Chapter 1
Parallel Phase-Shifting Digital Holography

Yasuhiro Awatsuji

Division of Electronics, Kyoto Institute of Technology, Japan

1.1 Chapter Overview

Parallel phase-shifting digital holography is a technique capable of not only instantaneously measuring the three-dimensional (3D) field but also motion picture measurement of time evolution in the 3D field. The recording and reconstruction flow of this technique are described. The technique has been experimentally demonstrated by a parallel phase-shifting digital holography system using a normal-speed camera, which lead to a high-speed camera being constructed and used so that 3D motion and phase motion picture capture were demonstrated at the rate of up to 262 500 frames per second (fps). As an ultrafast phase imaging technique, a parallel phase-shifting digital holography system using a femtosecond pulsed laser has been experimentally demonstrated. A portable parallel phase-shifting digital holography system will also be introduced here. Finally some function-extended parallel phase-shifting digital holography will be mentioned for the purpose of motion picture-measurement of 3D and color, 3D and spectral characteristics, 3D and polarization characteristics, and 3D motion picture microscopy.

1.2 Introduction

Holography is a technique for recording and reconstructing perfect wavefronts of objects [1]. The technique actively investigates not only three-dimensional (3D) displays but also 3D measurement of objects. In this technique, the complex amplitude distribution of an object is recorded as a form of an interference fringe image. The complex amplitude distribution consists of amplitude and phase distributions of objects, and can provide a 3D image. In conventional holography, a high-resolution photosensitive material, called the holographic plate, is used to record the interference fringe image. The medium in which the interference fringe image is recorded is the hologram.

Recently, there has been a great deal of progress in image sensors such as charge-coupled devices (CCDs) and complementary metal-oxide semiconductor (CMOS) image sensors, and such devices have been used in holography in place of holographic plates. Holography using image sensors is called digital holography [2, 3]. Digital holography has the following attractive features: it does not require a wet and chemical process for developing; quantitative evaluation is easy for 3D images of objects; and focused images of 3D objects at the desired depth can be instantaneously recorded without a mechanical focusing process. Also, this technique can quantitatively provide phase distribution of an object. Thus, digital holography can serve as a quantitative 3D and phase-imaging video camera. The technique is used in many fields such as shape and deformation measurement, particle measurement, microscopy, endoscopy, object recognition, information security, and so on.

Since the pixel size and pixel pitch of image sensors are too large to record fine interference fringes that would be recorded on a photographic plate, in-line digital holography is frequently applied. In in-line digital holography, the object and reference waves almost orthogonally irradiate the image sensor. Indeed, in-line digital holography allows instantaneous measurement of the object wave in principle, but the reconstructed image is degraded because the undesired images are superimposed on the desired object wave. To obtain just the object wave, phase-shifting digital holography has been proposed [4].

Although phase-shifting digital holography can only derive the complex amplitude of an object wave at an arbitrary depth, it needs multiple holograms to reconstruct the object wave free of undesired images. The multiple holograms are sequentially recorded by using reference waves with different phase retardations. Indeed phase-shifting digital holography allows reconstruction of a clear object wave, but is useless for instantaneous measurement of moving objects. To achieve a phase-shifting method that can perform instantaneous measurement, parallel phase-shifting digital holography has been investigated [5-27]. The technique uses an ingenious arrangement of image sensor pixels and a phase-shifting array device.

In this chapter, the basic concept and processing flow of parallel phase-shifting digital holography are explained. Three parallel phase-shifting digital holography experimental systems and their results are described [23-26]. Also, a portable system based on parallel phase-shifting digital holography is introduced [27]. Finally, some function-extended parallel phase-shifting digital holography techniques are mentioned [28-35].

1.3 Digital Holography and Phase-Shifting Digital Holography

Digital holography is a technique for recording the interference fringe image by an image sensor and reconstructing the complex amplitude distribution of an object by computer [2, 3]. A schematic of a system setup of digital holography is shown in Fig. 1.1. Generally, a laser is used as the optical source. A laser beam is divided into two beams. One beam illuminates the object and the beam scattered from the object is called the object wave. The object wave irradiates the image sensor. The other beam illuminates the image sensor directly and this beam is called a reference wave. An interference fringe image is generated by the object and reference waves and captured with the image sensor. The captured interference image is called a digital hologram. The complex amplitude distribution of the object is numerically reconstructed from the digital hologram by computer. Therefore, one instantaneous 3D image of an object can be reconstructed from a single hologram. By sequential capturing of holograms with a camera, a 3D motion picture image of the object can be recorded.

Figure 1.1 Schematic diagram of digital holography

To reconstruct the image in digital holography, a diffraction integral is generally applied to the hologram recorded with the image sensor. Although the use of only the diffraction integral is the simplest calculation scheme used to reconstruct the image and allows instantaneous measurement, the reconstructed image is degraded because the undesired images, which are the non-diffraction wave and the conjugate image, are superimposed on the desired object wave, which forms the image of the object. To extract just the object wave, phase-shifting digital holography has been proposed [4].

Figure 1.2 shows the optical setup schematic for phase-shifting digital holography [4]. More than two holograms are sequentially recorded using reference waves with different phase retardations. A method of four-step phase-shifting of the reference wave, such as 0, p/2, p, and 3p/2, is frequently adopted for phase-shifting digital holography. Usually, the retardation is sequentially changed by using a piezoelectric-transducer (PZT) mirror or wave plates. Indeed phase-shifting digital holography can only derive the complex amplitude of an object wave and is useless for moving objects. To obtain a clear reconstructed 3D image of moving objects, parallel phase-shifting digital holography has been proposed [5-27].

Figure 1.2 Schematic diagram of phase-shifting digital holography

1.4 Parallel Phase-Shifting Digital Holography

The essence of parallel phase-shifting digital holography [5-27] is a single-shot technique for implementing phase-shifting digital holography. The single-shot technique uses a single image sensor and space-division multiplexing of holograms. Figure 1.3 shows a schematic diagram of the principle of parallel phase-shifting digital holography. Multiple holograms needed for phase-shifting digital holography are stuffed into a single hologram by using space-division multiplexing of the holograms pixel by pixel. To implement the multiplexing of the holograms, several ideas have been proposed. A micro phase-retarder array such as the micro glass-plate array is inserted in the reference wave path and imaged onto the image sensor [5]. High light efficiency is achieved by this arrangement, but precise alignment of the optical system for imaging of the micro phase-retarder array onto the image sensor pixel by pixel is needed. To make alignment easy, a spatial light modulator (SLM) consisting of a liquid crystal is used in the micro phase-retarder array [17]. Also a micro polarization-element array was proposed to achieve the multiplexing of the holograms. In this arrangement, a micro polarization-element array is attached to the image sensor [6, 13, 16, 23-27]. The directions of the transmission axes of the micro polarizer array are alternately changed pixel by pixel. 2 × 2 configuration [5-7, 11] and 2 × 1 configuration [10, 11, 13, 14] of the unit of micro polarizer array have been reported for parallel four-step and parallel two-step phase-shifting digital holography, respectively. Light efficiency of this arrangement is lower than that using a micro phase-retarder array, but alignment of the optical element in the parallel phase-shifting digital holography system is quite easy.

Figure 1.3 Schematic diagram of principle of parallel phase-shifting digital holography

Figure 1.4 shows a schematic diagram of a flow for image reconstruction in parallel phase-shifting digital holography. This figure shows one example of the implementation of parallel four-step-phase-shifting...