БЕЛОРУССКИЙ ГОСУДАРСТВЕННЫЙ УНИВЕРСИТЕТ ИНФОРМАТИКИ И РАДИОЭЛЕКТРОНИКИ
Кафедра ЭТТ
РЕФЕРАТ
На тему:
«Астигматизм и кривизна изображения. Хроматические аберрации»
МИНСК, 2008
Астигматизм и кривизна изображения
Астигматизм появляется при значительном смещении точки предмета с оси и
добавляется ко всем остальным аберрациям. Сместим предмет с оси на
значительное расстояние (рис.1). Астигматизм состоит в том, что не
совпадают точки фокусов в меридиональной
picscalex100010009000003f500000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02400200021200000026060f001a00ffffffff000010000000c0ffffff
a6ffffffc0010000e60100000b00000026060f000c004d61746854797065000060001c00
0000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320ae0012401
010000006d791c000000fb0280fe0000000000009001010000000402001054696d657320
4e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d0101000400
0000f001000008000000320a800146000100000046791c000000fb0280fe000000000000
9001000000020002001053796d626f6c007740000000060a0a5f1643c7771f43c77720c0
c97700003000040000002d01000004000000f001010008000000320a6a01600101000000
a2790a00000026060f000a00ffffffff0100000000001c000000fb021000070000000000
bc02000000cc0102022253797374656d000000000a0021008a0100000000010000009cf3
12002942c777040000002d01010004000000f0010000030000000000 и сагиттальной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 плоскостях,
поэтому лучи бесконечно узкого пучка не сходятся в одной точке. Кривизна
заключается в том, что наилучшее изображение получается на искривленной
поверхности, а не на плоскости.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Разложение в ряд волновой аберрации при наличии астигматизма 3 и 5
порядков: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(1)
или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.
Количественно астигматизм и кривизна характеризуются продольными
астигматическими отрезками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 и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. Меридиональная
кривизна определяется отрезком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 – это
расстояние от плоскости параксиального изображения до меридионального
фокуса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. Сагиттальная
кривизна определяется отрезком
picscalex100010009000003f500000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c024002a0011200000026060f001a00ffffffff000010000000c0ffffff
a6ffffff60010000e60100000b00000026060f000c004d61746854797065000060001c00
0000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320ae001fd00
0100000073791c000000fb0280fe0000000000009001010000000402001054696d657320
4e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d0101000400
0000f001000008000000320a80014c00010000007a791c000000fb0280fe000000000000
9001000000020002001053796d626f6c0077400000003d0a0a631643c7771f43c77720c0
c97700003000040000002d01000004000000f001010008000000320a6a01fa0001000000
a2790a00000026060f000a00ffffffff0100000000001c000000fb021000070000000000
bc02000000cc0102022253797374656d000000000a0021008a010000000001000000fcf3
12002942c777040000002d01010004000000f0010000030000000000 – это
расстояние от плоскости параксиального изображения до сагиттального
фокуса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.
Средняя кривизна определяется полусуммой астигматических отрезков и
указывает положение наилучшего изображения для данного пучка: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.
(2)
Мера астигматизма в продольном измерении определяется разностью
астигматических отрезков: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.
(3)
В первом приближении средняя кривизна пропорциональна квадрату
расстояния от оси. Зависимость кривизны и астигматизма по полю
показывают графики продольных аберраций для внеосевых пучков (рис. 2).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Рисунок 2 – Астигматизм 3 порядка (продольные и поперечные аберрации)
Здесь – относительная предметная координата (на краю поля = 1 , на оси
= 0):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.
(4)
Для астигматизма более высоких порядков (5 и выше) графики могут
выглядеть, как показано на рис.3: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Рисунок 3 – Продольные аберрации при астигматизме 5 порядка.
В зависимости от положения плоскости изображения при астигматизме пятно
рассеяния может принимать форму эллипсов, отрезков или круга (рис.4).
Горизонтальный отрезок наблюдается, если плоскость изображения совпадает
с меридиональным фокусом, а вертикальный – если с сагиттальным.
