Abstract

An analytical expression is derived for the alignment of optical elements, such as the Dove or Pechan prism, that are used to rotate optical images. Improper alignment is characterized by a nutation of the system boresight as the prism is rotated. An analytical description is developed for this nutational boresight error in terms of specific misalignments between the prism, mechanical, and optical axes. This error is shown to be similar in form to that given by a mathematical expression commonly known as the limacon of Pascal. Unique nutation patterns are noted by which one can distinguish and measure specific misalignments. Proper alignment is seen to involve both lateral and angular adjustments. Appropriate adjustment axes are chosen, and suitable alignment procedures are developed.

© 1972 Optical Society of America

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Figures (6)

Fig. 1
Fig. 1

Image nutation due to misalignment of rotational prism.

Fig. 2
Fig. 2

Rotational prism axis. (A Pechan prism is the example used.)

Fig. 3
Fig. 3

Displaced input ray effects.

Fig. 4
Fig. 4

Tilted input ray effects.

Fig. 5
Fig. 5

Limacon of Pascal (ρ = ba cosθ).

Fig. 6
Fig. 6

General case angular or displacement relationships between optical, prism, and mechanical axes.

Tables (1)

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Table I Summary of Displacement and Angular Alignment Errors and Corresponding Nutation Pattern

Equations (5)

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ρ = 2 ( D M I cos θ - D M P ) ,
ρ = b - a cos θ .
cos θ = ( D M P + D P I ) / D M I .
ρ = D O P + D P I = 2 D P I .
ρ = 2 ( D M I cos θ - D M P ) .

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