Laser Doppler vibrometer

Last updated October 24, 2024

A laser Doppler vibrometer (LDV) is a scientific instrument that is used to make non-contact vibration measurements of a surface. The laser beam from the LDV is directed at the surface of interest, and the vibration amplitude and frequency are extracted from the Doppler shift of the reflected laser beam frequency due to the motion of the surface. The output of an LDV is generally a continuous analog voltage that is directly proportional to the target velocity component along the direction of the laser beam.

Some advantages of an LDV over similar measurement devices such as an accelerometer are that the LDV can be directed at targets that are difficult to access, or that may be too small or too hot to attach a physical transducer. Also, the LDV makes the vibration measurement without mass-loading the target, which is especially important for MEMS devices.

Principles of operation

A vibrometer is generally a two beam laser interferometer that measures the frequency (or phase) difference between an internal reference beam and a test beam. The most common type of laser in an LDV is the helium–neon laser, although laser diodes, fiber lasers, and Nd:YAG lasers are also used. The test beam is directed to the target, and scattered light from the target is collected and interfered with the reference beam on a photodetector, typically a photodiode. Most commercial vibrometers work in a heterodyne regime by adding a known frequency shift (typically 30–40 MHz) to one of the beams. This frequency shift is usually generated by a Bragg cell, or acousto-optic modulator.^[1]

A schematic of a typical laser vibrometer is shown above. The beam from the laser, which has a frequency f_o, is divided into a reference beam and a test beam with a beamsplitter. The test beam then passes through the Bragg cell, which adds a frequency shift f_b. This frequency shifted beam then is directed to the target. The motion of the target adds a Doppler shift to the beam given by f_d = 2*v(t)*cos(α)/λ, where v(t) is the velocity of the target as a function of time, α is the angle between the laser beam and the velocity vector, and λ is the wavelength of the light.

Light scatters from the target in all directions, but some portion of the light is collected by the LDV and reflected by the beamsplitter to the photodetector. This light has a frequency equal to f_o + f_b + f_d. This scattered light is combined with the reference beam at the photo-detector. The initial frequency of the laser is very high (> 10¹⁴ Hz), which is higher than the response of the detector. The detector does respond, however, to the beat frequency between the two beams, which is at f_b + f_d (typically in the tens of MHz range).

The output of the photodetector is a standard frequency modulated (FM) signal, with the Bragg cell frequency as the carrier frequency, and the Doppler shift as the modulation frequency. This signal can be demodulated to derive the velocity vs. time of the vibrating target.

Applications

LDVs are used in a wide variety of scientific, industrial, and medical applications. Some examples are provided below:

Aerospace – LDVs are being used as tools in non-destructive inspection of aircraft components.^[2]
Acoustic – LDVs are standard tools for speaker design, and have also been used to diagnose the performance of musical instruments.^[3]
Architectural – LDVs are being used for bridge and structure vibration tests.^[4]
Automotive – LDVs have been used extensively in many automotive applications, such as structural dynamics, brake diagnostics, and quantification of Noise, vibration, and harshness (NVH), measurement of accurate speed.^[5]
Biological – LDVs have been used for diverse applications such as eardrum diagnostics^[6] and insect communication.^[7]
Calibration – Since LDVs measure motion that can be calibrated directly to the wavelength of light, they are frequently used to calibrate other types of transducers.^[8]
Hard disk drive diagnostics – LDVs have been used extensively in the analysis of hard disk drives, specifically in the area of head positioning.^[9]
Dental Devices - LDVs are used in the dental industry to measure the vibration signature of dental scalers to improve vibration quality.^[10]
Landmine detection – LDVs have shown great promise in the detection of buried landmines. The technique uses an audio source such as a loudspeaker to excite the ground, causing the ground to vibrate a very small amount with the LDV used to measure the amplitude of the ground vibrations. Areas above a buried mine show an enhanced ground velocity at the resonance frequency of the mine-soil system. Mine detection with single-beam scanning LDVs,^[11] an array of LDVs,^[12] and multi-beam LDVs^[13] has been demonstrated.
Security – Laser Doppler vibrometers (LDVs) as non-contact vibration sensors have an ability of remote voice acquisition. With the assistance of a visual sensor (camera), various targets in the environment, where an audio event takes place, can be selected as reflecting surfaces for collecting acoustic signals by an LDV. The performance of the LDV greatly depends on the vibration characteristics of the selected targets (surfaces) in the scene, on which a laser beam strikes and from which it returns.^[14]
Materials Research – Due to the non-contact method, Laser Vibrometers, especially Laser Scanning Vibrometers, can measure surface vibrations of modern materials like carbon plates. The vibration information can help identify and study defects as materials with defects will show a different vibration profile compared to materials without defect.^[15]

