Review of 3D Imaging by Coded Aperture Correlation Holography (COACH)

Recent progress in digital holography with dynamic diffractive phase apertures [Invited]

Digital holography with diffractive phase apertures is a hologram recording technique in which at least one of the interfering waves is modulated by a phase mask. In this review, we survey several main milestones on digital holography with dynamic diffractive phase apertures. We begin with Fresnel incoherent correlation holography (FINCH), a hologram recorder with an aperture of a diffractive lens. FINCH has been used for many applications such as 3D imaging, fluorescence microscopy, superresolution, image processing, and imaging with sectioning ability. FINCH has played an important role by inspiring other digital holography systems based on diffractive phase aperture, such as Fourier incoherent single-channel holography and coded aperture correlation holography, which also are described in this review.

High-quality interferenceless coded aperture correlation holography with optimized high SNR holograms

Motivated by the key role of point spread function in an imaging system, we propose an interferenceless coded aperture correlation holographic (I-COACH) technology with low speckle and high energy efficiency annular sparse coded phase mask (CPM) as system pupil to improve imaging performance. In the proposed method, a modified Gerchberg-Saxton (GS) algorithm is proposed to obtain a low speckle and high energy efficiency annular sparse CPM and to suppress speckle and increase the intensity of the holograms. Therefore, the randomly distributed amplitude in the bandwidth of the GS algorithm is replaced by the annular amplitude to determine the spatial position, and the band-limited random phase and quadratic phase are used as the initial phase to approximately meet band-limited conditions; meanwhile, in the iterative process of the algorithm, appropriate constraints are imposed on the information within and outside the band limit. All are used for obtaining the CPM with low speckle and high energy efficiency. Therefore, the proposed technique here is coined as low speckle I-COACH owing to the characteristics of CPM and imaging performances. The experimental results show that, under the same experimental conditions, the proposed method can obtain holograms with low speckle and intensity enhancement of about 8%, and further improve the quality of reconstructed images due to the improvement signal-to-noise ratio (SNR) of the holograms. The proposed method provides a powerful reference method for further expanding the I-COACH system to the field of low-intensity optical signals detection and imaging.

Recording point spread functions by wavefront modulation for interferenceless coded aperture correlation holography

Coded aperture correlation holography (COACH) needs the point spread function (PSF) for image reconstruction. Utilizing a pinhole to generate a point light source is the most frequently adopted method for measuring PSF, which, however, has significant issues to resolve. One of the problems is that the resolution of the reconstructed result is limited by the cutoff frequency of the pinhole. The other is that the far-field PSF is undetectable because the amount of light illuminance decreases with the distance. In this work, we present a method for recording the PSF based on wavefront modulation. By modulating a plane wave with both the carrier spherical wave and the coded phase mask, we obtain a virtual point spread function (VPSF) that is used for image reconstruction. It is shown that the resolution of reconstructed results is not limited by the pinhole. We experimentally demonstrate high-resolution reconstruction by the VPSF.

COACH-based Shack-Hartmann wavefront sensor with an array of phase coded masks

Shack-Hartmann wavefront sensors (SHWS) are generally used to measure the wavefront shape of light beams. Measurement accuracy and the sensitivity of these sensors are important factors for better wavefront sensing. In this paper, we demonstrate a new type of SHWS with better measurement accuracy than the regular SHWS. The lenslet array in the regular SHWS is replaced with an array of coded phase masks, and the principle of coded aperture correlation holography (COACH) is used for wavefront reconstruction. Sharper correlation peaks achieved by COACH improve the accuracy of the estimated local slopes of the measured wavefront and consequently improve the reconstruction accuracy of the overall wavefront. Experimental results confirm that the proposed method provides a lower mean square wavefront error by one order of magnitude in comparison to the regular SHWS.

