Fig. 1. Schematic diagram and operation of the lensless polarimetric coded ptychography (pol-CP) platform. (a) A circular polarizer transforms linearly polarized light from the laser diode into circularly polarized light, which then interacts with the specimen. The exit wave is recorded by the integrated polarimetric coded image sensor. (b) Illustration of changes in the polarization state within the pol-CP system. (c) A 2 μL sample of goat blood is smeared onto the sensor’s coverglass and fixed with ethyl alcohol, forming a thin and dense blood-cell layer that acts as a high-performance scattering lens with a theoretically unlimited field of view. (d) An ultrathin polarizing film is adhered to the blood-cell layer, forming an integrated polarimetric coded image sensor. (e) The pol-CP prototype features a polarimetric coded sensor mounted on programmable stages, allowing control over both rotational and translational motions.

Fig. 2. Image acquisition and reconstruction process of pol-CP. (a) The captured four sets of raw images with the integrated coded sensor at four different orientations. (b) The recovered four images with the 0° orientation as the reference. (c), (d) The optic axis orientation and retardance maps are derived using Jones calculus. (e) A pseudo-colored birefringence map by encoding the optic axis orientation as color hue and the retardance information as intensity.

Fig. 3. Image quality quantification using a USAF resolution target. (a) The captured raw image of the resolution target. (b) The recovered image using the pol-CP platform. The recovered intensity (c1) and phase (c2) images of the blood-cell layer on the integrated coded sensor. The goat blood cells are smallest among all animals.

Fig. 4. Validating the pol-CP prototype using a quantitative phase target. The recovered (a) amplitude, (b) phase, and (c) color-coded birefringence map.

Fig. 5. Validation of the pol-CP prototype by imaging potato starch granules. (a) The captured raw diffraction measurement of the potato starch granules. (b) The reconstructed optic axis orientation using the pol-CP prototype. (c)–(e) Zoomed-in views of the highlighted regions of (b). The line traces show the measurements using the pol-CP prototype (black dotted line) and the conventional lens-based polarized light microscopy with a 10×, 0.45 NA objective (red dotted line).

Fig. 6. High-resolution, large field-of-view gigapixel birefringence imaging via pol-CP. (a) The captured raw image of the whole-slide starch grain sample. (b) The recovered birefringence map. (c)–(f) The magnified views of different regions in (b). (c1)–(f1) The captured raw images. (c2)–(f2) The recovered amplitude. (c3)–(f3) The recovered optic axis orientation. (c4)–(f4) The recovered retardance. (c5)–(f5) The birefringence maps where the color scale is used to encode the optic axis orientation and the gray scale is used to encode the retardance information.

Fig. 7. High contrast background-free imaging of a corn stem sample. (a) Captured raw image of corn stem. (b)–(d) The recovered amplitude, optic axis orientation, and birefringence map of (a). (e1)–(g3) Enlarged raw images of the highlighted regions in (a). (e1)–(g1) Raw images. (e2)–(g2) The recovered amplitude and phase of the wavefront at α=0°. (e3)–(g3) The reconstructed optic axis orientation, retardance, and birefringence map.

Fig. 8. Detecting malaria-infected blood cells using the lensless pol-CP prototype. (a) The recovered phase image of the sample. (b)–(d) The zoomed-in views of the raw diffraction measurements (left column), quantitative birefringence maps (middle column), and overlaid images of phase and birefringence maps (right column).

Fig. 9. Imaging of calcium phosphate crystal prepared from urine samples. (a1)–(a3) The captured raw images. (b1)–(b3) The recovered amplitude images at four polarization angles. (c1)–(c3) The recovered birefringence maps.

Fig. 10. Imaging of an unstained thyroid sample using the lensless pol-CP prototype. (a) Captured raw image. (b) Recovered amplitude. (c) Recovered birefringence map, where the calcium oxalate crystals are present within the colloid of thyroid follicles and contribute to the purple color in the birefringence map. (d) Captured autofluorescence image captured using a regular fluorescence microscope with a DAPI filter cube. The bright region indicates the autofluorescence signals from calcium oxalates. The results demonstrated here can be used to locate follicles on unstained cytology smears for rapid on-site evaluation.