Temporal Wavefront Research Articles

Temporally sliced photon primitives for time‐of‐flight rendering

AbstractWe derive a class of new Monte Carlo estimators for volumetric time‐of‐flight rendering, generalizing prior work on transient photon points and beams. Conceptually, our method starts with any steady‐state photon primitive – like a photon plane, parallelepiped, or parallelotope – and slices it with a temporal wavefront, producing a primitive of one dimension lower. We show how different unbiased temporally sliced primitives arise by analytically integrating any four dimensions within a novel extended spatio‐temporal path space formulation. The differences between these estimators reduce to the determinant of a 4×4 Jacobian matrix, with columns dictated by the chosen dimensions. We then show how to combine the relative strengths of different sliced primitives using multiple importance sampling. Finally, we implement several of the new estimators enabled by our theory and compare them to each other as well as previous techniques.

Robustness of prediction for extreme adaptive optics systems under various observing conditions

Context. For high-contrast imaging systems, such as VLT/SPHERE, the performance of the system at small angular separations is contaminated by the wind-driven halo in the science image. This halo is a result of the servo-lag error in the adaptive optics (AO) system due to the finite time between measuring the wavefront phase and applying the phase correction. One approach to mitigating the servo-lag error is predictive control. Aims. We aim to estimate and understand the potential on-sky performance that linear data-driven prediction would provide for VLT/SPHERE under various turbulence conditions. Methods. We used a linear minimum mean square error predictor and applied it to 27 different AO telemetry data sets from VLT/SPHERE taken over many nights under various turbulence conditions. We evaluated the performance of the predictor using residual wavefront phase variance as a performance metric. Results. We show that prediction always results in a reduction in the temporal wavefront phase variance compared to the current VLT/SPHERE AO performance. We find an average improvement factor of 5.1 in phase variance for prediction compared to the VLT/SPHERE residuals. When comparing to an idealised VLT/SPHERE, we find an improvement factor of 2.0. Under our 27 different cases, we find the predictor results in a smaller spread of the residual temporal phase variance. Finally, we show there is no benefit to including spatial information in the predictor in contrast to what might have been expected from the frozen flow hypothesis. A purely temporal predictor is best suited for AO on VLT/SPHERE. Conclusions. Linear prediction leads to a significant reduction in phase variance for VLT/SPHERE under a variety of observing conditions and reduces the servo-lag error. Furthermore, prediction improves the reliability of the AO system performance, making it less sensitive to different conditions.

High temporal resolution aberrometry in a 50-eye population and implications for adaptive optics error budget.

We formed a database gathering the wavefront aberrations of 50 healthy eyes measured with an original custom-built Shack-Hartmann aberrometer at a temporal frequency of 236 Hz, with 22 lenslets across a 7-mm diameter pupil, for a duration of 20 s. With this database, we draw statistics on the spatial and temporal behavior of the dynamic aberrations of the eye. Dynamic aberrations were studied on a 5-mm diameter pupil and on a 3.4 s sequence between blinks. We noted that, on average, temporal wavefront variance exhibits a n-2 power-law with radial order n and temporal spectra follow a f-1.5 power-law with temporal frequency f. From these statistics, we then extract guidelines for designing an adaptive optics system. For instance, we show the residual wavefront error evolution as a function of the number of corrected modes and of the adaptive optics loop frame rate. In particular, we infer that adaptive optics performance rapidly increases with the loop frequency up to 50 Hz, with gain being more limited at higher rates.

Temporal wavefront stability of an ultrafast high-power laser beam

We measured the temporal dynamics of wavefront aberrations in a beam produced by a commercial ultrafast high-power laser with a research-prototype real-time Hartmann-Shack wavefront sensor. Measurements were performed at two different temporal rates for a 7 mm diameter. Results showed that changes in the wavefront aberrations were always lower than 1%. The main contribution to the total root-mean-square (RMS) wavefront error was due to the effects of low order aberrations (defocus and astigmatism), which persisted even after cavity realignment. The potential improvement in the beam quality after correction of the different aberration modes was also shown. Real-time measurements of laser aberrations while modifying cavity parameters might be a useful tool to improve the beam quality.

Vibration-desensitized fiber-diffraction interferometer for industrial surface measurements

We describe an industrial interferometer designed to conduct high-precision surface measurements in the presence of severe vibration. The principle of common-path interferometry is realized by devising a single-mode fiber waveguide that generates the reference wave directly from the measurement wave, enabling removal of the temporal wavefront fluctuation caused by vibration. In addition, a continuous-scanning phase-measuring method is adopted to isolate spurious vibration residuals in interferometric fringes captured using a high-speed digital camera. Experimental tests prove that the proposed interferometer is suited for in-line measurements of large mirrors, silicon wafers, and flat display panels with no excessive ground isolation for anti-vibration.

Fourier-transform method of data compression and temporal fringe pattern analysis

Temporal fringe pattern analysis is invaluable in studies of transient phenomena but necessitates large data storage for two essential sets of data, i.e., fringe pattern intensity and deformation phase. We describe a compression scheme based on the Fourier-transform method for temporal fringe data storage that permits retrieval of both the intensity and the deformation phase. When the scheme was used with simulated temporal wavefront interferometry intensity fringe patterns, a high compression ratio of 10.77 was achieved, with a significant useful data ratio of 0.859. The average root-mean-square error in phase value restored was a low 0.0015 rad. With simulated temporal speckle interferometry intensity fringe patterns, the important paremeters varied with the modulation cutoff value applied. For a zero modulation cutoff value, the ratio of data points and the compression ratio values obtained were roughly the same as in wavelength interferometry, albeit the average root-mean-square error in the phase value restored was far higher. By increasing the modulation cutoff value we attained significant reduction and increase in the ratio of data points and the compression ratio, respectively, whereas the average root-mean-square error in the restored phase values was reduced only slightly.

Basin-scale internal-wave tomography using a large-aperture vertical array

Basin-scale acoustic transmissions which are received at a large-aperture vertical line array (VLA), like those deployed for the Acoustic Thermometry of Ocean Climate (ATOC) program, provide several acoustic fluctuation observables that can be used for internal-wave tomography. A single receiver provides observations of wavefront travel-time variance, pulse time spread, and temporal signal coherence. A VLA adds the observations of vertical wavefront coherence and modal time spread and time coherence. The combination of wavefront and modal observations provides tomographic vertical resolution of average internal-wave energies as a function of depth. In addition, vertical and temporal wavefront coherences are complementary observations, since spatial and temporal internal-wave variabilities are related through the dispersion relation. Also, vertical and temporal coherences help test the assumption of a separable internal-wave spectrum in terms of frequency and vertical wave number. First efforts to combine several of these acoustic fluctuation observations from the ATOC North Pacific VLAs in an internal-wave tomographic analysis will be presented. Directions for future research will be discussed.

Chaotic wavefront propagation in coupled map lattices

Chaotic wavefront propagation is numerically studied, with the use of coupled map lattices. If the front propagates with “velocity of light”, noise-induced period doublings are observed. For the “sublight” propagation there exist resonances leading to a regular temporal wavefront structure.