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Структура и качество оптического изображения (реферат)

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БЕЛОРУССКИЙ ГОСУДАРСТВЕННЫЙ УНИВЕРСИТЕТ ИНФОРМАТИКИ И РАДИОЭЛЕКТРОНИКИ

Кафедра ЭТТ

РЕФЕРАТ

На тему:

«Структура и качество оптического изображения»

МИНСК, 2008

Основные характеристики структуры изображения

Изображающие приборы могут давать изображение различного качества с
точки зрения передачи структуры предмета. Структура и форма светового
поля в пространстве изображений подобна структуре и форме предмета,
однако оптическая система вносит в эту структуру свои изменения, оценка
которых есть оценка качества изображения.

Передача структуры предмета или изображения – это отображение оптической
системой мелких деталей объекта. Для описания такого отображения
необходимо математическое описание предмета и изображения в виде функций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 и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. Эти функции описывают зависимость
распределения интенсивности от пространственных координат.

Представим предмет в виде совокупности бесконечного количества
светящихся точек. Для того, чтобы считать, что изображение предмета –
это совокупность изображений соответствующих точек предмета, оптическая
система должна удовлетворять свойствам линейности и инвариантности к
сдвигу.

Свойство линейности

Изображение суммы объектов равно сумме изображений каждого объекта:
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.
(1)

То есть, если предмет – это сумма точек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, то изображение
– сумма изображений этих точек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. Изображающие
оптические системы полностью линейны.

Свойство инвариантности к сдвигу (условие изопланатизма)

При смещении точки ее изображение только смещается на пропорциональную
величину (рис.1):
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,
(2)

где V – обобщенное увеличение.
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Рисунок.1 – Условие изопланатизма.

В отличие от условия линейности, условие изопланатизма в оптических
системах соблюдается приблизительно, поскольку характер изображения при
смещении изменяется. Изопланатизм, как правило, не соблюдается в
пределах всего поля, обычно он соблюдается только при небольших
смещениях.

Изопланатическая зона – это зона, в пределах которой соблюдается условие
изопланатизма. Чем больше размер изопланатической зоны, тем лучше
изопланатизм. Если зона полностью перекрывает предмет, то система
полностью изопланатична. Мы будем рассматривать структуру изображения в
пределах одной изопланатической зоны.

Функция рассеяния точки

В идеальной оптической системе точка изображается в виде точки, а в
реальной оптической системе точка изображается в виде пятна рассеяния
(рис.2).
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Рисунок 2 – Изображение точки в пределах изопланатической зоны.

Основной характеристикой, описывающей передачу структуры предмета
оптической системой является функция рассеяния точки.

Функция рассеяния точки (ФРТ, point spread function, PSF)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– это функция, описывающая зависимость распределения освещенности от
координат в плоскости изображения, если предмет – это светящаяся точка в
центре изопланатической зоны.

Зная функцию рассеяния точки, можно найти изображение любого предмета,
если разложить его на точки и найти ФРТ от каждой точки. Если есть
предмет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, то каждая его точка изображается в виде функции
picscalex1000100090000033d01000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c020002000b1200000026060f001a00ffffffff000010000000c0ffffff
c6ffffffc00a0000c60100000b00000026060f000c004d61746854797065000050001c00
0000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320a6001420a
01000000297908000000320a60018c05010000002c7908000000320a6001000101000000
28791c000000fb0280fe0000000000009001010000000402001054696d6573204e657720
526f6d616e001643c7771f43c77720c0c97700003000040000002d01010004000000f001
000008000000320a60019e0802000000567908000000320a600140060100000079790800
0000320a6001f40302000000567808000000320a60019c0101000000787808000000320a
60013a000100000068781c000000fb0280fe000000000000900100000002000200105379
6d626f6c007740000000740d0a131643c7771f43c77720c0c97700003000040000002d01
000004000000f001010008000000320a6001a207010000002d7808000000320a4a010007
01000000a27808000000320a6001f802010000002d7808000000320a4a01560201000000
a2780a00000026060f000a00ffffffff0100000000001c000000fb021000070000000000
bc02000000cc0102022253797374656d000000000a0021008a0100000000010000009cf3
12002942c777040000002d01010004000000f0010000030000000000, то есть ФРТ
смещается в точку с координатами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 (рис.2), а изображение
всего предмета будет представлять собой сумму этих изображений:
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.
(3)

Если увеличение V принять за единицу, то выражение (3) становится
сверткой (конволюцией).