Посередине между ними пятно рассеяния имеет форму круга. В остальных
положениях – пятна эллиптической формы.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Рисунок 4 – Пятна рассеяния астигматического пучка.
Дисторсия
Название происходит от латинского “искажение”.
Если кроме дисторсии других аберраций нет, то точка изображается в виде
точки (гомоцентрический пучок остается гомоцентрическим), но эта точка
смещена от идеальной (рис.5).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Рисунок 5 – Дисторсия.
Разложение в ряд волновой аберрации при наличии дисторсии: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(5)
или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.
При дисторсии величина изображения отличается от идеального: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.
(6)
Абсолютная дисторсия (выражается в тех же единицах, что и величина
изображения):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,
(7)
где V – увеличение системы для данной точки поля.
Относительная дисторсия: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 .
(8)
Дисторсия характерна тем, что ее величина нелинейно зависит от величины
предмета, то есть линейное увеличение различно для разных точек поля.
Абсолютная дисторсия 3 порядка определяется дифференцированием выражения
(8.38) и умножением на квадрат предметной координаты :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(9)
График относительной дисторсии 3 порядка приведен на рис.6. Для
сравнения показан примерный ход кривой дисторсии высшего порядка.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Рисунок 6 – Дисторсия 3 и высшего порядков.
Наличие дисторсии приводит к искажению прямых линий, не проходящих через
ось (рис.7). Если квадратный предмет изображается в виде подушки – это
положительная дисторсия. Если изображение квадрата имеет выпуклые
стороны (в виде бочки), то это отрицательная дисторсия.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Рисунок 7 – Дисторсия
Допустимая относительная дисторсия (то есть дисторсия, которая при
восприятии глазом не вызывает ощущения, что изображение искажено) около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. Исправление дисторсии важно в
измерительных приборах (в частности, в фотограмметрических системах),
так как наличие дисторсии приводит к нелинейной ошибке измерений.
Например, в фотолитографии допуск на абсолютную дисторсию не превышает
20 нм.
Хроматические аберрации
Хроматические аберрации – это проявление зависимости характеристик
оптической системы от длины волны света (хромо – цвет). Хроматические
аберрации приводят к тому, что в изображениях неокрашенных предметов
появляется окрашенность. Хроматические аберрации появляются из-за того,
что оптические системы изготовлены из оптических стекол с показателями
преломления, зависящими от длины волны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.
Существуют два основных вида хроматизма:
– хроматизм положения,
– хроматизм увеличения.
Хроматизм положения
Хроматизм положения – это аберрация, при которой изображения одной точки
предмета расположены на разном расстоянии от оптической системы для
разных длин волн (разные положения плоскости изображения). В этом случае
фокусы также расположены на разных расстояниях (рис.).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Рисунок 8 – Хроматизм положения.
На рис.9 представлен типичный график зависимости положения изображения
от длины волны.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Рисунок 9 – График зависимости положения изображения от длины волны.
Чем меньше длина волны, тем ближе изображение к оптической системе.
Численно хроматизм положения определяется разностью положений плоскости
изображения для крайних длин волн (1 и 2):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.
(10)
Естественный хроматизм возникает в оптической системе, если все линзы
сделаны из одного сорта стекла. В таком случае оптическая система
неахроматизована.
Устранение (коррекция) хроматизма может быть произведена двумя
способами:
– использование зеркальных систем, где хроматизм в принципе отсутствует
(катоптрические системы, например система Кассегрена),
– использование в линзовых (диоптрических) системах нескольких сортов
стекла с различными коэффициентами дисперсии e.
