The Application of Piecewise Regularization Reconstruction to the Calibration of Strain Beams.

Standard beams are mainly used for the calibration of strain sensors using their load reconstruction models. However, as an ill-posed inverse problem, the solution to these models often fails to converge, especially when dealing with dynamic loads of different frequencies. To overcome this problem, a piecewise Tikhonov regularization method (PTR) is proposed to reconstruct dynamic loads. The transfer function matrix is built both using the denoised excitations and the corresponding responses. After singular value decomposition (SVD), the singular values are divided into submatrices of different sizes by utilizing a piecewise function. The regularization parameters are solved by optimizing the piecewise submatrices. The experimental result shows that the MREs of the PTR method are 6.20% at 70 Hz and 5.86% at 80 Hz. The traditional Tikhonov regularization method based on GCV exhibits MREs of 28.44% and 29.61% at frequencies of 70 Hz and 80 Hz, respectively, whereas the L-curve-based approach demonstrates MREs of 29.98% and 18.42% at the same frequencies. Furthermore, the PREs of the PTR method are 3.54% at 70 Hz and 3.73% at 80 Hz. The traditional Tikhonov regularization method based on GCV exhibits PREs of 27.01% and 26.88% at frequencies of 70 Hz and 80 Hz, respectively, whereas the L-curve-based approach demonstrates PREs of 29.50% and 15.56% at the same frequencies. All in all, the method proposed in this paper can be extensively applied to load reconstruction across different frequencies.

Spherical wavefront measurement on modified cyclic radial shearing interferometry.

We propose a radial shearing interferometric approach to measure spherical wavefronts as both of the reflective and transmissive optical configurations. The modified cyclic radial shearing interferometer uses a single lens in the optical layout, which can conveniently adjust the radial shearing ratio between two shearing spherical wavefronts, and the use of a polarization camera enables to reconstruct the wavefront by a single image. The wavefront mapped onto the camera plane can be identified and quantified throughout an optimized wavefront reconstruction algorithm. In the experiments, plano-convex lenses and concave mirrors were used to generate spherical wavefronts, and the proposed system was able to reconstruct the surface figures after system characterization and calibration. Further investigations were performed to evaluate the system measurement accuracy by the radius of curvature comparison with design value and a commercial Shack-Hartmann wavefront sensor.

Correction of the air refractive index using a two-color method for absolute distance measurement without a dead zone.

In the fields of satellite formation, large-scale manufacturing, and ultra-precision machining, high-precision ranging based on the femtosecond laser is one of the necessary technologies. However, the fluctuations of the air refractive index and the limited tuning range of repetition rate restrict the measurement precision and range. Using only one femtosecond comb that corrects the air refractive index simultaneously, a method for ranging without the dead zone of measurement is described. A delay optical path is established in the ranging system to eliminate the dead zone of measurement by a comb. Meanwhile, in order to ensure the consistency of the pulse sequence between the fundamental frequency beam and the second-harmonic beam after the delay optical path, the second-harmonic beam generates on the delay optical path after the fundamental harmonic passes the long fiber. A two-color method is used to correct the effect of the air refractive index. The experimental result demonstrates the measurement precision of 7.2 µm at ∼0.8m with correction of the air refractive index, and the precision of measurement is 8.4 µm at ∼2.2m. Finally, the maximum deviation between our system and the reference standard is 5.0 µm.

Diverging cyclic radial shearing interferometry for single-shot wavefront sensing.

In this investigation, we describe a simple cyclic radial shearing interferometer for single-shot wavefront sensing. Instead of using the telescope lens system used in typical radial shearing interferometry, a single lens is used to generate two diverging radial shearing beams. This simple modification leads to the advantages of conveniently adjusting the radial shearing ratio, compactness of the system, and practical ease of alignment. With the aid of a polarization pixelated CMOS camera, the spatial phase-shifting technique is used to extract the phase with a single image. The most important feature is the fringe contrast enhancement by reducing the aberrations caused by the complicated optical system even though an incoherent light is used. The experimental results show the fringe contrast enhancement is at least 0.1 better than that of the conventional method, and the wavefronts are properly reconstructed with less than 0.071λ root-mean-squared wavefront error regardless of the coherence of the light.

Surface profile measurement of doped silicon using near-infrared low-coherence light.

A scanning interferometry system based on near-infrared low-coherence interferometry by using a superluminescent diode (SLD) as the light source is presented. The system cannot only measure the surface profile of doped double-sided polished silicon but also measure its optical thickness and refractive index. The measurement system uses near-infrared CCD to detect interferometric light in the near infrared, based on the Michelson interference principle. SLD has low temporal and high spatial coherence and high penetration to doped silicon wafers; thus, higher visibility can be obtained when measuring the rear side. Meanwhile, the optical thickness measured by low coherent scanning interference is compared with the optical thickness obtained by spectrally resolved interferometry to verify the accuracy of the system. Due to the periodic characteristics of interference fringes, the coherence length of the narrowband light source is usually greater than the path length difference of the interferometer. It gives the measurement a phase ambiguity of 2π, which may severely limit the application of the measurement. However, the short coherent length SLD light source used in the project can avoid 2π phase ambiguity problems. Besides, this system can perform full scanning in a larger step and achieve rapid on-line measurement of the target surface.