Plane wave analysis of coherent holographic image reconstruction by phase transfer (CHIRPT)

Abstract

Fluorescent imaging plays a critical role in a myriad of scientific endeavors, particularly in the biological sciences. Three-dimensional imaging of fluorescent intensity often requires serial data acquisition, that is, voxel-by-voxel collection of fluorescent light emitted throughout the specimen with a nonimaging single-element detector. While nonimaging fluorescence detection offers some measure of scattering robustness, the rate at which dynamic specimens can be imaged is severely limited. Other fluorescent imaging techniques utilize imaging detection to enhance collection rates. A notable example is light-sheet fluorescence microscopy, also known as selective-plane illumination microscopy, which illuminates a large region within the specimen and collects emitted fluorescent light at an angle either perpendicular or oblique to the illumination light sheet. Unfortunately, scattering of the emitted fluorescent light can cause blurring of the collected images in highly turbid biological media. We recently introduced an imaging technique called coherent holographic image reconstruction by phase transfer (CHIRPT) that combines light-sheet-like illumination with nonimaging fluorescent light detection. By combining the speed of light-sheet illumination with the scattering robustness of nonimaging detection, CHIRPT is poised to have a dramatic impact on biological imaging, particularly for in vivo preparations. Here we present the mathematical formalism for CHIRPT imaging under spatially coherent illumination and present experimental data that verifies the theoretical model.

Three-dimensional single-pixel imaging of incoherent light with spatiotemporally modulated illumination

“…Instead, an SSB is isolated by a time-dependent phase shift imparted to the illumination intensity that manifests as a carrier frequency in the temporal domain. This carrier frequency permits one to isolate all three components of the measured signal—$S_t^{\left(0\right)},S_t^{\left(1\right)}, \text{and} S_t^{\left(-1\right)}$ —with straightforward Fourier signal processing methods [13–15,23]. …”

“…Throughout the scan, the AC signal encodes redundant spatial frequency information that must be isolated to recover a unique image of the object. CHIRPT enables the extraction of an SSB without the need to collect multiple images with phase-shifted illumination patterns [13,14]. This is accomplished with a time-dependent phase shift that causes the illumination fringes to shift across the specimen while the spatial frequency of the fringes is scanned through the support of the objective lens [15].…”

“…From that analysis, it follows that CHIRPT will obtain the largest possible DOF for an imaging system because plane waves are eigenfunctions of the Helmholtz equation that describes wave propagation in the object. While the plane-wave model of CHIRPT matches experimental measurements remarkably well [13,14], the focused illumination light that is typically used in the experimental realization of CHIRPT limits the DOF.…”

“…We recently developed an SPI method dubbed coherent holographic image reconstruction by phase transfer (CHIRPT), an imaging technique that converts the spatial phase information carried by the illumination light pattern into temporal modulations of the measured light [13,14]. A key feature of CHIRPT is the ability to digitally refocus light collected from regions that lie well beyond the traditional depth of field (DOF) set by the numerical aperture (NA) of the microscope and illumination wavelength.…”

“…A key feature of CHIRPT is the ability to digitally refocus light collected from regions that lie well beyond the traditional depth of field (DOF) set by the numerical aperture (NA) of the microscope and illumination wavelength. We have previously presented a plane-wave model of the CHIRPT imaging process that captures much of the physics of image formation [13]. From that analysis, it follows that CHIRPT will obtain the largest possible DOF for an imaging system because plane waves are eigenfunctions of the Helmholtz equation that describes wave propagation in the object.…”