Detection and measurement of defect size and shape using ultrasonic fourier-transformed waveforms

1. A system comprising:

a data analysis device configured to:

receive from an ultrasonic waveform detector ultrasonic waveform data representative of an ultrasonic waveform that propagated through a sample and resonated within a defect within the sample;

select a portion of the ultrasonic waveform data;

apply a Fast Fourier Transform to the portion of the ultrasonic waveform data to transform the portion from a time domain to a frequency domain;

identify a characteristic frequency of the portion in the frequency domain; and

determine a characteristic of the defect by at least one of (1) comparing the characteristic frequency to a calibration curve or (2) calculating an approximate size of the defect using at least one equation that relates the characteristic frequency to the approximate size of the defect.

2. The system of claim 1 , wherein the data analysis device is configured to determine the characteristic of the defect by comparing the characteristic frequency to the calibration curve, and wherein the calibration curve comprises a plot of characteristic frequencies of defects of a known shape and known sizes versus an inverse of the known sizes.

3. The system of claim 1 , wherein the data analysis device is configured to determine the characteristic of the defect by calculating the approximate size of the defect using at least one equation that relates the characteristic frequency to the approximate size of the defect, and wherein the at least one equation comprises the equation:

D

=

17.87

⁢

d

f

2

3

wherein D is an approximate diameter of the defect, d is a diameter of a sound hole of the defect, and f is the characteristic frequency of the portion.

4. The system of claim 1 , wherein the data analysis device is configured to determine the characteristic of the defect by calculating the approximate size of the defect using at least one equation that relates the characteristic frequency to the approximate size of the defect, and wherein the at least one equation comprises the equation:

D

=

3

⁢

⁢

d

2

⁢

C

2

8

⁢

⁢

L

⁢

⁢

f

2

⁢

π

2

3

wherein D is an approximate diameter of the defect, d is a diameter of a sound hole of the defect, C is a speed of sound, L is a length of a neck of the defect, and f is the characteristic frequency of the portion.

5. The system of claim 1 , wherein the data analysis device is configured to determine the characteristic of the defect based on at least two equations that relate the characteristic frequency to a respective approximate size of the defect, and wherein the data analysis device is configured to output a range of approximate sizes based on the respective approximate sizes.

6. The system of claim 1 , wherein the data analysis device is configured to:

select a first portion of the ultrasonic waveform data;

apply a Fast Fourier Transform to the first portion of the ultrasonic waveform data to transform the portion from a time domain to a frequency domain;

identify a first characteristic frequency of the first portion in the frequency domain;

select a second portion of the ultrasonic waveform data;

apply a Fast Fourier Transform to the second portion of the ultrasonic waveform data to transform the portion from a time domain to a frequency domain;

identify a second characteristic frequency of the second portion in the frequency domain; and

generate a representation of at least the first characteristic frequency and the second characteristic frequency as a function of the portion.

7. The system of claim 6 , wherein the data analysis module is configured to:

receive an input from a user selecting at least one portion from the representation;

determine a representative characteristic frequency for the at least one portion; and

determine the characteristic of the defect based on the representative characteristic frequency of the at least one portion.

8. A method comprising:

with one or more processors, receiving from an ultrasonic waveform detector ultrasonic waveform data representative of an ultrasonic waveform that propagated through a sample and resonated within a defect within the sample;

with the one or more processors, selecting a portion of the ultrasonic waveform data;

with the one or more processors, applying a Fast Fourier Transform to the portion of the ultrasonic waveform data to transform the portion from a time domain to a frequency domain;

with the one or more processors, identifying a characteristic frequency of the portion in the frequency domain; and

with the one or more processors, determining a characteristic of the defect by at least one of (1) comparing the characteristic frequency to a calibration curve or (2) calculating an approximate size of the defect using at least one equation that relates the characteristic frequency to the approximate size of the defect.

9. The method of claim 8 , wherein the calibration curve comprises a plot of characteristic frequencies of defects of a known shape and known sizes versus an inverse of the known sizes.

10. The method of claim 8 , wherein determining the characteristic of the defect by at least one of (1) comparing the characteristic frequency to the calibration curve and (2) calculating the approximate size of the defect using at least one equation that relates the characteristic frequency to the approximate size of the defect comprises determining the characteristic of the defect based on:

D

=

17.87

⁢

d

f

2

3

wherein D is an approximate diameter of the defect, d is a diameter of a sound hole of the defect, and f is the characteristic frequency of the portion.

