An intracavity, second-harmonic generation, tunable, dual-frequency, passively Q-switched Nd:YAG laser based on a T-resonator configuration with polarization splitting is proposed, whose frequency difference could be doubled in comparison with fundamental lasing. The Nd:YAG, Cr4 + : YAG, and potassium titanyl phosphate (KTP) crystals were set at the shared arm, which could considerably reduce thermal fluctuation and pulse timing jitter between dual-frequency lasers. One birefringent filter consisting of a polarized beam splitter and a half-wave plate (HWP) is placed in each divided arm to select their single longitudinal mode. As a result, the p-polarized and s-polarized passively Q-switched components of 532 nm are simultaneously operated, whose power easily reaches to same and frequency is beneficial to tune theoretically throughout the whole gain bandwidth. The main characteristics of the power, longitudinal mode selection, and the pulse have been tested experimentally. Moreover, the frequency difference of the dual-frequency laser at 532 nm has been widely tuned from 9.6 to 117 GHz, by slightly adjusting the tilt angles of the HWPs. We offer a simple and widely tunable source with potential for portable frequency reference applications in absolute-distance interferometry, terahertz-wave generation, and other fields.
To stabilize the frequency difference of the two-cavity dual-frequency Nd:YAG laser at 1064 nm, a scheme of the phase modulation of the orthogonally and linearly polarized dual-frequency laser using single electro-optic phase modulator has been proposed, and a frequency-difference stabilizing system for a two-cavity dual-frequency Nd:YAG laser based on the single-modulator quadrature-demodulated Pound–Drever–Hall (SM-QD-PDH) method has been designed and established. The characteristics of phase modulation, frequency discrimination, frequency stabilization, and frequency-difference stabilization of the orthogonally and linearly polarized dual-frequency laser with a frequency difference of ∼24 GHz at 1064 nm have been investigated experimentally. The experimental results have indicated that during a period of 1 h, the laser frequency stabilities of the linear and right-angle cavities are estimated by Allan variance to be better than 1.6 × 10 − 11 and 2.0 × 10 − 11, respectively, corresponding to a frequency-difference stability of better than 2.9 × 10 − 7. The designed SM-QD-PDH frequency-difference stabilizing system is not only simple but also has better performances than that of the double-modulator QD-PDH frequency-difference stabilizing system. Such a frequency-difference-stabilized two-cavity dual-frequency Nd:YAG laser can be used as an ideal light source for the synthetic-wave absolute-distance interferometric system.
In order to obtain the dual-frequency laser output with tunable frequency-difference, a design scheme of dual-frequency Nd:YAG laser with two standing-wave cavities sharing the common gain medium has been proposed, which is based on the principle of longitudinal mode selection of the Fabry-Perot etalon. Both linear and right-angle cavities including a piece of Fabry-Perot etalon, the p- and s-polarized components of the 1064nm laser will be forced to oscillate simultaneously in single longitudinal mode in the linear and right-angle cavities, respectively. As a result the orthogonally and linearly polarized dual-frequency laser at 1064nm can be output; the frequency-difference can be tuned by adjusting the tilt angles of the intra-cavity Fabry-Perot etalons, the maximum frequency-difference is predicted theoretically to approach the oscillating bandwidth of the Nd:YAG laser. The principles of single longitudinal mode selection and frequency tuning of the Fabry-Perot etalon have been analyzed, and two fused quartz-made Fabry-Perot etalons have been designed and fabricated. An experimental system of diode-pumped two-cavity dual-frequency Nd:YAG laser at 1064nm has been established, the characteristics of single longitudinal mode oscillation and frequency tuning have been investigated experimentally. The orthogonally and linearly polarized dual-frequency laser output at 1064nm has been obtained, the frequency-difference of which being 21GHz and 76GHz, respectively. Such a two-cavity dual-frequency all-solid-state laser will be widely used in the synthetic-wave absolute-distance interferometry and other fields.
To obtain the dual-frequency laser output with large and tunable frequency difference, a design scheme of dual-frequency Nd:YAG laser with two standing-wave cavities sharing the common gain medium has been proposed, which is based on the principles of polarization splitting and single longitudinal mode selection of intracavity Fabry–Perot etalon. With each of the cavities containing a piece of Fabry–Perot etalon, the p- and s-polarized components of the laser at 1064 nm will be forced to oscillate simultaneously in single longitudinal mode in the linear and right-angle cavities, respectively. As a result, the orthogonally and linearly polarized dual-frequency laser at 1064 nm can be obtained. The principle of single longitudinal mode selection by use of the Fabry–Perot etalon has been analyzed, and the Fabry–Perot etalons have been designed. An experimental system of the two-cavity dual-frequency Nd:YAG laser at 1064 nm has been established, and the characteristics of single longitudinal mode oscillation of the two cavities have been investigated experimentally. The orthogonally and linearly polarized dual-frequency laser output at 1064 nm has been obtained; the main characteristics of the oscillating threshold and output power, the polarization state as well as the laser beam quality have been tested experimentally. The frequency difference of the dual-frequency laser has been tuned in turn to 16, 24, 37, and 76 GHz, by slightly adjusting the tilt angles of the intracavity Fabry–Perot etalons. Such a two-cavity dual-frequency Nd:YAG laser will be widely used in the synthetic-wave absolute-distance interferometry and other fields.