Функция изображения есть свертка функции предмета с функцией рассеяния
точки:
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(4)

Гармонический периодический объект

Предмет кроме разложения на отдельные точки можно разложить на другие
элементарные части – периодические решетки.

Периодическая решетка – это структура с белыми и черными полосами.

Гармоническая периодическая решетка – это структура, интенсивность
которой описывается гармонической функцией (рис.3).

В электронике существует аналог гармонической решетки – периодический во
времени сигнал на входе прибора.
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Рисунок 3 – Гармоническая периодическая решетка

Гармоническая периодическая решетка описывается выражением:
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,
(5)

где a – вещественная амплитуда, b – сдвиг, T – период, – угол
ориентации.

Вместо периода можно использовать пространственную частоту
picscalex1000100090000032901000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02c00120051200000026060f001a00ffffffff000010000000c0ffffff
c6ffffffe0040000860100000b00000026060f000c004d61746854797065000030001c00
0000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320a6001e203
0100000054791c000000fb0280fe0000000000009001000000000402001054696d657320
4e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d0101000400
0000f001000008000000320a60014c03010000002f7908000000320a6001740201000000
31791c000000fb0280fe0000000000009001000000020002001053796d626f6c00774000
00008a090a9c1643c7771f43c77720c0c97700003000040000002d01000004000000f001
010008000000320a60016601010000003d791c000000fb0280fe00000000000090010100
00020402001053796d626f6c007740000000f70c0a5d1643c7771f43c77720c0c9770000
3000040000002d01010004000000f001000008000000320a6001feff010000006e790a00
000026060f000a00ffffffff0100000000001c000000fb021000070000000000bc020000
00cc0102022253797374656d000000000a0021008a010000000000000000fcf312002942
c777040000002d01000004000000f0010100030000000000, а вместо вещественной
амплитуды и сдвига – комплексную амплитуду:
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,

(6)

Тогда интенсивность гармонической решетки в комплексной форме:
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,
(7)

Величину
picscalex100010009000003c900000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c024002c0011200000026060f001a00ffffffff000010000000c0ffffff
a6ffffff80010000e60100000b00000026060f000c004d61746854797065000060001c00
0000fb0220ff0000000000009001010000020402001053796d626f6c0077400000006d0d
0aaf1643c7771f43c77720c0c97700003000040000002d01000008000000320ae001f000
0100000071791c000000fb0280fe0000000000009001010000000402001054696d657320
4e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d0101000400
0000f001000008000000320a80014c000100000078790a00000026060f000a00ffffffff
0100000000001c000000fb021000070000000000bc02000000cc0102022253797374656d
000000000a0021008a010000000000000000fcf312002942c777040000002d0100000400
0000f0010100030000000000 можно выразить как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, тогда
интенсивность гармонической решетки будет зависеть от двух координат (x,
y):
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(8)

где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– частота в направлении x,
picscalex100010009000003c900000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c026002c0011200000026060f001a00ffffffff000010000000c0ffffff
a6ffffff80010000060200000b00000026060f000c004d61746854797065000070001c00
0000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320ae0011701
0100000079791c000000fb0280fe0000000000009001010000020402001053796d626f6c
007740000000df0d0a1f1643c7771f43c77720c0c97700003000040000002d0101000400
0000f001000008000000320a8001feff010000006e790a00000026060f000a00ffffffff
0100000000001c000000fb021000070000000000bc02000000cc0102022253797374656d
000000000a0021008a0100000000000000009cf312002942c777040000002d0100000400
0000f0010100030000000000 – частота в направлении y.

