Propagation phasor approach for holographic image reconstruction

Abstract

To achieve high-resolution and wide field-of-view, digital holographic imaging techniques need to tackle two major challenges: phase recovery and spatial undersampling. Previously, these challenges were separately addressed using phase retrieval and pixel super-resolution algorithms, which utilize the diversity of different imaging parameters. Although existing holographic imaging methods can achieve large space-bandwidth-products by performing pixel super-resolution and phase retrieval sequentially, they require large amounts of data, which might be a limitation in high-speed or cost-effective imaging applications. Here we report a propagation phasor approach, which for the first time combines phase retrieval and pixel super-resolution into a unified mathematical framework and enables the synthesis of new holographic image reconstruction methods with significantly improved data efficiency. In this approach, twin image and spatial aliasing signals, along with other digital artifacts, are interpreted as noise terms that are modulated by phasors that analytically depend on the lateral displacement between hologram and sensor planes, sample-to-sensor distance, wavelength, and the illumination angle. Compared to previous holographic reconstruction techniques, this new framework results in five- to seven-fold reduced number of raw measurements, while still achieving a competitive resolution and space-bandwidth-product. We also demonstrated the success of this approach by imaging biological specimens including Papanicolaou and blood smears.

Sparsity-based multi-height phase recovery in holographic microscopy

“…While the presented approach has been demonstrated for multi-height holographic imaging and phase recovery, other types of physical measurement diversities can also be utilized in the same sparse signal recovery framework, such as multi-angle illumination and wavelength scanning2627 which might benefit various applications in quantitative imaging of live biological samples, such as growing colonies of bacteria, fungi or other types of cells.…”

“…Furthermore, this technique can be potentially combined with a recently introduced phasor approach for high resolution and wide field-of-view imaging27 and/or multiplexed color imaging28 to further reduce the number of measurements in these holographic microscopy approaches. Enabled by novel algorithmic processing, this sparsity-based holographic image reconstruction technique can be regarded as another step forward in making lensfree on-chip holography more efficient, higher throughput and more appealing in microscopy-related applications.…”

Resolution Analysis in a Lens-Free On-Chip Digital Holographic Microscope

“…Because of the spatial aliasing/undersampling, the imaging sensor will fail to record holographic oscillation corresponding to high spatial frequency information of the specimen. To address this problem, pixel super-resolution (SR) methods have been proposed in which the hologram with a smaller effective pixel size can be synthesized from multiple low-resolution (LR) measurements through specific computational algorithms [17,18,25,26,30]. With these pixel SR methods, the imaging resolution of the LFOCDHM systems can be improved from Nyquist-Shannon limit (half-pitch lateral resolution of ∼ 2µm, effective NA of ∼ 0.1 − 0.2) to an effective numerical aperture of ∼ 0.4 − 0.5 [17,18,26,31].…”

Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy

“…In traditional multi-height reconstruction method 23,38 , many efforts are made to implement subpixel shift to achieve the super-resolution, but the pixel binning is not taken into account, which does not accord with actual physical process. Thus, involving the process of recording digital images in the reconstruction procedure has drawn attention, and the enhancement in resolution has been validated 30 . The process of recording digital images is a down-sampling process which is usually modeled as a spatial averaging operator [LR Pixel = ∑ a h k 2 (h = 0, 1...k 2 − 1) where a h is the gray value of the super-resolution intensity images, k is a decimation factor] as shown in Fig .4(a).…”

“…Furthermore, this method significantly simplifies the operation process and improve data efficiency. Meanwhile, the enhancement of resolution only by Z-scanning has been demonstrated 30,31 . This method depends on the perfect fit between the practical and theoretical imaging model, but it is difficult to achieve in actual operation.…”