3D differential phase contrast (3D DPC) microscopy uses asymmetric illumination patterns and axial scanning to recover volumetric maps of refractive index. To avoid the expense of automated axial scanning, we demonstrate 3D DPC without a z-stage by hand spinning the microscope’s defocus knob to scan the object axially while updating illumination patterns on the LED-array microscope. We utilize an inverse problem optimization to retrieve the sample’s volumetric information with measurements from unknown axial positions by jointly solving for each measurement’s axial position. Finally, we explore how to optimize the LED-array illumination patterns for varying axial sampling rates.
3D refractive index imaging methods usually rely on a weak-scattering approximation that does not allow for thick samples to be imaged accurately. Recent methods such as 3D Fourier ptychographic microscopy (FPM) instead use multiple-scattering models which allow for thicker objects to be imaged. In practice the illumination-side coding of 3D FPM requires redundant information and may produce inaccurate reconstructions for thick samples. Here, we propose augmenting 3D FPM with detection-side coding using a spatial light modulator (SLM) and optimize the SLM coding strategy with physics-based machine learned pupil coding designs that are optimized for 3D reconstructions. We compare our learned designs to random-, defocus-, Zernike aberrations-based pupil codes in simulated and experimental results.
KEYWORDS: 3D image processing, 3D modeling, Phase imaging, Luminescence, Inverse optics, Reconstruction algorithms, Data modeling, 3D metrology, Diffraction, Optical tomography
Phase imaging provides quantitative structural data about biological samples as an alternative or complementary contrast method to the functional information given by fluorescence imaging. In certain cases, fluorescence imaging is undesirable because it may harm the development of living cells or add time and complexity to imaging pipelines. However, current 3D phase reconstruction methods, such as optical diffraction tomography [1], are often limited to a single-scattering approximation. This limits the amount of scattering that such 3D reconstruction algorithms can successfully handle, and therefore effectively limits the sample thickness that can be successfully reconstructed. More recent methods such as 3D Fourier ptychographic microscopy (FPM) have used intensity-only images combined with multiple-scattering models in order to reconstruct 3D volumes [2]. In practice, however, continuous biological samples on the order of 100 um thick are not well-reconstructed by 3D FPM, due to a lack of diverse information across the volume which creates an ill-posed inverse problem. To mitigate this, we introduce simultaneous detection coding in the form of pupil control to the 3D FPM capture scheme. Simple pupil coding schemes enabled us to capture diverse information across our volume. In concert with a beam propagation model that takes into account multiple scattering, this combination of illumination- and detection-side coding allows us to more stably reconstruct 3D phase for larger-scale biological samples.
[1] E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[2] L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an LED array microscope,” Optica, 2, 104-111 (2015).
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