolution
  *Sample volume
  *Region of overlap
  *Limited maximum velocity- nyquist
  *Aliasing

Doppler Transducer

• Pulsed Doppler Transducer

  • At least 1 crystal

  • Dampened PZT

  • Low Q-factor

  • Wide bandwidth

  • Lower sensitivity

• CW Doppler Transducer

  • At least 2 crystals

  • Undampened PZT

  • High Q-factor

  • Narrow bandwidth

  • Higher sensitivity

Measuring

• Pulsed Wave

  • Accurately identifies location of flow

  • Range resolution

  • Moderately sensitive

  • Very good temporal resolution

  • Aliasing

  • Peak velocity measured

• Continuous Wave

  • ID highest velocity jets anywhere along beam

  • Range ambiguity

  • Most sensitive

  • Very good temporal resolution

  • No aliasing

  • Peak velocity measurement

• Color Flow

  • Provides 2D information directly on anatomic image

  • Range resolution

  • Moderately sensitive; size of color jet most affected by color Doppler gain settings

  • Reduced temp res due to multiple packets

  • Aliasing

  • Average velocity

• Power Mode

  • Used with low flow velocity or flow of small vessels

  • Range resolution

  • Greater sensitivity than color flow

  • Lowest temporal resolution

  • Subject to flash artifact, not aliasing

  • No velocity

Stenosis Effects

• Change in flow direction

• Increased velocity as a vessel narrows

• Turbulence downstream from stenosis

• Pressure gradient across stenosis

• Loss of pulsatility

Diaphragm Movement

• Inspiration

  • Diaphragm moves downward

  • Thoracic pressure decreases

  • Abdominal pressure increases

  • Venous flow to heart increases

  • Venous flow to legs decrease

• Expiration

  • Diaphragm moves up into thorax

  • Thoracic pressure increases

  • Abdominal pressure decreases

  • Venous flow to heart decreases

  • Venous flow to legs increase

Flow type

• Laminar

  • Open Window

  • After stenosis

• Turbulent

  • Disturbed

  • Bifurcation

  • Sharp curve

  • Spectral Broadening

  • Associated with pathology

Ultrasound Machine Assumption

• Sound travels in a straight line

• Sound travels directly to a reflector and back

• Sound travels at a rate of 1,540 m/s

• Reflections only arise from structures positioned in beams main axis

• Imaging plane is extremely thin

• Strength of reflection is related to characteristics of tissue creating the reflection

Artifact

• Reverberation

  • Multiple reflectors placed equally on display

  • Caused by sound bouncing between two strong reflectors

  • Places too many reflections on image

• Ring Down or Comet Tail Artifact

  • Form of reverberation

  • Comet tail by two close reflectors

  • Ring down by gas bubble that resonates

  • Hyperechoic line downward of reflector

• Shadow

  • Hypoechoic or anechoic under strong attenuator

  • Result of too much attenuation

  • Prevents visualization of anatomy under

  • Can provide diagnostic information

• Enhancement

  • Hyperechoic region under weakly attenuating structure

  • Bladder

  • Loss of visualization behind structure

  • Useful in diagnostic information

• Mirror Image

  • Replica placed deeper in image

  • Reflection off of strong, flat reflector

  • Bright mirroring reflector lies on straight line between artifact and transducer

  • Cross talk on spectral

• Focal Enhancement (Banding)

