Converting LED photometric to radiometric values

EELE 482 Electro-Optical Systems

J. A. Shaw F12

Converting LED photometric to radiometric values Light emitting diodes (LEDs) are used often in visual display applications. Consequently, it is standard for the optical power output of visible-wavelength LEDs to be specified in photometric units, which are radiometric units weighted according to the standard human eye response. Specifically, the radiometric values are weighted by the photopic, or lightadapted, eye response (as opposed to the scotopic response, which is only valid for truly dark-adapted vision). Tables listing values for these curves are included in our class notes, along with further details on radiometric and photometric units and terminology. The most common specification for the amount of light radiated by a visible-wavelength LED is “radiant intensity” in units of mcd (millicandelas). A candela is a lumen/steradian (lm/sr), while a lumen is the photometric unit of radiant flux that is just a scaled version of optical power in watts. Any photometric quantity can be obtained from its radiometric counterpart as follows: (1) xv  K m  x v( )d , where xv is a photometric quantity, x is the corresponding radiometric quantity, v() is the visual response function normalized to a peak value of one, and Km is the luminous efficacy, which serves as the scale factor carrying the proper value and units for v(). For the photopic response function, Km is 683 lumens/watt, corresponding to the peak of v() at a wavelength of 555 nm. Monochromatic conversions If the source radiates effectively only at one wavelength, equation (1) becomes a simple algebraic expression that can be solved easily in either direction (radiometric to photometric, or vice versa). xv  K m x v( ) . (2) For example, a red LED made of AlGaAs with model number LTST-C190CKT is listed on its data sheet as emitting a typical luminous intensity Iv = 20 mcd. If we assume the LED emits all of its light at the peak wavelength of 660 nm, then we can simply read from the v() table and perform the following simple algebraic conversion: Iv 0.020 [lm/sr] I   4.8  10 4 [w/sr]  0.48 [mw/sr]. (3) K m v(  660 nm) 683 [lm/w]  0.061 However, the data sheet actually lists two different wavelengths: a) peak wavelength 660 nm wavelength of actual peak emission b) dominant wavelength 638 nm wavelength of perceived emission The dominant (or human-perceived) wavelength is shorter than the peak-emission wavelength because the LED’s emission spectrum is several tens of nm wide and the photopic eye response is much higher at short wavelengths than at long wavelengths. Selecting between these two wavelengths requires consideration of non-monochromatic conversions through spectral integration. 1

EELE 482 Electro-Optical Systems

J. A. Shaw F12

Non-monochromatic conversions When a source does not emit at a single wavelength, the spectral distribution function must be considered when converting between radiometric and photometric values. For example, the LTST-C190CKT LED’s spectral emission function is plotted in Figure 1 and the photopic visual response function is plotted in Figure 2 over the same spectral range.

Figure 1. Spectral emission function for the LTST-C190CKT red LED,

Figure 2. The photopic visual response function over the LED’s spectral range.

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EELE 482 Electro-Optical Systems

J. A. Shaw F12

The human-perceived LED output is obtained by integrating the product of these two curves, as is shown in Figure 3. Here it is clear that the dominant wavelength for human perception is shorter than 660 nm (it is not clear that the best dominant wavelength value is 638 nm, which requires looking at the colorimetric coordinates of the emission on a CIE color diagram).

Figure 3. Product of LED emission spectrum and the photopic visual response function, showing that the human-perceived LED radiation is dominant at shorter wavelengths than the actual LED spectral emission function (Fig. 1). So the question naturally arises, ‘which wavelength gives the best monochromatic approximation of the radiometric output from the photometric data sheet value?’ To answer this rigorously requires inverting the integral equation (1). However, finding the radiometric value embedded inside of the integral from a single photometric number is not trivial. Doing this requires at least knowing the spectral distribution of the radiometric quantity. There are many people who make careers out of inverting integral equations to estimate an unknown quantity from imperfect measurements of another quantity. A non-monochromatic conversion can be performed at least approximately if we use the known LED spectral emission function together with the known photometric luminous intensity, as follows. Let’s express the radiometric intensity as a single value I [w/sr] multiplied by a dimensionless spectral distribution function f(), which is the curve shown in Figure 1. In this manner we can write (4) I v  683I  f ( )v( )d. The values of f() and v() used to create the graphs in Figures 1, 2, and 3 are listed in Table 1.

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EELE 482 Electro-Optical Systems

J. A. Shaw F12

Table 1. Values of the LED emission curve and the photopic response function _______________________________________________________ [nm]  f() v() 610 0 0.503 620 0.08 0.381 630 0.20 0.265 640 0.35 0.175 650 0.60 0.107 660 1.0 0.061 670 0.60 0.032 680 0.35 0.017 690 0.20 0.0082 700 0.08 0.0041 710 0 0.0021 ________________________________________________________

We can use a tool like Matlab to numerically approximate the integral in eq. (4), being careful to normalize so that the integral of f() over this spectral range gives a value of one, allowing the actual numerical value of the LED emission to be contained within I. i f i vi (5) I v  683I  f ( )v( )d  683I .  fi i

We can now algebraically solve for the desired radiometric intensity I: Iv  fi i I  3.41  10 4 [w/sr]  0.34 [mw/sr]. 683 f i vi

(6)

i

It is useful to note that the monochromatic conversion at the peak wavelength of 660 nm gave I = 0.48 mw/sr, while the monochromatic conversion at the dominant wavelength of approximately 640 nm gave I = 0.17 mw/sr. So apparently the peak wavelength is the better choice, but appears to slightly overestimate the radiometric intensity.

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