2019
DOI: 10.1364/ao.59.000190
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LED irradiance pattern at short distances

Abstract: Many emerging light-emitting diode (LED) applications require short-distance illumination. For that, we derive an exact formula of the illumination profile produced by Lambertian LEDs, in which all parameters are fundamental constants. Moreover, we propose a general, simple, but accurate mathematical model of the irradiance pattern, valid for Lambertian and non-Lambertian LEDs at short distances. This model provides the irradiance profile as a function of both the LED-target distance and the coordinates of eve… Show more

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Cited by 14 publications
(5 citation statements)
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“…Equation (6) describes the irradiance in W/m 2 of a square LED at a distance in any point at xy [ 31 ]: where is the flux in Watts, is the length of the LED, is the width and is the distance away from the LED emitting surface. Figure 5 shows the LED irradiance at the surface with a 1 mm 2 area away from the LED at different distances.…”
Section: Functional Principle and Designmentioning
confidence: 99%
“…Equation (6) describes the irradiance in W/m 2 of a square LED at a distance in any point at xy [ 31 ]: where is the flux in Watts, is the length of the LED, is the width and is the distance away from the LED emitting surface. Figure 5 shows the LED irradiance at the surface with a 1 mm 2 area away from the LED at different distances.…”
Section: Functional Principle and Designmentioning
confidence: 99%
“…We assume now the light source has a Lambertian emission pattern, i.e., its radiance L t is constant across locations on the transmitter surface. In this case, the integral in ( 15) has analytical solutions which can be obtained either by direct integration or by changing the surface integral into a contour integral in an R 3 space by applying the Stokes theorem [14], [20]. Here, we present the contour's integral method as we consider the integration conditions make the procedure simpler.…”
Section: Model For a Non-tilted Light Source And A Tilted Receiver A General Expression Of Irradiance For A Planar Sourcementioning
confidence: 99%
“…It is important to mention that we can derive the solution proposed in [14] for a receiver placed at a vertical distance z = −h from the transmitter and pointing toward the ceiling with a fixed orientation n r = [0, 0, 1] R from (20).…”
Section: B Case Of a Planar Rectangular Light Sourcementioning
confidence: 99%
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“…[20] While light uniformity can be improved by increasing vertical distance, the optical power density at the skin surface is significantly reduced by the long radiation distance and severe diffuse reflection. [21,22] Some researchers reported that only 10% of incident light could penetrate into a skin model when irradiated with a 630 nm light source at 2 cm distance. [23][24][25][26][27][28] In addition, excessive light exposure to compensate distance-induced optical loss can give rise to adverse effects related with thermal damages such as increased melanin production, low temperature burns, and eye damage, as displayed in Table S1B, Supporting Information.…”
Section: Introductionmentioning
confidence: 99%