Формы представления аберраций (поперечная, продольная, волновая). Монохроматические аберрации (реферат)

БЕЛОРУССКИЙ ГОСУДАРСТВЕННЫЙ УНИВЕРСИТЕТ ИНФОРМАТИКИ И РАДИОЭЛЕКТРОНИКИ

Кафедра ЭТТ

РЕФЕРАТ

На тему:

«Формы представления аберраций (поперечная, продольная, волновая).
Монохроматические аберрации»

МИНСК, 2008

В идеальной оптической системе все лучи, исходящие из точки A,
пересекаются в сопряженной с ней точке A?0. После прохождения реальной
оптической системы либо нарушается гомоцентричность пучка и лучи не
имеют общей точки пересечения, либо гомоцентричность сохраняется, но
лучи пересекаются в некоторой точке A?, которая не совпадает с точкой
идеального изображения (рисунок 1). Это является следствием аберраций.
Основная задача расчета оптических систем – устранение аберраций.
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Рисунок 1 – Идеальное и реальное изображения точки

Для вычисления аберраций необходимо определить точку референтного
(идеального) изображения A?0 , в которой должно находиться изображение
по законам гауссовой оптики. Относительно этой точки и определяют
аберрации.

Поперечные аберрации

Поперечные аберрации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 – это отклонения координат точки A?
пересечения реального луча с плоскостью изображения от координат точки
A?0 идеального изображения в направлении, перпендикулярном оптической
оси (рисунок 2):
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.
(1)

Если точки A? и A?0 совпадают, то поперечные аберрации равны нулю
picscalex1000100090000034501000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c020002e00a1200000026060f001a00ffffffff000010000000c0ffffff
c6ffffffa00a0000c60100000b00000026060f000c004d61746854797065000050001c00
0000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320a60011e0a
01000000297908000000320a60015e0901000000307908000000320a6001080501000000
2c7908000000320a60014e0401000000307908000000320a600134000100000028791c00
0000fb0280fe0000000000009001000000020002001053796d626f6c007740000000ab08
0af51643c7771f43c77720c0c97700003000040000002d01010004000000f00100000800
0000320a60012c08010000003d7908000000320a4a01720701000000a27908000000320a
6001c80501000000447908000000320a60011c03010000003d7908000000320a4a016202
01000000a27908000000320a6001be000100000044791c000000fb0280fe000000000000
9001010000000402001054696d6573204e657720526f6d616e001643c7771f43c77720c0
c97700003000040000002d01000004000000f001010008000000320a6001b20601000000
797908000000320a6001a8010100000078790a00000026060f000a00ffffffff01000000
00001c000000fb021000070000000000bc02000000cc0102022253797374656d00000000
0a0021008a0100000000010000009cf312002942c777040000002d01010004000000f001
0000030000000000.
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Рисунок 2 – Поперечные аберрации

Различают поперечные аберрации в сагиттальной плоскости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 и в меридиональной
плоскости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. Поперечные аберрации
для изображения ближнего типа выражаются в миллиметрах, для изображения
дальнего типа – в угловой мере. Для изображения дальнего типа поперечная
аберрация – это угловое отклонение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 между реальным
и идеальным лучом (рисунок 3).
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Рисунок 3 – Поперечные аберрации для удаленного изображения

У каждого луча в пучке своя величина поперечной аберрации. Для всего
пучка поперечные аберрации – это функции от зрачковых координат:
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 ,
(2)

Зрачковые канонические координаты.

Зрачковые координаты определяют положение луча в пучке. Канонические
(относительные) зрачковые координаты определяются следующим образом:
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 , (3)

где
picscalex1000100090000031501000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02600240051200000026060f001a00ffffffff000010000000c0ffffff
a6ffffff00050000060200000b00000026060f000c004d61746854797065000070001c00
0000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320a80017204
01000000297908000000320a80012e02010000002c7908000000320a8001340001000000
28791c000000fb0220ff0000000000009001010000000402001054696d6573204e657720
526f6d616e001643c7771f43c77720c0c97700003000040000002d01010004000000f001
000008000000320ae001ce0301000000797908000000320ae00194010100000078791c00
0000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000004000000f00101000800
0000320a8001fa0201000000507908000000320a8001ca000100000050790a0000002606
0f000a00ffffffff0100000000001c000000fb021000070000000000bc02000000cc0102
022253797374656d000000000a0021008a0100000000010000009cf312002942c7770400
00002d01010004000000f0010000030000000000,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 – входные и выходные реальные зрачковые
координаты,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,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 – входные и выходные апертуры. Апертуры
определяют максимальные значения зрачковых координат.

