Laser-based Non-destructive Evaluation and Monitoring
John S. Popovics
Summary
Lasers are devices that create a high intensity, directed light beam. The light beam can travel in air or through fiber optic cables. Lasers can be used to generate waves and detect stretching or motion in a solid material without direct contact with the material. Thus lasers are useful in many important engineering applications that require remote non-destructive evaluation (NDE) and sensing such as laser ultrasonics, “smart” structures and vibration sensing. In this lesson, necessary basic concepts about light, lasers, fiber optics and wave propagation are introduced. The basis of wave generation and sensing with lasers is given. Finally specific engineering applications that make use laser-based techniques are described.
(I) Introductory Concepts
(A) Harmonic motion and wave propagation
Many natural phenomena arise from simple harmonic motion. For example, consider a mass hanging vertically from the end of a spring. At first the mass is at rest. If the mass is slightly displaced downward, it will move up and down for some time under the downward action of gravity and the upward restoring action of the spring. A plot of the vertical position of the mass with respect to time shows a general sinusoidal form, and this type of motion is termed “harmonic.” The maximum value gives the “displacement amplitude” of the motion. The frequency of the wave motion () is defined as
= 1/T (1)
where T is the period of the wave motion. Harmonic motion that has a low value of T therefore has a high value of , and vice versa. T is measured in units of seconds (s), and thus in units of 1/s. Usually the Hertz (Hz) is used as the name for the unit of frequency instead of 1/s, although they have the same meaning.
Propagating waves also cause harmonic motion at a sensed point. Propagating waves are disturbances that travel through a medium with a certain velocity (V). The type of disturbance depends on the type of propagating wave. It is important to understand that no mass is transported by wave itself. Rather, the wave is a passing disturbance that causes motion (or some other disturbance) at a single location in the medium. It is this disturbance at a point, caused by the passing wave, which exhibits harmonic motion. Usually, the resulting motion is described by a combination of individual harmonic motions each with different frequency and amplitude. Audible sound (disturbance of air pressure), ultrasound, RADAR and visible light all exhibit properties of propagating harmonic waves, even though the specific phenomena for each are very different. As an example, consider a piano that is recorded by a nearby microphone. The output of the microphone is electrical voltage that is directly related to the variation in pressure of the air near the front of the microphone. If we play a single key on the left-hand side of the piano keyboard, we hear sound with low pitch. Until the sound dies out, the output of the microphone will look like harmonic wave motion with characteristic values T and . (As a reference, the middle “A” key on the piano has a frequency () of 440 Hz and a period (T) of 2.27x10-3 s.) If we now play a single key on the right-hand side of the keyboard, we hear sound with high pitch. The output of the microphone again looks like harmonic wave motion, but now T is much smaller and therefore much higher. Thus frequency is interpreted as the pitch in the case of audible sound. If we now play a chord on the piano (several keys played together), the microphone output is a complicated signal that does not look like harmonic motion. However, this complicated signal can be broken down into three individual harmonic signals, each with specific values of T and .
All harmonic propagating waves obey the fundamental frequency-wavelength relation and exhibit reflection, refraction and interference behaviors. Equation 2 relates the frequency of the wave to the wavelength () in terms of the wave propagation velocity (V)
V = (2)
Consider again the piano and the microphone. It is known that the velocity of sound waves in air is approximately 330 m/s. If the microphone is 1 m away from the piano, the sound waves will reach the microphone 3.03x10-3 s after the moment that the key (let’s say the middle “A” key) is played. After the wave-front reaches the microphone, the characteristic frequency ( = 440 Hz) of the harmonic wave motion can be determined from the harmonic signal. The wavelength of the resulting sound in air can be computed (using equation 2) to be 0.75 m. It can be seen that has units of length and can be visualized as the distance in space (in this case air) between two points of the same phase of the harmonic wave. Assuming constant wave velocity, is inversely related to .
When a propagating wave traveling in a medium impinges on an interface with another medium, wave reflection and refraction occurs. A portion of the incident wave energy will propagate back into the original medium (reflection) while the remaining wave energy will propagate through into the second medium (refraction). Another important property that harmonic waves display is interference. If two identical harmonic waves (same frequency and amplitude) are combined together, the amplitude of the
resulting combined wave depends on the alignment (phase delay) of the two individual waves. The amplitude of the combined wave will be maximal if the individual waves are perfectly aligned; this is called constructive interference and the individual waves are “in phase.” If one wave is shifted with respect to the other, the amplitude of the combined
wave will be lower than that obtained from constructive interference. In one special case, called destructive interference, the combined signal has zero amplitude. This occurs when one wave signal has a phase delay of T/2 with respect to the other.