Любой объект, как было сказано выше, можно разложить на элементарные
гармонические объекты, тогда изображение – это совокупность изображений
элементарных объектов. Эти изображения для реальных оптических систем
всегда имеют искажения, что связано с законом сохранения энергии.
Идеальные оптические системы нарушают закон сохранения энергии, так как
они для сохранения неизменной структуры предмета должны передавать
бесконечно большую энергию.

Изображение гармонического объекта можно описать, если в выражение (9.3)
подставить в качестве распределения интенсивности на предмете функцию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 (8):
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.
(9)

Если выразить координаты предмета и изображения в едином масштабе, то
V=1, следовательно:
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.

После замены переменных
picscalex100010009000003e501000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02400440151200000026060f001a00ffffffff000010000000c0ffffff
c7ffffff00150000070400000b00000026060f000c004d617468547970650000e0001c00
0000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320a9f03fc13
01000000777908000000320a9f03741101000000797908000000320a9f03fe0e01000000
797908000000320a9f03b60b02000000647708000000320a9f03c6070200000064790800
0000320a9f03040301000000797908000000320a9f035e0001000000797908000000320a
5f01021101000000787908000000320a5f01a40e01000000787908000000320a5f01620b
01000000647908000000320a5f01780702000000647808000000320a5f01da0201000000
787808000000320a5f014c000100000078781c000000fb0280fe00000000000090010000
00020002001053796d626f6c007740000000990b0a941643c7771f43c77720c0c9770000
3000040000002d01010004000000f001000008000000320a9f03d612010000002d780800
0000320a8903341201000000a27808000000320a9f031810010000003d7808000000320a
9f03d80a010000002d7808000000320a9f03a009010000003d7808000000320a9f031e04
010000003d7808000000320a9f03c001010000002d7808000000320a89031e0101000000
a27808000000320a5f015e12010000002d7808000000320a4901bc1101000000a2780800
0000320a5f01b80f010000003d7808000000320a5f01840a010000002d7808000000320a
5f014c09010000003d7808000000320a5f01ee03010000003d7808000000320a5f01a801
010000002d7808000000320a4901060101000000a2781c000000fb0280fe000000000000
9001010000020402001053796d626f6c007740000000610d0ac21643c7771f43c77720c0
c97700003000040000002d01000004000000f001010008000000320a9f033e0501000000
777808000000320a5f014213010000006e7808000000320a5f01220c010000006e780800
0000320a5f010205010000004a780a00000026060f000a00ffffffff0100000000001c00
0000fb021000070000000000bc02000000cc0102022253797374656d000000000a002100
8a0100000000010000009cf312002942c777040000002d01010004000000f00100000300
00000000 получим:
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или, после переобозначения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:
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. (10)

Двойной интеграл в выражении (9.10) – это некоторая функция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, зависящая от пространственных частот.

Обозначим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, и запишем распределение интенсивности на изображении
гармонического объекта в следующем виде:
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.
(11)

Как показывают соотношения (8) и (11), изображение от предмета
отличается только комплексной амплитудой, то есть изображение
гармонической решетки любой оптической системы есть гармоническая
решетка с той же частотой. Поэтому гармоническую решетку удобно
использовать для исследования и оценки передачи структуры изображения.
Изменение комплексной амплитуды гармонической решетки – это и есть
действие оптической системы.

Оптическая передаточная функция (ОПФ)

Оптическая передаточная функция (optical transfer function, OTF)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характеризует передачу структуры предмета оптической системой как
функция пространственных частот:
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.
(12)

ОПФ связана с ФРТ интегральным преобразованием – преобразованием Фурье:
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(13)

или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или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,

где F – обозначение Фурье преобразования:
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.
(14)

ФРТ показывает, как оптическая система изображает точку, а ОПФ
показывает, как оптическая система изображает гармоническую решетку, то
есть как меняется комплексная амплитуда решетки в зависимости от
частоты.

