NDT Solution
Effect of Ultrasonic Beam Frequency and
Focalization on Detectability and
Resolution of Minute Discontinuities
This article gives the practical aspects of ultrasonic testing. The author has successfully demonstrated the influence of excitation frequency, transducer focal length and the sample thickness on the resolution of the technique. Readers should find this article useful as it reexamines the relationship between various parameters of ultrasonic testing and the capability of the system in resolving minute discontinuities.
G.P Singh
Associate Technical Editor
Introduction
According to fundamental principles of discontinuity detection, in order to detect and reliably resolve tiny discontinuities, the wavelength of ultrasound should be chosen as close as possible to the discontinuity size. For instance, to resolve 1 mm (3.9 x 10-5 in.) discontinuities, the ultrasound wavelength should be in the range of several micrometers. Detection of discontinuities of this size will require the use of an ultrasound frequency in the range of 0.5 to 1 GHz. Unfortunately, at these frequencies, the ultrasound does not penetrate sufficiently into the target material, reaching only the very thin, immediate undersurface layer several micrometers thick. Therefore, these frequencies cannot be used for discontinuity detection inside the specimen beyond the immediate undersurface layer. However, even frequencies in the range of 50 MHz cannot be used for material through thickness discontinuity testing since the ultrasound is still severely attenuated by the material texture (Hirsekorn et al., 1994).
When the focal zone is too long, the test resolution and detectability may degrade significantly.
Thus, even lower frequencies have to be used to detect discontinuities located relatively deeply in the specimen. The frequencies ranging between 5 to 25 MHz are commonly used for industrial discontinuity detection. It should be mentioned that although higher frequencies in the range of 15 to 25 MHz are typically employed to improve the test resolution, it is at the expense of ultrasonic penetration depth. On the contrary, lower frequencies of 5 to 10 MHz are used to improve the ultrasonic penetration depth and detectability, although at the expense of the test resolution. In reality, the ultrasound frequency should be chosen carefully based on test objectives and, to some extent, as a tradeoff between detectability and resolution.
The other parameter to be chosen carefully is the transducer focal length. It is important to choose the appropriate focal length since it will eventually affect the length of the focal zone. Reduction in the focal zone length enhances the beam energy concentration that may significantly improve both detectability and resolution. A certain relationship (Krautkramer and Krautkramer, 1990) exists between the transducer focal length and the focal zone length. Namely, shortening the focal length results in simultaneous shortening of the focal zone and vice versa. When the focal zone is too long, the test resolution and detectability may degrade significantly. Therefore, when higher resolution and detectability are required, it is important to choose shorter focal lengths. The actual length of the -6 dB focal zone can be estimated using Equation 1 (Panametrics, Inc., 1995).
(1) 
where
Fz = focal zone length
F = transducer focal length
SF = F/N (normalized focal length)
N = D2f/4c (near field distance)
f = frequency
D = transducer diameter
c = sound velocity.
In the test described below, two transducers with frequencies of 10 and 15 MHz and focal lengths of 50.8 and 76.2 mm (2 and 3 in.), respectively, were compared for their ability to detect minute discontinuities.
Experiment
One focused, broadband, immersion transducer of 15 MHz frequency, 12.5 mm (0.5 in.) diameter and 50.8 mm (2 in.) focal length and one of 10 MHz frequency, 9.5 mm (0.4 in.) diameter and 76.2 mm (3 in.) focal length are employed. Two specimens, an aluminum flat bottom hole 100-3 specimen with the hole measuring 100 µm (3.9 x 10-3 in.) and a copper flat bottom hole 250-6 specimen with the hole measuring 250 µm (0.01 in.), are tested. The first number in the specimen identification designates the flat bottom hole diameter (in micrometers), while the second indicates the distance (in millimeters) between the flat bottom hole surface and the front surface of the specimen. Discontinuity free 99.999% purity low alloyed aluminum with 0.5 weight percent copper and 99.999% purity copper were used to make these specimens.During the test, the ultrasonic pulse is introduced into the specimen at a normal incidence through a water column in the C-scan tank. The echo, which is reflected back from the flat bottom hole, is received by the same transducer and processed by the computer based data acquisition system. The data acquisition system employs a receiver with a signal conditioning circuitry, low noise tuned preamplifier, low noise gated linear amplifier and a peak detector loaded with a 12 bit analog to digital converter.
