Abstract
We demonstrate 3D phase and absorption recovery from partially coherent intensity images captured with a programmable LED array source. Images are captured through-focus with four different illumination patterns. Using first Born and weak object approximations (WOA), a linear 3D differential phase contrast (DPC) model is derived. The partially coherent transfer functions relate the sample's complex refractive index distribution to intensity measurements at varying defocus. Volumetric reconstruction is achieved by a global FFT-based method, without an intermediate 2D phase retrieval step. Because the illumination is spatially partially coherent, the transverse resolution of the reconstructed field achieves twice the NA of coherent systems and improved axial resolution.
Highlights
Standard commercial microscopes use partially spatially coherent illumination for better spatial resolution, higher light throughput and reduction of speckle artifacts, as compared to coherent illumination
The resulting non-interferometric 3D quantitative phase method is simple to implement in a commercial microscope, achieves the incoherent resolution limit (2× the coherent resolution limit) and is accurate for most biological samples
The transverse Fourier coverage of the differential phase contrast (DPC) transfer function spans a bandwidth 2× larger than the NA of the objective (N A⊥,max = 2 × N A), so phase and absorption may be recovered with resolution that is 2× the coherent resolution limit
Summary
Standard commercial microscopes use partially spatially coherent illumination for better spatial resolution, higher light throughput and reduction of speckle artifacts, as compared to coherent illumination. When diffraction effects become prominent (e.g. in the visible regime), a diffraction tomography model [12,18] is needed This assumes knowledge of the complex-field at each angle, requiring a two-step inverse problem: 2D phase retrieval, followed by tomography to reconstruct 3D. With partially coherent light, one can use 2D phase retrieval at multiple focus planes to reconstruct 3D refractive index. We present a 3D DPC model that recovers 3D absorption and refractive index from intensity images taken at different focus planes with each of the 4 half-circle source patterns (Fig. 1). The resulting non-interferometric 3D quantitative phase method is simple to implement in a commercial microscope, achieves the incoherent resolution limit (2× the coherent resolution limit) and is accurate for most biological samples
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