Принципы ахроматизации оптических систем
Возьмем две тонких линзы из разных сортов стекла. Если линзы расположены
вплотную друг к другу, то получается тонкая система. Задача
ахроматизации сводится к тому, чтобы оптическая сила системы линз не
зависела от длины волны. Оптическая сила системы из двух тонких линз: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(11)
Оптическая сила каждой линзы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. Пусть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, при этом оптическая сила каждой линзы
меняется на величину
picscalex1000100090000033102000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c026002c0101200000026060f001a00ffffffff000010000000c0ffffff
a6ffffff80100000060200000b00000026060f000c004d61746854797065000070001c00
0000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320a8001fa0f
01000000297908000000320a8001e60a01000000287908000000320a8001960901000000
297908000000320a8001f4030100000028791c000000fb0220ff00000000000090010000
00000402001054696d6573204e657720526f6d616e001643c7771f43c77720c0c9770000
3000040000002d01010004000000f001000008000000320ae001530f0100000032790800
0000320ae001560c0100000031791c000000fb0260ff0000000000009001000000000402
001054696d6573204e657720526f6d616e001643c7771f43c77720c0c977000030000400
00002d01000004000000f001010008000000320a1802f40801000000327908000000320a
1802b1050100000031791c000000fb0280fe000000000000900101000002040200105379
6d626f6c007740000000a70d0a9f1643c7771f43c77720c0c97700003000040000002d01
010004000000f001000008000000320a8001600e01000000727908000000320a80017c0b
0100000072791c000000fb0220ff0000000000009001010000020402001053796d626f6c
0077400000007a0a0a8c1643c7771f43c77720c0c97700003000040000002d0100000400
0000f001010008000000320ae0017608010000006c7908000000320ae001450501000000
6c791c000000fb0280fe0000000000009001000000020002001053796d626f6c00774000
0000a70d0aa01643c7771f43c77720c0c97700003000040000002d01010004000000f001
000008000000320a8001340d010000002d7908000000320a8001500a01000000d7790800
0000320a80018f06010000002d7908000000320a8001c202010000003d7908000000320a
80013a000100000044791c000000fb0280fe000000000000900101000000040200105469
6d6573204e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d01
000004000000f001010008000000320a8001af07010000006e7908000000320a80017e04
010000006e791c000000fb0280fe0000000000009001010000cc0402001054696d657320
4e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d0101000400
0000f001000008000000320a8001240101000000d4790a00000026060f000a00ffffffff
0100000000001c000000fb021000070000000000bc02000000cc0102022253797374656d
000000000a0021008a0100000000000000009cf312002942c777040000002d0100000400
0000f0010100030000000000. Зная число Аббе для любого интервала длин волн
picscalex100010009000003cf01000003001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02c00440081200000026060f001a00ffffffff000010000000c0ffffff
bcffffff000800007c0400000b00000026060f000c004d61746854797065000010010800
0000fa0200001000000000000000040000002d0100000500000014024002a40205000000
13024002e4071c000000fb0260ff0000000000009001000000000402001054696d657320
4e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d0101000800
0000320a6404340701000000327908000000320a6404f10301000000317908000000320a
0202aa040100000030791c000000fb0280fe000000000000900100000000040200105469
6d6573204e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d01
020004000000f001010008000000320a6a018a060100000031791c000000fb0220ff0000
000000009001010000020402001053796d626f6c007740000000a90d0af91643c7771f43
c77720c0c97700003000040000002d01010004000000f001020008000000320a2c04b606
010000006c7908000000320a2c048503010000006c7908000000320aca012f0401000000
6c791c000000fb0280fe0000000000009001010000020402001053796d626f6c00774000
0000080d0a8e1643c7771f43c77720c0c97700003000040000002d01020004000000f001
010008000000320aa002feff010000006e791c000000fb0280fe00000000000090010100
00000402001054696d6573204e657720526f6d616e001643c7771f43c77720c0c9770000
3000040000002d01010004000000f001020008000000320acc03ef05010000006e790800
0000320acc03be02010000006e7908000000320a6a016803010000006e791c000000fb02
80fe0000000000009001000000020002001053796d626f6c007740000000080d0a8f1643
c7771f43c77720c0c97700003000040000002d01020004000000f001010008000000320a
cc03cf04010000002d7908000000320a6a019405010000002d7908000000320aa0026601
010000003d790a00000026060f000a00ffffffff0100000000001c000000fb0210000700
00000000bc02000000cc0102022253797374656d000000000a0021008a01000000000100
0000fcf312002942c777040000002d01010004000000f0010200030000000000, можно
получить следующее выражение: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.
