In the optical interferometry fields, the phase extracted by the arctangent function is a 2π-wrapped phase, it is necessary to carry out the phase unwrapping to obtain a correct continuous phase distribution. However the undersampled phase occurs due to too low sampling frequency and higher fringe density, thus the common unwrapping algorithms will fail. Aimed at the undersampled problem, a phase unwrapping algorithm based on lateral shearing and zooming is presented in the paper. The algorithm combines least square phase unwrapping based on second lateral shearing and bicubic interpolation to obtain larger anti-undersampled range. Taking peaks function as object, the anti-undersampled ranges are analyzed for different phase unwrapping algorithms. It can be shown that the presented algorithm retrieves the continuous phase of 2750 times the peaks function. The algorithm can provide a phase unwrapping solution for the serious undersampled phase, and the analyses of anti-undersampled capability for different phase unwrapping algorithms also are as a reference for future measurement.
A multiple mode rate equations model of the dual-cavity solid-state vortex laser has been established and used to investigate the dynamic process of the Laguerre-Gaussian (LG) modes competition. We calculated the dynamic processes of the modes LG01, LG02 and LG03. The results show that the laser exhibits a complex cross-spiking and cross-relaxation characteristic during the early stage of mode competition. The later start of a mode would cause the cross-spiking and cross-relaxation process, and ultimately the mode started firstly may even not be the one that can be sustained at steady state. To ensure the successful mode selection, the reflectivity of the secondary cavity should be larger than that of the primary cavity, but a too large one would decrease the stable output power of the mode LG01, even to its suppression. The pumping beam distribution has a great influence on the dynamic process and the stable output power of the modes, so the radius and the order of the pumping beam should be optimized. In our case, the optimized beam radius is 0.4 mm, slightly larger than the beam radius of the mode LG00, i.e.0.3 mm, and the optimized order is 4. Moreover, if the laser do not have proper reflectivities of output couplers and pumping beam distribution, the mode selection may not be demonstrated only by optimization of the aperture radius, which would only delay the crossspiking.
Elasticity modulus is a critical parameter to determine the mechanical characters of the human tissue and materials.The new stimulated Brillouin scattering (SBS) method possesses the unique characters of high speed and resolution. In this study, a SBS measurement system of elasticity modulus has been developed using a passively Q-switched dual-frequency Nd:YAG laser as the source, where two beams acting as pump and pumping lights are employed to generate the seed mode of SBS and then amplify it on ectogenous area, respectively. Thus the frequency shift and line width of SBS can be easily got from heterodyne method. Both the oscillation and output characteristics of the dual-frequency pulse laser have been investigated. The simple and efficient SBS setup allows for the generation and amplification of SBS, which will provide a reference of the application SBS of detecting dynamic change on human tissue and materials in biomechanics and medicine science.
The refractive indexes of prisms are affected by temperature, hence the optical characteristics of triangular prisms ring cavity is disturbed enough to affect the stability of the laser gyro. Considering the temperature perturbation, the transmission matrices of the reflected and refracted beams on the prism surfaces have been modified. The modified results are the old 2×2 beam transfer matrices are corrected to new 3×3 matrices and the temperature perturbations are added. According to the self-consistent theory of the laser ring cavity, a physical model of the ring cavity light transmission with the temperature disturbance has been established. The theoretical analysis shows that when the temperature varies from -40℃ to 70℃, the changes of the optical cavity-length, frequency offset, and scale factor are 49μm, 0.011MHz and 1.96×10-10, respectively. An experimental system of the prism laser gyroscope has been established whose temperature can be changed, and the experimental results agree with the theoretical values.
Proc. SPIE. 11053, Tenth International Symposium on Precision Engineering Measurements and Instrumentation
KEYWORDS: Ferroelectric materials, Digital signal processing, Optical amplifiers, Modulation, Phase shift keying, Demodulation, Signal processing, Laser stabilization, Signal detection, Laser systems engineering
Based on the principle of orthogonal demodulation, a Pound-Drever-Hall laser frequency locking scheme is developed. In the orthogonal demodulation Pound-Drever-Hall system, three sine signals are generated simultaneously using a direct digital synthesizer. A 0° phase sine signal is used to drive an electro-optic modulator to produce the phase sidebands, and 180° and 270° phase sine signals are used as reference signals for phase demodulation. The phase-modulated laser beam is coupled with a reference Fabry–Pérot cavity, and the reflected beam is sent into a photo-detector, whose output is mixed with two orthogonal reference signals to obtain two orthogonal components of the error signal. Using an analogto- digital converter, the two orthogonal components are processed using orthogonal phase sensitive detection to obtain the error signal on a host computer. The Pound-Drever-Hall laser frequency discrimination and tracking system is established and investigated experimentally using the orthogonal demodulation method. A frequency discrimination curve is obtained, and it is observed that the resonant frequency of the Fabry–Pérot cavity can automatically track laser frequency variation.
A T-shaped cavity dual-frequency Nd:YAG laser with electro-optical modulation is proposed, which consists of both p- and s-cavities sharing the same gain medium of Nd:YAG. Each cavity was not only able to select longitudinal mode but also tune frequency using an electro-optic birefringent filter polarization beam splitter + lithium niobate. The frequency difference of dual frequency was tuned through the whole gain bandwidth of Nd:YAG, which is far above the usually accepted free spectral range value in the case of a single-axis laser. As a result, the simultaneous operation of orthogonally and linearly polarized dual-frequency laser was obtained, which coincides with the theoretical analysis based on Jones matrices. The obtained frequency difference ranges from 0 to 132 GHz. This offers a simple and widely tunable source with potential for portable frequency reference applications in terahertz-wave generation and absolute-distance interferometry measurement areas.
