Fig. 1. Overview of the proposed computational imaging paradigm. (a) Architecture of the proposed imaging system. A transfer lens is placed between the object and the image sensor to collect and deliver the object information. (b) Prototype of the proposed imaging paradigm. (c) The object is reconstructed from the measured intensity patterns by use of a backward wave propagation model.

Fig. 2. The optimal spatial information transfer lens. (a) Design process of the spatial information transfer lens. (b) Ray tracing of the transfer lens. (c) Spot diagrams on the observation plane. (d) Intensity distributions at sampled points on the observation plane. (e) Retrieved spectrum distributions in image space in the two examples. (f) Fabricated transfer lens. (g) Surface error maps of the entrance and exit surfaces of the transfer lens.

Fig. 3. Key steps of the full path optical diffraction calculation. (a) Illustration of the two intensity measurements. (b) Flowchart of the dual phase retrieval algorithm.

Fig. 4. Illustration of decomposition operation in the full path optical diffraction calculation. (a) Perspective view of the decomposed lens with a set of cutting planes. (b) Front view of the two identical annuluses p1 and p2, which are the projections of the p-th surface slice on the p-th and (p+1)-th plane, respectively. Since the two annuluses are identical, only one annulus is shown here for simplicity. (c) Side view of two identical annuluses on the p-th plane and the (p+1)-th plane and illustration of the phase compensation.

Fig. 5. Reconstruction of the USAF 1951 resolution test chart. (a) Two intensity patterns recorded by the image sensor. (b) Amplitude distribution in the tangent plane at the vertex of the exit surface. (c) Change of SVFG. (d) Reconstructed object with the transfer lens. (e) Reconstructed object without the transfer lens. (f) Reconstructed object with thin lens approximation.

Fig. 6. Reconstruction of a mouse ovarian tissue. (a) Two intensity patterns recorded by the image sensor. (b) Amplitude distribution in the tangent plane at the vertex of the exit surface. (c) Full FOV image of the mouse ovarian cells. (d1), (e)–(g) Vignette high-resolution views of the image in (c). (d2), (d3) Images taken by a commercial microscope with a 2× (d2) and a 20× (d3) objective lens, for comparison.

Fig. 7. Influence of key factors on the quality of image reconstruction. (a) Reconstruction results of the standard test chart with the number of decomposed slices of 10, 30, and 50. (b) Change of the reconstruction resolution when the decenter of the lens is increased from 0.01 mm to 0.05 mm. (c) Change of the reconstruction resolution when the tilt of the lens is increased from 0.1° to 0.5°.

Fig. 8. Influence of the initial phase on the final reconstruction results. Final reconstruction results generated from (a) a uniform phase and (b) a random phase.

Fig. 9. Two intensity patterns are measured to recover the complex amplitude.

Fig. 10. Convergence of the dual plane phase retrieval.

Fig. 11. Illustration of the lens decomposition: the annuluses projected from the slices to the adjacent planes are marked in green to better show the full path diffraction calculation process.