(12)
Допустим, что эти линзы изготовлены из разных сортов стекла, тогда
условие ахроматизации будет выглядеть так: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(13)
где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 – оптическая
сила системы для основной длины волны,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 – оптические силы
первой и второй линз для основной длины волны,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– коэффициенты дисперсии
стекла первой и второй линз.
Решив систему линейных уравнений (13), получим уравнения ахроматизации
для двух сортов стекла: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(14)
У стекол должны быть разные коэффициенты дисперсии, причем коэффициент
дисперсии первой линзы должен быть больше коэффициента дисперсии второй
линзы (1 > 2), иначе может получится так, что система будет состоять из
двух компонентов с близкими по величине, но противоположными по знаку
оптическими силами. Это приведет к необходимости увеличения оптической
силы компонентов, и как следствие, к появлению больших монохроматических
аберраций. Обычно для системы из двух линз выбирают 1 60 (крон), 2 30
(флинт). Тогда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(рис.10).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Рисунок 10 – Ахроматическая система из двух линз.
В этом случае график зависимости положения изображения от длины волны
будет выглядеть, как показано на рис.11. У такой системы нет хроматизма
положения: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.
–––
–––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Рисунок 11 – График хроматизма положения для системы из двух линз.
Разность на краях спектра сводится к нулю, но остается разность
положений изображения для центральной 0 и крайних (1, 2) длин волн. Это
вторичный хроматизм или вторичный спектр. Его величина определяется
следующим образом: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.
(15)
Вторичный спектр гораздо меньше первичного хроматизма положения, но тем
не менее, он влияет на качество изображения. Для исправления вторичного
спектра требуется не меньше трех сортов стекла с различными
коэффициентами дисперсии и относительной частной дисперсией (такие
системы называются апохроматы). Если при коррекции хроматизма
используется еще больше стекол, то такая система называется
суперапохроматом.
На рис.12 приведены графики продольного хроматизма первого порядка
неахроматизированной и ахроматизированной систем.
picscalex960100090000032a0200000200a20100000000a201000026060f003a03574d4
643010000000000010004970000000001000000180300000000000018030000010000006
c000000000000000000000008000000100000000000000000000000983a0000180d00002
0454d4600000100180300001200000002000000000000000000000000000000000500000
004000040010000f000000000000000000000000000000000e2040080a90300160000000
c000000180000000a0000001000000000000000000000000900000010000000580200008
f000000250000000c0000000e000080250000000c0000000e000080120000000c0000000
1000000520000007001000001000000f1ffffff000000000000000000000000900100000
00000cc04400022430061006c00690062007200690000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
0001100ccad11001000000030b11100b0ae1100cb4f603230b1110028ae1100100000009
8af110014b111001c4f603230b1110028ae110020000000e9e12f3128ae110030b111002
0000000ffffffff7c0bee0064e22f31ffffffffffff0180ffff01800fff0180ffffffff0
00000000008000000080000e8ba120001000000000000006000000025000000372e9001c
c00020f0502020204030204ef0200a07b20004000000000000000009f000000000000004
30061006c006900620072000000000000000000f0ae1100e2882f31e8ad083250b211005
cae1100df382731080000000100000098ae110098ae1100307a253108000000c0ae11007
c0bee006476000800000000250000000c00000001000000250000000c000000010000002
50000000c00000001000000180000000c000000000000025400000054000000000000000
00000000800000010000000010000000000c8410080bb41000000000d000000010000004
c000000040000000000000000000000580200008f0000005000000020000077090000004
6000000280000001c0000004744494302000000ffffffffffffffff59020000900000000
00000004600000014000000080000004744494303000000250000000c0000000e0000802
50000000c0000000e0000800e00000014000000000000001000000014000000040000000
3010800050000000b0200000000050000000c028f005802040000002e0118001c000000f
b021000070000000000bc02000000cc0102022253797374656d000000000000000000000
0000000000000000000000000000000040000002d010000040000002d010000040000000
20101001c000000fb02f1ff0000000000009001000000cc0440002243616c69627269000
00000000000000000000000000000000000000000000000040000002d010100040000002
d010100040000002d010100050000000902000000020d000000320a0d000000010004000
000000058028f0020ea0900040000002d010000040000002d010000030000000000
Рисунок 12 – Продольный хроматизм первого порядка.
