Main Title Slide
SRAS: Generation
Using Fourier theory
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SRAS Signal Generation
We have this process:
Laser with a temporal response illuminates sample over extended area
Spatial pattern of ‘hot’ spots on the sample
Produces sound waves
Waves propagate under detector spot
Produces a temporal signal on the photodiode
Building generation pattern from simple functions
Pulse train with spacing λa
Rectangle shape
Pulse train spacing τrr
Gaussian pulse of laser
Intensity profile of laser beam
SRAS Generation
The pulse width of laser is important
It determines the upper limit of the frequencies available to use.
Take FFT of the pulse width to see the frequency content.
The exact form of the laser pulse depends on the type of the laser.
This the same for spatial frequencies too!
Small spatial extent object has wide spatial frequency content.
Rep rate of laser
SRAS Generation
The laser is imaged to the sample surface illuminating an area on the sample. The size of this region will determine the frequency content of the generated sound waves. Here a delta function type spot will produce wide frequency content. We can convert from spatial domain to time domain (for our case) by the acoustic velocity of the sample.
Convert via sample velocity
SRAS Generation
Changing to line generation reduces the maximum possible frequency.
Here a ‘top hat’ response looks like a sinc response in the frequency domain
Width in time 1/ width is where first zero crossing is in spectra.
Example: 12μm width 4ns in time, 1/4ns = 250MHz width of sinc function
SRAS Generation
If we have a series of single spots then we modify the frequency again
Here a comb function in space is a comb function in frequency
Comb spacing in time domain Δt give comb spacing in frequency domain of 1/Δt
24μm 8ns 125MHz spacing
SRAS Generation
If we have a grating pattern we combine the two responses from before
Notice that the zero of the sinc removes the second harmonic.
SRAS Generation
If we have a grating pattern we combine the two responses from before
Notice that the zero of the sinc removes the second harmonic.
Quick Check for sanity:
We see our fundamental signal is at 125MHz
We used line spacing of 24μm and acoustic velocity of 3000m/s
3000=24μm*125MHz
This is correct.
SRAS Generation
We can take the inverse FFT to see what the signal will look like in the time domain.
SRAS Generation
How we actually make the pattern:
Relay optics
Laser beam
SRAS Generation
An additional limitation we have overlooked so far comes from the spatial resolution of the imaging system and it’s ability to accurately reproduce the pattern of lines on the sample.
The optical resolution of an imaging system depends on the numerical aperture of the system. If you do Optics and Photonics technology in Yr 4 this will be covered in detail there.
The resolution limit is on the order of 1 micron in size – leading to a upper frequency limit of a few Gigahertz waves. This is generally much higher than is used in NDE applications so it was ok to neglect it here.
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