Оптическая передаточная функция – это комплексная функция:
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.
(15)

Модуль ОПФ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 называется
модуляционной передаточной функцией (МПФ) или частотно-контрастной
характеристикой (ЧКХ). Аргумент (фаза) ОПФ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 называется фазовой передаточной
функцией (ФПФ) или частотно-фазовой характеристикой (ЧФК).

Частотно-контрастная характеристика показывает передачу вещественной
амплитуды гармонического объекта:
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,

(16)

где a – амплитуда на предмете, a – амплитуда на изображении.

Амплитуда изображения гармонического объекта тесно связана с контрастом.
Контраст для периодических (гармонических) изображений (рис.9.4)
определяется выражением:
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.
(17)
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Рисунок 4 – Контраст гармонического объекта.
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. Абсолютный контраст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 получается, когда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 (рис.5.а). Контраст
в изображении нулевой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, когда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 – изображение
практически отсутствует (рис.5.б).
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Рисунок 5 – Абсолютный и нулевой контраст гармонического объекта

Чем больше контраст, тем лучше различаются мелкие детали изображения.
Изображение нельзя зарегистрировать или увидеть в случае, если:
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,
(18)

где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 – порог
контраста, зависящий от приемника изображения (например, для глаза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).

Контраст для изображения гармонического объекта может быть выражен через
постоянную a0 и a переменную составляющие изображения гармонического
объекта (рис.6):
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.
(19)
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Рисунок 6 – Постоянная и переменная составляющие изображения
гармонического объекта

Если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, то ЧКХ, как следует из выражения (16) будет определяться
следующим соотношением:
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,

(20)

где k – контраст изображения, k – контраст предмета.

Частотно-контрастная характеристика показывает зависимость контраста
изображения гармонической решетки от частоты решетки, если считать, что
на предмете контраст единичный (рис.7). Для идеальной оптической системы
ЧКХ – прямая, параллельная оси.
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Рисунок 7 – Частотно-контрастная характеристика.

Для ближнего типа предмета или изображения пространственная частота
измеряется в [лин/мм]. Для дальнего типа пространственная частота
измеряется в [лин/рад].

Итак, передача структуры изображения описывается ФРТ или ОПФ, которые
связаны через взаимно однозначные преобразования Фурье. Наглядно
отобразить двумерную функцию ОПФ можно в виде:

– графиков сечений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 или
picscalex1000100090000032901000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02600200041200000026060f001a00ffffffff000010000000c0ffffff
a6ffffffc0030000060200000b00000026060f000c004d61746854797065000070001c00
0000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320a80013503
01000000297908000000320a80012a010100000028791c000000fb0220ff000000000000
9001010000000402001054696d6573204e657720526f6d616e001643c7771f43c77720c0
c97700003000040000002d01010004000000f001000008000000320ae001910201000000
79791c000000fb0280fe0000000000009001010000000402001054696d6573204e657720
526f6d616e001643c7771f43c77720c0c97700003000040000002d01000004000000f001
010008000000320a800122000100000054791c000000fb0280fe00000000000090010100
00020402001053796d626f6c007740000000cb0b0a9f1643c7771f43c77720c0c9770000
3000040000002d01010004000000f001000008000000320a80017801010000006e790a00
000026060f000a00ffffffff0100000000001c000000fb021000070000000000bc020000
00cc0102022253797374656d000000000a0021008a0100000000000000009cf312002942
c777040000002d01000004000000f0010100030000000000,

– изометрического изображения “поверхности”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,

– карты уровней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.

Схема формирования оптического изображения

Существует два фактора, которые влияют на структуру и качество
изображения в оптической системе: дифракция и аберрации. Эти факторы
действуют совместно. Если аберрации малы и преобладает дифракция, то
такие системы называются дифракционно-ограниченными. Если аберрации
велики, и дифракция теряется на фоне аберраций, то такие системы
называются геометрически-ограниченными (формирование изображения вполне
корректно описывается с позиций геометрической оптики, без привлечения
теории дифракции).
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Рисунок 8 – Схема формирования оптического изображения.

