Complex Hologram Research Articles

Spatial–temporal demodulation technique for heterodyne optical scanning holography

Abstract In optical scanning holography (OSH), the object is raster scanned by a heterodyne fringe pattern. The light scattered from the object is detected by a photodetector. Traditionally, the photo-electric signal is demodulated by a dual-channel lock-in amplifier (LIA) to extract a complex hologram. The use of LIA complicates the detection module of the system and increases the cost, especially when the heterodyne frequency is high. In this paper, an alternative demodulation method called a spatial–temporal demodulation technique (STDT) is studied. In STDT, the photo-electric temporal signal is directly digitized as scanning lines. The spectrum of each scanning line is band-pass filtered to remove the zeroth-order term and the complex conjugate term. Finally, a complex hologram is obtained from the filtered spectrum. The first merit of STDT is that the phase of the demodulated complex hologram is insensitive to the modulation error. Thus it is easily applied to the applications of particle holography. Besides, the bandwidth of the zeroth-order term in STDT is narrow, which allows the system to be operated in a wide range of heterodyne frequency. This feature enables STDT-based OSH to be applied in low-cost and high-speed dynamic holographic imaging.

High resolution integral holography using Fourier ptychographic approach.

An innovative approach is proposed for calculating high resolution computer generated integral holograms by using the Fourier Ptychographic (FP) algorithm. The approach initializes a high resolution complex hologram with a random guess, and then stitches together low resolution multi-view images, synthesized from the elemental images captured by integral imaging (II), to recover the high resolution hologram through an iterative retrieval with FP constrains. This paper begins with an analysis of the principle of hologram synthesis from multi-projections, followed by an accurate determination of the constrains required in the Fourier ptychographic integral-holography (FPIH). Next, the procedure of the approach is described in detail. Finally, optical reconstructions are performed and the results are demonstrated. Theoretical analysis and experiments show that our proposed approach can reconstruct 3D scenes with high resolution.

Embedding image into a phase-only hologram

Past research has demonstrated that with error diffusion, a complex Fresnel hologram can be converted into a phase-only hologram, and capable of preserving high fidelity on its reconstructed image. Furthermore, the phase-only hologram can be embedded with an image that is of the same size as the hologram. This is achieved by replacing the least M least significant bits (LSB) of each hologram pixel with the M most significant bits (MSB) of the embedded image in the error diffusion process. The phase-only hologram obtained in this manner is known as a Data Embedded Error Diffusion (DEED) hologram. Despite the success, the quality of the embedded image is rather poor for small value of M. However, if M is increased to preserve the quality of the embedded image, the phase-only hologram will be jeopardized. The DEED hologram also has no protection on the access of the embedded image, as it can be retrieved by simply extracting the M least significant bits of the hologram pixels. In this paper, a method for overcoming the above problems is reported. Briefly, the image to be embedded is first converted into an M bit data with the use of error diffusion. Next, a fixed window is reserved in the binary bit-string of each hologram pixel, within which M bits are randomly selected and replaced with the embedded image data. As such, the bit selection configuration in each hologram pixel can be taken as an encryption key for retrieving the embedded image. The image embedded phase-only hologram realized with such means, which is referred to as the Image Encrypted Error Diffusion (IEED) hologram, is capable of preserving high fidelity on the content of the hologram, as well as favorable visual quality on the embedded image if the correct encryption key is presented.

광 스캐닝 홀로그래피와 스펙클 잡음에 의한 오염도 평가

In this paper we record the complex hologram of a real object with optical scanning holography (OSH). We reconstruct the complex hologram using a numerical process, and then we evaluate the degree of contamination by speckle noise between the reconstruction of the complex hologram and the image captured by a CCD camera. We use the contrast of the speckle pattern for quantitative evaluation.Keywords: Holography, Speckle noise, Optical Scanning HolographyOCIS codes: (090.1995) Digital holography; (090.2870) Holographic display

Automatic decomposition of a complex hologram based on the virtual diffraction plane framework

