led chip and optimized optics one typically increases the number of led chips arranging the leds in an array one example of an led array is depicted in fig5 at 130 in array 130 there are five exemplary columns 132 134 136 138 140 and five exemplary rows 142 144 146 148 150 of the leds 114 since electrical connections must exist for each individual led it is difficult to achieve packing densities much higher than 70 for any arbitrary m u00d7 n array in which either n or m is greater than two for fig5 m and n are each 5 for example if fig5 depicts an array of 1 mm 2 led chips in a 5 u00d7 5 array with a packing density of approximately 62 then along either the vertical axis 152 or horizontal axis 154 the ratio of non imaging non emitting to emitting surface area is slightly less than 80 regarding the led 120 of fig4 the vertical axis h in fig5 would be collinear with the focusing direction h in fig4 spreading the emission away from the focal line by spreading the led chips apart reduces the emission concentration at the image focal line f 2 the non emitting gaps between the led chips also reduce the overall surface irradiance if the led chips in the array 130 could be replaced by a single large led with the same emitting area such as 5 mm u00d7 5 mm both the source irradiance and the irradiance at f 2 would be significantly higher because all of the led emission would be concentrated in the smallest possible distance along h leading to the highest concentration at f 2 stated otherwise using a single large led.