Designing efficient LED luminary, LCD backlight
Achieving an optimal design may involve investment in higher efficacy LEDs, improved switching regulator design, and/or compromises to the industrial design. Optimal designs feature reduced heat sink size and minimal heat output, yielding a desirable industrial design while sipping a bare minimum of electrical power.
The Commission Internationale De L'Eclairage (CIE) is the key international governing body of colourimetry. CIE has defined two sets of colour-matching functions that are the cornerstone for the calculations used throughout this article. The CIE1931 colour-matching functions define light in fields with two degrees of angular subtense to the viewer and are used when matching colours in a small area, such as accent lighting. The CIE1964 colour-matching functions define light in fields with 10 degrees of angular subtense to the viewer. These supplementary functions are used when matching colours over a broader area, such as lights used to wash a wall.
Efficacy with respect to lighting typically refers to the amount of light (lumens) produced by a luminary (lamp, light bulb, LED, and so on), as a ratio of the amount of electrical power (watts) consumed to produce it. A lumen is defined to be unity for a radiant energy of 1/683 watt at a frequency of 540THz. In air at standard temperature and pressure (STP), light with a frequency of 540THz corresponds to a wavelength of 555.017 nm.
Depending on the colour-matching functions used (CIE1931 or CIE1964), the maximum possible efficacy changes slightly. The peak of the CIE1931 luminosity function occurs at 555 nm; 555.017 nm on the CIE1931 luminosity curve corresponds to 0.999997, which equates to 683 / 0.999997 = 683.002 lm/W. The peak of the CIE1964 luminosity function is slightly offset from the CIE1931 peak at 557 nm. Whereas, 555.017 nm on the CIE1964 luminosity curve corresponds to 0.999122 or 683 / 0.999122 = 683.601 lm/W. These definitions only apply if the light source is monochromatic and green (555 nm or 557 nm accordingly). For simplicity, all calculations assume a maximum efficacy of 683 lm/W regardless of the chosen colour-matching curves. Light sources with differing chromaticity coordinates and/or spectral distributions have lower maximum efficacies.
Optical efficiency is calculated by dividing the maximum possible efficacy at the corresponding chromaticity coordinates into the measured efficacy at the same coordinates. Since the maximum possible efficacy will change depending on the spectral distribution (and thus chromaticity coordinates), using 683 lm/W as a maximum efficacy for all colours will yield incorrect results. Exercise care to ensure that the spectral distribution of the light source equates to that used to calculate the maximum value.
Limits of the visible spectrum
Optical calculations, particularly ones dealing with maximum efficiency, are impacted greatly by the definition of the visible spectrum. Meaningful comparisons demand a consistent definition.
A wide variety of definitions are available from various sources. CIE has published 5 nm colour-matching tables for monochromatic light that include wavelengths between 380 – 780 nm. Colour-matching tables with 1 nm increments, including wavelengths between 360 – 830 nm, are also available. The 1988 Photopic Luminous Efficiency Function from CIE (figure 1) shows visible light between the wavelengths of 380 – 780 nm. Additionally, a narrower spectrum of light between 400 – 700 nm is frequently used as 99.93% of the optical energy beneath the photopic curve falls between these wavelengths.
Calculations, particularly those dealing with ideal black body models, can change drastically depending on the definition of what wavelength of light is visible. Both the full photopic range (380 – 780 nm) and the narrower alternate range (400 – 700 nm) will be considered as standard throughout the rest of the discussion.
Figure 1: The 1988 photopic curve defines the visible spectrum as containing wavelengths between 380 – 780 nm. Alternate limits between 400 – 700 nm contain 99.93% of the total visible optical energy.
Calculating maximum efficacy from a spectral density curve
Chromaticity coordinates  and maximum efficacy can be calculated after normalizing the total energy beneath the spectral density curve. Once normalized, multiplying the Y coordinate by 683 lm/W yields the maximum efficacy of the light source.
The spectral density curve in figure 2 can be digitized using a number of free software tools . Once digitized, the resulting data is then normalized (green curve) such that the sum of the power underneath the curve totals 1. Chromaticity coordinates are calculated using the normalized data.
Figure 2: Digitized data is indexed, smoothed, and normalized before calculating chromaticity coordinates and maximum efficacy.