Abstract

The automatic wavefront error sensor has been developed for determining the wavefront error of an optical system. The instrument, which provides a null test for a parabola, measures the ray intercept error and automatically converts this to a wavefront error. Both the ray fan plot and the wavefront error curve are plotted simultaneously. Ray intercept errors smaller than 0.1 μm can be measured, providing wavefront error information with interferometric sensitivity.

© 1973 Optical Society of America

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Figures (14)

Fig. 1
Fig. 1

Major elements of the automatic wavefront error sensor.

Fig. 2
Fig. 2

Pentaprism rotations.

Fig. 3
Fig. 3

Ray intercept detector.

Fig. 4
Fig. 4

Beam displacement in a parallel plate. d[(n − 1)/n].

Fig. 5
Fig. 5

Beam displacement as a function of plate rotation.

Fig. 6
Fig. 6

Parallel plate in a converging cone.

Fig. 7
Fig. 7

Aberrations of parallel plate at paraxial focus.

Fig. 8
Fig. 8

Aberrations of parallel plate at optimum focus.

Fig. 9
Fig. 9

Plate motion necessary for no aberrations.

Fig. 10
Fig. 10

Postdetection electronics.

Fig. 11
Fig. 11

Tracking error of servo.

Fig. 12
Fig. 12

Noise in wavefront error output.

Fig. 13
Fig. 13

(a) Ray fan and (b) wavefront error curves of f/4 parabola.

Fig. 14
Fig. 14

Wavefront error of f/6 parabola. (a) 0.254-mm inside focus, (b) 0.127-mm inside focus, (c) best focus, (d) 0.127-mm outside focus, (e) 0.254-mm outside focus, (f) 0.381-mm outside focus.

Equations (9)

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( y ) = - 2 F [ W ( x , y ) / y ] ,
W ( y ) = - 1 2 F - 1 1 ( y ) d y .
S = ( β - ϕ - α ϕ ) x ^ + ( ϕ 2 ) y ^ + z ^ .
Pitch : S = z ^ . Roll : S = ( β ) x ^ + z ^ . Yaw : S = ( - ϕ ) x ^ + ( ϕ 2 ) y ^ + z ^ .
β - ϕ - α ϕ < 0.65 ( 10 - 3 ) rad = 2.23 arc min .
d = t sin θ [ 1 - cos θ ( n 2 - sin 2 θ ) 1 / 2 ] ,
d t θ [ ( n - 1 ) / n ] .
= ( 1 / 2 F ) δ z y + ( 1 / 4 F ) [ ( n - 1 ) / n ] y u ¯ 2 t + ( 1 / 2 F ) [ ( n 2 - 1 ) / n 3 ] u ¯ 2 t y + 3 8 ( 1 / F 2 ) [ ( n 2 - 1 ) / n 3 ] y 2 u ¯ t + ( 1 / 16 F 3 ) [ ( n 2 - 1 ) / n 3 ] y 3 t ,
= 0.08333 δ z y + 0.01388 y u ¯ 2 t + 0.03086 u ¯ 2 t y + 0.003858 y 2 u ¯ t + 0.000107 y 3 t .

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