11. The method of claim 8 , wherein determining the characteristic of the defect by at least one of (1) comparing the characteristic frequency to the calibration curve and (2) calculating the approximate size of the defect using at least one equation that relates the characteristic frequency to the approximate size of the defect comprises determining the characteristic of the defect based on:

D

=

3

⁢

⁢

d

2

⁢

C

2

8

⁢

⁢

L

⁢

⁢

f

2

⁢

π

2

3

wherein D is an approximate diameter of the defect, d is a diameter of a sound hole of the defect, C is a speed of sound, L is a length of a neck of the defect, and f is the characteristic frequency of the portion.

12. The method of claim 8 , wherein determining the characteristic of the defect by at least one of (1) comparing the characteristic frequency to a calibration curve and (2) calculating an approximate size of the defect using at least one equation that relates the characteristic frequency to the approximate size of the defect comprises determining the characteristic of the defect based on at least two equations that relate the characteristic frequency to an approximate size of the defect, further comprising outputting a range of approximate sizes based on the approximate sizes determined based on the at least two equations.

13. The method of claim 8 , wherein:

selecting the portion of the ultrasonic waveform data comprises selecting a first portion of the ultrasonic waveform data;

applying the Fast Fourier Transform to the portion of the ultrasonic waveform data comprises applying a Fast Fourier Transform to the first portion of the ultrasonic waveform data to transform the portion from a time domain to a frequency domain;

identifying the characteristic frequency of the portion in the frequency domain comprises identify a first characteristic frequency of the first portion in the frequency domain; and

wherein the method further comprises:

with the one or more processors, selecting a second portion of the ultrasonic waveform data;

with the one or more processors, applying a Fast Fourier Transform to the second portion of the ultrasonic waveform data to transform the portion from a time domain to a frequency domain;

with the one or more processors, identifying a second characteristic frequency of the second portion in the frequency domain; and

with the one or more processors, generating a representation of at least the first characteristic frequency and the second characteristic frequency as a function of the portion.

14. The method of claim 13 , further comprising:

with the one or more processors, receiving an input from a user selecting at least one portion from the representation;

with the one or more processors, determining a representative characteristic frequency for the at least one portion; and

with the one or more processors, determining the characteristic of the defect based on the representative characteristic frequency of the at least one portion.

15. A non-transitory computer readable medium comprising instructions that cause a programmable processor to:

receive from an ultrasonic waveform detector ultrasonic waveform data representative of an ultrasonic waveform that propagated through a sample and resonated within a defect within the sample;

select a portion of the ultrasonic waveform data;

apply a Fast Fourier Transform to the portion of the ultrasonic waveform data to transform the portion from a time domain to a frequency domain;

identify a characteristic frequency of the portion in the frequency domain; and

determine a characteristic of the defect by at least one of (1) comparing the characteristic frequency to a calibration curve or (2) calculating an approximate size of the defect using at least one equation that relates the characteristic frequency to the approximate size of the defect.

16. The non-transitory computer readable medium of claim 15 , wherein the calibration curve comprises a plot of characteristic frequencies of defects of a known shape and known sizes versus an inverse of the known sizes.

17. The non-transitory computer readable medium of claim 15 , wherein the instructions cause the programmable processor to:

select a first portion of the ultrasonic waveform data;

apply a Fast Fourier Transform to the first portion of the ultrasonic waveform data to transform the portion from a time domain to a frequency domain;

identify a first characteristic frequency of the first portion in the frequency domain;

select a second portion of the ultrasonic waveform data;

apply a Fast Fourier Transform to the second portion of the ultrasonic waveform data to transform the portion from a time domain to a frequency domain;

identify a second characteristic frequency of the second portion in the frequency domain; and

generate a representation of at least the first characteristic frequency and the second characteristic frequency as a function of the portion.

18. The non-transitory computer readable medium of claim 17 , wherein instructions cause the programmable processor to generate a false color map of the first characteristic frequency and the second characteristic frequency as a function of the portion.

19. The non-transitory computer readable medium of claim 18 , further comprising instructions that cause the programmable processor to:

receive an input from a user selecting at least one portion from the representation;

determine a representative characteristic frequency for the at least one portion; and

determine the characteristic of the defect based on the representative characteristic frequency of the at least one portion.

20. The non-transitory computer readable medium of claim 19 , wherein the representative characteristic frequency comprises at least one of a mean of the characteristic frequencies of the at least one portion, a median of the characteristic frequencies of the at least one portion, or a mode of the characteristic frequencies of the at least one portion.