KEYWORDS: Carbon dioxide, LIDAR, Signal detection, Absorption, Denoising, Signal processing, Modal decomposition, Pulse signals, Interference (communication), Signal to noise ratio
Differential Absorption Lidar (DIAL) serves as a pivotal technique for profiling atmospheric CO2 concentrations, yet its efficacy is hampered by the presence of noise. Traditional denoising methods, such as Empirical Mode Decomposition (EMD) and its variant (EEMD), have been employed to mitigate this issue. However, these methods are not underpinned by a robust mathematical framework and are prone to the phenomenon of mode mixing, which can compromise the quality of signal decomposition. In this research, we present a novel denoising method for Differential Absorption Lidar (DIAL) signals, employing Successive Variational Mode Decomposition (SVMD) integrated with Pearson correlation coefficients. The algorithm initiates by decomposing the echo signal into a multitude of intrinsic mode functions (IMFs) through the SVMD process. Subsequently, Pearson correlation coefficients are utilized to quantitatively assess the degree of similarity between each IMF and the original signal. Only those IMFs that meet a pre-defined threshold of similarity are integrated back into the reconstruction process, yielding a refined, denoised signal. The efficacy of our proposed denoising methodology is substantiated through a comparative analysis with simulated DIAL echo signals. The results highlight the algorithm's ability to effectively reduce noise in echo signals, thereby improving the precision and effective range of CO2 concentration profile retrievals.
Fizeau interferometry is widely used to measure the surface of optical components and the wavefront aberration of optical systems due to common-path configuration, high accuracy and easy implementation. However, due to the existence of wavefront slope, when the transmission light is not perfectly perpendicular to the reflection flat (RF), the gap between the RF and the test piece will cause the reflected beam to be slightly misaligned from the transmission beam in the transmission test, which is also called beam walk-off error. If the beam walk-off error is less than 1/4 of the pixel spacing, its effects can be ignored. In this work, we will analyze the wavefront slope tolerance of 800mm aperture Fizeau interferometry and suppress it by optimizing the design of the beam expansion system, which is the key component that affects the overall wavefront slope. For the camera with 2048×2048 pixel array, the wavefront slope should be less than 9.77μrad to neglect the influence of beam walk-off error within a cavity length of 5000mm. To obtain the 800mm aperture test light, a Galilean beam expander is designed to expand and collimate the 100mm aperture light into an 800mm aperture test light. Compared with the Keplerian design, the Galilean design can decrease spherical aberration by the combination of positive and negative lenses. Tested by interferometry, the slope of the transmitted wavefront of the Galilean beam expander is 3.83μrad, which ensures the high-precision measurement.
Holograms captured by digital holographic microscopic systems that use high-coherence lasers as light sources are heavily influenced because of coherent noise. The contrast of interferograms will be affected although coherent noise can be suppressed by using short coherence light sources. This paper develops a reflective common-path digital holographic microscopy (DHM) combined with partially coherent illumination. The light is scattered by a rotating diffuser and coupled into a multimode fiber, which form into an extended light source. After passing through an imaging system, the designed blazed grating generated by spatial light modulator (SLM) works as a polarization point diffraction plate at the Fourier plane, which has a circular area playing the role of a reflective pinhole at the position corresponded to the image of the multimode fiber. Being benefit from the polarization-selective modulation property of the particular blazed grating, polarization directions of diffracted component and non-diffracted component are modulated to be orthogonal. Because of the common-path configuration, the length of the object and reference path is equal and high contrast polarization phase-shifted interferograms are captured by polarization camera. Quantitative phase images are further obtained. A resolution target and a standard step plate are measured with the proposed system. The result of the resolution target shows that the lateral resolution is 715nm at least, which is higher than the reference method and close to the diffraction limit. Otherwise, the measured height of the standard step plate is 92nm and has only 4.76% deviation from the actual height, which represents high vertical resolution.
The measurement of large aperture optical components becomes much more critical as they are increasingly being used in high power systems and astronomical systems. Large aperture transmissive optical elements always suffer from stressinduced birefringence, which leads to the difference of profiles for linearly polarized beams with different orientations. A spatially varying optical path difference is introduced into the measurement result as wavefront aberration in a dynamic interferometer based on the polarization phase-shifting method. This paper proposed a method to measure and correct the birefringence effect for a 600mm aperture dynamic interferometer based on the rotation of the incident polarized beam, needing no more additional elements. The interferometer includes a Kepler beam expander system consisting of two collimators with 100mm and 600mm aperture. The 600mm aperture collimator is viewed as a transmitting element between the interference cavity of a 100mm TF and a 600mm RF. The polarization state of the incident beam can be switched between P light and S light, where a phase difference can be obtained between two measurements. The difference between the two distributions can be viewed as the birefringence effect on the dynamic interferometer. Besides, the system error can be removed during the data subtraction. Experiments are conducted on a 600mm dynamic interferometer and the correction result is compared with a wavelength tuning method which is free of polarization errors brought by the stress-induced birefringence stress. A comparison is also conducted with the correction result realized via a wave plate model proposed before.
Null interferometric microscope (NIM) is an effective method for detecting the isolated defects on the ICF capsule’s surfaces thanks to its null interference and high-resolution imaging ability. However, the limited depth-of-focus (DOF) caused by the large numerical aperture is the main drawback that prevents measuring defects in the full field of view (FOV) on the curved surface. In this work, a depth-of-focus (DOF) extension method based on numerical propagation is proposed to expand the field of view (FOV) of the NIM. The capability of the proposed DOF extension method is proved by the measurement of a 1-mm diameter ICF capsule. Experiment results indicate that the FOV of NIM is expanded from 140 μm to 320 μm.