Types

Single-point vibrometers – This is the most common type of LDV.^[16] It can measure one directional out of plane movement.^[17]
Scanning vibrometers – A scanning LDV adds a set of X-Y scanning mirrors, allowing the single laser beam to be moved across the surface of interest.
Holographic laser Doppler vibrometry (HLDV) – An extended-illumination LDV that relies on digital holography for image rendering to capture the motion of a surface at many points simultaneously.^[18]^[19]

holographic vibrometry of the cantilevers of a musical box by frequency-division multiplexing CantileversLaserDopplerHolography.jpg — holographic vibrometry of the cantilevers of a musical box by frequency-division multiplexing

3-D vibrometers – A standard LDV measures the velocity of the target along the direction of the laser beam. To measure all three components of the target's velocity, a 3-D vibrometer measures a location with three independent beams, which strike the target from three different directions. This allows a determination of the complete in-plane and out-of-plane velocity of the target.^[20]
Rotational vibrometers – A rotational LDV is used to measure rotational or angular velocity.
Differential vibrometers – A differential LDV measures the out-of-plane velocity difference between two locations on the target.
Multi-beam vibrometers – A multi-beam LDV measures the target velocity at several locations simultaneously.
Self-mixing vibrometers – Simple LDV configuration with ultra-compact optical head.^[21] These are generally based on a laser diode with a built-in photodetector.^[22]^[23]
Continuous scan laser Doppler vibrometry (CSLDV) – A modified LDV that sweeps the laser continuously across the surface of the test specimen to capture the motion of a surface at many points simultaneously

Related Research Articles

The Doppler effect is the change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave. The Doppler effect is named after the physicist Christian Doppler, who described the phenomenon in 1842. A common example of Doppler shift is the change of pitch heard when a vehicle sounding a horn approaches and recedes from an observer. Compared to the emitted frequency, the received frequency is higher during the approach, identical at the instant of passing by, and lower during the recession.

Lidar is a method for determining ranges by targeting an object or a surface with a laser and measuring the time for the reflected light to return to the receiver. Lidar may operate in a fixed direction or it may scan multiple directions, in which case it is known as lidar scanning or 3D laser scanning, a special combination of 3-D scanning and laser scanning. Lidar has terrestrial, airborne, and mobile applications.

A Doppler radar is a specialized radar that uses the Doppler effect to produce velocity data about objects at a distance. It does this by bouncing a microwave signal off a desired target and analyzing how the object's motion has altered the frequency of the returned signal. This variation gives direct and highly accurate measurements of the radial component of a target's velocity relative to the radar. The term applies to radar systems in many domains like aviation, police radar detectors, navigation, meteorology, etc.

<span class="mw-page-title-main">Interferometry</span> Measurement method using interference of waves

Interferometry is a technique which uses the interference of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, spectroscopy, quantum mechanics, nuclear and particle physics, plasma physics, biomolecular interactions, surface profiling, microfluidics, mechanical stress/strain measurement, velocimetry, optometry, and making holograms.

Flow measurement is the quantification of bulk fluid movement. Flow can be measured using devices called flowmeters in various ways. The common types of flowmeters with industrial applications are listed below:

Time of flight (ToF) is the measurement of the time taken by an object, particle or wave to travel a distance through a medium. This information can then be used to measure velocity or path length, or as a way to learn about the particle or medium's properties. The traveling object may be detected directly or indirectly. Time of flight technology has found valuable applications in the monitoring and characterization of material and biomaterials, hydrogels included.

The Michelson interferometer is a common configuration for optical interferometry and was invented by the 19/20th-century American physicist Albert Abraham Michelson. Using a beam splitter, a light source is split into two arms. Each of those light beams is reflected back toward the beamsplitter which then combines their amplitudes using the superposition principle. The resulting interference pattern that is not directed back toward the source is typically directed to some type of photoelectric detector or camera. For different applications of the interferometer, the two light paths can be with different lengths or incorporate optical elements or even materials under test.

