Section 7 Gaussian Reduction .edu

OPTI-201/202 Geometrical and Instrumental Optics ? Copyright 2018 John E. Greivenkamp

7-1

Section 7 Gaussian Reduction

OPTI-201/202 Geometrical and Instrumental Optics ? Copyright 2018 John E. Greivenkamp

7-2 Paraxial Raytrace Equations

Refraction occurs at an interface between two optical spaces. The transfer distance t' allows the ray height y' to be determined at any plane within an optical space (including virtual segments).

nu

n nC

t n

Refraction:

nu nu y

y

Transfer:

n

n

u

y

u

P P

u t

y y tu

y

y

nu

t n

y y

y z

OPTI-201/202 Geometrical and Instrumental Optics ? Copyright 2018 John E. Greivenkamp

7-3 Gaussian Reduction

Gaussian reduction is the process that combines multiple components two at a time into a single equivalent system. The Gaussian properties (power, focal lengths, and the location of the cardinal points) are determined.

Two component system ? System Power:

Trace a ray parallel to the optical axis in object space. This ray must go through the rear focal point of the system.

Paraxial raytrace:

Refraction Transfer

nu nu y

y

y y nut n y y

1

2

u = u1 = 0

y1

u1 = u2

y2

P1 P1

P P2

P2

n1 = n

n2 = n1

u = u2

F

z

n3 = n2 = n

t = t

Define the system power by applying the refraction equation to the system:

2 y1

0

y1

OPTI-201/202 Geometrical and Instrumental Optics ? Copyright 2018 John E. Greivenkamp

7-4 Two Component System ? System Power

1

2

u = u1 = 0

y1

u1 = u2

y2

P1 P1

P P2

P2

n1 = n

n2 = n1

u = u2

F

z

n3 = n2 = n

Trace the ray:

t = t

2 1 1 y11 y11 y2 y1 1 2 2 y22

y11 y1 1 2 y11 y12 y11 2 y1 1 2 12 y1

t n2

y1

System power:

1 2 12

OPTI-201/202 Geometrical and Instrumental Optics ? Copyright 2018 John E. Greivenkamp

7-5 Two Component System ? Rear Cardinal Points

The system rear principal plane is the plane of unit system magnification.

1

2

u = u1 = 0

y1

u1 = u2

y2

P1 P1

P P2

P2

n1 = n

n2 = n1

u = u2

F

z

n3 = n2 = n

y2 y1 1 1 2 y11 y1

d y2 y1 u

d 1 u

d n

1

y11 y1

t = t d

d 1 1 t

n

n2

Note that the shift d' of the system rear

principal plane P' from the rear principal plane of the second element P2 occurs in the system image space n'.

P2F fR

P2F

y2 u

f

R

P2

F

d

f R

n

If P2 is the rear vertex of the system, then the distance P2F is the BFD.

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