Phase distribution analysis of tissues based on the off-axis digital holographic hybrid reconstruction algorithm

Abstract

Off-axis digital holography (DH) has great potential in histopathology for its high efficiency and precision. Phase distribution, usually extracted by the angular spectrum (AS) algorithm from a digital hologram, reflects important structural information of biological tissues. However, the complex structure of tissues introduces spectrum aliasing of the hologram, making the AS algorithm hard to realize and accurate phase analysis difficult to conduct. Here, we present a hybrid reconstruction algorithm, combining Fresnel reconstruction in spatial domain with the AS algorithm in frequency domain, to solve aliasing by spatial filtering. Through simulation, we demonstrate the feasibility and superiority of the hybrid algorithm and verified the precision (10^-3 rad) of the hybrid algorithm with spectrum aliasing. We extract phase distributions from normal urothelial and bladder cancer tissues by the hybrid algorithm and make quantitative analysis through histogram and standard deviation. The result shows the hybrid algorithm in off-axis DH has great advantage for the high-precision phase extraction of tissues and supplies significant information for cancer diagnosis.

Keywords: (070.6110) Spatial filtering; (090.1995) Digital holography; (100.5070) Phase retrieval; (170.6930) Tissue.

Fig. 1

Schematic diagram of optical system.

Fig. 2

Basic procedure of hybrid algorithm.

Fig. 3

Simulated digital hologram: (a) phase distribution; (b) amplitude distribution; (c) simulated off-axis digital hologram based on (a) and (b).

Fig. 4

Spectrum of simulated hologram and object information selection by two algorithm: (a) spectrum of simulated hologram; (b) spectrum of zero-order diffraction; (c) new hologram without spectrum aliasing; (d) spectrum of new hologram; (e) image of Fresnel amplitude reconstruction and spatial filtering; (f) complete object spectrum after back calculation.

Fig. 5

Phase distributions: (a) 2D phase distribution extracted by hybrid algorithm; (b) 2D phase distribution extracted by AS algorithm; (c) comparison of phase curves.

Fig. 6

Error analysis without spectrum aliasing: (a) hybrid algorithm error value distribution; (b) AS algorithm error value distribution; (c) histogram.

Fig. 7

Spectral selection: (a) spectrum of simulated hologram; (b) image of Fresnel amplitude reconstruction and spatial filtering; (c) complete object spectrum after back calculation.

Fig. 8

Phase distribution: (a) and (b) 2D phase distributions extracted by AS algorithm; (c) 2D phase distribution extracted by hybrid algorithm; (d) comparison of phase curves.

Fig. 9

Error analysis with spectrum aliasing: (a) and (b) error value distributions of AS algorithm1 and AS algorithm2; (c) error value distributions of hybrid algorithm; (d) histogram.

Fig. 10

Digital hologram of bladder tissues and spectral selection. (a) digital hologram; (b) spectrum; (c) object image of Fresnel amplitude reconstruction and spatial filtering; (d) spectrum of object image by hybrid algorithm.

Fig. 11

Phase distribution extraction of bladder tissues by two algorithms. (a) and (b) 2D phase distribution extracted from spectrum in yellow and red box in Fig. 10(b) by AS algorithm; (c)2D phase distribution of the spectrum by hybrid algorithm; (d)-(f) 3D display maps of (a)-(c).

Fig. 12

Comparison between H&E stained image and phase distribution. (a) and (b) stained image and phase distribution of normal urothelial tissue; (c) local zoom (framed in (b)); (d) and (e) stained image and phase distribution of bladder cancer tissue ; (f) local zoom (framed in (e)).

Fig. 13

Data analysis. (a) phase histograms of 10 regions in Fig. 12(b); (b) phase histograms of 10 regions in Fig. 12(e); (c) standard deviation of normal urothelial and bladder cancer tissues samples.