Sub-Pixel Scale Structured Illumination for Lateral Resolution Enhancement of Non-Diffraction-Limited Flow Imaging

TL;DR

This work presents a practical, low-cost sub-pixel structured illumination approach to overcome instrument-limited lateral resolution in flow imaging. By projecting linearly shifting, sub-pixel SI patterns and capturing four-frame quasi-static sets, it reconstructs high-resolution images that double the lateral sampling and enhance flow-gradient estimation in both static and dynamic scenarios. The FPPOCS-based reconstruction pipeline incorporates flat-field correction, precise sub-pixel registration, and phase-based recombination to produce HR images, demonstrated on static text and a micro-jet flow with quantified improvements in gradient detail and mixing-layer thickness. While effective, the method introduces higher background noise and requires careful alignment, grating control, and synchronization; future work aims to optimize optics and motion accuracy for higher-speed, broader-applicability flow imaging.

Abstract

In fluid flow imaging, intensity gradients are a good measure of spatial variations in scalar properties, which play an important role in controlling transport processes. However, current flow imaging techniques exhibit system-limited spatial resolutions, thus inhibiting the ability to accurately detect intensity gradients. To address this challenge, we present a method and system, inspired by Structured Illumination Microscopy (SIM), which can be implemented in dynamic flow imaging to enhance pixel resolution and, thereby, the estimation of scalar gradients. We utilize sub-pixel-scale patterned light matching the system pixel scale and multi-frame imaging that creates quasi-static images over four frames, with scalability for high-speed imaging. These multi-frame images are then processed using a bespoke recombination algorithm that produces a new image with twice the pixel resolution compared to the original images. The sub-pixel spatial-resolution enhancement capabilities are shown with static images and dynamic fluid flow, for which enhancement in the flow gradient is demonstrated.

Figures (5)

• Figure 1: Grating example and visualization of misalignment during setup. (a) Sample grating with the expected captured image in the camera showing no visible sub-pixel pattern. (b) Simulation of the camera image arising in the case of an aligned illumination pattern (left) and Moiré patterns occurring when the system pixel size does not match the grating (right).
• Figure 2: General overview of the system and method. (a) Illustration of the structured illumination pathway. (b) Schematic illustration of the sub-pixel structured illumination process in which a subject is illuminated with a sub-pixel pitch grating, captured with a camera, and combined to create a reconstructed high resolution image. (c) CAD model of the developed imaging system.
• Figure 3: Workflow of the image reconstruction algorithm for a continuous set of n images. For each set of 4 images, an initial (1) flat field correction and (2) position registration are applied and calculated. (3a) Interpolated upscaling, (3b) position alignment, and (3c) average are performed on the 4 images to generate an upscaled HR image. (4a) Position alignment to HR grid and (4b) recombination are performed on the 4 images to generate a superimposed recombined HR image. (5) Crop and discrete fast Fourier transform (FFT) are applied on both the superimposed and upscaled HR images. Merging of the two images is achieved using an average phase difference-based update algorithm (6). An inverse discrete Fourier transform (IDFT) is applied (7), creating the resulting reconstruction HR image. Applying these steps to all consecutive sets of 4 images results in (8) set generation.
• Figure 4: Example of spatial resolution enhancement for static text of the words 'UCSD' and 'California'. (a) Text enhancement at sampling rates below the Nyquist–Shannon criterion. (b) Text enhancement at sampling rates above the Nyquist–Shannon criterion. (c) Intensity plots for line-cuts of 'California' imaged at sampling rates above the Nyquist–Shannon criterion. Scale bars are 2.12 mm.
• Figure 5: Flow imaging with an example mass flow rate of 160 $mm/h$ captured at 40 fps and enhanced with structured illumination. Flow enhancement is visualized through line cuts and gradient plots. (a) Captured low-resolution (cLR) and reconstructed high-resolution (rHR) images with labels denoting which frames are utilized to create a high-resolution (rHR) image for flow developing over 8.75 seconds. (b,c) Magnified image of the flow at 0 (part b) and 8.75 seconds (part c). Line-cuts in regions (i)-(iii) (shown in insets) exhibit an increase in the pixel resolution. Scale bars are 1.76 mm. (d,e) Flow gradient magnitudes for captured low-resolution and reconstructed high-resolution images at 0 (part d) and 8.75 seconds (part c). Gradients are shown as intensity per mm. Bottom panel: line cut of the center of each cropped gradient.