In incoherent digital holography (IDH) and in any imaging technique, the lateral and axial resolutions are intertwined and consequently changing one characteristic affects the other. In this study, we present two new hybridization techniques HM-1, and HM-2 for IDH, one for real-time and another for post-recording of holograms respectively, to engineer the axial resolution independent of lateral resolution. Two optical functions namely a lens and an axicon, with a low focal depth and a high focal depth respectively are considered. In both hybridization techniques, the axial resolution can be tuned between the limits of the axial resolutions of lens and axicon, while maintaining a constant lateral resolution. In HM-1, the axial resolution was engineered using a special phase mask designed using a modified version of Gerchberg-Saxton algorithm that can generate a spherical beam and Bessel beam for every object point and create self-interference between them. By controlling the strengths of the two beams, the axial resolution can be tuned without changing the lateral resolution. This method requires an active optical device such as a spatial light modulator. HM-2 involves two recordings of the same scene, one with a lens and another with an axicon which are then combined after recording. By controlling the weights of the two recordings, the axial resolution can be tuned between the limits of lens and the axicon independent of lateral resolution. In this case, passive diffractive or refractive optical elements are sufficient. Both hybridization techniques are implemented in indirect imaging mode consisting of three steps: recording point spread hologram, object hologram and reconstruction by Lucy-Richardson-Rosen algorithm.
Fresnel incoherent correlation holography (FINCH) is a well-established incoherent digital holography technique for imaging objects with an enhanced transverse resolution. In FINCH, light from an object point is split into two and modulated using two different quadratic phase masks and interfered to obtain the self-interference hologram. The two beams can be generated either by spatial random multiplexing or polarization multiplexing, with the former being power efficient and the latter exhibits a high signal to noise ratio. At least three such holograms are recorded with phase shifts 0, 2π/3 and 4π/3 radians and combined to obtain a complex hologram. This complex hologram can be numerically propagated to reconstruct any plane of the object. Under special beam matching condition, FINCH can exhibit a transverse resolution that is 1.5 times better than incoherent lens-based direct imaging systems with the same numerical aperture. To summarize, FINCH records 3D information with a high resolution at the expense of reduced temporal resolution. Several techniques have been developed in the past to improve the temporal resolution of FINCH by sacrificing transverse resolution and field of view. In this study, a recently developed phase mask design algorithm called Transport of Amplitude into Phase based Gerchberg-Saxton Algorithm (TAP-GSA) and reconstruction algorithm called Lucy-Richardson-Rosen algorithm (LR2A) has been implemented in FINCH. The modified approach with the TAP-GSA and LR2A significantly improved the performance of FINCH with an improved temporal resolution, light throughput and signal to noise ratio.
Manufacturing diffractive lenses with a high numerical aperture (NA) is often a challenging task. The challenge stems from the fundamental limit of lithography techniques and the diffraction limit. Photolithography and femtosecond ablation are some of the well-established rapid lithography techniques for manufacturing large-area diffractive lenses for the visible region. First, when high NA diffractive lenses are designed, the outermost width of the zone becomes a sub-lithography limit (~ 2 μm) while still being super-wavelength. In advanced photolithography and most femtosecond ablation methods, the lithography limit is sub-wavelength, but scalar diffraction is not applicable, and the device becomes polarization sensitive. In this study, a holographic solution to overcome the above limitations is proposed. Fresnel incoherent correlation holography (FINCH) is a super-resolution incoherent imaging technique. In this project, a FINCH-inspired optical configuration is proposed to image beyond the lithography and diffraction limit of the diffractive lens. In a regular imaging system, the light from an object is collected by a diffractive lens and imaged, and recorded by an image sensor in the image plane. In this work, the intensity distribution is not recorded at the image plane but at a plane where the light modulated by the diffractive lens interferes with the unmodulated light outside the diffractive lens. This intensity distribution has spatial frequencies beyond the limit of the NA of the diffractive lens, resulting in super-resolution. Using the newly developed Lucy-Richardson-Rosen algorithm (LR2A), the image is reconstructed. We believe that the developed technique will improve the performance of imaging systems based on high-NA diffractive lenses.
Designing a pure phase multifunctional diffractive optical element (M-DOE) is a challenging task, as the regular summation of multiple pure phase functions results in a complex function. One of the widely used multiplexing methods to design a pure phase M-DOE is the random multiplexing method. In this method, different pure phase functions are multiplied to mutually exclusive binary random functions before summation. However, M-DOEs designed using the random multiplexing method are prone to scattering noise. In this study, a novel approach based on a modified Gerchberg-Saxton algorithm (GSA) has been proposed and demonstrated for the design of pure-phase multifunctional DOEs. In this approach, the complex M-DOE obtained by regular summation is used as a reference, and with suitable constraints, the amplitude component of the complex M-DOE is transported into the phase component, resulting in a pure phase MDOE. This modified algorithm is called Transport of Amplitude into Phase based on GSA (TAP-GSA). This method has been demonstrated on a well-established incoherent digital holography technique called Fresnel incoherent correlation holography (FINCH). In FINCH, it is necessary to multiplex two-phase masks, which can be achieved using random multiplexing or polarization multiplexing, resulting in reconstruction noise and low light throughput, respectively. Under low-light conditions, random multiplexing is a better choice than the polarization multiplexing method. The M-DOE designed using TAP-GSA for FINCH improved the light throughput and exhibited a higher SNR in comparison to the random multiplexing method.
A computational imaging technique using a lens and Lucy-Richardson-Rosen algorithm (LRRA) has been developed for 3D imaging. A deep 3D point spread function (PSF) was recorded in the first step. A single camera shot of an object was recorded next. Using the 3D PSF and the LRRA, the complete 3D information of the object was reconstructed. In this configuration, direct imaging and indirect imaging concepts co-exist: when the imaging condition is satisfied, an image of the object is directly obtained and in other cases it is indirectly obtained. The proposed single lens incoherent digital holography system will be attractive for numerous imaging applications.
The near infrared (NIR) part of the infrared synchrotron beam is usually discarded to improve the signal to noise ratio of spectral imaging at the Australian Synchrotron. In this study, NIR synchrotron beam has been extracted and used for three-dimensional (3D) imaging. A Fresnel zone aperture (FZA) was fabricated on barium fluoride windows using femtosecond ablation. The 3D point spread functions (PSFs) were recorded using the FZA mounted between the pinhole and the image sensor. An object is then placed within the boundaries of the PSF library and an object intensity distribution was recorded. Computational reconstruction methods were applied to reconstruct the object information.
The near infrared (NIR) part of the infrared synchrotron beam is usually dumped to improve the signal to noise ratio of spectral imaging. In this study, this NIR synchrotron beam has been extracted and used for three-dimensional (3D) phase imaging. A pinhole was inserted in the path of the fork shaped NIR synchrotron beam and the Airy diffraction pattern was aligned with biochemical samples and the diffracted intensity distribution was captured using an image sensor sensitive to NIR. A phase retrieval algorithm was used to estimate the 3D phase distribution at the object plane from the recorded intensity distribution.
A 4D computational incoherent imaging technique using accelerating Airy beams (A2-beams) and nonlinear reconstruction (NLR) has been developed. The phase mask was designed as a binary version for the generation of a sparse random array of A2-beams. The imaging process consist of three steps. In the first step a 4D point spread function (PSF) was recorded at different wavelengths and depths. In the next step, a multicolor, multiplane object was loaded and a single camera shot was recorded. Finally, the 4D information of the object was reconstructed by processing the object intensity distribution and 4D PSFs. The simulation results for the imaging concept are presented.
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