Рассмотрим формирование изображения некоторой точки (рис.8).
Гомоцентрический пучок лучей выходит из точки A0, и после идеальной
оптической системы сходится в точке A0. Наряду с пучками лучей можно
также рассматривать сферические волновые фронты Sw и Sw. Действие
реальной оптической системы сводится к следующим факторам:

– преобразование расходящегося пучка лучей (волнового фронта) в
сходящийся,

– ограничение размеров проходящего пучка лучей или волнового фронта,

– ослабление интенсивности (энергии) проходящего поля,

– нарушение гомоцентричности пучка или сферичности волнового фронта, то
есть изменение фазы проходящего поля.

Рассмотрим поле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 на
выходной сфере (в области выходного зрачка). Волновой фронт близок к
выходной сфере, но отличается от нее на величину волновой аберрации.
Поле на волновом фронте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. Оптический путь из
центра предмета до волнового фронта для всех лучей одинаковый, так как
волновой фронт – поверхность равного эйконала. Поскольку для
формирования изображения важна разность фаз между выходной сферой и
волновым фронтом, а не сама фаза, то можно принять, что фаза волнового
фронта равна нулю =0. При отсутствии аберраций амплитуда поля единичная,
следовательно поле на волновом фронте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. Набег фазы от выходной сферы
до волнового фронта:

picscalex100010009000003f301000003001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02600320081200000026060f001a00ffffffff000010000000c0ffffff
acffffffe00700000c0300000b00000026060f000c004d61746854797065000050000800
0000fa0200000800000000000000040000002d0100000500000014025901c20505000000
13025901c3071c000000fb0220ff0000000000009001010000020402001053796d626f6c
007740000000cb0a0a961643c7771f43c77720c0c97700003000040000002d0101000800
0000320a45027e06010000006c7908000000320a9101f9040100000070791c000000fb02
80fe0000000000009001010000020402001053796d626f6c007740000000100b0a381643
c7771f43c77720c0c97700003000040000002d01020004000000f001010008000000320a
c0022401010000006a791c000000fb0220ff000000000000900101000000040200105469
6d6573204e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d01
010004000000f001020008000000320aff001407010000006e7908000000320aff005906
010000006c7908000000320a91016f050100000069791c000000fb0280fe000000000000
9001010000000402001054696d6573204e657720526f6d616e001643c7771f43c77720c0
c97700003000040000002d01020004000000f001010008000000320ac002be0301000000
65791c000000fb0220ff0000000000009001000000020002001053796d626f6c00774000
0000cb0a0a981643c7771f43c77720c0c97700003000040000002d01010004000000f001
020008000000320af200870701000000a27908000000320aff00d90601000000d7790800
0000320af200a50601000000a27908000000320aff00d1050100000044791c000000fb02
80fe0000000000009001000000020002001053796d626f6c007740000000100b0a3a1643
c7771f43c77720c0c97700003000040000002d01020004000000f001010008000000320a
c0028c02010000003d7908000000320ac0023a000100000044791c000000fb0220ff0000
000000009001000000000402001054696d6573204e657720526f6d616e001643c7771f43
c77720c0c97700003000040000002d01010004000000f001020008000000320a91018704
0100000032790a00000026060f000a00ffffffff0100000000001c000000fb0210000700
00000000bc02000000cc0102022253797374656d000000000a0021008a01000000000200
00009cf312002942c777040000002d01020004000000f0010100030000000000,

(21)

где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 – расстояние
между волновым фронтом и выходной сферы вдоль луча.

Поле на выходной сфере математически можно представить в виде:
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,
(22)

где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 – волновая аберрация,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 – зрачковая функция.

В выражении (22) учитывается одновременно ограничение пучков и наличие
аберраций.