For a simultaneous phase-shifting interferometer (SPSI), typically four interferograms with different phase shifts are captured at different areas on the detector target by a single-shot capture method. Prior to calculating phase distribution, the region segmentation should be conducted to obtain four separated interferograms. A registration method is also necessary to eliminate the mismatch errors between the interferograms. A spatial mismatch calibration method based on fast partial phase correlation is proposed to register the spatial positions between the phase-shifting interferograms. By tilting the reflective flat, four carrier interferograms are captured to extract four phase distributions using the Fourier transform technique. Partial phase distribution is used as match characteristics to register the interferograms rapidly by employing the correlation operation. The simulation and experimental results show that the ripple error generated by spatial mismatch is suppressed well by the proposed method.
In this paper, we demonstrate a spectral beam combining scheme of two ytterbium-doped fiber lasers, running at different wavelengths. An edge filter with high damage threshold (>20 MW/cm2 ) and steep rising edge (<2 nm) is employed as the combining element to overlap the two output beams in the near and far fields. 6.2 kW combined output power is achieved with an efficiency of 97%, which proves the high efficiency of the filter for both the reflection and transmission cases. Despite the broad emission spectrum of the single channel, the beam quality of the output is approximate with the incident emitters in horizontal and vertical directions. In terms of the measurement result conducted with thermal imaging camera, the growth of temperature on the edge filter during the combining process is well within the acceptable range. Compared with the grating based spectral beam combining (SBC) schemes, it permits the efficient combining of broader spectrum and arbitrarily large beams, which shows the potential of the filter-based spectral beam combination system. Scaling by additional and more powerful channels, higher combined output power appears to be feasible.
The conjugate differential method has been applied to the absolute test of flat, cylindrical, and axicon surfaces. In the
previous work, simulations and correspond experiments have been carried out to verify the feasibility of the method. To
analyze the influences of different factors upon the measurement result, the conjugate differential method is discussed in
detail. Considering the characteristics of the test surface such as surface types and surface profiles, the application ranges
of the conjugate differential method are discussed into three parts. According to the three surface types using the
conjugate differential method, the method can be extended to the absolute test of the spherical surfaces based on
spherical coordinate system. The reconstructed errors caused by different aberrations expressed as Zernike polynomial
terms show that they are more sensitive to high order aberration terms of the surface under test. And for surfaces with
different frequency distributions, the surface with less mid-spatial frequency information is less sensitive to the sampling
frequency. The influence from the other factors in interferometric test are also discussed into three parts. The influences
from the uncertainty of shifts are correlated with the increased aperture diameters, since the integration error caused by
the shift error increases gradually with the expanding of the integration path. The integration error changes by the
influences from the coherent noise and pixel noise related to pixel deviations. The reconstructed deviations get increased
while the peak pixel deviation is increasing. For the balance of the differential deviation and integration error, the
optimization of sampling resolution should take considered for accuracy improvement.
Multilayer defects which reside on the top or inside the multilayer are one of the most critical concerns in the extreme ultraviolet lithography (EUVL) manufacturing process. We proposed the transport of intensity equation and partial least-square regression (TIE & PLSR) method to inspect the defect and reconstruct its geometric parameters: height and full width at half maximum (FWHM). The transport of intensity equation (TIE) is employed to retrieve the phase of the multilayer defect from the two scattering images, which collected at two adjacent propagation distances. Comparing the simulated ideal phase, the phase deformations caused by different top heights and widths of the defects are analyzed. The optical properties maximum, minimum and fitting Zernike coefficients are used to parameterize the phase deformation. Partial least-squares regression (PLSR) is applied to associate the optical properties of the phase deformation with the geometric parameters of the defects, and reconstruct geometric parameters of the measured defect from the established data library. The reconstruction error is less than 0.2% in simulation experiment.
An absolute testing method for cylindrical surfaces is presented in a null test setup with a computer-generated hologram. The absolute test exploits the symmetry of cylinders, which allows us to introduce a certain shift of the test surface both parallel to and rotated about the centerline while the null test condition is still maintained. With two shifts of the cylindrical surface, four measurements belonging to two groups in conjugate positions can be accomplished to obtain the absolute differential map with the interferometer and null optics errors removed. The absolute surface can be obtained by wavefront reconstruction from local differential data. A simulation of the method is presented to estimate the error propagation. Experimental absolute test results of a concave cylindrical surface with 100-mm radius are given. The measured profiles are compared with those obtained from a commercial profiler, showing a difference of less than 15 nm (root-mean-square).
Optical freeform surfaces are complex surfaces with non-rotational symmetry that break through the limitations of conventional optical element, and are widely used in advanced optics application for system configuration simplifying and performance enhancing. Due to the geometrical complexity and optical particularity of optical freeform surfaces, there is, as yet, a lack of precision freeform surfaces testing. Computer generated hologram (CGH) null testing method are discussed in this paper to test the optical freeform surfaces such as off-axis aspheric surfaces. CGH design based on ray tracing and NURBS interpolation are included. Simuation in Zemax is given to verify the result of calculation. The alignment and fiducial sections are added to the CGH to lead the alignment of the freeform surface and CGH with sixdimensional adjustment. The CGH was designed and fabricated to test an off-axis aspheric with Fizeau configuration.
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