Matrix methods in paraxial optics

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Matrix methods in paraxial optics. Wednesday September 25, 2002. Matrices in paraxial Optics. Translation (in homogeneous medium). .  0. y. y o. L. Matrix methods in paraxial optics. Refraction at a spherical interface. . y. ’. . φ. ’. n. n’.

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### Matrix methods in paraxial optics

Wednesday September 25, 2002

Matrices in paraxial Optics

Translation

(in homogeneous medium)

0

y

yo

L

Matrix methods in paraxial optics

Refraction at a spherical interface

y

’

φ

’

n

n’

Matrix methods in paraxial optics

Refraction at a spherical interface

y

’

φ

’

n

n’

Matrix methods in paraxial optics

Lens matrix

n

nL

n’

For the complete system

Note order – matrices do not, in general, commute.

Matrices: General Properties

For system in air, n=n’=1

System matrix: Special Cases

(a) D = 0  f = Cyo (independent of o)

f

yo

Input plane is the first focal plane

yf

o

System matrix: Special Cases

(b) A = 0  yf = Bo (independent of yo)

Output plane is the second focal plane

yf

System matrix: Special Cases

(c) B = 0  yf = Ayo

yo

Input and output plane are conjugate – A = magnification

o

f

System matrix: Special Cases

(d) C = 0  f = Do (independent of yo)

Telescopic system – parallel rays in : parallel rays out

Examples: Thin lens

Recall that for a thick lens

For a thin lens, d=0

Examples: Thin lens

Recall that for a thick lens

For a thin lens, d=0

In air, n=n’=1

Imaging with thin lens in air

’

o

yo

y’

Input

plane

Output plane

s

s’

Imaging with thin lens in air

For thin lens: A=1B=0D=1 C=-1/f

y’ = A’yo + B’o

Imaging with thin lens in air

For thin lens: A=1B=0D=1 C=-1/f

y’ = A’yo + B’o

For imaging, y’ must be independent of o

 B’ = 0

B’ = As + B + Css’ + Ds’ = 0

s + 0 + (-1/f)ss’ + s’ = 0

Examples: Thick Lens

H’

’

yo

y’

f’

n

nf

n’

x’

h’

h’ = - ( f’ - x’ )

Cardinal points of a thick lens

Recall that for a thick lens

As we have found before

h can be recovered in a similar manner, along with other cardinal points