Abstract

We discuss the use of total internal reflection for the production of sensors with high angular resolution. These sensors are intended for measurement of the angle between a sensor’s axis and the direction to a source of radiation or reflecting object. Sensors of this type are used in controlling the position of machine parts in robotics and industry, orienting space vehicles and astronomic devices in relation to the Sun, and as autocollimators for checking angles of deviation. This kind of sensor was used in the Apollo space vehicle some 20 years ago. Using photodetectors with linear and area CCD arrays has opened up new application possibilities for appropriately designed sensors. A generalized methodology is presented applicable to a wide range of tasks. Some modifications that can improve the performance of the basic design are described.

© 1996 Optical Society of America

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References

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  1. L. Ivin, I. Shavirin, “Displacement angle amplification at the border of full internal reflection,” Opt. Mekh. Prom. No. 10, 12–14 (1975)
  2. N.t., L. Ivin, I. Shavirin, U.S. patent3,414,213 (1968)
  3. N.t., L. Ivin, I. Shavirin, USSR patent1,498,150 (26November1988).

1975

L. Ivin, I. Shavirin, “Displacement angle amplification at the border of full internal reflection,” Opt. Mekh. Prom. No. 10, 12–14 (1975)

Ivin, L.

L. Ivin, I. Shavirin, “Displacement angle amplification at the border of full internal reflection,” Opt. Mekh. Prom. No. 10, 12–14 (1975)

N.t., L. Ivin, I. Shavirin, U.S. patent3,414,213 (1968)

N.t., L. Ivin, I. Shavirin, USSR patent1,498,150 (26November1988).

Shavirin, I.

L. Ivin, I. Shavirin, “Displacement angle amplification at the border of full internal reflection,” Opt. Mekh. Prom. No. 10, 12–14 (1975)

N.t., L. Ivin, I. Shavirin, U.S. patent3,414,213 (1968)

N.t., L. Ivin, I. Shavirin, USSR patent1,498,150 (26November1988).

Opt. Mekh. Prom. No.

L. Ivin, I. Shavirin, “Displacement angle amplification at the border of full internal reflection,” Opt. Mekh. Prom. No. 10, 12–14 (1975)

Other

N.t., L. Ivin, I. Shavirin, U.S. patent3,414,213 (1968)

N.t., L. Ivin, I. Shavirin, USSR patent1,498,150 (26November1988).

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Figures (15)

Fig. 1
Fig. 1

Schematic of a position-sensitive sensor.

Fig. 2
Fig. 2

Operating principle of a high-resolution sensor.

Fig. 3
Fig. 3

Specifications of sensor parameters.

Fig. 4
Fig. 4

Aperture diaphragms.

Fig. 5
Fig. 5

Parameters for calculation of image plane light distribution.

Fig. 6
Fig. 6

Further parameters for flux calculation.

Fig. 7
Fig. 7

Three-dimensional topographical maps of image plane light intensity distributions for a conical prism.

Fig. 8
Fig. 8

Three-dimensional topographical maps of image plane light intensity distributions for a pyramidal prism.

Fig. 9
Fig. 9

Measured image plane light distributions.

Fig. 10
Fig. 10

Linear slice intensity plots of a conical prism.

Fig. 11
Fig. 11

Measured image plane light distributions.

Fig. 12
Fig. 12

Linear slice intensity plots of a pyramidal prism.

Fig. 13
Fig. 13

Schematic of the experimental rig.

Fig. 14
Fig. 14

Experimental rig showing waveforms of pulsed signals.

Fig. 15
Fig. 15

Schematic of the peak finding circuit.

Equations (15)

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θ = arccos { η sin [ Y arcsin ( sin φ η ) ] } .
θ = 2 φ cos Y .
θ = arccos [ η ( 1 { cos Y [ 1 ( 1 η sin ω ) 2 ] 1 / 2 + sin Y 1 η sin ω cos ( U α ) } 2 ) 1 / 2 ]
θ = { 2 cos Y [ ω cos ( u α ) ω cr ] } 1 / 2 ,
ω cr = η sin Y 1 cos Y ,
Y = arcsin 1 η + ω 0 η .
τ ( ω ) = 2 θ ( 1 + sin 2 Y ) 2 θ + sin Y cos Y .
d E inp = L d Ω cos ω,
d 2 Φ = τ app τ d 2 Φ inp ,
d E = τ app τ d 2 E inp d σ d Q 2 .
E = o oo sin 2 2 Y ( 1 + sin 2 Y ) φ x 2 φ ˜ x θ ( cot Y + 1 θ ) 2 2 θ + sin Y cos Y × { ω 0 2 ω x 2 ω 0 2 ω x 2 L ( ω x , ω y ) y } x ,
θ = [ 2 cos Y ( ω x ω c 2 ) ] 1 / 2 , φ ˜ x = { φ x 1 if 0 ρ ρ cr ω 0 if ρ cr < ρ ρ max , φ x 1 , 2 = θ 1 , 2 2 2 cos Y + ω cr , θ 1 , 2 = ( 2 R 1 , 2 ρ sin 2 Y cot Y ) 1 , ω cr = ω cr φ 0 cos ( u o α ) , ρ cr = 2 R 1 sin 2 Y ( cot Y + 1 θ cr ) , ρ max = 2 R 2 sin 2 Y ( cot Y + 1 θ cr ) ,
θ cr = [ 2 cos Y ( ω 0 ω cr ) ] 1 / 2 .
φ x = ω 0 + o oo ( 2 R 1 ρ x sin 2 Y cot Y ) 2 cos 1 Y ,
φ y = ω 0 + o oo ( 2 R 1 ρ y sin 2 Y cot Y ) 2 cos 1 Y ,

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