# # Graph the light intensity from a one dimensional array of isotropic # LEDs along a line parallel to the array of LEDs using gnuplot(1): # # For an isotropic light source a perpendicular distance, d, from a # point, p, in a plane, the light intensity measured at a distance, l, # from p in the plane would be proportional to the hypotenuse, h, # squared, i.e.: # # h^2 = d^2 + l^2 # I is proportional to 1 / h^2 # I is proportional to 1 / (d^2 + l^2), by substitution # # If l = 0, (i.e., the reference value directly under the # isotropic light source): # # I(0) = 1 / d^2 # I(l) / I(0) = (1 / (d^2 + l^2)) / (1 / d^2) # = d^2 / (d^2 + l^2) # = 1 / (1 + (l^2 / d^2)) # # Note that this value is the RELATIVE intensity of light at a # distance l from the perpendicular under the light source in the # plane, (i.e., relative to directly under the isotropic light # source.) If l = 0, this value is unity. # # So, the value of the intensity of an isotropic light source, at a # perpendicular distance, d, from a plane decreases at 1 / d^2. The # RELATIVE intensity of light at a distance l in the plane to that # value is 1 / (1 + (l^2 / d^2)), which is useful for calculating the # variation in the intensity of light projected on the plane from an # array of identical isotropic light sources. # # d = distance between LED array and parallel line, inches # # l = distance between LEDs, inches, (60 LEDs per meter for SMD 5050, # which are approximated as an isotropic radiator) # d = 5 l = 39.37 / 60 # set grid show grid # set title "Relative Light Intensity, (to one isotropic LED)" set xlabel "X, Inches" set ylabel "Light Intensity" # # One LED: # plot [-15:15] 1 / (1 + (((x + (0 * l)) / d) ** 2)) title "One LED" with lines # # Linear array of 15 LEDs: # plot [-15:15] 1 / (1 + (((x + (-7 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (-6 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (-5 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (-4 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (-3 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (-2 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (-1 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (+0 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (+1 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (+2 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (+3 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (+4 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (+5 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (+6 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (+7 * l)) / d) ** 2)) \ title "15 LEDs" with lines # # Linear array of 10 LEDs: # plot [-10:10] 1 / (1 + (((x + (-5 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (-4 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (-3 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (-2 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (-1 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (+0 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (+1 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (+2 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (+3 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (+4 * l)) / d) ** 2)) + \ 1 / (1 + (((x + (+5 * l)) / d) ** 2)) \ title "10 LEDs" with lines # set terminal jpeg font "/usr/share/fonts/truetype/freefont/FreeSans.ttf,10" set output "isotropic.array.jpg" set terminal wxt # exit