Зрачковая функция (pupil function, PF) показывает влияние оптической
системы на прохождение электромагнитного поля от точки предмета до
выходного зрачка и в общем случае в канонических координатах описывается
выражением:
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,
(23)

где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 – канонические зрачковые
координаты,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– функция пропускания по зрачку,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 – область зрачка в канонических координатах.

Теперь нужно перейти от поля на выходном зрачке к полю на изображении.
Вблизи изображения геометрическая оптика не применима, поэтому для
описания поля на изображении следует использовать теорию дифракции.
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Рисунок 9 – Формирование комплексной амплитуды в плоскости изображения.

Для вычисления комплексной амплитуды поля в плоскости изображения
применим принцип Гюйгенса в форме интеграла Гюйгенса-Френеля.
Рассматриваемая область находится вблизи центра выходной сферы (рис. 9):
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.
(23)

Используя зрачковую функцию, выражение (9.23) можно записать в виде:

picscalex1000100090000030103000004001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c022005e0171200000026060f001a00ffffffff000010000000c0ffffff
beffffffa0170000de0400000b00000026060f000c004d617468547970650000c0000800
0000fa0200000800000000000000040000002d01000005000000140247011a1105000000
13024701631208000000fa0200001000000000000000040000002d010100050000001402
4003010f0500000013024003b3121c000000fb02c0fd0000000000009001000000020002
001053796d626f6c007740000000b40c0a241643c7771f43c77720c0c977000030000400
00002d01020008000000320a2a045a0702000000f2f21c000000fb0280fe000000000000
9001000000020002001053796d626f6c0077400000000f0b0a0f1643c7771f43c77720c0
c97700003000040000002d01030004000000f001020008000000320ab6040d1101000000
a2f208000000320aa0031c06010000003df208000000320a8a03de0401000000a2f20800
0000320a8a03160301000000a2f208000000320a8a03660101000000a2f21c000000fb02
20ff0000000000009001000000020002001053796d626f6c007740000000b40c0a251643
c7771f43c77720c0c97700003000040000002d01020004000000f001030008000000320a
e000271201000000a2f208000000320ae0008e1101000000a2f21c000000fb0220ff0000
000000009001010000000402001054696d6573204e657720526f6d616e001643c7771f43
c77720c0c97700003000040000002d01030004000000f001020008000000320a00040117
0100000079f208000000320a0004b2140100000078f208000000320aed00b41101000000
6ef208000000320aed0029110100000072f208000000320a7f01c7100100000069f20800
0000320a0004a30d0100000079f208000000320a0004660b0100000078f21c000000fb02
80fe0000000000009001010000000402001054696d6573204e657720526f6d616e001643
c7771f43c77720c0c97700003000040000002d01020004000000f001030008000000320a
a0033a150100000064f208000000320aa003f5120100000064f208000000320acc045910
0100000072f208000000320aae02150f0100000065f208000000320aa0030d0901000000
66f208000000320aa0031e040100000079f208000000320aa0035c020100000078f20800
0000320aa00316000100000055f21c000000fb0280fe0000000000009001010000020402
001053796d626f6c0077400000000f0b0a111643c7771f43c77720c0c977000030000400
00002d01030004000000f001020008000000320aa003fa150100000072f208000000320a
a003b5130100000072f208000000320aa0039c0c0100000072f208000000320aa003690a
0100000072f21c000000fb0220ff0000000000009001010000020402001053796d626f6c
007740000000b40c0a271643c7771f43c77720c0c97700003000040000002d0102000400
0000f001030008000000320a33027a11010000006cf208000000320a7f01501001000000
70f21c000000fb0220ff0000000000009001000000000402001054696d6573204e657720
526f6d616e001643c7771f43c77720c0c97700003000040000002d01030004000000f001
020008000000320a7f01de0f0100000032f21c000000fb0280fe00000000000090010000
00000402001054696d6573204e657720526f6d616e001643c7771f43c77720c0c9770000
3000040000002d01020004000000f001030008000000320aa003470e0100000029f20800
0000320aa003000c010000002cf208000000320aa003d3090100000028f208000000320a
a00338050100000029f208000000320aa0036a03010000002cf208000000320aa003c001
0100000028f20a00000026060f000a00ffffffff0100000000001c000000fb0210000700
00000000bc02000000cc0102022253797374656d000000000a0021008a01000000000300
00009cf312002942c777040000002d01030004000000f0010200030000000000.
(24) Поскольку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 и,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 то множитель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 можно представить в
виде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. Множитель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, следовательно его можно вынести за интеграл, и не учитывать,
так как нас интересует только относительное распределение комплексной
амплитуды. Тогда выражение (24) преобразуется так:
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(25)

