Pixel-size-maintained image reconstruction of digital holograms on arbitrarily tilted planes by the angular spectrum method

Angle Multiplexing Optical Image Encryption in the Fresnel Transform Domain Using Phase-Only Computer-Generated Hologram

We propose an angle multiplexing method for optics-based image encryption using a phase-only computer-generated hologram (POCGH) in the tilted Fresnel transform (TFrT) domain. Modified Gerchberg-Saxton algorithms, based on the three types of rotation manipulation in both the hologram and reconstruction planes, are used with their corresponding TFrT parameters to extract the phase-only functions (POFs) of the target images. All the extracted POFs are then phase-modulated and summed to obtain the final POCGH, which is capable of multiplexing and avoiding overlap in the reconstructed images. The computer simulation results show that the images corresponding to the various rotation manipulations at the hologram and image reconstruction planes can be successfully restored with high correlation coefficients. Due to the encrypted nature of the multiplexed images, a higher system security level can be achieved, as the images can only be correctly displayed when all the required parameters in the TFrT are available. The angle sensitivity on the image quality for each manipulation is also investigated.

Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes

The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.

Light propagation analysis using a translated plane angular spectrum method with the oblique plane wave incidence

A novel angular spectrum method was proposed to numerically analyze off-axis free-space light propagation on a translated plane to an arbitrary angle. Utilizing a shifted angular spectrum method based on an oblique incident plane wave assumption, a generalized light propagation formulation was obtained in a wide range of both tilt angles and sampling intervals, which overcame the limitations of prior attempts. A detailed comparison of the proposed angular spectrum method with prior methods is numerically presented for diffractive optics and computer-generated holograms. The validity of the proposed method was confirmed experimentally by reconstructing a digital holographic image using a spatial light modulator.

Wavelet-based depth-of-field extension, accurate autofocusing, and particle pairing for digital inline particle holography

Depth-of-field extension and accurate 3D position location are two important issues in digital holography for particle characterization and motion tracking. We propose a method of locating the axial positions of both opaque and transparent objects in the reconstructed 3D field in the wavelet domain. The spatial-frequency property of the reconstructed image is analyzed from the viewpoint of the point spread function of the digital inline holography. The reconstructed image is decomposed into high- and low-frequency subimages. By using the variance of the image gradient in the subimages as focus metrics, the depth-of-field of the synthesis image can be extended with all the particles focalized, and the focal plane of the object can be accurately determined. The method is validated by both simulated and experimental holograms of transparent spherical water droplets and opaque nonspherical coal particles. The extended-focus image is applied to the particle pairing in a digital holographic particle tracking velocimetry to obtain the 3D vector field.

Direct calculation of a three-dimensional diffracted field

We present an approach to calculating the complex amplitude of a three-dimensional (3D) diffracted light field in the paraxial approximation based on a 3D Fourier transform. Starting from the Huygens-Fresnel principle, the method is first developed for the computation of the light distribution around the focus of an apertured spherical wave. The method, with modification, is then extended to treat the 3D diffraction of an aperture with an arbitrary transmittance function.

Optical section imaging of the tilted planes by illumination-angle-scanning digital interference holography

A new method of optical imaging that can generate the section images of arbitrarily tilted planes has been developed from illumination-angle-scanning digital interference holography. A set of complex object fields are reconstructed from the holograms captured as the illumination angle is varied with uniform intervals. After the complex fields are modified with phase ramps that match the tilt (relative to the hologram plane) of a desired observation plane, the image of the object sliced along the tilted plane is obtained from their superposition. The axial resolution of a system employing this method is measured with a step height standard, and it is applied to the tomographic inspection of a microelectromechanical system.

Shifted angular spectrum method for off-axis numerical propagation

A novel method is proposed for simulating free-space propagation from an input source field to a destination sampling window laterally shifted from that in the source field. This off-axis type numerical propagation is realized using the shifted-Fresnel method (Shift-FR) and is very useful for calculating non-paraxial and large-scale fields. However, the Shift-FR is prone to a serious problem, in that it causes strong aliasing errors in short distance propagation. The proposed method, based on the angular spectrum method, resolves this problem. Numerical examples as well as the formulation are presented.

Quantitative imaging of cellular adhesion by total internal reflection holographic microscopy

Total internal reflection (TIR) holographic microscopy uses a prism in TIR as a near-field imager to perform quantitative phase microscopy of cell-substrate interfaces. The presence of microscopic organisms, cell-substrate interfaces, adhesions, and tissue structures on the prism's TIR face causes relative index of refraction and frustrated TIR to modulate the object beam's evanescent wave phase front. We present quantitative phase images of test specimens such as Amoeba proteus and cells such as SKOV-3 and 3T3 fibroblasts.

Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields

A novel method is proposed for simulating free-space propagation. This method is an improvement of the angular spectrum method (AS). The AS does not include any approximation of the propagation distance, because the formula thereof is derived directly from the Rayleigh-Sommerfeld equation. However, the AS is not an all-round method, because it produces severe numerical errors due to a sampling problem of the transfer function even in Fresnel regions. The proposed method resolves this problem by limiting the bandwidth of the propagation field and also expands the region in which exact fields can be calculated by the AS. A discussion on the validity of limiting the bandwidth is also presented.

Creating an extended focus image of a tilted object in Fourier digital holography

We present a new method to numerically reconstruct images on a tilted plane by digital holography in Fourier configuration. The proposed technique is based on a quadratic deformation of spatial coordinates of the digital hologram. By this approach we demonstrate that it is possible to recover the extended focus image (EFI) of a tilted object in a single reconstruction step from the deformed hologram.

Controlling depth of focus in 3D image reconstructions by flexible and adaptive deformation of digital holograms

We show here that through an adaptive deformation of digital holograms it is possible to manage the depth of focus in 3D imaging reconstruction. Deformation is applied to the original hologram with the aim to put simultaneously in focus, and in one reconstructed image plane, different objects lying at different distances from the hologram plane (i.e., CCD sensor). In the same way, by adapting the deformation it is possible to extend the depth of field having a tilted object entirely in focus. We demonstrate the method in both lensless as well as in microscope configuration.