![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABKcAAAaVCAIAAABhzzulAAAACXBIWXMAABYlAAAWJQFJUiTwAAAgAElEQVR42uzasRHAIBADQctD/y3LBTgi5NktQQncQNo+AAAADPWaAAAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAADVZwIAAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAVJ8JAAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAFB9JgAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAABA9ZkAAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAANVnAgAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABUnwkAAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAUH0mAAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACqDwAAgIMtEwDAJEmMAPy1NcK1vPUBAABMFtEPAAAwmLc+AAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAcLtlgpslMQLAQdoaAYDta7/zAwAAYDA/PAEAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAAD42ruD0DjL/IHjT5YJHiZFXUhIaZam0ENd6HTBQzATqLIzCLYgolQmnvdQdBOKJxG08eJJipE/FTz0lCkGRAXNsnZEiplAQNBOaHcPizv9m9IhA1Uwc8oL8z+82+x/datJmzTv+87nc1hQap153ulmvj7v+3tQfQAAAKg+AAAA1QcAAIDqAwAAIPlylgCAtOvr67MIAL+s2+1ahJ5lrw8AACDL+kQ/AABAhtnrAwAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAL0uZwl6WV9fn0UgXbrdrkUAANje135foQAAADLMHZ4AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAADVBwAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACoPgAAAFQfAAAAqg8AAADVBwAAgOoDAABA9QEAAKg+AAAAVB8AAACqDwAAANUHAACA6gMAAED1AQAAoPoAAABUHwAAAKoPAAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqg8AAADVBwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAANUHAACA6gMAAED1AQAAoPoAAABQfQAAAKg+AAAA1QcAAIDqAwAAQPUBAACg+gAAAFB9AAAAqD4AAABUHwAAgOoDAABA9QEAAKD6AAAAUH0AAACoPgAAAFQfAAAAqg8AAED1AQAAoPoAAABQfQAAAKg+AAAAVB8AAACqDwAAANUHAACg+gAAAFB9AAAAqD4AAABUHwAAAKoPAAAA1QcAAIDqAwAAyLqcJQAg8+r1+vz8fLvdjv/yxRdfLBaLlgWAHtHX7XatAgBZVa1WX3755Vartfl3hoeHP/vss6NHj1ocAHqEOzwByKZ2u10ul1944YUQwjvvvLO2ttbtdrvd7s2bN/9/8i0sLDSbTcsFQIbZ6wMgg5rN5mOPPdZqtUql0kcffZTP5//rL+t0OgMDAyGExcVF93wCkFX2+gDImnq9fujQoVarNTMz85e//OVOyRdCyOfzi4uLIYSJiYlqtWrpAMgke30AZM3k5OTFixfn5uYmJye38uvb7XahUGi1Wnb8AFB9AJAOzWZzdHR0679+ZWWlUCiEEP75z39u6x8EANUHAOlQr9cnJiaGh4e/++67XM7JRgBkh+f6AMiIKIru5R8vFoszMzOtVuvll1+2mABkib0+ALKg3W4PDQ1t/Vm+O3Xjo48+2mg03OcJQJbY6wMgC+LYe+ihh+7lN8nlch9//HEI4emnn77HnUMAUH0AsGPq9XqtVqtUKk899dQ9/lajo6Nzc3ONRmN+ft7CApAN7vAEIN2iKPrd737XarXW1tYGBwd35Decn58/deqUmS4AZIOfZwCk27vvvhsfyL4jyRdCyOVy9/JwIAAkjb0+AFKs0+kMDAw4bgEAfoHn+gBIsbfeeiv+311Kvk6nY5EBSDt7fQCkVRRF/exuaA8AAAzGSURBVP39u7fRNz09PTs7u76+ns/nrTYA6WWvD4C0isdsvvrqq7u00Xfq1KlwezsRANLLXh8AqbQ5unNX9+KOHTvWaDQ2NjY8NAhAetnrAyCVVldX49Gdu3r75ZtvvhlubyoCQErZ6wMgrTqdzgMPPLCru3Cbjw7evHnTggOQUvb6AEirfD6/2zde5nK5mZmZVqtVr9ctOAApZa8PAH5Js9k8dOhQqVS6dOmS1QBA9QHAroui6Pvvvx8cHLxv/8Z4posjHABIKXd4ApAyy8vLQ0NDCwsL9+3fGM90uXDhgsUHII3s9QGQMuVyuVarra2t3bftvk6nMzAwUCgUrly5Yv0BSB17fQCkSafTqdVqhULhft7hmc/nK5VKo9Fot9suAQCqDwB2UXybZXzL5f30yiuvLC4uPvzwwy4BAKnjDk8A0iS+vdNgFQDYOnt9AKRGfHtnqVSSfACg+gDIoMuXL4cQzpw5YykAQPUBkEHnzp0LIRw/fnyvXkC1Wi2Xyy4EAKoPAHZeEm7v/Mc//lGr1VZWVlwOAFQfAOywJNze+cwzz4QQPvzwQ5cDANUHADvsr3/9a9jT2ztDCEePHg0hfPDBBy4HACmSswQApMKTTz4ZQtjz6Z1TU1Ozs7Ptdvt+HhMPAPfCeX0AsA31en1iYmJubm5yctJqAJAK7vAEgG34wx/+EEK4cOGCpQAgLez1AcD2lMvlWq22sbGRy3lQAoAUsNcHQNJ1Op2FhYVOp5OQ1/P000+HEP72t7+5NACoPgDYARcuXDhx4sQ333yTkNcTzxGNT5IAgORzhycASRffUbm+vr7nAzz//eOzr69QKFy5csXVASD57PUBkGhRFNVqtUKhkJzkCyFUKpVGo5Gcm04BQPUBkFbLy8shhGeffTZRr+q9995bW1tLVIgCwJ0YPgZAon3++echhD/+8Y+JelX5fF7yAZAWnusDINGOHTvWaDQS9VAfAKSLOzwBSK4oihqNRqlUknwAoPoAyKD4TLz4fLykWVlZKZfL9XrdZQJA9QHAXYrPxIvPx0uaffv21Wq1+LFDAFB9AHA3Pv744xDCI488ksDXNjo6GkL44IMPXCYAVB8A3KVarVYqlXK5hE6cnpqacmofAMnn5AYAkmtubu7gwYOJfXljY2MhhG+++aZYLLpYACSWvT4AkmtycjLJQTU+Ph5C+Prrr10pAFQfAGRQ/Ghf/PAhAKg+AMigSqVSq9WsAwCqDwC2J4qihYWF5A9KiW/ybDabLhkAqg8AtmF5efnEiRPJv3kyPktwaWnJJQNA9QHANsSnn8c7aUkWnyW4vLzskgGQWH3dbtcqAJA05XK5VqttbGwk9rC+Tfv37w8h3Lx501UDQPUBwJZ/PvX1FQqFK1euJP+lttvtEMLg4KCrBkAyOaUdgMSJh6M8/vjjqXi1eg+AhPNcHwCJc+3atRDC2NiYpQAA1QdABn311VchDaNcAED1AcDd+PLLL0MIIyMjaXnB9Xp9enrahQNA9QHAltRqtUKhkPzpnZvm5+dnZ2ejKHLtAFB9APAr0jXKJRY/gri6uuryAaD6AOBX/PjjjyFto1yOHj0aQlhaWnL5AFB9APDrKpVKuVxO0QseHh4OISwvL7t2ACSQU9oBYCd+oKbnWHkAeo29PgDYAZVKpdFoWAcAVB8AZNORI0fC7VE0AKD6ANieKIp65FSAKIra7XYaX/nhw4dDCNeuXfNxBUD1AbCNBIqP/+7v7++RSSHz8/NDQ0Np3DEbHx8PIXz11Vc+twAkTc4SACTQysrKhx9+eP78+VarFUIoFAo98sZv3boVQsjn86l75SMjIyGEv//97z69AKg+AO6o3W6fP39+M/aGh4dnZmZOnz49ODjYIysQH3mXxveby+UKhcIXX3zhYwxA0ji5ASARsff++++/99578RDI4eHh06dPP/PMM/HZ3z1l//79Q0NDKT3/oF6vhxCKxaKPNACJYq8PYM90Op3Lly+fO3euVqvFf2dqaurUqVNjY2O5XC/+/3MURa1W64knnkjp69d7AKg+AP7VNsvLy2fPnt2MvVKpdPbs2Z6NvU2rq6shhJMnT/qQAIDqA0hr7M3Pz8/Ozm7G3pkzZ44fP57G4SW7IT724ODBg5YCAFQfQJr8fCDnn/70p+eff753ZrRs0bfffhtCOHDgQHrfgkf7AFB9AD3EQM7tigd4jo6OpvctPPfccyGEmzdvupoAJIcZngA7H3sGct6dVA/wjE1OTl68eHFjY6PHH9EEIFH8TALYGQZy3qO0D/CMHTlyJISwurqa6h1LAFQfAP/RKgZy7ojvv/9+eHg47QM8Dx8+HEK4ceOG6gNA9QFkIfYM5NxBg4ODGXgcbnx8PIRw/fp1A10AUH0AaWUgJ78gbv7l5eXJyUmrAYDqA0gTAznZivjz0G63LQUAyWGGJ8CvxJ6BnGxLuVyu1Wp+vAKQHL+xBAA/1+l0FhYWyuXy0NDQn//850ajMTU1tbi4+N1337322muSbzf09fW98cYbGXgjv//970MIURS5pgAkhDs8Af7NQM69Et8S+dvf/jYD72VsbCw4vAEA1QeQwNgzkHMPdTqdzFRf7Nq1a6oPANUHsPcM5EyIpaWlEEI2bp0tl8uVSuXBBx90WQFQfQB7xkDOpLl161YIYd++fRl4L4ODg9Vq1TUFQPUB7E3s/WQg58zMjIGcSRDv9Y2MjFgKAFB9ANvW6XQuX7587ty5zRktU1NTp06dMqMlUUEeQnA5AED1AWyDgZwpUqvVSqVSlt5Rp9N54IEHfNIASALn9QEZjL16vT49Pd3f3z8xMRHnxKeffrq+vn7p0qViseiLeAIDKYSQpYcqq9XqwMDA6uqqiwtAEvjqA2SHgZwpFd/eOT4+nrH39eOPP7q4AKg+gJ1pBgM5U+3GjRshW4f1HTx4MISwsrJiUBAAqg/gnmLPQM5suH79esjWXt+BAwfC7eMoAGDP9XW7XasApIiBnJm8pu12e2RkJDNXMIqi/v7+SqXi4D4AksA3JCA1X6MN5MyqfD6fz+cz9cM1lwu3n1cEANUH8OuxNz8/Pzs7uxl7Z86cOX78eMY6gYwplUqb/4UCAFQfwH9hICepFn9QoyiyFw3AnnNeH5As7Xb7jTfe2L9/f6FQeP3110MIMzMza2trV65ceemllyRf9nQ6nWq1Wq/XM/a+Tp48GUJwZB8ASeA/QAJJiT0DOXv20r/wwgvvvPNOsVi0GgCg+oCsMZCT7B3WF4sPolhaWhodHXWVAVB9QM8xkJNN8WF98bHmAIDqA7IQewZy8nPxseZZMjIysr6+7oMNgOoDeoWBnNzJJ598EkLIXh3lcjkb1wCoPiD72u32+fPnN2MvntFy+vRpscdP+EgAgOoDUhZ7BnKyRVevXh0eHrYOAKD6gBQwkJO70Gg0KpVKJt9atVr95JNPqtWqqwzA3nJKO3Cvoiiq1+vlcnlgYODEiRO1Wq1UKi0uLm5sbLz99tvFYlHy8Qsfnmy/wYsXLzabTRcagL3lqxhw99/XDeTkHq2uroYQTp48aSkAQPUBCWIgJ2xF/CDrjRs3HNQOgOoD0sFATnZDpVIpl8uZfGv79u0LIVy/fr1YLLrQAKg+INGxZyAnu2R0dDTDw07c6gxAQvR1u12rAPycgZywAz9l+/oqlYoxngDsLV/dgP8Qz2g5e/bsZuyVSqWzZ8+KPQAA1QekPvYM5ISdVSqVrl69ah0AUH3AXjKQkz107NixoaGhS5cuZfUNDg4Obm6bA4DqA+4rAzlJgkajUalUMvwG/YECQPUBexB7BnKSEFEUhRCOHDmS4fc4NjYWQmg2m47sA0D1AbvLQE4SaHV1NYRw+PDhDL/H8fHxubk5O34AqD5gtxjICXtrdHTULh8Aqg/YrdgzkJOEu3btWghhfHzcUgCA6gO2ykBOUuSHH36wCACg+oAtMZCTNLp161YvvM1ms5nP5/1hBED1AXcZewZykl5LS0shhMw/9nbo0KFKpVKtVl1xAFQfsFUGckK6XL161SIAoPqAX2cgJ1oojUql0uafWQBQfcAdY89ATrKn0WiUSqXMv01P9AGg+oA7MpCTbOt2u1EU9Uj1RVFkTx4A1Qf8i4Gc9NAPoR4IobGxsRDC6uqq49oBUH0g9gzkBABA9UHmGMgJAMCu+o0lgD0RRVG9Xi+XywMDAydOnKjVaqVSaXFxcWNj4+233y4Wi5KPbFtZWZmenm42m5l/p+Pj4+H24YQAoPqgV2Jvenq6v79/YmIijr1PP/10fX390qVLYo+eqr7Z2dkbN25YCgDYbb5fwv37jmsgJ/zEgQMHLAIA7La+brcbQgjhN/9zsPvS/4Zw+68BAADIgP8D2gFuZTBwffMAAAAASUVORK5CYII=)
光学設計ノーツ 42 ver.1.01
結像における余弦則により正弦条件を求める
本連載 17 回よりクラウジウスの関係から、輝度不変則を導き、さらに正弦条件を導出し
た。また 18 回においては共役関係にない二つの微小光斑の間でのストローベルの定理を導
出し、エタンデューと呼ばれる量が得られた。
また 19 回では輝度不変則によらずに、17,18 回とは異なる考え方で正弦条件を導いた。
今回はこの、19 回での手法を再び取り上げ、そこに含まれていた結像における余弦則とい
うものをクローズアップし、輝度不変則、正弦条件、ハーシェルの条件等について改めて考
えを廻らせたい。
1. 結像における余弦則
基本的は 19 回1節における導出と同じであるが、軸外に範囲を一般化し、角度の取り方
等も変えて、異なった表示方法を試みる。
図1において、Aの像 A’が収差無く結像していて、そこから微小距離
dr
離れた物点 Pの
像P’にも同様の無収差の結像が起きているとする。まず、Aから A’に到達する光線を考え
る。また同様に Pを出発して P’に到達する光線を考える。両点において無収差結像が起こ
っているとすれば、こうした光線は無数にあるが、光線 AA’が線分 AP(つまり物体面を表
す)となす角度をφとする。また光線 PP’も物界では線分 AP に対し同じ角度φで Pを出発
しているとする。また像界では光線 AA’は像平面の一部、線分 A’P’(長さ dr’)に対して
φ‘の角度を為して存在するとする。
さて、この時、AP の長さが微小であって光線 PP’もA’P’に対して同じように角度φ'をな
していると仮定しよう。すると、二つの光線の光路長を考えれば図から明らかな様に、
coscos ndrAArdnPP
coscos ndrrdnAAPP
(1)
となる。
P
n