picscalex100010009000003d100000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02a00160021200000026060f001a00ffffffff000010000000c0ffffff
c6ffffff20020000660100000b00000026060f000c004d61746854797065000020001c00
0000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320a60012401
0100000072791c000000fb0280fe0000000000009001000000020002001053796d626f6c
007740000000240c0a971643c7771f43c77720c0c97700003000040000002d0101000400
0000f001000008000000320a4a01d80101000000a27908000000320a60013a0001000000
44790a00000026060f000a00ffffffff0100000000001c000000fb021000070000000000
bc02000000cc0102022253797374656d000000000a0021008a0100000000000000009cf3
12002942c777040000002d01000004000000f0010100030000000000 можно выразить
через
picscalex1000100090000030501000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02000260031200000026060f001a00ffffffff000010000000c0ffffff
c6ffffff20030000c60100000b00000026060f000c004d61746854797065000050001c00
0000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320a60010e02
01000000797908000000320a60014c000100000078791c000000fb0280fe000000000000
9001000000020002001053796d626f6c007740000000f50b0a381643c7771f43c77720c0
c97700003000040000002d01010004000000f001000008000000320a4a01ce0201000000
a27908000000320a4a01060101000000a2791c000000fb0280fe00000000000090010000
00000402001054696d6573204e657720526f6d616e001643c7771f43c77720c0c9770000
3000040000002d01000004000000f001010008000000320a60015a01010000002c790a00
000026060f000a00ffffffff0100000000001c000000fb021000070000000000bc020000
00cc0102022253797374656d000000000a0021008a0100000000010000009cf312002942
c777040000002d01010004000000f0010000030000000000 и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 (рис. 10).

picscalex1000100090000032a0200000200a20100000000a201000026060f003a03574d
464301000000000001003c76000000000100000018030000000000001803000001000000
6c000000000000000000000008000000100000000000000000000000071c0000c1100000
20454d460000010018030000120000000200000000000000000000000000000000050000
0004000040010000f000000000000000000000000000000000e2040080a9030016000000
0c000000180000000a00000010000000000000000000000009000000100000001f010000
b7000000250000000c0000000e000080250000000c0000000e000080120000000c000000
01000000520000007001000001000000f1ffffff00000000000000000000000090010000
000000cc04400022430061006c0069006200720069000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
00001100ccad11001000000030b11100b0ae1100cb4f603230b1110028ae110010000000
98af110014b111001c4f603230b1110028ae110020000000e9e12f3128ae110030b11100
20000000ffffffff3c18ee0064e22f31ffffffffffff0180ffff01800fff0180ffffffff
000000000008000000080000e8ba120001000000000000006000000025000000372e9001
cc00020f0502020204030204ef0200a07b20004000000000000000009f00000000000000
430061006c00690062007200000000000020ee05d59f603267cd120a1c18ee00644bdf00
5cae1100df382731080000000100000098ae110098ae1100307a253108000000c0ae1100
3c18ee006476000800000000250000000c00000001000000250000000c00000001000000
250000000c00000001000000180000000c00000000000002540000005400000000000000
000000000800000010000000010000000000c8410080bb41000000000d00000001000000
4c0000000400000000000000000000001f010000b7000000500000002000000009000000
46000000280000001c0000004744494302000000ffffffffffffffff20010000b7000000
000000004600000014000000080000004744494303000000250000000c0000000e000080
250000000c0000000e0000800e0000001400000000000000100000001400000004000000
03010800050000000b0200000000050000000c02b7001f01040000002e0118001c000000
fb021000070000000000bc02000000cc0102022253797374656d00000000000000000000
00000000000000000000000000000000040000002d010000040000002d01000004000000
020101001c000000fb02f1ff0000000000009001000000cc0440002243616c6962726900
000000000000000000000000000000000000000000000000040000002d01010004000000
2d010100040000002d010100050000000902000000020d000000320a0d00000001000400
000000001f01b700204f0900040000002d010000040000002d010000030000000000