There are many different types of propagating waves, several of which are classified as “mechanical waves.” These waves propagate a mechanical disturbance in a medium, such as pressure or motion. For example audible sound, ultrasound and vibrations all are mechanical wave phenomena. In fluids and gasses, the mechanical wave propagates a disturbance of pressure. Only this type of disturbance is possible, and this wave is often called an “acoustic” wave. In solid materials, however, more than one mechanical wave mode can exist. In solids, the wave propagates as a disturbance in motion (displacement). The type of the wave is defined by the direction of local particle motion with respect to the direction of wave propagation. “Longitudinal” waves (L-waves) have particle motion coincident with the propagation direction, while “transverse” waves (T-waves) have particle motion perpendicular to the propagation direction. L-waves and T-waves propagate throughout a solid. Another type of wave, the Rayleigh surface wave (R-wave), propagates only along the free surface of a solid, and the particle motion is a combination of parallel and perpendicular motions. Each of these wave types travel with different velocity defined by the mechanical properties of the medium through which they propagate. For a given medium, L-waves have the highest velocity and R-waves the lowest.
Mechanical waves exhibit reflection and refraction when they impinge on an interface. The magnitude of the reflection is primarily controlled by the differences in mechanical properties between the two media (for example material stiffness and density.) If the two materials have very different mechanical properties, the amount of reflection will be very high. Thus most mechanical wave energy is reflected at the interface between a solid and air. As a result most sound energy (acoustic wave in air) will reflect back from a distant solid wall (an echo). Similarly, most ultrasonic wave energy traveling in a solid will reflect from an air-filled crack in the solid material.
(B) Optics
Light is a form of electromagnetic radiation, which behaves as a propagating harmonic wave. All electromagnetic radiation propagates through vacuum with a velocity of approximately 3.0x108 m/s, which is much higher than that for mechanical waves. The constant velocity of electromagnetic waves in vacuum is commonly referred to as “c.” In actual materials such as air, the velocity of propagation is slightly slower, depending on the refractive index of the material. The refractive index of a material is the propagation velocity of electromagnetic waves in vacuum divided by that in the material, and is greater than or equal to 1.0. The refractive index of air at atmospheric pressure is very close to 1.0, so we can assume that the wave velocity air is effectively the same as that in vacuum. Electromagnetic radiation is a disturbance in the electric and magnetic fields, which propagates through a given medium. During propagation, the wave energy is transferred between electric and magnetic fields, which are normally perpendicular to each other and to the direction of propagation. The plane that contains both the direction of the electric field and the direction of wave propagation is called the plane of polarization. Light is unusual in that it can behave both as a wave and also as a collection of discrete packets (photons) of energy. Like ordinary wave propagation, light waves obey the fundamental relation between wavelength () and frequency () (related by the wave velocity c). The full electromagnetic spectrum covers a wide range of frequencies: 104 Hz (long radio waves) to 1021 Hz (high-energy gamma rays). The optical spectrum occupies a small portion of the full spectrum, ranging from 1x1014 Hz (high end of infra-red spectrum) to 5 x1015 Hz (low end of ultraviolet spectrum.) Further, visible light occupies a range of frequencies within the optical spectrum, bounded by the infra-red and ultraviolet spectra. In the case of visible light, the frequency of the wave is interpreted as the color of the light. For example, red light has a frequency of 4x1014 Hz while violet light has 8x1014 Hz. Assuming that waves travel with a velocity c, the frequency limits of the visible light spectrum correspond to wavelengths of 700 x10-9 m and 400x10-9 m, respectively.
In addition light reflects and refracts at an interface. For light, the nature of reflection and refraction are controlled by the refractive indices of the two materials. Unlike ordinary wave propagation however, photons of light can absorb or emit a finite amount of energy (a quantum). The amount of energy is related to the wave frequency through Planck’s constant (h)
E = h (3)
where E is the change in energy (typically reported in units of electron volts or eV), and h= 4.14 eV s. Atomic and molecular systems have many discrete energy states in which they can exist. The lowest energy state is termed the “ground state” and the multiple higher energy states are collectively termed “excited states.” Quantum theory states that the energy change associated with transition from the ground state to a specific excited state (E) is associated with a specific frequency, as seen in equation 3.