KEYWORDS: Nd:YAG lasers, Laser stabilization, Ferroelectric materials, Signal detection, Signal processing, Digital signal processing, Crystals, Optical engineering, Laser applications, Demodulation
To stabilize the frequency-difference of the two-cavity dual-frequency Nd:YAG laser at 1064 nm, a quadrature-demodulated Pound–Drever–Hall (QD-PDH) frequency-difference stabilizing system has been designed, which is composed of two sets of QD-PDH frequency stabilizing subsystems sharing the same Fabry–Perot cavity as the frequency reference. Both phase modulators are driven by the signals with the same frequency of 10 MHz generated by a single direct digital synthesizer (DDS), and the DDS also outputs the other two orthogonal signals as the demodulation reference signals of both frequency stabilizing subsystems. A QD-PDH frequency-difference stabilizing system for a two-cavity dual-frequency Nd:YAG laser with a frequency-difference of ∼24 GHz at 1064 nm has been established and investigated experimentally. The experimental results have indicated that during a period of 1 h, the laser frequency stabilities of the linear and right-angle cavities are estimated by Allan variance to be better than 2.3 × 10 − 11 and 2.7 × 10 − 11, respectively, corresponding to frequency-difference stability of better than 4.2 × 10 − 7. Such a frequency-difference-stabilized two-cavity dual-frequency Nd:YAG laser can be used as an ideal light source for the synthetic-wave absolute-distance interferometric system.
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.
The coherent noise appears in the constructed image of digital holographic microscopy due to the laser source; thus, the imaging quality is degraded. A method of coherent noise reduction using a laterally shifting hologram aperture is presented. An original hologram with coherent noise is captured by a camera first. A series of holograms are sampled by laterally shifting the digital aperture in the original hologram. Instead of extracting the specimen’s part information, each sampled hologram, which includes the whole specimen, is reconstructed. The coherent noise is reduced by averaging the different reconstructed images. The experiment demonstrates the feasibility of the approach. The presented approach with a single recorded hologram realizes the coherent noise reduction without loss of spatial resolution, which is useful for real-time measurement.
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.
The adaptive spatial filtering method is commonly adopted to extract the +1 term spectrum in digital holography for real-time dynamic analysis. However, the typical filtering method is not satisfactory for automatic analysis, because the reset of the filtering window is needed to extract the area of the +1 term spectrum. Therefore, an adaptive spatial filtering method based on region growing and the characteristic of the spectrum separation is proposed. Its filtering window is automatically formed by region growing. The key parameters, including threshold and seed point, are set by the intensity distribution of the hologram spectrum. Then the adaptive filtering extracting the +1 term spectrum is realized by multiplying the hologram spectrum by the filtering window. Compared to the typical filtering method, the experimental results of a microhole array and a phase step show that the proposed method has better adaptability and a higher precision. Moreover, the applicability of this method for different uses is also demonstrated by experiments with a microhole array and a phase step.
The telecentric arrangement in digital holographic microscopy (DHM), considered to be a pure-physical compensation for defocus aberration introduced by microscope objective (MO), shows shift-invariant behavior. Its optical arrangement requires precise adjustment of the distance between MO aperture stop and collimated lens. However, it is difficult to measure and quantify the distance even by monitoring the spatial frequency spectrum of recorded hologram in the absence of object. Thus the misalignment results in the residual defocus aberration in the telecentric arrangement. The total aberrations compensation for misalignment of telecentric arrangement in DHM is presented, in which a posteriori surface fitting method based on Zernike polynomials is performed to eliminate the residual defocus aberration as well as other primary aberrations. The approach reduces the difficulty in precise alignment of the telecentric arrangement and decreases the measurement error caused by aberrations in construction. Three-dimensional retrieval of the height for micro-hole arrays with high-spatial-frequency content demonstrates the feasibility of the method.
Digital holographic microscopy (DHM) has been widely applied for the topography measurement of microscopic
specimen. A total surface fitting method based on Zernike polynomials is presented to remove aberrations in DHM, in
which Zernike polynomial coefficients enable to provide quantitative measurement of primary aberrations. The phase
free of aberrations is obtained by subtracting out the surface fitting result from the reconstructed phase. The method
carries out the total phase aberrations compensation automatically by only one hologram, instead of knowing the
physical parameters of optical setup and the aberration mathematical model in advance. The optical system of off-axis
DHM is set up and the experiment results are given. Compared with the double-exposure method, the Zernike surface
fitting method obtains better phase information owing to removing residual tilt aberration.
In order to obtain the non-overlapping and high-quality reconstructed image, this paper analyzes the system parameters
in digital holographic microscopy. Nowadays a few scholars have analyzed the system parameters which need to satisfy
the sampling theorem and spectrum separation conditions. In this paper, not only the sampling theorem and spectrum
separation but also the size relationship between the reconstructed plane and the magnified image are studied. Then
relationships of system parameters are proposed. First, the maximum object size is directly proportional to the
wavelength and microscope objective focal length, inversely proportional to the sampling interval. Second, the minimum
magnification is described accurately. Finally, the paper gives the range of recoding distance. Experiments further
demonstrate the proposed conclusion’s validity.
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 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.
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