Calculating a composition for a preparation for treating hair fibers

A method of calculating a composition for a preparation for treating hair fibers, the method comprising:

• obtaining a target specification, comprising one or more numerical parameters defining a desired appearance of the hair fibers;
• providing a second computational model describing an interaction of light with hair fibers;
• obtaining, for the first image, a first set of hair fiber optical parameters, which describes the hair fibers in the first image;
• modifying the first set of fiber optical parameters, to produce a second set of hair fiber optical parameters describing a plurality of modified hair fibers;
• simulating, using the second computational model and the second set of hair fiber optical parameters, how light would interact with the modified hair fibers;
• rendering, based on a result of the simulation, a first synthetic image showing an appearance of the modified hair fibers;
• and
• providing said first synthetic image as the modified image;
• providing a first computational model that relates a chemical composition of the preparation to a predicted appearance of the hair fibers when treated by that preparation;
• and
• calculating, using the first computational model and the target specification, a composition for the preparation that is predicted to produce in the hair fibers an appearance similar or identical to the desired appearance,
• wherein the preparation comprises a plurality of dye compounds of one type present in respective dosages and wherein, in calculating the composition using the first computational model, the dosages of all of the dye compounds of that type in the preparation are variable independently of one another,
• wherein said type is one of:
• primary dye compounds;
• coupler dye compounds;
• and direct dye compounds.