A controller for a holographic display apparatus comprising a spatial light modulator, the controller being configured to: generate a first frame hologram data signal including information of a first frame hologram pattern for reproducing a first frame hologram image for a first frame and a first frame diffraction pattern data signal including information of a first frame periodic diffraction pattern for adjusting a location of the first frame hologram image to be reproduced; generate a first final signal by multiplying the first frame hologram data signal by the first frame diffraction pattern data signal; provide the first final signal to the spatial light modulator; generate a second frame hologram data signal including information of a second frame hologram pattern for reproducing a second frame hologram image for a second frame and a second frame diffraction pattern data signal including information of a second frame periodic diffraction pattern for adjusting a location of the second frame hologram image to be reproduced; generate a second final signal by multiplying the second frame hologram data signal by the second frame diffraction pattern data signal; and provide the second final signal to the spatial light modulator, wherein each of the first frame hologram image and the second frame hologram image comprises a first color image, a second color image, and a third color image, the first color image, the second color image and the third color image are red, green and blue colors respectively, and wherein each of the first frame periodic diffraction pattern and the second frame periodic diffraction pattern comprises a first periodic diffraction pattern for adjusting a location of the first color image, a second periodic diffraction pattern for adjusting a location of the second color image, and a third periodic diffraction pattern for adjusting a location of the third color image, the first periodic diffraction pattern, the second periodic diffraction pattern, and the third periodic diffraction pattern having different periods from each other, and further characterised in that the controller is configured to generate the first frame diffraction pattern data signal and the second frame diffraction pattern data signal such that the second frame periodic diffraction pattern formed on the spatial light modulator in the second frame derives from the first frame periodic diffraction pattern formed on the spatial light modulator in the first frame by translation along a predetermined direction, further characterised in that the controller is configured to set the periods of the first, second and third periodic diffraction patterns to be proportional to wavelengths of light of first, second and third colors, respectively. generate a first frame hologram data signal including information of a first frame hologram pattern for reproducing a first frame hologram image for a first frame and a first frame diffraction pattern data signal including information of a first frame periodic diffraction pattern for adjusting a location of the first frame hologram image to be reproduced; generate a first final signal by multiplying the first frame hologram data signal by the first frame diffraction pattern data signal; provide the first final signal to the spatial light modulator; generate a second frame hologram data signal including information of a second frame hologram pattern for reproducing a second frame hologram image for a second frame and a second frame diffraction pattern data signal including information of a second frame periodic diffraction pattern for adjusting a location of the second frame hologram image to be reproduced; generate a second final signal by multiplying the second frame hologram data signal by the second frame diffraction pattern data signal; and provide the second final signal to the spatial light modulator, wherein each of the first frame hologram image and the second frame hologram image comprises a first color image, a second color image, and a third color image, the first color image, the second color image and the third color image are red, green and blue colors respectively, and wherein each of the first frame periodic diffraction pattern and the second frame periodic diffraction pattern comprises a first periodic diffraction pattern for adjusting a location of the first color image, a second periodic diffraction pattern for adjusting a location of the second color image, and a third periodic diffraction pattern for adjusting a location of the third color image, the first periodic diffraction pattern, the second periodic diffraction pattern, and the third periodic diffraction pattern having different periods from each other, and further characterised in that the controller is configured to generate the first frame diffraction pattern data signal and the second frame diffraction pattern data signal such that the second frame periodic diffraction pattern formed on the spatial light modulator in the second frame derives from the first frame periodic diffraction pattern formed on the spatial light modulator in the first frame by translation along a predetermined direction, further characterised in that the controller is configured to set the periods of the first, second and third periodic diffraction patterns to be proportional to wavelengths of light of first, second and third colors, respectively.