Holography is a technique for capturing the hologram of a three-dimensional scene. In many applications, it is often pertinent to retain specific items of interest in the hologram, rather than retaining the full information, which may cause distraction in the analytical process that follows. For a real optical image that is captured with a camera or scanner, this process can be realized by applying image segmentation algorithms to decompose an image into its constituent entities. However, because it is different from an optical image, classic image segmentation methods cannot be applied directly to a hologram, as each pixel in the hologram carries holistic, rather than local, information of the object scene. In this paper, we propose a method to perform automatic decomposition of a complex hologram based on a recently proposed technique called the virtual diffraction plane (VDP) framework. Briefly, a complex hologram is back-propagated to a hypothetical plane known as the VDP. Next, the image on the VDP is automatically decomposed, through the use of the segmentation on the magnitude of the VDP image, into multiple sub-VDP images, each representing the diffracted waves of an isolated entity in the scene. Finally, each sub-VDP image is reverted back to a hologram. As such, a complex hologram can be decomposed into a plurality of subholograms, each representing a discrete object in the scene. We have demonstrated the successful performance of our proposed method by decomposing a complex hologram that is captured through the optical scanning holography (OSH) technique.

Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging.

We report an imaging scheme, termed aperture-scanning Fourier ptychography, for 3D refocusing and super-resolution macroscopic imaging. The reported scheme scans an aperture at the Fourier plane of an optical system and acquires the corresponding intensity images of the object. The acquired images are then synthesized in the frequency domain to recover a high-resolution complex sample wavefront; no phase information is needed in the recovery process. We demonstrate two applications of the reported scheme. In the first example, we use an aperture-scanning Fourier ptychography platform to recover the complex hologram of extended objects. The recovered hologram is then digitally propagated into different planes along the optical axis to examine the 3D structure of the object. We also demonstrate a reconstruction resolution better than the detector pixel limit (i.e., pixel super-resolution). In the second example, we develop a camera-scanning Fourier ptychography platform for super-resolution macroscopic imaging. By simply scanning the camera over different positions, we bypass the diffraction limit of the photographic lens and recover a super-resolution image of an object placed at the far field. This platform's maximum achievable resolution is ultimately determined by the camera's traveling range, not the aperture size of the lens. The FP scheme reported in this work may find applications in 3D object tracking, synthetic aperture imaging, remote sensing, and optical/electron/X-ray microscopy.

Fast conversion of digital Fresnel hologram to phase-only hologram based on localized error diffusion and redistribution

Past research has demonstrated that a digital, complex Fresnel hologram can be converted into a phase-only hologram with the use of the bi-direction error diffusion (BERD) algorithm. However, the recursive nature error diffusion process is lengthy and increases monotonically with hologram size. In this paper, we propose a method to overcome this problem. Briefly, each row of a hologram is partitioned into short non-overlapping segments, and a localized error diffusion algorithm is applied to convert the pixels in each segment into phase only values. Subsequently, the error signal is redistributed with low-pass filtering. As the operation on each segment is independent of others, the conversion process can be conducted at high speed with the graphic processing unit. The hologram obtained with the proposed method, known as the Localized Error Diffusion and Redistribution (LERDR) hologram, is over two orders of magnitude faster than that obtained by BERD for a 2048×2048 hologram, exceeding the capability of generating quality phase-only holograms in video rate.

Data-embedded-error-diffusion hologram (Invited Paper)

This paper describes a method for converting a complex Fresnel hologram into a phase-only hologram that can be embedded with large amount of data. Briefly, each row of pixels in the hologram is scanned sequentially in a left-to-right direction. The magnitude of each visited pixel is set to a constant, and its phase is embedded with the data. Subsequently, the error is diffused to the neighborhood pixels. The phase hologram realized with such means, which is referred to as the data-embedded-error-diffusion (DEED) hologram, is capable of preserving high fidelity on the content of the hologram and the embedded data.