Laser Doppler velocimetry, also known as laser Doppler anemometry, is the technique of using the Doppler shift in a laser beam to measure the velocity in transparent or semi-transparent fluid flows or the linear or vibratory motion of opaque, reflecting surfaces. The measurement with laser Doppler anemometry is absolute and linear with velocity and requires no pre-calibration.

<span class="mw-page-title-main">Imaging radar</span> Application of radar which is used to create two-dimensional images

Imaging radar is an application of radar which is used to create two-dimensional images, typically of landscapes. Imaging radar provides its light to illuminate an area on the ground and take a picture at radio wavelengths. It uses an antenna and digital computer storage to record its images. In a radar image, one can see only the energy that was reflected back towards the radar antenna. The radar moves along a flight path and the area illuminated by the radar, or footprint, is moved along the surface in a swath, building the image as it does so.

<span class="mw-page-title-main">Pulse-Doppler radar</span> Type of radar system

A pulse-Doppler radar is a radar system that determines the range to a target using pulse-timing techniques, and uses the Doppler effect of the returned signal to determine the target object's velocity. It combines the features of pulse radars and continuous-wave radars, which were formerly separate due to the complexity of the electronics.

<span class="mw-page-title-main">Homodyne detection</span> Sensor implementation technique

In electrical engineering, homodyne detection is a method of extracting information encoded as modulation of the phase and/or frequency of an oscillating signal, by comparing that signal with a standard oscillation that would be identical to the signal if it carried null information. "Homodyne" signifies a single frequency, in contrast to the dual frequencies employed in heterodyne detection.

Laser-ultrasonics uses lasers to generate and detect ultrasonic waves. It is a non-contact technique used to measure materials thickness, detect flaws and carry out materials characterization. The basic components of a laser-ultrasonic system are a generation laser, a detection laser and a detector.

Holographic interferometry (HI) is a technique which enables the measurements of static and dynamic displacements of objects with optically rough surfaces at optical interferometric precision. These measurements can be applied to stress, strain and vibration analysis, as well as to non-destructive testing and radiation dosimetry. It can also be used to detect optical path length variations in transparent media, which enables, for example, fluid flow to be visualised and analyzed. It can also be used to generate contours representing the form of the surface.

Optical heterodyne detection is a method of extracting information encoded as modulation of the phase, frequency or both of electromagnetic radiation in the wavelength band of visible or infrared light. The light signal is compared with standard or reference light from a "local oscillator" (LO) that would have a fixed offset in frequency and phase from the signal if the latter carried null information. "Heterodyne" signifies more than one frequency, in contrast to the single frequency employed in homodyne detection.

Photon Doppler velocimetry (PDV) is a one-dimensional Fourier transform analysis of a heterodyne laser interferometry, used in the shock physics community to measure velocities in dynamic experiments with high temporal precision. PDV was developed at Lawrence Livermore National Laboratory by Oliver Strand. In recent years PDV has achieved popularity in the shock physics community as an adjunct or replacement for velocity interferometer system for any reflector (VISAR), another time-resolved velocity interferometry system. Modern data acquisition technology and off-the-shelf optical telecommunications devices now enable the assembly of PDV systems within reasonable budgets.

<span class="mw-page-title-main">Continuous-scan laser Doppler vibrometry</span> Method of measuring vibration across a surface

Continuous-scan laser Doppler vibrometry (CSLDV) is a method of using a laser Doppler vibrometer (LDV) in which the laser beam is swept across the surface of a test subject to capture the motion of a surface at many points simultaneously. This is different from scanning laser vibrometry (SLDV) in which the laser beam is kept at a fixed point during each measurement and quickly moved to a new position before acquiring the next measurement.

A laser surface velocimeter (LSV) is a non-contact optical speed sensor measuring velocity and length on moving surfaces. Laser surface velocimeters use the laser Doppler principle to evaluate the laser light scattered back from a moving object. They are widely used for process and quality control in industrial production processes.