Таким образом, верхний луч пучка имеет координаты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, нижний луч пучка –
picscalex1000100090000035101000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c026002400a1200000026060f001a00ffffffff000010000000c0ffffff
a6ffffff000a0000060200000b00000026060f000c004d61746854797065000070001c00
0000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320a80015609
01000000317908000000320a80012e04010000002c7908000000320a8001740301000000
30791c000000fb0280fe0000000000009001000000020002001053796d626f6c00774000
0000270d0ab51643c7771f43c77720c0c97700003000040000002d01010004000000f001
000008000000320a80018408010000002d7908000000320a80014c07010000003d790800
0000320a80014202010000003d791c000000fb0220ff0000000000009001010000000402
001054696d6573204e657720526f6d616e001643c7771f43c77720c0c977000030000400
00002d01000004000000f001010008000000320ae001480601000000797908000000320a
e00142010100000078791c000000fb0280fe000000000000900101000002040200105379
6d626f6c007740000000270d0ab61643c7771f43c77720c0c97700003000040000002d01
010004000000f001000008000000320a8001420501000000727908000000320a80014600
0100000072790a00000026060f000a00ffffffff0100000000001c000000fb0210000700
00000000bc02000000cc0102022253797374656d000000000a0021008a01000000000000
0000fcf312002942c777040000002d01000004000000f0010100030000000000,
главный луч пучка –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, сагиттальный луч –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 (рисунок 4).
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Рисунок 4 – Канонические зрачковые координаты

Канонические зрачковые координаты можно выразить через полярные
координаты ? и ?:

picscalex1000100090000036301000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02800420081200000026060f001a00ffffffff000010000000c0ffffff
c0ffffffe0070000400400000b00000026060f000c004d617468547970650000f0001c00
0000fb0280fe0000000000009001010000020402001053796d626f6c007740000000e30b
0ad51643c7771f43c77720c0c97700003000040000002d01000008000000320aaf03cb06
010000006a7908000000320aaf03950301000000727908000000320aaf03460001000000
727908000000320a66018706010000006a7908000000320a660187030100000072790800
0000320a660146000100000072791c000000fb0280fe0000000000009001000000000402
001054696d6573204e657720526f6d616e001643c7771f43c77720c0c977000030000400
00002d01010004000000f001000009000000320aaf03b50403000000636f736509000000
320a6601a1040300000073696e651c000000fb0280fe0000000000009001000000020002
001053796d626f6c007740000000e30b0ad61643c7771f43c77720c0c977000030000400
00002d01000004000000f001010008000000320aaf035102010000003d6908000000320a
66014302010000003d691c000000fb0220ff000000000000900101000000040200105469
6d6573204e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d01
010004000000f001000008000000320a0f044d0101000000796908000000320ac6014301
0100000078690a00000026060f000a00ffffffff0100000000001c000000fb0210000700
00000000bc02000000cc0102022253797374656d000000000a0021008a01000000000000
00009cf312002942c777040000002d01000004000000f0010100030000000000 ,
(4)

где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.

Волновая аберрация

Волновая аберрация – это отклонение реального волнового фронта от
идеального (рисунок 5), измеренное вдоль луча в количестве длин волн:
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 (5)

Из выражения (5) следует, что волновая аберрация пропорциональна
отклонениям оптических длин лучей пучка. Поэтому влияние волновой
аберрации на качество изображения не зависит от типа изображения, а
определяется тем, сколько длин волн она составляет.
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Рисунок 5 – Волновая аберрация

Референтная сфера – это волновой фронт идеального пучка с центром в
точке идеального изображения A?0, проходящий через центр выходного
зрачка O?. При нахождении волновой аберрации с референтной сферой
сравнивается ближайший к ней волновой фронт.

Для всего пучка волновая аберрация – это функция канонических зрачковых
координат:
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.
(6)

Поперечная и волновая аберрации – это разные формы представления одного
явления, они связаны между собой соотношениями:
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. (7)

Таким образом, поперечные аберрации прямо пропорциональны первым частным
производным волновой аберрации по каноническим координатам.