Если в оптической системе присутствуют монохроматические аберрации
третьего и пятого порядка, то графики продольного хроматизма будут
выглядеть, как показано на рис.13 и рис.14.
picscalex930100090000032a0200000200a20100000000a201000026060f003a03574d4
6430100000000000100ee050000000001000000180300000000000018030000010000006
c000000000000000000000008000000100000000000000000000000723800004a0f00002
0454d4600000100180300001200000002000000000000000000000000000000000500000
004000040010000f000000000000000000000000000000000e2040080a90300160000000
c000000180000000a000000100000000000000000000000090000001000000042020000a
7000000250000000c0000000e000080250000000c0000000e000080120000000c0000000
1000000520000007001000001000000f1ffffff000000000000000000000000900100000
00000cc04400022430061006c00690062007200690000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
0001100ccad11001000000030b11100b0ae1100cb4f603230b1110028ae1100100000009
8af110014b111001c4f603230b1110028ae110020000000e9e12f3128ae110030b111002
0000000ffffffff7c0bee0064e22f31ffffffffffff0180ffff01800fff0180ffffffff0
00000000008000000080000e8ba120001000000000000006000000025000000372e9001c
c00020f0502020204030204ef0200a07b20004000000000000000009f000000000000004
30061006c006900620072000000000000000000f0ae1100e2882f31e8ad083250b211005
cae1100df382731080000000100000098ae110098ae1100307a253108000000c0ae11007
c0bee006476000800000000250000000c00000001000000250000000c000000010000002
50000000c00000001000000180000000c000000000000025400000054000000000000000
00000000800000010000000010000000000c8410080bb41000000000d000000010000004
c00000004000000000000000000000042020000a70000005000000020000008090000004
6000000280000001c0000004744494302000000ffffffffffffffff43020000a80000000
00000004600000014000000080000004744494303000000250000000c0000000e0000802
50000000c0000000e0000800e00000014000000000000001000000014000000040000000
3010800050000000b0200000000050000000c02a7004202040000002e0118001c000000f
b021000070000000000bc02000000cc0102022253797374656d000000000000000000000
0000000000000000000000000000000040000002d010000040000002d010000040000000
20101001c000000fb02f1ff0000000000009001000000cc0440002243616c69627269000
00000000000000000000000000000000000000000000000040000002d010100040000002
d010100040000002d010100050000000902000000020d000000320a0d000000010004000
00000004202a70020ea0900040000002d010000040000002d010000030000000000
Рисунок 13 – Продольный хроматизм в присутствии аберраций
третьего порядка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Рисунок 14 – Присутствуют аберрации третьего и пятого порядков.
Кривые хроматизма могут быть взаимно наклонены, это так называемый
сферохроматизм, то есть хроматизм сферической аберрации (рис.15).
