How it works

The optical path setup of the digitial lensless holographic microscope consists of only three components: an illumination source is placed in a bench-top system above a transparent sample that is directly above the image sensor.  The spacing between illumination source and the sample is kept at around 10cm, while the spacing between the sample and the imaging chip is kept being <1mm. The optical path setup is extremely simplistic and hence guarantees portable, cost-effective, and accessible use in immediate medical applications such as cell counting and diagnosis. 

By discarding the use of lenses in traditional optical microscopes, the digital lensless holographic microscope is able to decoupole the trade-off between field of view (FOV) and resolution. That is, it is able to see nearly 100 times larger volume of cells with a just as resolved quality of image. This is substantial to aiding large volume of cell inspection while ensuring accuracy and precision.

The setup is designed to be able to take holograms at various heights of the sample. This allows the combination of these images at different depths to merge into a higher quality image.  

Instead of traditional use of laser light source for holography techniques, the digital lensless holographic microscope employs a LED light source.  While LED light, unlike lasers, do not produce speckle noises due to its low temporal coherence, its low spatial coherence also reduces the interference effects on the hologram. To overcome the limitation of low cohereence, a small pinhole was utilized to ensure good spatial coherence and quality of image, while suppressing minimal noises. For the particular setup, a pinhole of diameter ≈100μm is used. 

Given that the resolution of the phase reconstructed profile is highly dependent on the distance chosen, a bad estimation of distances can lead to poorly resolved image. Since the range of height adjustments are often in degrees of ≈ 100 μm, it is impractical to perform manual measurements. Hence, an auto-focusing (AF) algorithm is incorporated to improve the performance of the gs algorithm. Before processing the hologram any further, an auto-focusing algorithm is used to find the exact focus distance from which the image is taken.  The algorithm involves hologram reconstruction at several planes within the suspected measurement volume through pre-determined upper and lower search boundaries. Subsequently, the hologram is back propagated to the object plane to produce reconstructed image accordingly. A Sobel edge detecting function is utilized to examine the resolution and sharpness of the edges of each reconstructed image through contrast measure .  Ultimately, the reconstruction distance at which the output exhibits a minima or maxima is considered as the object focal plane location. In order to shorten the time frame, a rough search is first implemented with larger step sizes to search for, and a finer search is followed to find the more exact distance.The object image evaluated at this distance is taken as the image at focus.
 

Digital Lensless Holographic Microscopy (DLHM) operates by recording holograms of the specimen's interaction with an incident coherent light source, capturing both amplitude and phase information. These holograms are typically acquired at different heights (or axial positions) relative to the specimen, creating a stack of 2D holographic images. The Multi-Height Gerchberg-Saxton (MHGS) algorithm comes into play when we aim to reconstruct a high-resolution 3D image of the specimen from this stack.

The core challenge in Digital Lensless Holographic Microscopy (DLHM) is phase retrieval, which involves recovering the phase information from the recorded intensity patterns. The intensity measurements alone are insufficient for a complete reconstruction since they lack the phase information that carries valuable 3D structural details. The Multi-Height Gerchberg-Saxton (MHGS) algorithm addresses this issue by iteratively refining the phase estimate.

1. Initialization: To begin the MHGS algorithm, an initial guess for the complex wavefront of the specimen is required. This estimate is often obtained using a simpler technique like the Fourier Transform Method (FTM) or the Angular Spectrum Method (ASM). The initial guess is assigned to each height plane.

2. Iteration: The algorithm iterates between two main steps: the Gerchberg-Saxton (GS) and the Multi-Height (MH) steps.

• Gerchberg-Saxton (GS) Step:
  • For each height plane, the complex wavefront estimate is propagated back and forth between the object and hologram planes using the Fresnel diffraction equation.
  • The intensity of the propagated wavefront in the hologram plane is compared to the recorded hologram.
  • A correction factor is calculated based on the phase difference between the propagated and recorded hologram, and the phase of the wavefront estimate is updated accordingly.
• Multi-Height (MH) Step:
  • After performing the GS step for all height planes, the algorithm considers the phase estimates from multiple heights to compute a weighted average phase correction.
  • This step aims to reduce phase errors and increase the accuracy of the phase retrieval process by exploiting information from multiple heights.

3. Convergence Criteria: The iterations continue until a convergence criterion is met, such as a maximum number of iterations or when the phase estimates stop changing significantly.

4. Final Reconstruction: Once convergence is achieved, the final reconstructed 3D image of the specimen is obtained by combining the phase estimates from all height planes. This 3D image represents the object's complex refractive index distribution.

The implementation of the phase unwrapping algorithm in a digital lensless holographic microscope (DLHM) is a crucial step for extracting valuable quantitative information from holographic images. DLHM records both the amplitude and phase of light, with the phase holding vital details about the specimen's refractive index distribution and morphology. However, the phase information is typically wrapped within a limited range, which can hinder precise quantitative analysis. The phase unwrapping algorithm plays a pivotal role in DLHM by reconstructing the unwrapped phase from these wrapped values, enabling accurate and meaningful measurements.

In a DLHM system, holographic images are captured as complex-valued images, where the phase information encodes variations in the optical path length of the specimen. Due to the limited dynamic range of imaging sensors and the inherent periodicity of phase, these recorded phase values are wrapped within a range typically spanning from -π to π radians. This wrapping creates phase discontinuities and ambiguity, making it challenging to interpret the data accurately.

A global gradient-based unwrapping algorithm is applied for the digital lensless holographic microscope. The global gradient-based approach aims to resolve these phase ambiguities across an entire image by leveraging the phase gradients.

1. Initialization: The algorithm begins with a wrapped phase map, typically represented as a 2D grid of phase values, where each pixel has a wrapped phase within the [-π, π] range. This initial map often contains phase jumps and discontinuities.

2. Gradient Computation: The first step involves calculating the gradients of the wrapped phase map. This is done by computing the spatial derivatives of the phase with respect to both the x and y directions. Essentially, this step quantifies how rapidly the phase is changing in the horizontal and vertical directions at each pixel.

3. Branch Cut Initialization: In the global gradient-based approach, phase discontinuities are often referred to as "branch cuts." These branch cuts are initially placed at locations where phase gradients are the steepest, indicating a likely phase discontinuity. The locations of branch cuts are determined by analyzing the gradient magnitude and direction.

4. Region Growing: The algorithm proceeds by iteratively growing regions from the initial branch cuts. It identifies pixels connected to each branch cut, forming "seed regions." These regions expand by incorporating neighboring pixels with phase values close to the current region's phase. This process continues until all pixels in the image are assigned to a region.

5. Phase Unwrapping: Once the regions have been grown and all pixels have been assigned, the phase unwrapping process occurs. The algorithm systematically unwraps the phase in each region while maintaining phase continuity across the branch cuts. This is achieved by adjusting the phase values of each pixel within a region so that they align with the phase of a reference pixel, which is often chosen as a seed pixel with a known phase.

6. Global Consistency: One of the key advantages of the global gradient-based approach is that it takes into account the entire image's gradient information. This global perspective helps ensure that phase unwrapping is consistent across the entire image and minimizes errors that might arise from local decisions.

7. Iterative Refinement: In some cases, residual phase ambiguities may persist after the initial phase unwrapping. Iterative refinement techniques can be applied to further improve the unwrapped phase map's accuracy and completeness.

8. Quality Control: As with any phase unwrapping method, it is essential to assess the quality and reliability of the unwrapped phase map. Validation techniques and error estimation may be used to evaluate the accuracy of the unwrapped phase values.