Method of hologram calculation

A holographic projector comprising:

• a display device comprising an array of light-modulating pixels, wherein each light-modulating pixel is a cell containing liquid crystal operable to modulate both amplitude and phase;
• a display driver arranged to drive the display device to display a hologram by independently-driving each light-modulating pixel at a respective complex modulation level selected from a plurality of allowable complex modulation levels, each having an amplitude modulation value and phase modulation value;
• and
• a hologram engine configured to calculate a hologram to be displayed by the display driver, the hologram having an amplitude and a phase component and being calculated by a method comprising the ordered steps of:
• (i) receiving an input image comprising a plurality of data values representing amplitude;
• (ii) assigning a random phase value to each data value of the plurality of data values to form a complex data set;
• (iii) performing an inverse Fourier transform of the complex data set;
• (iv) constraining each complex data value of the complex data set to one of a plurality of allowable complex data values, each comprising an amplitude modulation value and a phase modulation value, to form a hologram, wherein for each complex data value of a second complex data set, the step of constraining comprises replacing the amplitude and phase component with the amplitude and phase component of the nearest allowable complex data value in the complex plane,
• wherein the plurality of allowable complex modulation levels comprises phase modulation values which span 2π, and wherein at least one of the complex modulation levels has an amplitude modulation value of zero;
• and
• wherein the plurality of allowable complex data values are defined on a line in the complex plane, wherein the line is a spiral towards the origin comprising a first section which is a closed loop around the origin and a second section which extends inwardly from the circumference of the loop towards the origin of the complex plane.