<span class="mw-page-title-main">Laser Doppler imaging</span>

Laser Doppler imaging (LDI) is an imaging method that uses a laser beam to image live tissue. When the laser light reaches the tissue, the moving blood cells generate Doppler components in the reflected (backscattered) light. The light that comes back is detected using a photodiode that converts it into an electrical signal. Then the signal is processed to calculate a signal that is proportional to the tissue perfusion in the imaged area. When the process is completed, the signal is processed to generate an image that shows the perfusion on a screen.

<span class="mw-page-title-main">Laser scanning vibrometry</span> Device for measurement and imaging of vibration

The scanning laser vibrometer or scanning laser Doppler vibrometer, was first developed by the British loudspeaker company, Celestion, around 1979, further developed in the 1980s, and commercially introduced by Ometron, Ltd around 1986. It is an instrument for rapid non-contact measurement and imaging of vibration.

References

↑ Lutzmann, Peter; Göhler, Benjamin; Hill, Chris A.; Putten, Frank van (2016). "Laser vibration sensing at Fraunhofer IOSB: review and applications". Optical Engineering. 56 (3): 031215. Bibcode:2017OptEn..56c1215L. doi:10.1117/1.OE.56.3.031215. ISSN 0091-3286. S2CID 125618909.
↑ Kilpatrick, James M.; Markov, Vladimir (2008). "<title>Matrix laser vibrometer for transient modal imaging and rapid nondestructive testing</title>". In Tomasini, Enrico P (ed.). Eighth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications. Vol. 7098. p. 709809. doi:10.1117/12.802929. S2CID 109520649.
↑ Bissinger, George.; Oliver, David (July 2007). "3-D Laser Vibrometry on Legendary Old Italian Violins" (PDF). Sound and Vibration. Retrieved 2013-01-24.
↑ GmbH, Polytec. "Civil Engineering". www.polytec.com.
↑ Baldini, Francesco; Moir, Christopher I.; Homola, Jiri; Lieberman, Robert A. (2009). "Miniature laser doppler velocimetry systems". In Baldini, Francesco; Homola, Jiri; Lieberman, Robert A (eds.). Optical Sensors 2009. Vol. 7356. pp. 73560I–73560I–12. doi:10.1117/12.819324. S2CID 123294042.
↑ Huber, Alexander M; Schwab, C; Linder, T; Stoeckli, SJ; Ferrazzini, M; Dillier, N; Fisch, U (2001). "Evaluation of eardrum laser doppler interferometry as a diagnostic tool" (PDF). The Laryngoscope. 111 (3): 501–7. doi:10.1097/00005537-200103000-00022. PMID 11224783. S2CID 8296563.
↑ Fonseca, P.J.; Popov, A.V. (1994). "Sound radiation in a cicada: the role of different structures". Journal of Comparative Physiology A. 175 (3). doi:10.1007/BF00192994. S2CID 22549133.
↑ Sutton, C. M. (1990). "Accelerometer Calibration by Dynamic Position Measurement Using Heterodyne Laser Interferometry". Metrologia. 27 (3): 133–138. Bibcode:1990Metro..27..133S. doi:10.1088/0026-1394/27/3/004. S2CID 250757084.
↑ Abdullah Al Mamun; GuoXiao Guo; Chao Bi (2007). Hard Disk Drive: Mechatronics And Control. CRC Press. ISBN 978-0-8493-7253-7 . Retrieved 24 January 2013.
↑ "Vibrations Inc. – Laser Doppler Vibrometers". www.vibrationsinc.com.
↑ Xiang, Ning; Sabatier, James M. (2000). "<title>Land mine detection measurements using acoustic-to-seismic coupling</title>". In Dubey, Abinash C; Harvey, James F; Broach, J. Thomas; et al. (eds.). Detection and Remediation Technologies for Mines and Minelike Targets V. Vol. 4038. p. 645. doi:10.1117/12.396292. S2CID 12131129.
↑ Burgett, Richard D.; Bradley, Marshall R.; Duncan, Michael; Melton, Jason; Lal, Amit K.; Aranchuk, Vyacheslav; Hess, Cecil F.; Sabatier, James M.; Xiang, Ning (2003). "Mobile mounted laser Doppler vibrometer array for acoustic landmine detection". In Harmon, Russell S; Holloway, Jr, John H; Broach, J. T (eds.). Detection and Remediation Technologies for Mines and Minelike Targets VIII. Vol. 5089. p. 665. doi:10.1117/12.487186. S2CID 62559102.
↑ Lal, Amit; Aranchuk, Slava; Doushkina, Valentina; Hurtado, Ernesto; Hess, Cecil; Kilpatrick, Jim; l'Esperance, Drew; Luo, Nan; Markov, Vladimir (2006). "<title>Advanced LDV instruments for buried landmine detection</title>". In Broach, J. Thomas; Harmon, Russell S; Holloway, Jr, John H (eds.). Detection and Remediation Technologies for Mines and Minelike Targets XI. Vol. 6217. p. 621715. doi:10.1117/12.668927. S2CID 62566351.
↑ Rui Li; Tao Wang; Zhigang Zhu; Wen Xiao (2011). "Vibration Characteristics of Various Surfaces Using an LDV for Long-Range Voice Acquisition". IEEE Sensors Journal. 11 (6): 1415. Bibcode:2011ISenJ..11.1415L. doi:10.1109/JSEN.2010.2093125. S2CID 37916336.
↑ Polytec, GmbH. "Material Research". www.polytec.com.
↑ Laura Rodríguez, High temperature surface measurement with Aries Laser Vibrometer, VELA. Original paper presented at AIVELA Conferences 2012.June 2012.
↑ "Single-Point Vibrometers".
1 2 Verrier, Nicolas and Atlan, Michael. Optics Letters 5 (2013); https://doi.org/10.1364/ol.38.000739; https://arxiv.org/abs/1211.5328
1 2 François Bruno, Jérôme Laurent, Daniel Royer, and Michael Atlan. Appl. Phys. Lett. 104, 083504 (2014); https://doi.org/10.1063/1.4866390; https://arxiv.org/abs/1401.5344
↑ Jorge Fernández Heredero, 3D Vibration Measurement using LSV. Original paper presented at AdMet 2012.February 2012.
↑ "OMS – Laser Doppler Vibrometers". www.omscorporation.com.
↑ Scalise, Lorenzo; Paone, Nicola (2000). "Self-mixing laser Doppler vibrometer". In Tomasini, Enrico P (ed.). Fourth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications. Vol. 4072. pp. 25–36. doi:10.1117/12.386763. S2CID 119778488.
↑ Heterodyned self-mixing laser diode vibrometer – US Patent 5838439 Archived 2011-06-12 at the Wayback Machine . Issued on November 17, 1998. Patentstorm.us. Retrieved on 2013-06-17.