Single shot holographic super-resolution microscopy

An exceptionally simple and versatile advance in super-resolution microscopy has been created by adding a new birefringent FINCH holographic lens system including an inexpensive uncooled CMOS camera to a standard microscope. Resolution, after only a single image capture, is equivalent to or better than other more complex popular methods such as SIM, Airyscan and a number of image scanning microscopy methods that boost resolution about two-fold. This new FINCH implementation uniquely works for any objective power and NA and is solid state, fast, and calibration-free. In addition to being as easy to operate and maintain as a standard fluorescence microscope, it can uniquely create super-resolved images with any type or wavelength of light including fluorescence, bioluminescence or reflected light because its principle depends only on emitted light from objects and requires no prior training or knowledge about the sample being imaged. This microscope technique increases the utility and availability of super-resolution microscopy for any user in any research lab.

Incoherent coded aperture correlation holographic imaging with fast adaptive and noise-suppressed reconstruction

Fast and noise-suppressed incoherent coded aperture correlation holographic imaging is proposed, which is utilized by employing an annular sparse coded phase mask together with adaptive phase-filter cross-correlation reconstruction method. Thus the proposed technique here is coined as adaptive interferenceless coded aperture correlation holography (AI-COACH). In AI-COACH, an annular sparse coded phase mask is first designed and generated by the Gerchberg-Saxton algorithm for suppressing background noise during reconstruction. In order to demonstrate the three-dimensional and sectional imaging capabilities of the AI-COACH system, the imaging experiments of 3D objects are designed and implemented by dual-channel optical configuration. One resolution target is placed in the focal plane of the system as input plane and ensured Fourier transform configuration, which is employed as reference imaging plane, and moved the other resolution target to simulate different planes of a three-dimensional object. One point spread hologram (PSH) and multiple object-holograms without phase-shift at different axial positions are captured by single-exposure sequentially with the annular sparse CPMs. A complex-reconstruction method is developed to obtain adaptively high-quality reconstructed images by employing the cross-correlation of PSH and OH with optimized phase filter. The imaging performance of AI-COACH is investigated by imaging various type of objects. The research results show that AI-COACH is adaptive to different experimental conditions in the sense of autonomously finding optimal parameters during reconstruction procedure and possesses the advantages of fast and adaptive imaging with high-quality reconstructions.

Depth-of-field engineering in coded aperture imaging

Extending the depth-of-field (DOF) of an optical imaging system without effecting the other imaging properties has been an important topic of research for a long time. In this work, we propose a new general technique of engineering the DOF of an imaging system beyond just a simple extension of the DOF. Engineering the DOF means in this study that the inherent DOF can be extended to one, or to several, separated different intervals of DOF, with controlled start and end points. Practically, because of the DOF engineering, entire objects in certain separated different input subvolumes are imaged with the same sharpness as if these objects are all in focus. Furthermore, the images from different subvolumes can be laterally shifted, each subvolume in a different shift, relative to their positions in the object space. By doing so, mutual hiding of images can be avoided. The proposed technique is introduced into a system of coded aperture imaging. In other words, the light from the object space is modulated by a coded aperture and recorded into the computer in which the desired image is reconstructed from the recorded pattern. The DOF engineering is done by designing the coded aperture composed of three diffractive elements. One element is a quadratic phase function dictating the start point of the in-focus axial interval and the second element is a quartic phase function which dictates the end point of this interval. Quasi-random coded phase mask is the third element, which enables the digital reconstruction. Multiplexing several sets of diffractive elements, each with different set of phase coefficients, can yield various axial reconstruction curves. The entire diffractive elements are displayed on a spatial light modulator such that real-time DOF engineering is enabled according to the user needs in the course of the observation. Experimental verifications of the proposed system with several examples of DOF engineering are presented, where the entire imaging of the observed scene is done by single camera shot.

Partial aperture imaging system based on sparse point spread holograms and nonlinear cross-correlations

Partial aperture imaging system (PAIS) is a recently developed concept in which the traditional disc-shaped aperture is replaced by an aperture with a much smaller area and yet its imaging capabilities are comparable to the full aperture systems. Recently PAIS was demonstrated as an indirect incoherent digital three-dimensional imaging technique. Later it was successfully implemented in the study of the synthetic marginal aperture with revolving telescopes (SMART) to provide superresolution with subaperture area that was less than one percent of the area of the full synthetic disc-shaped aperture. In the study of SMART, the concept of PAIS was tested by placing eight coded phase reflectors along the boundary of the full synthetic aperture. In the current study, various improvements of PAIS are tested and its performance is compared with the other equivalent systems. Among the structural changes, we test ring-shaped eight coded phase subapertures with the same area as of the previous circular subapertures, distributed along the boundary of the full disc-shaped aperture. Another change in the current system is the use of coded phase mask with a point response of a sparse dot pattern. The third change is in the reconstruction process in which a nonlinear correlation with optimal parameters is implemented. With the improved image quality, the modified-PAIS can save weight and cost of imaging devices in general and of space telescopes in particular. Experimental results with reflective objects show that the concept of coded aperture extends the limits of classical imaging.