Продольные аберрации

Продольные аберрации – это отклонения координаты точки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 пересечения
реального луча с осью от координаты точки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 идеального изображения вдоль оси (рисунок 6):
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 ,
(8)

где S? – положение точки пересечения луча с осью, S?0 – положение
идеальной точки пересечения.
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Рисунок 6 – Продольные аберрации осевого пучка для изображения ближнего
типа

Для изображения ближнего типа продольные аберрации выражаются в
миллиметрах, для изображения дальнего типа (рис.8.7) продольные
аберрации выражаются в обратных миллиметрах:
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. (9)
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Рисунок 7 – Продольные аберрации осевого пучка для изображения дальнего
типа

Продольные аберрации связаны с поперечными, и, следовательно, с
волновыми тоже:
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, (10)

где А?0 – задняя апертура осевого пучка.

Выражение (10) приближенное, оно может использоваться только для случая
небольших апертур.

Итак, из выражений (7) и (10) следует, что волновая, поперечная и
продольная аберрация – это разные формы представления одного явления
нарушения гомоцентричности пучков. При оценке качества изображения за
исходную модель аберрационных свойств оптической системы берут волновую
аберрацию (по величине волновой аберрации судят о качестве оптической
системы). Однако, если аберрации велики, то более целесообразно
использовать для оценки качества изображения поперечные аберрации.

Монохроматические аберрации

Аберрации делятся на монохроматические и хроматические.
Монохроматические аберрации присутствуют, даже если оптическая система
работает при монохроматическом излучении.

Монохроматические аберрации делятся на несколько типов:

– сферическая,

– кома,

– астигматизм и кривизна изображения,

– дисторсия.

Обычно все последующие аберрации добавляются к уже существующим. Но мы
будем рассматривать каждый тип аберрации по отдельности, как если бы
только он и существовал.

Разложение волновой аберрации в ряд

Если в оптической системе присутствуют все типы аберраций, то для
описания отдельных типов аберраций волновую аберрацию можно разложить в
ряд по степеням относительных зрачковых координат в следующем виде:
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(11)

или в полярных координатах:
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 , (12)

где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 (n – степень , m – степень cos) – коэффициент,
значение которого определяет вклад конкретного типа (и порядка)
аберрации в общую волновую аберрацию:
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 – постоянная составляющая, которая может быть
сведена к нулю соответствующим выбором референтной сферы,
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 и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 – сферическая аберрация 3 и 5 порядка,
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 – дисторсия,

picscalex1000100090000038f01000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02600200101200000026060f001a00ffffffff000010000000c0ffffff
b7ffffffc00f0000170200000b00000026060f000c004d61746854797065000060001c00
0000fb0280fe0000000000009001010000020402001053796d626f6c007740000000b70c
0a6f1643c7771f43c77720c0c97700003000040000002d01000008000000320aa001ae0e
010000006a7908000000320aa001c00a01000000727908000000320aa001370601000000
6a7908000000320aa0014d020100000072791c000000fb0280fe00000000000090010000
00000402001054696d6573204e657720526f6d616e001643c7771f43c77720c0c9770000
3000040000002d01010004000000f001000009000000320aa001980c03000000636f7365
09000000320aa001210403000000636f73651c000000fb0220ff00000000000090010000
00000402001054696d6573204e657720526f6d616e001643c7771f43c77720c0c9770000
3000040000002d01000004000000f001010008000000320af400ca0b01000000356f0800
0000320a0002c60902000000353108000000320af400570301000000333108000000320a
000253010200000033311c000000fb0280fe000000000000900101000000040200105469
6d6573204e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d01
010004000000f001000008000000320aa001890801000000573108000000320aa0011600
0100000057311c000000fb0280fe0000000000009001000000020002001053796d626f6c
007740000000b70c0a711643c7771f43c77720c0c97700003000040000002d0100000400
0000f001010008000000320aa0018707010000002b310a00000026060f000a00ffffffff
0100000000001c000000fb021000070000000000bc02000000cc0102022253797374656d
000000000a0021008a0100000000010000009cf312002942c777040000002d0101000400
0000f0010000030000000000 – кома 3 и 5 порядка,
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 – астигматизм 3 и 5 порядка.

В разложении могут участвовать и более высокие порядки, но мы их
рассматривать не будем.

Порядок аберрации определяется по степени координаты ? в разложении
поперечной аберрации в ряд.

Этот ряд получаем путем дифференцирования выражения (12). Таким образом,
поперечная аберрация определяется следующим образом:
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 . (13)

Разложение в ряд продольной аберрации имеет вид:
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 . (14)

Радиально симметричные аберрации (дефокусировка и сферическая аберрация)

Радиально симметричные аберрации (расфокусировка и сферическая
аберрация) анализируются и изучаются при рассмотрении осевой точки
предмета. Для описания радиально симметричных аберраций достаточно
использовать одну радиальную зрачковую координату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:
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 .
(15)

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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