The maximum amplitude of the radio frequency signal is converted into the analog output, which is digitized by the analog to digital converter and stored in the memory of the computer for future processing. The radio frequency signal is also displayed on the oscilloscope screen (Figure 1).
Figure 1 - The radio frequency signal displayed on the oscilloscope screen: (a) echo waveform from the 100 µm (3.9 x 10-3 in.) aluminum flat bottom hole 100-3, amplified; (b) echo waveforms from the surface and the aluminum flat bottom hole 100-3
The focalization curve for each of these two transducers is determined for both specimens. The curves are developed by varying the echo round trip delay time. The delay time (measured in microseconds) can be easily converted into round trip distance in millimeters (or inches) by multiplying the delay time by the ultrasonic velocity of the water at known temperature. The round trip delay time, as well as water path, completely defines the location of the focal spot and the length and the location of the (-6 dB) focal zone inside the specimen (Krautkramer and Krautkramer, 1990).
Results
The results show that the decrease in the frequency with the simultaneous increase in the focal length cause the focal zone to extend, but as is mentioned above, at the expense of test sensitivity (Figure 2). This effect is more pronounced for the copper specimen (Figure 2b) due to a stronger ultrasonic attenuation. As a result of ultrasonic interaction with specimen texture, a texture noise caused by wave diffraction and attenuation should also be accounted for.Figure 2 - Effect of frequency and focal length on test sensitivity: (a) signal to noise ratio versus round trip water path delay for aluminum flat bottom hole 100-3; (b) signal to noise ratio versus water path round trip delay for copper bottom hole 250-6.
This noise causes echoes from minute discontinuities to be buried within a texture noise, especially at low echo intensities. As seen in Figure 3b, even relatively large flat bottom holes, such as 250 µm (0.01 in.), become nearly invisible when the 10 MHz transducer is used. The focal zone of the transducers can be estimated using Equation 1. As it follows from the equation, the increase in the focal length from 50.8 to 76.2 mm (2 to 3 in.) as well as the decrease in both the frequency from 15 MHz to 10 MHz and transducer diameter from 12.5 to 9.5 mm (0.5 to 0.4 in.) result in the focal zone increase from 12.4 to 61.6 mm (0.49 to 2.4 in.) in water. A similar change occurs for the aluminum and copper specimens, where the focal zone length is changed from 3 to 14.5 mm (0.1 to 0.6 in.) in aluminum and from 4 to 20 mm (0.2 to 0.8 in.) in copper.
Figure 3 - Effect of frequency and focal length on signal to noise ratio: (a) aluminum flat bottom hole 100-3; (b) copper flat bottom hole 250-6.
At first glance, the increase in the transducer focal length looks very promising since it allows us to test thicker layers of the material with relatively uniform sound pressure intensity over a focal zone. However, as is shown in Figures 2 and 3, this will occur at the expense of test sensitivity. Therefore, the 10 MHz with longer focal length transducer has a certain disadvantage regarding detection of minute discontinuities since minute discontinuities remain almost invisible for this transducer. Therefore, shortening the focal zone and increasing the ultrasonic frequency provide a certain advantage in the case of minute discontinuity detection.
Finally, it should be noted that neither transducer is capable of scanning through the entire thickness of the specimen when the specimen thickness exceeds the focal zone length. Hence, in every case when the specimen thickness exceeds the -6 dB focal zone, the test result should be considered a statistical sampling for the material. Therefore, the final judgment - as to what kind of sampling (with shorter or longer focal zone) is better suited for the particular test - can be based on the test objectives.
References
Hirsekorn, S., S. Pangraz, W. Bernauer, G. Weides and W. Arnold, "Material Characterization and Nondestructive Testing by Acoustic Imaging Techniques," Acta Acustica, Vol. 2, 1994, pp. 195-204.Krautkramer, J. and H. Krautkramer, Ultrasonic Testing of Materials, fourth edition, New York, Springer-Verlag, 1990.
Panametrics, Inc., Ultrasonic Transducers P395, 1995.
* Tosoh SMD, Inc., 3600 Gantz Rd., Grove City, OH 43123; (614) 875-7912; fax (614) 875-0031; e-mail <alex.leybovich@tsmd.com>.
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