Novel method for converting digital Fresnel hologram to phase-only hologram based on bidirectional error diffusion

We report a novel and fast method for converting a digital, complex Fresnel hologram into a phase-only hologram. Briefly, the pixels in the complex hologram are scanned sequentially in a row by row manner. The odd and even rows are scanned from opposite directions, constituting to a bidirectional error diffusion process. The magnitude of each visited pixel is forced to be a constant value, while preserving the exact phase value. The resulting error is diffused to the neighboring pixels that have not been visited before. The resulting novel phase-only hologram is called the bidirectional error diffusion (BERD) hologram. The reconstructed image from the BERD hologram exhibits high fidelity as compared with those obtained with the original complex hologram.

Speckle-free digital holographic recording of a diffusely reflecting object

We demonstrate holographic recording without speckle noise using the digital holographic technique called optical scanning holography (OSH). First, we record a complex hologram of a diffusely reflecting (DR) object using OSH. The incoherent mode of OSH makes it possible to record the complex hologram without speckle noise. Second, we convert the complex hologram to an off-axis real hologram digitally and finally we reconstruct the real hologram using an amplitude-only spatial light modulator (SLM) without twin-image noise and speckle noise. To the best of our knowledge, this is the first time demonstrating digital holographic recording of a DR object without speckle noise.

Computational hologram synthesis and representation on spatial light modulators for real-time 3D holographic imaging

In dynamic computer-generated holography that utilizes spatial light modulators, both hologram synthesis and hologram representation are essential in terms of fast computation and high reconstruction quality. For hologram synthesis, i.e. the computation step, Fresnel transform based or point-source based raytracing methods can be applied. In the encoding step, the complex wave-field has to be optimally represented by the SLM with its given modulation capability. For proper hologram reconstruction that implies a simultaneous and independent amplitude and phase modulation of the input wave-field by the SLM.In this paper, we discuss full complex hologram representation methods on SLMs by considering inherent SLM parameter such as modulation type and bit depth on their reconstruction performance such as diffraction efficiency and SNR. We review the three implementation schemes of Burckhardt amplitude-only representation, phase-only macro-pixel representation, and two-phase interference representation. Besides the optical performance we address their hardware complexity and required computational load. Finally, we experimentally demonstrate holographic reconstructions of different representation schemes as obtained by functional prototypes utilizing SeeReal's viewing-window holographic display technology. The proposed hardware implementations enable a fast encoding of complex-valued hologram data and thus will pave the way for commercial real-time holographic 3D imaging in the near future.

Overview of techniques applicable to self-interference incoherent digital holography.

Self-interference incoherent digital holography (SIDH) retrieves the complex hologram from the object illuminated by the incoherent light. Supported by the adaptive optic feature, SIDH is readily applicable to the ocular imaging to investigate the human retinal cells. Considering the practical issues, issues related to resolution, phase-shifting, and contrast should be addressed to implement the viable SIDH system which is capable of recording the holographic information of human retinal cells under the incoherent illumination. Super resolution image reconstruction technique can be directly applied to SIDH to enhance the resolution of the system without any change of configuration. We present the improved way to incorporate the phase-shifting itself into the lateral shift required by the super resolution technique. To deal with the phase-shifting issue, we present an arbitrary phase shift retrieval algorithm which can reduce the number of phase-shift and accept the blind phase-shift. The single-shot imaging is also possible by adopting the off-axis configuration of SIDH. We will provide the detailed procedures to retrieve the complex hologram using the proposed arbitrary phase shifting algorithm and the off-axis configuration.

Digital holographic three-dimensional imaging spectrometry

A fully interferometric technique for obtaining hypermultispectral components of three-dimensional (3D) images has been tested for a polychromatic object that consists of spatially incoherent, planar light sources of different shapes. Each planar source has different continuous spectra, located at different 3D positions. The method is based on measurement of a five-dimensional (5D) interferogram. By applying synthetic aperture technique and spectral decomposition to that 5D interferogram, one obtains a set of complex holograms of different spectral components. From these holograms, 3D images of multiple spectral components have been retrieved. A decomposed continuous spectrum of each planar light source is also shown to demonstrate the potential applicability to identify materials of a particular part of an object under illumination by white light.

