Holographic representation: Hologram plane vs. object plane

https://doi.org/10.1016/j.image.2018.08.006Get rights and content

Highlights

  • Online database containing several sets of four interference patterns acquired by the phase shifting holography technique and the holograms generated from them.

  • Encoding performance in both propagation planes, hologram and object planes, is analyzed and compared.

  • Coding efficiency of Real-Imaginary versus Amplitude-Phase representation on computer generated and experimental holographic data is analyzed.

  • Quality assessment, in both propagation planes, hologram and object planes, is analyzed and compared.

Abstract

Digital holography allows the recording, storage and subsequent reconstruction of both amplitude and phase of the light field scattered by an object. This is accomplished by recording interference patterns that preserve the properties of the original object field essential for 3D visualization, the so-called holograms.

Digital holography refers to the acquisition of holograms with a digital sensor, typically a CCD or a CMOS camera, and to the reconstruction of the 3D object field using numerical methods.

In the current work, the different representations of digital holographic information in the hologram and in the object planes are studied. The coding performance of the different complex field representations, notably Amplitude-Phase and Real-Imaginary, in both the hologram plane and the object plane, is assessed using both computer generated and experimental holograms. The HEVC intra main coding profile is used for the compression of the different representations in both planes, either for experimental holograms or computer generated holograms.

The HEVC intra compression in the object plane outperforms encoding in the hologram plane. Furthermore, encoding computer generated holograms in the object plane has a larger benefit than the same encoding over the experimental holograms. This difference was expected, since experimental holograms are affected by a larger negative influence of speckle noise, resulting in a loss of compression efficiency.

This work emphasizes the possibility of holographic coding on the object plane, instead of the common encoding in the hologram plane approach. Moreover, this possibility allows direct visualization of the Object Plane Amplitude in a regular 2D display without any transformation methods. The complementary phase information can easily be used to render 3D features such as depth map, multi-view or even holographic interference patterns for further 3D visualization depending on the display technology.

Introduction

Holography provides the possibility to fully reconstruct a complex wavefield by recording its interference with a coherent reference beam. It was first presented by D. Gabor in 1948 while trying to improve electron microscopy [1]. Shortly after the invention of Light Amplification by Stimulated Emission of Radiation (LASER), E. Leith and Upatnieks developed the first transmission hologram in 1962 [[2], [3]], while Y. Denisyuk developed the first reflection hologram [4]. Traditionally, a hologram is an interference fringe pattern that is recorded in a photosensitive film using an appropriate optical setup. When that pattern is illuminated with the reference light, the diffracted wavefield fully reconstructs the captured object field along with all its properties: light intensity, parallax, and depth. In theory, there is no optical difference between the original and reconstructed object field.

Those earlier works lead in a short time to the production of the first Computer Generated Hologram (CGH). Lohmann and Paris made that breakthrough in 1967 using the limited computing capabilities at that time [5]. In 1980, Yaroslavskii and Merzlyakov established the theoretical background for CGH [6]. A digital hologram differs from a CGH in the sense that the generation of the interference patterns is performed optically instead of being artificially generated by numerical means. After Goodman and Lawrence [7] studies, digital holography development was followed by Kronrod et al. [8] who digitized optically enlarged parts of in-line and Fourier holograms to obtain numerical reconstructions of the original object fields. Later on, Onural and Scott made significant improvements in reconstruction algorithms [[9], [10]]. However, a major step in digital holography occurred in the 1990’s, when full digital recording and processing was made possible with the development of the first Charged Coupled Device (CCD). Schnars and Juptner presented the first direct recording of Fresnel holograms using this technique [11].

The referred advances in holography defined an important research topic, which is making its way into the most diverse applications including data storage [[12], [13], [14]], security [[15], [16]], medical imaging [[17], [18]], deformation/displacement measurement [19], and inevitably 3D displays [[20], [21]]. Holographic 3D displays are certainly a promising technology, which found their interest in early Hollywood sci-fi movies. Currently, most advanced prototypes, the so-called light-field or holographic displays, can already display holographic information in full 3D, despite the limited resolution, and viewing angle.

The first proposal for digital hologram coding and transmission dates from 1991, when Sato et al. [22] captured the holographic fringes using a camera, which was then modulated into a TV signal and transmitted to the receiver. In 1993, Yoshikawa realized that it is impractical to apply 2D image compression directly to the hologram. Instead, he proposes compressing hologram segments that correspond to different reconstruction perspectives. The segments were compressed with MPEG-1 and MPEG-2 [[23], [24]]. In 2002, Naughton et al., studied the compressibility of phase-shifting digital holography using several lossless compression algorithms [25]. They concluded that better compression rates might be expected when the digital hologram is stored in an intermediate coding of separate data streams for real and imaginary components. Lossy compression techniques such as subsampling and quantization were also applied in [25]. Quantization proved to be a very effective technique. The effectiveness of quantization in both numerical simulation and optical experiments was confirmed by Mills and Yamaguchi [26]. The quantization on reconstruction domain of phase shifting holograms was analyzed by Darakis and Soraghan [27]. Naughton et al. in 2003 and Darakis et al. in 2006, demonstrated that the direct application of standard wavelets to holograms is not very efficient, since standard wavelets are typically designed to process piecewise smooth signals [[28], [29], [30]]. These authors proposed the use of a family of wavelet bases, named Fresnelets. Fresnelets were also applied in 2003 by Libeling et al. [31]. A similar study to [25] was provided by Frauel [32]. In 2006, Seo et al. proposed compressing hologram segments using multi-view and temporal prediction within a modified MPEG-2 [[33], [34]]. Mills and I. Yamaguchi [26], Seo et al. [35], and Shortt et al., 2007 [36], considered the improvement of quantization of Real-Imaginary information. In 2010, Darakis et al. [37] determined the highest compression ratio that can be achieved on holograms while maintaining reconstruction quality at visually lossless levels. They used both MPEG-4 AVC and Dirac in their experiments. Based on scalar quantization, a multiple description coding method was applied to Amplitude-Phase information using maximum-a-posteriori [38]. It turned out to be a powerful mechanism to mitigate channel errors on digital holograms.

