Maréchal condition and the effect of aberrations on Strehl intensity

Use of pupil-difference moments for predicting optical performance impacts of generalized mid-spatial frequency surface errors

In this work, we present a methodology for predicting the optical performance impacts of random and structured MSF surface errors using pupil-difference probability distribution (PDPD) moments. In addition, we show that, for random mid-spatial frequency (MSF) surface errors, performance estimates from the PDPD moments converge to performance estimates that assume random statistics. Finally, we apply these methods to several MSF surface errors with different distributions and compare estimated optical performance values to predictions based on earlier methods assuming random error distributions.

The Effect of the Position Determination Error for Flexible Linear Array Elements on the Tomogram Focusing

In the article, the study of the quality of tomogram focusing during the inspection of objects with curved surfaces by flexible acoustic array was described. The main goal of the study was theoretically and experimentally define the acceptable deviation limits of the elements' coordinates values. The tomogram reconstruction was performed by the total focusing method. The Strehl ratio was chosen as a criterion for assessing the quality of tomogram focusing. The ultrasonic inspection procedure were simulated and validated experimentally by means of convex and concave curved arrays. In the study, it was proven that the elements coordinates of the flexible acoustic array were determined with an error of no more than 0.18λ and the tomogram image was obtained in sharp focus.

Inversion-free image recovery from strong aberration using a minimally sampled transmission matrix

A transmission matrix (TM), a characteristic response for an input-output relation of an optical system, has been used for achieving diffraction-limited and aberration-free images through highly-aberrant imaging systems. However, its requirement of acquiring a huge-size TM along with its heavy computational load limit its widespread applications. Here we propose a method for TM-based image reconstruction, which is more efficient in terms of data manipulation and computational time. Only 10% of the TM elements for a fish-eye (FE) lens with strong aberration were sampled compared to that required for the image reconstruction by the conventional inversion method. The missing information was filled in by an iterative interpolation algorithm working in k-space. In addition, as a replacement of the time-consuming matrix inversion process, a phase pattern was created from the minimally sampled TM in order to compensate for the angle-dependent phase retardation caused by the FE lens. The focal distortion could be corrected by applying the phase correction pattern to the angular spectrums of the measured object images. The remaining spatial distortion could also be determined through the geometrical transformation also determined by the minimally sampled TM elements. Through the use of these procedures, the object image can be reconstructed 55 times faster than through the use of the usual inversion method using the full-sized TM, without compromising the reconstruction performances.

Strehl ratio as the Fourier transform of a probability density of error differences

To give useful insight into the impact of mid-spatial frequency structure on optical performance, the Strehl ratio is shown to correspond to the Fourier transform of a simple statistical characterization of the aberration in the exit pupil. This statistical description is found simply by autocorrelating a histogram of the aberration values. In practice, the histogram itself can often be approximated by a convolution of underlying histograms associated with fabrication steps and, together with the final autocorrelation, it follows from the central limit theorem that the Strehl ratio as a function of the scale of the phase error is generally approximated well by a Gaussian.