  • Abnormal brightness at focus

  • Can be reduced by TGC

• Speed Error

  • Sound travels through medium other than soft tissue

  • Correct number of reflectors at incorrect depths

  • Makes image appear split or cut

  • When medium faster that soft tissue, reflector placed too shallow

  • When medium slower than soft tissue, reflector placed too deep

• Lobes

  • When sound wave is transmitted in direction other than beams main axis

  • Degradation of lateral resolution

  • Reflection of strong reflector may appear

  • Subdicing or apodization fixes

• Refraction

  • Pulse changes direction during transmission

  • Occurs at oblique boundary with different propagation speed

  • Degrades lateral resolution

  • Second copy of true reflector is usually produced nearly side by side

  • Change angle to fix

• Slice Thickness Artifact

  • Geometry of the beam

  • Seen in anechoic regions and this hyperechoic line

• Speckle

  • Form of noise

  • Tissue texture close to transducer

  • Harmonics fixes

Intensities

• Unfocused : 100 mW/cm²

• Focused: 1 W/cm²

Formulas

• $Power \propto amplitude^2$$$Power \propto amplitude^2$$

• $Intensity (W/cm^2) = \frac{Power (W)}{Area (cm)}$$$Intensity (W/cm^2) = \frac{Power (W)}{Area (cm)}$$

• $Intensity \propto amplitude^2$$$Intensity \propto amplitude^2$$

• $Intensity \propto power$$$Intensity \propto power$$

• $Wavelength (mm) = \frac{1.54mm/us}{Frequency}$$$Wavelength (mm) = \frac{1.54mm/us}{Frequency}$$

• $Speed (m/s) = frequency (Hz) \times wavelength (mm)$$$Speed (m/s) = frequency (Hz) \times wavelength (mm)$$

• Pulse Duration (us) = #cycles \times period (us)$$Pulse Duration (us) = #cycles \times period (us)$$

• Pulse Duration(us) = \frac{#cycles}{Frequency (MHz)}$$Pulse Duration(us) = \frac{#cycles}{Frequency (MHz)}$$

• Spatial Pulse Length (mm)= #cycles \times wavelength (mm)$$Spatial Pulse Length (mm)= #cycles \times wavelength (mm)$$

• $PRF= \frac{1}{PRP}$$$PRF= \frac{1}{PRP}$$

• $PRP=\frac{1}{PRF}$$$PRP=\frac{1}{PRF}$$

• $Rayleigh Scattering \propto Frequency^4$$$Rayleigh Scattering \propto Frequency^4$$

• $Attenuation Coefficient (dB/cm)= \frac{Frequency}{2}$$$Attenuation Coefficient (dB/cm)= \frac{Frequency}{2}$$

• $Total Attenuation (dB) = Attenuation Coefficient (dB/cm) \times distance (cm)$$$Total Attenuation (dB) = Attenuation Coefficient (dB/cm) \times distance (cm)$$

• $Impedance (Rayls) = Density (kg/cm^3) \times propagation speed (m/s)$$$Impedance (Rayls) = Density (kg/cm^3) \times propagation speed (m/s)$$

• $Incident Intensity (starting) = reflected intensity + transmitted intensity$$$Incident Intensity (starting) = reflected intensity + transmitted intensity$$

• $100\% intensity = reflection coefficient (IRC\%) + intensity transmission coefficient (ITC\%)$$$100\% intensity = reflection coefficient (IRC\%) + intensity transmission coefficient (ITC\%)$$

• $$IRC\%= \frac{Z2-Z1}{Z2+Z1} \times 100$$

• $ITC\%=\frac{transmitted \ intensity}{Reflected \ intensity} \times 100$$$ITC\%=\frac{transmitted \ intensity}{Reflected \ intensity} \times 100$$

• $= 1- intensity reflection coefficient$$$= 1- intensity reflection coefficient$$

• $Incident intensity (W/cm²) = Reflected \ intensity + Transmitted \ intensity$$$Incident intensity (W/cm²) = Reflected \ intensity + Transmitted \ intensity$$

• $Angle \ of \ incidence \ = Angle \ of \ reflection$$$Angle \ of \ incidence \ = Angle \ of \ reflection$$

• $Snells \ Law:$$$Snells \ Law:$$

• $$\frac{Sin (Transmission \ angle)}{Sin (Incident \ angle)} = \frac{Speed \ of \ medium \ 1}{Speed \ of \ medium