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Aerial LiDAR measurements at 7474 oil and gas production facilities in the Permian Basin yield a measured methane emission rate distribution extending to the detection sensitivity of the method, 2 kg/h at 90% probability of detection (POD). Emissions are found at 38.3% of facilities scanned, a significantly higher proportion than reported in lower-sensitivity campaigns. LiDAR measurements are analyzed in combination with measurements of the heavy tail portion of the distribution (>600 kg/h) obtained from an airborne solar infrared imaging spectrometry campaign by Carbon Mapper (CM). A joint distribution is found by fitting the aligned LiDAR and CM data. By comparing the aerial samples to the joint distribution, the practical detection sensitivity of the CM 2019 campaign is found to be 280 kg/h [256, 309] (95% confidence) at 50% POD for facility-sized emission sources. With respect to the joint model distribution and its confidence interval, the LiDAR campaign is found to have measured 103. 6% [93.5, 114.2%] of the total emission rate predicted by the model for equipment-sized emission sources (∼2 m diameter) with emission rates above 3 kg/h, whereas the CM 2019 campaign is found to have measured 39. 7% [34.6, 45.1%] of the same quantity for facility-sized sources (150 m diameter) above 10 kg/h. The analysis is repeated with data from CM 2020−21 campaigns with similar results. The combined distributions represent a more comprehensive view of the emission rate distribution in the survey area, revealing the significance of previously underreported emission sources at rates below the detection sensitivity of some emissions monitoring campaigns.

Gradient-index (GRIN) media offer advantages over thin optical elements for beam shaping of strongly diffracting fields. A numerical GRIN design method is presented, where diffraction effects are considered in solving for the refractive index profile. The index profile is found by specifying a desired beam transformation throughout the GRIN volume and solving a series of phase retrieval problems. A Gaussian to flat-top beam shaper and a coherent beam combiner are shown as examples. Reduced beam distortion is demonstrated in comparison to a purely geometric design method.

Aerial LiDAR measurements of methane emissions at 7920 oil and gas production facilities in the Permian Basin yield an emission rate distribution extending to the detection sensitivity of the method, 2 kg/h at 90% probability of detection. The LiDAR measurements are analyzed in combination with the heavy tail portion (> 600 kg/h) of a distribution obtained from an intensive airborne solar infrared imaging spectrometry study by Cusworth et al. to yield a more complete emission rate distribution. Comparison of the data sets supports an assessment of the detection sensitivity of the solar infrared study at 300 kg/h at 50% probability of detection. Emissions detected by LiDAR increase the total emission rate for the survey region by a factor of 3.0 after controlling for scale factors such as survey area and number of scans per facility. Additionally, the role of spatial aggregation is highlighted as the cumulative emission rate distribution shifts toward larger source emission rates by a factor of three when detections are aggregated to facility size scales (150 m) rather than resolved to equipment size scales (2 m). The combined distribution derived for this study represents previously underreported emission sources at rates below 300 kg/h resolved at equipment-level spatial precision.

In this paper gradient-index beam shapers are fabricated using the ultrafast laser inscription method. This method enables the fabrication of two-dimensional refractive index profiles inside silica glass, resulting in highly robust and compact beam shapers. The magnitude of this refractive index change can be tailored by adjusting the laser pulse energy, enabling arbitrary two-dimensional refractive index profiles to be manufactured. The process is then demonstrated by fabricating planar waveguides with quadratic index profiles that predictably resize Gaussian beams. Then a more complex two-dimensional refractive index profile is fabricated to transform an input Gaussian beam into a super-Gaussian (flat-top) beam.

A numerical design method is demonstrated for gradient refractive index (GRIN) beam shapers embedded in a medium. The three-dimensional refractive index profile Δn(x, y, z) gradually changes the spatial characteristics of a beam during propagation. Diffraction effects such as beam expansion are controlled and compensated by the refractive index profile, resulting in efficient field transformations with no coherent artifacts. The solution is found using phase retrieval and a paraxial scalar wave beam propagation model. An example design is shown in which small changes in refractive index (Δn < 10−3) are used to transform a beam over a device length of 10 mm.

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