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[LutzmannGoehler2016-1] Lutzmann, Peter; Göhler, Benjamin; Hill, Chris A.; Putten, Frank van (2016). "Laser vibration sensing at Fraunhofer IOSB: review and applications". Optical Engineering. 56 (3): 031215. Bibcode:2017OptEn..56c1215L. doi:10.1117/1.OE.56.3.031215. ISSN 0091-3286. S2CID 125618909.

[2] Kilpatrick, James M.; Markov, Vladimir (2008). "<title>Matrix laser vibrometer for transient modal imaging and rapid nondestructive testing</title>". In Tomasini, Enrico P (ed.). Eighth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications. Vol. 7098. p. 709809. doi:10.1117/12.802929. S2CID 109520649.

[3] Bissinger, George.; Oliver, David (July 2007). "3-D Laser Vibrometry on Legendary Old Italian Violins" (PDF). Sound and Vibration. Retrieved 2013-01-24.

[4] GmbH, Polytec. "Civil Engineering". www.polytec.com.

[BaldiniMoir2009-5] Baldini, Francesco; Moir, Christopher I.; Homola, Jiri; Lieberman, Robert A. (2009). "Miniature laser doppler velocimetry systems". In Baldini, Francesco; Homola, Jiri; Lieberman, Robert A (eds.). Optical Sensors 2009. Vol. 7356. pp. 73560I–73560I–12. doi:10.1117/12.819324. S2CID 123294042.

[6] Huber, Alexander M; Schwab, C; Linder, T; Stoeckli, SJ; Ferrazzini, M; Dillier, N; Fisch, U (2001). "Evaluation of eardrum laser doppler interferometry as a diagnostic tool" (PDF). The Laryngoscope. 111 (3): 501–7. doi:10.1097/00005537-200103000-00022. PMID 11224783. S2CID 8296563.

