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Log out of ReadCube. The response lag in the optical frequency change of a laser diode behind the injection current change was experimentally measured, showing that there were several time constants in the optical frequency response. The interference signals in the FMCW reflectometry were theoretically calculated by taking account of the response lag.

From these calculations, the beat frequency becomes low just after the turning point of the optical frequency sweep; this is due to the response lag in the optical frequency response.

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As a result, the spectrum of the interference signal is spread out toward the low frequency region and spatial resolution is degraded. Moreover, the spatial resolution is seriously degraded with increasing the diagnosing distance due to the nonlinearity in the optical frequency sweep. The calculated results agree well with the measured results. The full text of this article hosted at iucr. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account. If the address matches an existing account you will receive an email with instructions to retrieve your username.

Frequency-Modulated, Continuous-Wave Laser Ranging Using Photon-Counting Detectors

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Optical frequency-modulated continuous-wave (FMCW) interferometry - PDF Free Download

Please review our Terms and Conditions of Use and check box below to share full-text version of article. This is his first monograph. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Buy eBook. Buy Hardcover. Buy Softcover. FAQ Policy. About this book This book introduces the optical frequency-modulated continuous-wave FMCW interferometry - a new field of optics that is derived from radar. Thermal radiation gives a continuously spread spectrum that can be described by using the parameter of temperature. Incandescent sources are the typical incoherent optical sources.

Luminescent sources, such as electric discharge lamps and light-emitting diodes, emit light by using the inner energy of the constituent particles and give discrete spectra or specific limited-band spectra that generally cannot be described by using the parameter of temperature. Some luminescent sources are frequently used as partially coherent optical sources.

Lasers are based on the phenomenon of stimulated emission and produce a highly directional, highly intense beam. The single-longitudinal-mode lasers have an extremely narrow spectral bandwidth and can be used as ideal coherent optical sources. Various types of lasers are now available and have been widely 46 Chapter 3 Optical Sources for Optical FMCW Interference used in industrial processes, precision measurements, optical holography, optical communications, and medical treatments.

For optical FMCW interference, the optical source should meet the following essential requirements: 1 Changeable frequency: The optical frequency of the optical source must be capable of being continuously modulated. In addition, other factors, such as the lasing efficiency, physical size, reliability, durability, and cost, are also important to the real application.

In practice, only lasers are capable of satisfying the requirements above, and thus far semiconductor lasers are believed to be the best optical sources for optical FMCW interference because they have a number of superior features, such as high efficiency, direct current modulation, acceptable modulation linearity, high modulation rate, large modulation excursion, compact size, and low cost.

In the following two sections, we will first introduce the general principles of lasers and then apply these concepts to semiconductor lasers. To understand the operating principles of lasers, we have to understand what is meant by stimulated emission and under what conditions we can achieve the amplification of light by stimulated emission. In the energy domain, these particles can be characterized by discrete energy levels or states.

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  • The lowest level has the lowest energy and usually is referred to as the ground state, while the upper levels have a higher energy and usually are re- 3. Each constituent molecule or atom can exist in one of the allowed levels, but normally it prefers to stay in the lower levels.

    For a nondegenerate substance in thermal equilibrium, the population density N i. Such an amount of energy equals the difference between the two energy levels and can be in the form of light energy i. Transitions involving emission or absorption of photons are called radiative transitions. The rate of stimulated absorption depends on both the number of particles present in the lower energy level and the energy density of radiation present in the substance.

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    • The rate of spontaneous transition depends only on the number of particles present in the higher energy level. The average value of the time period for which a particle can stay in a higher energy level before downward transition by spontaneous emission is called lifetime.

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      An excited state with a long lifetime is referred to as a metastable level. Electron Photon c Stimulated emission. Figure 3. Radiative transitions. The rate of stimulated emission depends on both the number of particles in the higher energy level and the energy density of the external radiation. Notice that the most important aspect of stimulated emission is that the emitted photon is identical with the stimulating photon. They have the same frequency, same polarization state, and same propagation direction.

      Therefore, stimulated emission can produce an amplification of the stimulating radiation. The active medium may be a collection of molecules, atoms, or ions and may be in the solid, liquid, or gaseous form, which usually is addressed as an atomic system. In an atomic system, in the presence of external radiation, the probability of absorption per atom is the same as the probability of stimulated emission per atom. However, such a population distribution contradicts the normal population distribution in the atomic system in thermal equilibrium.

      This usually is called population inversion. Hence, population inversion is the necessary condition for light amplification. In other words, for a two-level atomic system, increasing the radiation energy density by an external radiation cannot cause population inversion. In some other atomic systems and under certain conditions, however, the population distribution may be inverted between a pair of levels. For instance, in the three-level the ground state and two excited states atomic system illustrated in Figure 3. Excitation of an atomic system by an external means is often called pumping.

      Pumping can be done optically by using a specific lamp, electrically by electric discharge, chemically by chemical reaction, etc. The excited atoms in level 3 can make a downward transition to level l by spontaneous and stimulated emission.

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      This transition may be achieved either by a onestep transition from level 3 to level 1 or by a two-step transition from level 3 to level 2 and then to level 1. In the latter case, at a given pumping rate, if the rate of transition from level 3 to level 2 exceeds the rate of transition from level 2 to level 1 this requires level 2 to be in a metastable state , then atoms would start accumulating in level 2, and the population of level 2 would increase with the pumping rate.

      In the three-level system above, population inversion is achieved between an excited state level 2 and the ground state level l. Because the population of the ground state in thermal equilibrium is much larger than that in any excited 3. Energy level diagrams of active media. Assuming radiative transition takes place between levels 3 and 2, if the rate of transition from level 4 to level 3 and the rate of transition from level 2 to level 1 are large compared with the rate of radiative transition from level 3 to level 2, population inversion can be achieved between levels 3 and 2.

      Since the lower level of the radiative transition is no longer the ground state, the required threshold pumping power for population inversion usually is much lower. Therefore, it is easier to achieve population inversion with the four-level system than with the three-level system. This is why, in practice, most lasers employ four-level atomic systems. Therefore, the gain in radiation actually is frequency-dependent.

      Lorentzian-linetype gain spectrum. Collisional broadening is a type of homogeneous broadening, while Doppler broadening is a type of inhomogeneous broadening. However, to obtain a highly coherent, highly intense, and highly directional laser beam, the active medium has to be placed in an optical resonator.

      The optical resonator or optical resonant cavity , similar to a Fabry-Perot etalon, consists of two mirrors M1 and M2 separated by a suitable distance, as shown in Figure 3. The mirrors may be planar or spherical and may either be attached to the ends of the active medium or be located outside it. Usually, one of the mirrors say M1 is almost totally reflecting and the other mirror M2 is partially reflecting so that a small fraction of optical energy can escape from the resonator as the output beam. The optical resonator has two major functions.

      The first function is to provide a positive-feedback mechanism to the active medium. The light reflected back from the front and rear mirrors serves as positive feedback, so that an optical oscillation can build up and sustain. Structure of a laser. However, this situation cannot last for long since increasing the power density induces more stimulated emissions, which results in faster depletion of the atoms from the excited state and reduces the population inversion and the gain coefficient.

      Frequency-Modulated Continuous-Wave (FMCW) Radar

      Soon, the radiation goes to a saturation state and the gain coefficient gets clamped at the threshold value. The second function of the optical resonator is to establish the characteristic properties of the output beam.