Optical surface reconstruction technique through combination of zonal and modal fitting

Adaptive optics for a time-resolved Förster resonance energy transfer (FRET) and fluorescence lifetime imaging microscopy (FLIM) in vivo

Förster resonance energy transfer (FRET) and fluorescence lifetime imaging (FLIM) have been coupled with multiphoton microscopy to image in vivo dynamics. However, the increase in optical aberrations as a function of depth significantly reduces the fluorescent signal, spatial resolution, and fluorescence lifetime accuracy. We present the development of a time-resolved FRET-FLIM imaging system with adaptive optics. We demonstrate the improvement of our adaptive optics (AO)-FRET-FLIM instrument over standard multiphoton FRET-FLIM imaging. We validate our approach using fixed cellular samples with FRET standards and in vivo with live imaging in a mouse kidney.

Algorithm based on the optimal block zonal strategy for fast wavefront reconstruction

Fast wavefront reconstruction is crucial for improving the temporal frequency of adaptive optics systems, in which a mass of subapertures is used. In this paper, we present a novel block zonal reconstruction algorithm based on Southwell geometry to speed up the wavefront reconstruction from Shack-Hartmann wavefront sensor measurements. Therein, we use the theory of computational complexity to install a novel optimal block zonal strategy to get the best size of the subwavefront and give the verification through simulations. Compared with the classical Southwell entire wavefront reconstruction algorithm, the algorithm based on the optimal block zonal strategy needs only a few milliseconds to finish the reconstruction process from 100×100 subapertures. Moreover, we analyze the superiority to use our algorithm to realize the phase reconstruction of the unconnected subwavefront, which cannot be reconstructed via traditional methods. Further, the simulation and experiments show that the precision of the algorithm based on the proposed optimal block zonal strategy is comparable with the commercial wavefront sensor HASO, the time consumption is much less than that of the traditional zonal reconstruction, and it is applicable to the square wavefront, circular wavefront, and local unconnected wavefront. Our proposed algorithm can be widely utilized in astronomical observation, laser transmission, and remote sensing.

Improved method for rapid shape recovery of large specular surfaces based on phase measuring deflectometry

Incorporating the modal and zonal estimation approaches into a unifying scheme, we introduce an improved three-dimensional shape reconstruction version of specular surfaces based on phase measuring deflectometry in this paper. The modal estimation is first implemented to derive the coarse height information of the measured surface as initial iteration values. Then the real shape can be recovered utilizing a modified zonal wavefront reconstruction algorithm to simultaneously achieve consistently high accuracy and dramatically rapid convergence. Moreover, the iterative process based on an advanced successive over-relaxation technique shows a consistent rejection of measurement errors, guaranteeing the stability and robustness in practical applications. The reconstruction results of numerical examples of the sphere, hyperbolic, and arbitrary surfaces, as well as an experimentally measured sphere mirror demonstrate the validity and efficiency of the proposed improved method. In the simulations, the proposed method increases the rate of convergence by fourfold compared with the existing zonal approach and realizes three orders of magnitude improvement in reconstruction accuracy compared with the modal technique when handling the sample points of 401×401  pixels of a sphere surface. Furthermore, the computation time decreases approximately 74.92% in contrast to the zonal estimation, and the surface error is about 6.68 μm with reconstruction points of 391×529  pixels of an experimentally measured sphere mirror. In general, this new method can be conducted with fast convergence speed and high accuracy, providing an efficient, stable, and real-time approach for shape reconstruction in practical situations.

Eigencorneas: application of principal component analysis to corneal topography

PURPOSE

To determine the minimum number of orthonormal basis functions needed to accurately represent the great majority of corneal topographies from a normal population.

METHODS

Principal Component Analysis was applied to the elevation topographies of the anterior and posterior corneal surfaces and central thickness of 368 eyes of 184 healthy subjects. PCA was applied directly to the input elevation data points and after fitting them to Zernike polynomials (up to 8th order, 8 mm diameter). The anterior and posterior surfaces, as well as right eye and left eye data, were analysed both separately and jointly. A threshold based on the amount of explained variance (99%) was applied to determine the minimum number of basis functions (eigencorneas) or degrees of freedom (DoF) in the population.

RESULTS

The eigenvectors directly obtained from elevation data resemble Zernike polynomials. The separate principal component analysis on the Zernike coefficients of anterior and posterior surfaces yielded 5 and 9 DoF, respectively. An additional reduction to 11 DoF (instead of 15 DoF) was achieved when performing a joint PCA that included both surfaces as well as central thickness. Finally, a further reduction was obtained by pooling right and left eye data together, to only 18 DoF.

CONCLUSIONS

The combination of Zernike fit and Principal Component Analysis yields a strong reduction of dimensionality of elevation topography data, to only 19 independent parameters (18 DoF plus population average), which indicates a high degree of correlation existing between anterior and posterior surfaces, and between eyes. The resulting eigencorneas are especially well suited for practical applications, as they are uncorrelated and orthonormal linear combinations of Zernike polynomials.

Describing the corneal shape after wavefront-optimized photorefractive keratectomy

PURPOSE

To develop a procedure for describing wavefront-optimized photorefractive keratectomy (PRK) corneas and to characterize PRK-induced changes in shape.

METHODS

We analyzed preoperative and postoperative corneal elevation data of 41 eyes of 41 patients (mean [±SD] age, 38 [±11] years) who underwent a myopia-correcting (preoperative spherical equivalent refraction -3.9 [±1.5] diopters) wavefront-optimized PRK, assessed with Scheimpflug imaging. Zernike polynomials were fitted to the elevation data. The diameter of the greatest corneal zone that could be analyzed and the number of Zernike orders needed to make a reliable fit were determined, based on the fitting error. The PRK-induced changes in corneal shape were studied.

RESULTS

All subjects could be included for analysis of zones up to 6 mm in diameter. This was 90, 83, and 44% for 7, 8, and 9 mm, respectively. The number of Zernike orders (terms) needed for an accurate fit ranged from four (15) for a 4-mm analyzed zone diameter to eight (45) for 8 mm. For the anterior surface, the spherical aberration term decreased significantly (p < 0.01) after PRK for the 4-mm analyzed zone diameter (-0.09 μm), remained unchanged for 5 mm (+0.01 μm; p = 0.56), and increased significantly for 6 mm (+0.40 μm) and above (p < 0.01). There was no significant change in any other higher-order Zernike term, but the square root of the sum of the squares of all higher-order terms increased significantly for all analyzed zone diameters. Photorefractive keratectomy did not influence the posterior corneal shape.

CONCLUSIONS

The cornea after wavefront-optimized PRK can be described as accurately as a healthy cornea and with a similar number of Zernike polynomials. The anterior corneal shape changes significantly after treatment, whereas the posterior corneal shape remains unchanged. The observed effect of wavefront-optimized ablation on the spherical aberration term depends on the diameter of the analyzed zone.