Wide-field, high-resolution Fourier ptychographic microscopy

Abstract

In this article, we report an imaging method, termed Fourier ptychographic microscopy (FPM), which iteratively stitches together a number of variably illuminated, low-resolution intensity images in Fourier space to produce a wide-field, high-resolution complex sample image. By adopting a wavefront correction strategy, the FPM method can also correct for aberrations and digitally extend a microscope's depth-of-focus beyond the physical limitations of its optics. As a demonstration, we built a microscope prototype with a resolution of 0.78 μm, a field-of-view of ~120 mm², and a resolution-invariant depth-of-focus of 0.3 mm (characterized at 632 nm). Gigapixel colour images of histology slides verify FPM's successful operation. The reported imaging procedure transforms the general challenge of high-throughput, high-resolution microscopy from one that is coupled to the physical limitations of the system's optics to one that is solvable through computation.

Keywords: digital pathology; gigapixel microscopy; high-throughput imaging; phase retrieval.

Fig. 1. FPM’s iterative recovery procedure (5 steps)

N low-resolution intensity images captured under variable illumination are used to recover one high-resolution intensity image and one high-resolution phase map. Steps 1–5 illustrate FPM’s algorithm, following principles from phase retrieval. Step 1: Initialize the high-resolution image, $\sqrt{I_h}{e}^{i{\phi }_h}$. Step2: Generate a low-resolution image $\sqrt{I_l}{e}^{i{\phi }_l}$, corresponding to an oblique plane wave incidence. Step 3: Replace I_l by the intensity measurement I_lm (i.e., $\sqrt{I_l}{e}^{i{\phi }_l}\to \sqrt{I_{lm}}{e}^{i{\phi }_l}$), and update the corresponding region of $\sqrt{I_h}{e}^{i{\phi }_h}$ in Fourier space (the area within the red circle). Step 4: Repeat steps 2–3 for other plane wave incidences (total N intensity images). Step 5: Repeat steps 2–4 for one more time.

Fig. 2. FPM prototype setup

(a) Diagram of the setup. A programmable LED matrix is placed beneath the sample. The i^th LED illuminates the sample with wave-vector $k_x^i$. (b) The LED matrix and microscope used in experiment, where (Inset) each LED can provide red, green, and blue narrow-band illumination. (c1) A full-FOV raw image of a USAF resolution target. (c2) A magnified view of the raw image, exhibiting a pixel size of 2.75 μm. (d) Our FPM reconstruction of the same region, where we achieve a reconstructed pixel size of 0.275 μm (refer to the discussion of FPM’s sampling requirement in Supplementary Note 3). In this reconstruction, the corresponding maximum synthetic NA of the reconstructed image is 0.5, set by the maximum angle between the optical axis and an LED. The entire recovery process is demonstrated in Supplementary Video 1.

Fig. 3. Extending depth-of-focus with digital wavefront correction

(a) The principle of FPM’s digital wavefront correction technique. A digital pupil function is introduced in steps 2 and 5 to model the connection between the actual sample profile and the captured intensity data, which may exhibit aberrations caused by defocus. Step 2: multiply a phase factor e^{iφ(k_x, k_y)} in the Fourier domain. Step 5: multiply an inverse phase factor e^{−iφ(k_x, k_y)} in the Fourier domain (refer to Fig. S5 for the FPM flowchart with digital wavefront correction). (b) One raw low-resolution image of the USAF target placed at z₀ = −150 μm. High-resolution FPM reconstructions without (c) and with (d) steps 2 and 5 added to the iterative recovery procedure.

Fig. 4. Gigapixel colour imaging via FPM

(a) A wide-FOV colour image of a pathology slide, with a SBP of approximately 0.9 gigapixels. (b, c1, d, and e): Vignette high-resolution views of the image in (a). Images taken by a conventional microscope with a 20× (c2) and a 2× (c3) objective lens, for comparison. A colour image sensor (DFK 61BUC02, Image Source Inc.) is used for capturing (c2 and c3).