Data amount circulated in the world is increasing year by year. Most of data are not desirable to erase even though the access frequency is not so high. To store the data, a data storage with long lifetime is required. TV program archives are the one of them and the data amount are increased with increasing the pixel number of display devices. Therefore, holographic data storage with large data capacity and long lifetime is expected for UHD TV. In holographic data storage, coded images called data pages are recorded on a recording medium by volume holography. However, the image quality is reduced by low-pass spatial frequency filtering, optical system error, and characteristics of recording medium. When the properties of optical system including recording medium are precisely known, the change of data page pattern can be expressed by an analytical function. In reconstruction, a deteriorated data page pattern from a volume hologram is captured by an image sensor. Then, an image sensor pixel detects signals from multiple data page pixels because a pixel pattern is spread. The weight coefficients from all data page pixels to an image sensor pixel can be calculated by using the analytical function. When the weight coefficients are calculated at all image sensor pixels, simultaneous equations are obtained. Original data page patterns can be reconstructed by solving the simultaneous equations. In this paper, the expression method of a deteriorated data page pattern with an analytical function is discussed.