High-resolution imaging system with an annular aperture of coded phase masks for endoscopic applications

Partial aperture imaging is a combination of two different techniques; coded aperture imaging and imaging through an aperture that is only a part of the complete disk, commonly used as the aperture of most imaging systems. In the present study, the partial aperture is a ring where the imaging through this aperture resolves small details of the observed scene similarly to the full disk aperture with the same diameter. However, unlike the full aperture, the annular aperture enables using the inner area of the ring for other applications. In this study, we consider the implementation of this special aperture in medical imaging instruments, such as endoscopes, for imaging internal cavities in general and of the human body in particular. By using this annular aperture, it is possible to transfer through the internal open circle of the ring other elements such as surgical tools, fibers and illumination devices. In the proposed configuration, light originated from a source point passes through an annular coded aperture and creates a sparse, randomly distributed, intensity dot pattern on the camera plane. A combination of the dot patterns, each one recorded only once, is used as the point spread hologram of the imaging system. The image is reconstructed digitally by cross correlation between the object intensity response and the point spread hologram.

Programmable liquid crystal display based noise reduced dynamic synthetic coded aperture imaging camera (NoRDS-CAIC)

Besides traditional lens-based imaging techniques, coded aperture imaging (CAI) can also provide target images but without using any optical lenses, therefore it is another solution in imaging applications. Most CAI methods reconstruct target image only from a single-shot coded image using a fixed coding mask; however, the collected partial information inevitably deteriorates the reconstruction quality. Though multi-exposure CAI methods are designed, these existed algorithms can hardly improve reconstruction signal-to-noise ratio (SNR) and spatial resolution simultaneously; additionally, dynamic coding mask display still requires expensive devices and complicated systems. In order to reconstruct target image with both enhanced spatial resolution and SNR but using cost-effective devices and a simple system, we design a noise reduced dynamic synthetic coded aperture imaging camera (NoRDS-CAIC) in this paper. The NoRDS-CAIC only consists of a programmable liquid crystal display (LCD) and an image recorder, and both of them are integrated with a three-dimensional printed shell with the compact size of 19 cm × 15 cm × 16 cm and controlled by our designed software to automatically realize coding mask display, coded image recording and target image reconstruction. When using the NoRDS-CAIC, the optimized coding mask is first sent to the programmable LCD and displayed, then the corresponding coded image is automatically captured using the image recorder. Next, cycle the above procedures to capture enough coded images with previously known coding masks and measured point spread functions (PSFs), and the target image can be finally reconstructed using our designed NoRDS-CAIC decoding algorithm, which is shown with better noise suppression capability and higher reconstruction resolution compared to other classical CAI algorithms. According to the experimental verifications, the NoRDS-CAIC can reach the high resolution of 99.2 µm and the high SNR of 19.43 dB, proving that the designed NoRDS-CAIC can be potentially used for lensless imaging in practical applications.

Sampling requirements and adaptive spatial averaging for incoherent digital holography

Incoherent digital holography (IDH) enables passive 3D imaging under spatially incoherent light; however, the reconstructed images are seriously affected by detector noise. Herein, we derive theoretical sampling requirements for IDH to reduce this noise via simple postprocessing based on spatial averaging. The derived theory provides a significant insight that the sampling requirements vary depending on the recording geometry. By judiciously choosing the number of pixels used for spatial averaging based on the proposed theory, noise can be reduced without losing spatial resolution. We then experimentally verify the derived theory and show that the associated adaptive spatial averaging technique is a practical and powerful way of improving 3D image quality.