(C) Lasers
High amplitude waves that are made up of a single frequency and forced into a highly-directed beam are often needed for engineering applications. This situation is relatively easy to achieve with mechanical waves and some electromagnetic waves such as RADAR. However it is not easy to achieve with visible light using standard technology. The advent of lasers now allows single frequency light amplification and beam confinement. Actually, the word laser is an acronym of Light Amplification by the Stimulated Emission of Radiation. From the previous section, we know that light is emitted when something (for example an electron in an atom) drops from a higher energy state to a lower one and that this change in energy is associated with a specific frequency. If this energy change occurs without any outside influence, it is called “spontaneous emission.” However if we can somehow influence many similar energy drops in a medium at once, we can generate high amplitude light that is made up of primarily one frequency. This is “stimulated emission,” and it can be promoted in a laser medium. For example, imagine that a photon of light energy is passing through a laser medium and then interacts with an atom (electron) that happens to be in a higher energy state. If the original photon has just the right amount of energy, it can induce the atom to reduce to a lower energy. The result is a second identical photon. Since there are now two photons instead of one, the light is amplified.
Stimulated emission by itself may not be sufficient for engineering application purposes since the light is not confined, but is emitted in all directions similar to the light emitted by a bulb, and has low intensity. In order to generate a beam of intense light, we
must amplify the light and confine it to one propagation direction. Suppose that we are able to guide light along one narrow column of a certain length in a laser medium. (For example, we can confine light using the concept of total internal reflection, as described in the following section.) Since this material along that light path can be manipulated to provide stimulated emission (being a laser medium), the light is amplified along the path. If we now add mirrors to each end of the confined light path, the light along that defined path will continue to propagate and progressively amplify as the light travels back and forth along the path. Emitted light rays that travel in other directions simply leak away and have low amplitude. In essence a light “resonator” is set up, and with each pass the internally reflected light stimulates further emission thereby increasing the intensity of the light along that path. If one of the end mirrors allows a portion of the built-up light energy to pass through, then the amplified light will emanate from the end and propagate outward along a confined beam. That is, a laser beam will be generated containing directed light made up of primarily one frequency. (Note that this described resonant cavity scheme is just one of many possible light amplification and confinement schemes.) The described system is capable of generating a laser beam continuously, provided that pumping (see inset above) is continuously applied. Such systems are called continuous-wave (CW) lasers, and are important in some engineering applications. In other engineering applications however intermittent laser light is needed, and pulsed laser systems are used to provide laser beams with short duration. There are several different schemes used to obtained laser pulses.
Laser light is characterized by the frequency content (or alternatively wavelength content), power, directionality and coherence length of the beam. These characteristics are primarily controlled by the laser system used to generate the light. Lasers have highly controlled beam directionality compared to conventional light sources. A laser beam can be visualized as a cone with an extremely small angle of divergence, typically a few milliradians. Thus the beam is column-like (typically a few millimeters wide) and can propagate long distances through air (several meters) without appreciable signal losses due to beam spreading. Coherence describes how well a light beam maintains classic harmonic form and is an important characteristic for CW lasers. Light is completely incoherent if there is no predictable phase behavior with respect to either space or time. Laser light starts out coherent but soon becomes incoherent as it propagates. The propagation distance within which the light is reasonably coherent is called the coherence length. The coherence length is essentially controlled by the frequency content of the light: the more monochromatic the light, the larger the coherence length. For example, a fairly monochromatic He-Ne laser has a coherence length of the order of 200 mm.
(D) Optical fibers
We now know that a highly column-like light beam can be generated using a laser. As a result, we can control the direction of the light beam and transmit the light over a large distance. However, we cannot transmit the light through physical barriers, such as walls, and we cannot bend the light beam in air to go around obstacles. However, it is possible to transmit light across great distances and around obstacles if we can guide the light along some sort of light “pipe.” Thin transparent glass fibers can be designed to pipe light. More generally, these are called optical fibers. Optical fibers work because they make use of the concept of total internal reflection, which was introduced earlier. If total internal reflection is achieved in a thin fiber, the light can travel along the fiber without losing intensity simply because no light is allowed to leak out to the material outside of the fiber. Optical fiber (core and cladding) is usually made of very pure glass (because it is very transparent) with a typical diameter of about 0.125 mm – about the size of monofilament fishing line. A plastic coating is often added to the outer surface to