[7] Fonseca, P.J.; Popov, A.V. (1994). "Sound radiation in a cicada: the role of different structures". Journal of Comparative Physiology A. 175 (3). doi:10.1007/BF00192994. S2CID 22549133.

[8] Sutton, C. M. (1990). "Accelerometer Calibration by Dynamic Position Measurement Using Heterodyne Laser Interferometry". Metrologia. 27 (3): 133–138. Bibcode:1990Metro..27..133S. doi:10.1088/0026-1394/27/3/004. S2CID 250757084.

[MamunGuo2007-9] Abdullah Al Mamun; GuoXiao Guo; Chao Bi (2007). Hard Disk Drive: Mechatronics And Control. CRC Press. ISBN 978-0-8493-7253-7 . Retrieved 24 January 2013.

[10] "Vibrations Inc. – Laser Doppler Vibrometers". www.vibrationsinc.com.

[11] Xiang, Ning; Sabatier, James M. (2000). "<title>Land mine detection measurements using acoustic-to-seismic coupling</title>". In Dubey, Abinash C; Harvey, James F; Broach, J. Thomas; et al. (eds.). Detection and Remediation Technologies for Mines and Minelike Targets V. Vol. 4038. p. 645. doi:10.1117/12.396292. S2CID 12131129.

[12] Burgett, Richard D.; Bradley, Marshall R.; Duncan, Michael; Melton, Jason; Lal, Amit K.; Aranchuk, Vyacheslav; Hess, Cecil F.; Sabatier, James M.; Xiang, Ning (2003). "Mobile mounted laser Doppler vibrometer array for acoustic landmine detection". In Harmon, Russell S; Holloway, Jr, John H; Broach, J. T (eds.). Detection and Remediation Technologies for Mines and Minelike Targets VIII. Vol. 5089. p. 665. doi:10.1117/12.487186. S2CID 62559102.

[13] Lal, Amit; Aranchuk, Slava; Doushkina, Valentina; Hurtado, Ernesto; Hess, Cecil; Kilpatrick, Jim; l'Esperance, Drew; Luo, Nan; Markov, Vladimir (2006). "<title>Advanced LDV instruments for buried landmine detection</title>". In Broach, J. Thomas; Harmon, Russell S; Holloway, Jr, John H (eds.). Detection and Remediation Technologies for Mines and Minelike Targets XI. Vol. 6217. p. 621715. doi:10.1117/12.668927. S2CID 62566351.

[Li2001-14] Rui Li; Tao Wang; Zhigang Zhu; Wen Xiao (2011). "Vibration Characteristics of Various Surfaces Using an LDV for Long-Range Voice Acquisition". IEEE Sensors Journal. 11 (6): 1415. Bibcode:2011ISenJ..11.1415L. doi:10.1109/JSEN.2010.2093125. S2CID 37916336.

[15] Polytec, GmbH. "Material Research". www.polytec.com.

[16] Laura Rodríguez, High temperature surface measurement with Aries Laser Vibrometer, VELA. Original paper presented at AIVELA Conferences 2012.June 2012.

[17] "Single-Point Vibrometers".

[Verrier-18] 1 2 Verrier, Nicolas and Atlan, Michael. Optics Letters 5 (2013); https://doi.org/10.1364/ol.38.000739; https://arxiv.org/abs/1211.5328

[Bruno-19] 1 2 François Bruno, Jérôme Laurent, Daniel Royer, and Michael Atlan. Appl. Phys. Lett. 104, 083504 (2014); https://doi.org/10.1063/1.4866390; https://arxiv.org/abs/1401.5344

[20] Jorge Fernández Heredero, 3D Vibration Measurement using LSV. Original paper presented at AdMet 2012.February 2012.

[21] "OMS – Laser Doppler Vibrometers". www.omscorporation.com.

[22] Scalise, Lorenzo; Paone, Nicola (2000). "Self-mixing laser Doppler vibrometer". In Tomasini, Enrico P (ed.). Fourth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications. Vol. 4072. pp. 25–36. doi:10.1117/12.386763. S2CID 119778488.

[23] Heterodyned self-mixing laser diode vibrometer – US Patent 5838439 Archived 2011-06-12 at the Wayback Machine . Issued on November 17, 1998. Patentstorm.us. Retrieved on 2013-06-17.

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