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

Kwanjun Park,Taedong Kong,Hyuk Soon Choi,Jung Min Lee,Hyung-Jin Kim,Hoon Jai Chun,Youngwoon Choi,Beop-Min Kim,Taeseok Daniel Yang

doi:10.1038/s41598-018-38027-y

Abstract

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.

Highlights

Accurate visualization of an object of interest often provides immediate solutions for problems under consideration
When being illuminated with a plane wave, the object generates a wave, EOP(x′, y′), where (x′, y′) is the spatial coordinate for object plane (OP). When this wave propagates through the imaging system, the light disturbance resulting in the output image EIP(x, y) can be described by the transmission matrix T of the optical system as[17,19,20]
Acquiring a huge data set is essential for the transmission matrix (TM) inversion method, the concomitant increase in the processing time significantly ruins the benefit of the slight increase in the image quality

Summary

Introduction

Accurate visualization of an object of interest often provides immediate solutions for problems under consideration. The variation of magnification along the radial direction causes image deformation, which is known to appear as a pincushion or a barrel distortion These two types of distortion, focal and spatial distortion, make the compact optical systems equipped with wide-viewing lenses in such small dimensions non-suitable for high-resolution and high-precision measurements. The environmental aberration was shown to be corrected with the AO technique in the presence of multiple scattering[14] These methods have been successful in suppressing the image deterioration induced by the aberrant effect, but the level of complexity required for their implementation is very high due to the requirement for the wavefront control by optical instruments such as spatial light modulators (SLMs), digital micro-mirror devices (DMDs), and deformable mirrors (DMs). The TM-based image reconstruction has lagged far behind real-time imaging, even in the case of simple aberration correction

Methods

Results

Conclusion