Abstract

Numerical and analytical techniques are presented that allow three-dimensional, asymmetric, refractive index fields to be reconstructed from optical pathlength measurements, which can be obtained using multidirectional holographic interferometry. Analytical reconstruction techniques that have been used in radioaptronomy and electron microscopy for a number of years, and recently in interferometry, are presented in the context of interferometric applications in the refractionless limit. These techniques require that optical pathlength data be collected over a 180° angle of view. The required pathlength sampling rate is discussed. An efficient numerical procedure is developed for direct inversion of the data. Several numerical techniques are developed that do not require that data be collected over a full 180° angle of view. All such techniques require redundant data to achieve accurate reconstructions. The required degree of redundancy increases as the angle of view decreases. Numerical simulations using six different reconstruction techniques indicate that with a 180° angle of view, all are capable of providing accurate reconstructions. Four of the techniques were used to analyze simulated interferometric data recorded over an angle of view of less than 180°. Examples of reasonably accurate reconstructions using data with angles of view as low as 45° are presented.

© 1973 Optical Society of America

Tomography for reconstructing continuous fields from ill-posed multidirectional interferometric data

Soyoung S. Cha and Hongwei Sun
Appl. Opt. 29(2) 251-258 (1990)

Three-dimensional image reconstruction using interferometric data from a limited field of view with noise

S. Bahl and J. A. Liburdy
Appl. Opt. 30(29) 4218-4226 (1991)

Reconstruction of multidirectional interferometric data using an isoparametric finite-element method

Yan Zhang and Gary A. Ruff
Appl. Opt. 34(28) 6361-6372 (1995)

Tomographic reconstruction of three-dimensional refractive index fields by use of a regularized phase-tracking technique and a polynomial approximation method

Chao Tian, Yongying Yang, Yongmo Zhuo, Tao Wei, and Tong Ling
Appl. Opt. 50(35) 6495-6504 (2011)

Weighted reconstruction of three-dimensional refractive index in interferometric tomography

Satoshi Tomioka, Shusuke Nishiyama, Naoki Miyamoto, Daichi Kando, and Samia Heshmat
Appl. Opt. 56(24) 6755-6764 (2017)