Analysis of Effect of Phase Error Sources of Polarization Components in Incoherent Triangular Holography

We derive the point-spread function of the reconstructed image from a point-source complex hologram, which includes phase error caused by polarization components, in the longitudinal direction of the point-spread function and analyze the effect of the error sources of polarization components having influence on image reconstruction of a point-source complex hologram in incoherent triangular holography.

Image encryption based on the reality-preserving multiple-parameter fractional Fourier transform and chaos permutation

In recent years, a number of methods have been proposed in the literature for the encryption of two-dimensional information by use of the fractional Fourier transform, but most of their encryptions are complex value and need digital hologram technique to record their encrypted information, which is inconvenience for digital transmission. In this paper, we first propose a novel reality-preserving multiple-parameter fractional Fourier transform which share real-valuedness outputs as well as most of the properties required for a fractional transform. Then we propose a new approach for image encryption based on the real-valuedness of the reality-preserving multiple-parameter fractional Fourier transform and the decorrelation property of chaotic maps in order to meet the requirements of the secure image transmission. In the proposed scheme, the image is encrypted by juxtaposition of sections of the image in the reality-preserving multiple-parameter fractional Fourier domains and the alignment of sections is determined by chaotic logistic maps. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.

Image encryption based on the reality-preserving multiple-parameter fractional Fourier transform

In recent years, a number of methods have been proposed in the literature for the encryption of two-dimensional information by using the fractional Fourier transform, but most of their encryptions are complex values and need digital hologram technique to record information, which is inconvenient for digital transmission. In this paper, we propose a new approach for image encryption based on the real-valuedness and decorrelation property of the reality-preserving multiple-parameter fractional Fourier transform in order to meet the requirements of the secure image transmission. In the proposed scheme, the original and encrypted images are respectively in the spatial domain and the reality-preserving multiple-parameter fractional Fourier transformed domain determined by the encryption keys. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.

Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging

Fresnel Incoherent Correlation Holography (FINCH) enables holograms to be recorded from incoherent light with just a digital camera and spatial light modulator. We previously described its application to general three dimensional incoherent imaging and specifically to fluorescence microscopy, wherein one complex hologram contains the three dimensional information in the field of view, obviating the need for scanning or serial sectioning. We have now further analyzed FINCH in view of linear system theory and in comparison to conventional coherent and incoherent two dimensional imaging systems. We demonstrate, theoretically and experimentally, improved resolution by FINCH, when compared to conventional imaging.

Complex Fresnel hologram display using a single SLM

We propose a novel optical method to display a complex Fresnel hologram using a single spatial light modulator (SLM). The method consists of a standard coherent image processing system with a sinusoidal grating at the Fourier plane. Two or three position-shifted amplitude holograms displayed at the input plane of the processing system can be coupled via the grating and will be precisely overlapped at the system's output plane. As a result, we can synthesize a complex hologram that is free of the twin image and the zero-order light using a single SLM. Because the twin image is not removed via filtering, the full bandwidth of the SLM can be utilized for displaying on-axis holograms. In addition, the degree of freedom of the synthesized complex hologram display can be extended by involving more than three amplitude holograms.

Low-bit-rate computer-generated color Fresnel holography with compression ratio of over 1600 times using vector quantization [Invited

We propose a method for compressing a digital color Fresnel hologram based on vector quantization (VQ). The complex color hologram is first separated into three complex holograms, each representing one of the primary colors. Subsequently, each hologram is converted into what we call a real Fresnel hologram and compressed with VQ based on a universal codebook. Experimental evaluation reveals that our scheme is capable of attaining a compression ratio of over 1600 times and still preserving acceptable visual quality on the reconstructed images. Moreover, the decoding process is free from computation and highly resistant to noise contamination on the compressed data.

Optimal complex field holographic projection

We describe a technique that uses complex field holograms to project three-dimensional light patterns. Holographic projection commonly uses phase-only encoding since accurately representing complex holograms using both amplitude and phase spatial light modulators reduces the optical throughput significantly. Here, we use a lossless projection via the generalized phase contrast method to produce the necessary amplitude pattern required for complex field holographic projection. We numerically evaluate the technique and demonstrate high optical throughput with reduced undesired high diffraction orders.