Рисунок 10 – Связь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 с радиусом
выходной сферы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 и расстоянием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от выходной сферы до точки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Отрезок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, причем
picscalex1000100090000036e01000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c022002a0081200000026060f001a00ffffffff000010000000c0ffffff
a6ffffff60080000c60100000b00000026060f000c004d61746854797065000050001c00
0000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320a80011107
01000000417908000000320a80013a00010000006e791c000000fb0220ff000000000000
9001010000000402001054696d6573204e657720526f6d616e001643c7771f43c77720c0
c97700003000040000002d01010004000000f001000008000000320ae0019f0401000000
41791c000000fb0280fe0000000000009001000000020002001053796d626f6c00774000
00008b0a0a5f1643c7771f43c77720c0c97700003000040000002d01000004000000f001
010008000000320a6a01fb0701000000a27908000000320a8001bb05010000003d790800
0000320a6a01960401000000a27908000000320a6a01060101000000a2791c000000fb02
80fe0000000000009001010000020402001053796d626f6c007740000000f60b0a631643
c7771f43c77720c0c97700003000040000002d01010004000000f001000008000000320a
80016a030100000073791c000000fb0280fe000000000000900100000000040200105469
6d6573204e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d01
000004000000f001010009000000320a800184010300000073696e650a00000026060f00
0a00ffffffff0100000000001c000000fb021000070000000000bc02000000cc01020222
53797374656d000000000a0021008a010000000001000000fcf312002942c77704000000
2d01010004000000f0010000030000000000 – для крайнего луча, а для
остальных лучей: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,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. Теперь интеграл (25) можно записать
так:
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.
(26)

Введем канонические (приведенные) координаты на предмете и изображении:
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 .
(27)

Тогда в канонических координатах получим:
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. (28)

Так как зрачковая функция вне зрачка равна нулю, интегрирование
происходит внутри зрачка. Комплексная амплитуда в изображении точки в
канонических координатах, как следует из выражения (28), связана со
зрачковой функцией через обратное преобразование Фурье:
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.
(29)

Комплексная амплитуда поля в изображении точки есть обратное
Фурье-преобразование от зрачковой функции в канонических координатах.

Функция рассеяния точки – это распределение не амплитуды поля, а
интенсивности, то есть квадрата модуля комплексной амплитуды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. Тогда для ФРТ можно получить
следующее выражение:
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.
(30)

Оптическую передаточную функцию также можно выразить в канонических
координатах:
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,

(31)

где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 – канонические
пространственные частоты:
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(32)

Канонические частоты безразмерные: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. В этих координатах получаем
простую связь зрачковой функции с оптической передаточной функцией:
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.
(33)

Это выражение в соответствии со свойством преобразования Фурье можно
представить через автокорреляцию зрачковой функции:
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, (34)

где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 – площадь зрачка в канонических координатах.

ЛИТЕРАТУРА

1. Бегунов Б.Н., Заказнов Н.П. и др. Теория оптических систем. – М.:
Машиностроение, 2004

2. Дубовик А.С. Прикладная оптика. – М.: Недра, 2002

3. Нагибина И.М. и др. Прикладная физическая оптика. Учебное пособие.-
М.: Высшая школа, 2002

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