picscalex1000100090000032a0200000200a20100000000a201000026060f003a03574d
464301000000000001008f02000000000100000018030000000000001803000001000000
6c000000000000000000000008000000100000000000000000000000e33a0000a70f0000
20454d460000010018030000120000000200000000000000000000000000000000050000
0004000040010000f000000000000000000000000000000000e2040080a9030016000000
0c000000180000000a00000010000000000000000000000009000000100000005b020000
ab000000250000000c0000000e000080250000000c0000000e000080120000000c000000
01000000520000007001000001000000f1ffffff00000000000000000000000090010000
000000cc04400022430061006c0069006200720069000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
00001100ccad11001000000030b11100b0ae1100cb4f603230b1110028ae110010000000
98af110014b111001c4f603230b1110028ae110020000000e9e12f3128ae110030b11100
20000000ffffffff7c0bee0064e22f31ffffffffffff0180ffff01800fff0180ffffffff
000000000008000000080000e8ba120001000000000000006000000025000000372e9001
cc00020f0502020204030204ef0200a07b20004000000000000000009f00000000000000
430061006c006900620072000000000000000000f0ae1100e2882f31e8ad083250b21100
5cae1100df382731080000000100000098ae110098ae1100307a253108000000c0ae1100
7c0bee006476000800000000250000000c00000001000000250000000c00000001000000
250000000c00000001000000180000000c00000000000002540000005400000000000000
000000000800000010000000010000000000c8410080bb41000000000d00000001000000
4c0000000400000000000000000000005b020000ab000000500000002000000809000000
46000000280000001c0000004744494302000000ffffffffffffffff5c020000ac000000
000000004600000014000000080000004744494303000000250000000c0000000e000080
250000000c0000000e0000800e0000001400000000000000100000001400000004000000
03010800050000000b0200000000050000000c02ab005b02040000002e0118001c000000
fb021000070000000000bc02000000cc0102022253797374656d00000000000000000000
00000000000000000000000000000000040000002d010000040000002d01000004000000
020101001c000000fb02f1ff0000000000009001000000cc0440002243616c6962726900
000000000000000000000000000000000000000000000000040000002d01010004000000
2d010100040000002d010100050000000902000000020d000000320a0d00000001000400
000000005b02ab0020ea0900040000002d010000040000002d010000030000000000
Рисунок 15 – Сферохроматизм в присутствии аберраций 3 и 5 порядков
Как видно из рис.8.33, обычно сферохроматизм исправляется для значения
20.5.
Хроматизм увеличения
Хроматизм увеличения – это аберрация, при которой увеличение оптической
системы зависит от длины волны (рис.16). Вследствие этого вместо
изображения точки образуется цветная полоска.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Рисунок 16 – Хроматизм увеличения.
Численно абсолютный хроматизм увеличения (первичный спектр) определяется
как разность величины изображения для крайних длин волн: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.
(16)
Вторичный спектр (вторичный хроматизм увеличения) определяется как
разность величины изображения для центральной и крайних длин волн: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(17)
Хроматизм увеличения измеряется в тех же единицах, что и величина
изображения: для ближнего типа – в миллиметры, для дальнего типа – в
угловой мере.
Относительный хроматизм увеличения:
первичный спектр: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(18)
вторичный спектр: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(19)
Если выразить увеличение для различных длин волн в виде: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,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, то относительный
хроматизм увеличения можно записать в следующем виде: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.
(20)
Хроматизм увеличения принято рассматривать только в одной плоскости
установки. Поскольку типы хроматических аберраций не связаны друг с
другом, хроматизм увеличения может исправляться независимо от хроматизма
положения. В частности, если оптическая система тонкая (рис. 17), а
апертурная диафрагма совпадает с ней, то хроматизм положения
присутствует, а хроматизма увеличения нет.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Рисунок 17 – Хроматизм положения и увеличения тонкой линзы.
Если в системе исправлен первичный хроматизм увеличения, то это ахромат
по хроматизму увеличения, если исправлен вторичный хроматизм увеличения,
то это апохромат по хроматизму увеличения, если хроматизм увеличения не
исправлен, то это неахромат по хроматизму увеличения.
ЛИТЕРАТУРА
1. Бегунов Б.Н., Заказнов Н.П. и др. Теория оптических систем. – М.:
Машиностроение, 2004
2. Заказнов Н.П. Прикладная оптика. – М.: Машиностроение, 2000
3. Дубовик А.С. Прикладная оптика. – М.: Недра, 2002
4. Нагибина И.М. и др. Прикладная физическая оптика. Учебное пособие.-
М.: Высшая школа, 2002
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