## 1 Introduction  
Holographic data storage (HDS) has been researched as a next-generation mass optical storage solution [1; 2; 3]. With HDS, information is recorded as a volume hologram in thick photopolymer media. Therefore, it can achieve a higher storage capacity than that of conventional planar optical disks. As a recording medium, photopolymer material is preferred [4; 5; 6] for the following reasons: (1) it is suitable for recording a thick phase-type hologram; (2) it has potential to achieve high diffraction efficiency with low noise, such as scattering; (3) the spectral sensitivity of the medium can be selected with comparative freedom; and (4) deterioration in the hologram does not easily occur. Issues associated with using photopolymer material, such as recording sensitivity and reliability, have been greatly improved, and this medium is currently expected to become a practical medium for HDS applications.  
HDS with photopolymer media is promising for archival storage. A reduction in power consumption is an expected requirement, although hard-disk drive (HDD) technology with relatively high power requirements is currently used for archival storage in data centers. If HDS replaces HDD as an archival storage solution, a reduction in power consumption of at least 40% is expected. Considering the progress of magnetic tape or hard-disk technologies used for archival storage, the capacity required by HDS is expected to be 1-10 TB/disk in the near future. These trends indicate that improvement of the recording and reproduction methods of HDS will be required in the future; photopolymer media represents an opportunity to achieve such high-capacity storage.  
The multiplexing method plays a key role in determining storage capacity, and numerous multiplexing methods have been previously proposed. Such methods can be classified roughly into Bragg-based and other techniques [3]. Bragg-based methods include angle [7; 8; 9], wavelength [10; 11], phase-code [12; 13], peristrophic [14; 15; 16], shift [17; 18], and correlation multiplexing [2]. These methods depend on the effect of Bragg selectivity, which is determined by calculating the thickness of the medium and the wavelength and geometry of the optical system. Multiplexing methods based on other principles include polytopic [19] and aperture multiplexing [20], which are based on conservation of momentum and optical correlation.  
In the present study, we examine the potential of achieving high recording density in the recording and reproduction method by combining peristrophic multiplexing and shift multiplexing with spherical reference waves [21]. In the latter method, multiplex recording is enabled simply by displacing the recording medium. However, results of our previous research indicated that the insensitivity of shift selectivity in the radial, or \(y\)-axis, direction becomes an obstruction factor to high-density recording; however, shift selectivity in the track direction and that vertical to the medium direction, or \(z\)-axis, were sensitive [22; 23]. Thus, it became necessary to enhance shift multiplexing to achieve the target storage capacity by combining it with a peristrophic-multiplexing method that changes the direction of the hologram transportation wave and provides multiple records.