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Grasp the science behind color mixing

Posted: 04 Jul 2012 ?? ?Print Version ?Bookmark and Share

Keywords:HB LEDs? Colour mixing? linear transformation?

Colour mixing these three LEDs can generate any colour that lies within this triangle. This area is called the colour gamut. However, in the CIE 1931 standard, the colour distribution is not homogeneous and contains discontinuities. Therefore, linear transformation cannot be applied to decide the proportion of primary colour required to generate the desired secondary colour.

Colour-mixing algorithm
In colour-mixing applications, the firmware inputs values in CIE chromaticity coordinate form. It converts the coordinates into appropriate dimming values for each LED channel. A dimming value is simply the percentage of maximum luminous flux to which an LED must be dimmed. If the current of an LED is quickly switched on and off in an intelligent fashion, the LED has its flux output controlled.

The firmware combines this coordinate with its preprogrammed knowledge of the characteristics of the LEDs in the system. It then completes the necessary transfer function that correctly converts the chromaticity coordinate into a dimming value for each LED. This process enables their light outputs to mix together to create the colour of the chromaticity coordinate input into the system.

Multi-channel colour mixing
In a three-channel colour mix, if the colour points of three LEDs are mapped onto the CIE 1931 chart, it forms a triangle. If the three LEDs are red, green, and blue then the triangle formed is called the colour gamut (figure 2). The area inside the triangle is the gamut of achievable colours with this particular set of three LEDs. Any (x, y) coordinate within the triangle is input into the system. This provides a broad range and high resolution of unique colours that is produced with this system.

Four-channel colour-mixing solution is based on the principle of superposition. It uses three-channel colour-mixing algorithm as its base. For four-channel colour mixing, if the colour points of four LEDs are mapped onto a colour space chart, it becomes apparent that there are exactly four triangles formed by the lines drawn between the four LED colour point (figure 3).

Figure 3: Superposition on four-channel colour mixing.

The method described here is easily expandable to more than four LED colours. In figure 3, the four triangles are made up of the following LED triplets: TR1(R,G,B), TR2(R,A,B), TR3(R,G,A), and TR4(G,A,B).

Each triangle is solved for dimming values using three-channel colour mixing functions. Out of these four triangles, two give all non-negative dimming values and two have one or all dimming values negative. Triangles with any or all negatives values are not valid and are discarded. Dimming arrays with all positive values are accumulated.

The interpretation of negative dimming values is that the desired point lies outside the triangle formed by three basic colours. For example, in figure 4, RGB triangle returns all non negative values for P1; for P2, at least one dimming value is negative.

Two positive dimming values for each desired colour are added and scaled appropriately. A negative dimming value implies that the desired colour is not inside the gamut so that cannot be generated using the particular base colours.

Figure 4: Positive and negative dimming values.

Colour-mixing implementation details
The firmware uses CIE 1931 colour space to input colour requests. A particular point in the CIE 1931 colour space is represented with three values (x, y, Y). The point is defined by (x, y) where x and y value represent the colour hue and saturation. Hue is one of the dimensions of CIE 1931 colour space. Saturation is the second dimension of this colour space. The third value of (x, y, Y) vector specifies the luminous flux, in lumens (lm). The firmware must have inputs in the (x, y, Y) vector that specifies its colour and flux output at some rated current and junction temperature.

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