Due to the advantages of traditional lighting solutions, the application of high brightness (HB) LEDs is becoming more and more popular. One of the advantages of high-brightness LEDs is their ability to generate different colors, which opens up a new world of decorative lighting.
The essence of color mixing is the process of generating secondary colors by mixing the underlying primary colors in an appropriate ratio. This article will explain the science behind color mixing, including the mathematical formulas involved and how to apply them effectively.
The science behind color mixing and multi-point excitation spaces
Primary colors are not the basic properties of light, but often involve the psychological response of the eye to light. It is believed that the primary colors are completely independent of one another, but can be combined to create a useful color range (gamut).
Similar to the mathematical representation of any other physical phenomenon, the color model can be expressed in different ways. Each model has its own advantages and disadvantages. The goal of modeling is to minimize the complexity and number of variables of the formula while maximizing "substance" and coverage.
Traditionally, three of them are sufficient to describe all colors, regardless of what they are assigned to variables: RGB, hue-saturation-brightness (HSB), other hue-saturation-based models such as L&TImes; a&TImes;b and xyY. A common feature of them is the number or dimension of variables.
In the multi-point excitation space, the color excitation is marked by the letters R, Q, G, B, and A. Q refers to the excitation of any color; the letters R, G, B, and A are reserved for the expression of the selected fixed basic excitation for the color matching experiment. Red, green, blue and amber are basic motivations.
Color matching refers to an additive mixture obtained by mixing a given excitation Q with various basic excitations R, G, B, and A in an appropriate amount, which can be expressed by a vector equation (Formula 1):
Formula 1
In multidimensional space, the color excitation Q is represented by a multi-point excitation vector Q; where: scalar megaTIpliers RQ, GQ, BQ, and AQ are respectively metrics for the given basic excitations R, G, B, and A. Units to measure, they are called multi-point excitation values ​​of Q.
Figure 1 is a geometric representation of the linear multidimensional space of Equation 1. The unit vectors R, G, B, and A represent basic stimuli that define the space. They have a common starting point and point to four different directions.
Figure 1: Multidimensional color space.
The vector Q is the same as the origin of R, G, B, and A. Its four components are located at the axes defined by R, G, B, and A; the lengths are equal to the multi-point excitation values ​​RQ, GQ, BQ, and AQ, respectively. The direction and length can be obtained from a simple vector equation defined by equation (1). The space defined by R, G, B, and A is called a multi-excitation space. In this space, the color excitation Q can be regarded as a multi-excitation vector (RQ, GQ, BQ, and AQ). In the color blending algorithm, the firmware calculates what these values ​​should be to obtain a color stimulus Q.
Color mixing
Figure 2 shows the CIE 1932 chromaticity diagram. There are three LEDs in the picture: red, green and blue. By mixing the two primary colors (such as red and blue) in an appropriate ratio, the colors on their lines can be produced; likewise, when blue and green are mixed, can the blue and green lines be produced? ? There are colors.
Figure 2: CIE chromaticity diagram.
Mixing these three LED colors can produce any color that lies within this triangle. This area is called the color gamut. However, in the CIE 1931 standard, the color distribution is uneven and discontinuous. Therefore, when it is decided to generate the required secondary color and calculate the ratio of the primary colors, linear transformation cannot be employed.
In a color mixing application, the firmware enters values ​​in the form of CIE chromaticity coordinates. For each LED channel, it converts the coordinates to the appropriate dimming value. Simply put, the dimming value is the ratio of the maximum luminous flux that the LED must have in the dimming range. If the operating current of the LED is quickly turned on and off in an intelligent manner, the luminous flux output of the LED can be controlled.
The firmware combines this coordinate with the knowledge of the characteristics of the LEDs used in the preprogrammed system. It then completes the necessary conversion function to correctly convert the chromaticity coordinates to the brightness value of each LED. This process causes their light outputs to be mixed together to generate chromaticity coordinates of the colors input into the system.
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