Complementary to the extensive studies on the performance of lossless coding and quantization methods, work on holographic data compression focused on lossy compression with wavelets transform were proposed. In 2013, Blinder et al. [39] investigated alternative wavelet decomposition on off-axis holograms. In 2014, Viswanathan et al. [40] used Morlet wavelets for transforming a hologram, and in 2015, Xing et al. [41] combined wavelet transform and joint encoding methods to compress phase-shifting holographic data.

In 2014, Still, Xing and Dufaux studied lossy coding based on scalar and vector quantization [42]. The same authors proposed a vector lifting scheme that exploits mutual redundancy [43].

More recently, Peixeiro et al. [44] performed a benchmark of the main available image coding standard solutions for digital holographic data, along with the main alternative representation formats. The standard image codecs: JPEG, JPEG 2000, H.264/AVC intra, HEVC intra main coding profile were compared. The authors concluded that the HEVC intra main coding profile is the best standardized coding solution and that the best representation formats are the Phase-Shifted Distances and Real-Imaginary.

Also in 2016, Dufaux et al. [[45], [46]] reviewed the state of the art of the compression of digital holographic data. Several research lines were proposed by the authors, from which we point out the following three: the need for common datasets for a fair comparison of the proposed compression methods; the pursuit of better performance assessment methodologies; and finally, the urge to understand at which stage of the processing pipeline compression needs to be performed. This paper gives some contributions to these three points raised by Dufaux [46].

The first contribution of this paper is a database available online,1 named EmergImg-HoloGrail, containing several sets of four interference patterns acquired in “Universidade da Beira Interior”, by the phase shifting holography technique [47]. The sets of four phase-shifted holograms that are used to generate holograms can be found in the database. The Matlab codes for algebraic combination and numerical reconstruction of the interference patterns are also made available.

The second contribution is related with the choice of the compression plane. As presented above, several coding methods were used to study the characteristics of different representations. In the previous studies, the compression has been mostly applied to the hologram plane. Darakis and Soraghan [27] consider the compression on the object plane. These authors compare the quantization of the complex amplitudes on camera plane versus the quantization of complex amplitudes on the reconstruction plane. A single object acquired hologram and the normalized root-mean-square (NMRS) error for comparison, were used. They shown that the compression on reconstruction plane outperforms the compression on camera plane [27]. Furthermore, the application of Fresnelets can be understood as using a B-spline wavelet transform on the object plane. The Fresnelets coefficients are compressed more efficiently than the corresponding wavefront, since they reveal a higher spatially correlation [30]. In [30] the SPIHT coding of Fresnelets was proposed. They used the proposed method to compress one hologram representing a die. In the current study a similar analysis is overtaken. However, the Amplitude-Phase and Real-Imaginary representations are considered and coded independently. Moreover, the HEVC intra main coding profile is used since it was considered the best standardized coding solution for both hologram plane [44] and object plane [48]. Furthermore, experimental holograms and CGHs are considered in this study. Some of the holograms have multiple objects.

Finally, as last contribution, the quality was assessed in both hologram and object planes. Usually, reconstruction of the object is performed for quality assessment. However, as both planes were considered for quality assessment, the relation between them was also analyzed.

The present work analyses the coding efficiency of (1) Real-Imaginary versus Amplitude-Phase representation; (2) Hologram versus Object plane; and for (3) Computer generated and experimental holographic data.

Section snippets

Optical recording

The evaluated digital holograms were acquired using phase-shifting holography. The recording setup comprises a Mach–Zehnder type interferometer working in the reflection mode and using an in-line configuration (see Fig. 1). According to this setup, a laser beam, produced by a randomly polarized HeNe laser with 5mW and 632.8nm wavelength, is divided into a reference and an object beams by means of a variable beam splitter. The light reflected by the object is then combined with the reference

Method of analysis

The goal of the present work is to analyze the impact of codification in each propagation plane, hologram or object planes (see Fig. 3) for the different complex representation formats, namely Amplitude-Phase or Real-Imaginary, using experimental holograms and CGHs. This section presents the used data, the considered representations, the coding scheme, and finally the quality assessment methodology.

Results and global analyses

In this section, the results obtained for the impact of HEVC in each Amplitude-Phase and Real-Imaginary representations, on the hologram and on the object plane in experimental holograms and CGHs are analyzed.

Figs. 10, 11, and 12 represent the bpp/PSNR relations for CGHs from Interfere-I, Interfere-II, and experimental holograms, respectively. All the relations are presented, namely, the two coding planes and the two assessment planes possibilities. More specifically, both Real-Imaginary (RI)

Conclusion

In this work, the coding performance of Amplitude-Phase and Real-Imaginary representations, on hologram and object propagation planes, for experimental holograms and CGHs, was analyzed. The assessment in both hologram and object planes is also studied.

The experimental holograms used in this work are made available in an open-access database. The optical recording, phase-shifting, and numerical reconstruction are detailed and the necessary MATLAB codes are also provided. The CGHs were selected

Acknowledgments

The authors are very grateful to the Portuguese FCT-Fundação para a Ciência e Tecnologia and co-funded by FEDER-PT2020 , Portugal partnership agreement under the project PTDC/EEI-PRO/2849/ 2014 - POCI-01-0145-FEDER-016693, and under the project UID/EEA/50008/2013.

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