Proc. SPIE. 9446, Ninth International Symposium on Precision Engineering Measurement and Instrumentation
KEYWORDS: Signal to noise ratio, Oscillators, Detection and tracking algorithms, Modulation, Interference (communication), Phase shift keying, Signal processing, Laser stabilization, Laser systems engineering, Phase shifts
The Pound-Drever-Hall (PDH) laser frequency stabilization is a wide spread adopted technique for narrow linewidth and ultra-stable lasers, and a phase shifter is an important part in a traditional PDH frequency stabilization system. A PDH laser frequency stabilization system without phase shifter was proposed, in which quadrature coherent detection method was used to extract the frequency drifts. Orthogonal reference signals are generated using direct digital frequency synthesizer (DDS) and mixed with the output of a photo-detector. Over-sampling technique and cumulative average algorithm were used to improve the detection resolution and SNR, orthogonal phase sensitive detection algorithm was adopted to obtain the frequency drifts. Both the quadrature demodulation system structure and the signal processing methods were adopted, the systematic detection error is reduced, the anti-noise performance is raised and long term frequency stability is improved with the PDH laser frequency stabilization system without phase shifter.
Two-cavity dual-frequency Nd:YAG laser with large frequency difference can be used as an ideal light source for synthetic-wave absolute-distance interferometric system. The operation principle of the two-cavity dual-frequency Nd:YAG laser with large frequency difference has been introduced, and the frequency locking principle of the Pound-Drever-Hall (PDH) method has been analyzed. A FPGA-based digital PDH frequency stabilizing system for the two-cavity dual-frequency Nd:YAG laser has been designed, in which the same frequency reference of a high finesse Fabry-Perot cavity is used and two separate heterodyne interference sub-systems are employed so that two electrical error signals can be obtained. Having been processed through FPGA, the output signals are applied to drive the PZT frequency actuators attached on the two-cavity dual-frequency Nd:YAG laser, as a result both operating frequencies of the two-cavity dual-frequency Nd:YAG laser can be simultaneously frequency-locked to two resonant frequencies of the Fabry-Perot cavity. A frequency stability of better than 10-10 will be obtained by use of the digital PDH frequency locking system, which can meet the needs of synthetic-wave absolute-distance interferometry.
When a new birefringent filter consisting of a polarizing beam splitter (PBS) and a half wave-plate (&lgr;/2), i.e.,
PBS-&lgr;/2 was included in a 1064nm Nd:YAG laser cavity, the laser was enforced to oscillate in single longitudinal
mode. The single longitudinal mode selecting ability of the intra-cavity filter of PBS-&lgr;/2 had been studied
experimentally by rotating the half wave-plate around the laser cavity axis, and the tuning characteristics of the
single-frequency laser output power versus the rotation angle of the half wave-plate had also been studied. An
orthogonally and linearly polarized dual-frequency Nd:YAG laser at 1064nm had been designed and demonstrated,
which included two standing-wave cavities sharing the same gain medium of Nd:YAG crystal and the birefringent filter
of PBS-&lgr;/2, the p-and s-components of the 1064nm laser light simultaneously oscillated in single longitudinal mode in
each cavity. The frequency-difference of the dual-frequency laser at 1064nm was measured to be approximately
1.87GHz, limited by the free spectral range of the scanning Fabry-Perot interferometer. It is predicted theoretically that
the frequency-difference of the dual-frequency laser at 1064nm can be tuned in a range from zero up to the lasing
bandwidth of the Nd:YAG laser.
A new scheme of a liquid crystal Fabry-Perot etalon (LCFPE) had been proposed and designed on the basis of the electronically controlled birefringence of liquid crystal, some main aspects in the LCFPE design had also been considered, and such a birefringent LCFPE element with a free spectral range (FSR) of 125-GHz had been fabricated. An oscillation of 1064-nm single longitudinal mode had been observed when an empty LCFPE (i.e., without liquid crystal material) was inserted in a diode-pumped Nd:YAG laser cavity with an optical length of approximately 43-mm. In addition, the transmitted resonant mode splitting of a birefringent Fabry-Perot etalon had been investigated theoretically, and the dependence of splitting magnitude on the path difference between ordinary light and extra-ordinary light inside the Fabry-Perot resonant cavity had been given. The theoretically analyzed results indicate that the transmitted resonant mode of the birefringent Fabry-Perot etalon can split over a whole FSR, and the splitting magnitude changes linearly with the optical path difference.
A novel displacement sensor based on diode-end-pumped solid-state laser technology has been investigated theoretically and experimentally. The investigation results indicate that provided the average radius of the pump beam in the gain medium is much smaller than the radius of the waist of the TEMoo laser beam, the exponential of the laser output power will change in a manner of a Gaussian function when the waist of the pump beam is displaced axially. Both the measurement range and the sensitivity of the displacement sensor depend on the pump power, the measurement range will be enlarged and the sensitivity be enhanced when the pump power is increased. For the experimental system of the diode-end-pumped 1064-nm Nd:YAG laser sensor, the measurement range and the sensitivity are 13.045-mm and 0.148-mW/μm, respectively, when the input optical power is 7.24-Watt (corresponding to a maximum output power of 1.926-Watt). Several main error sources that affect measurement accuracy of the displacement sensor have also been analyzed.