Abstract

Three different commonly used methods of measuring the length and fan angle of a light line or a light fan produced by a laser line generator were analyzed, tested, and compared. One measurement method is proposed as the standard method, and the resultant 1/e 2 intensity fan angle is proposed as the standard parameter to describe the line generator.

© 1998 Optical Society of America

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Figures (5)

Fig. 1
Fig. 1

Laser line generator consisting of a laser beam and a cylindrical lens. The beam that propagates in the z direction is incident on the cylindrical lens and the cylindrical lens transforms the laser beam into a light fan in the y–z plane centered at focal point o of the cylindrical lens. The light fan forms a light line on a working plane at a working distance W from the cylindrical lens. The angular intensity distribution Ia(ϕ) of the light fan can be measured by method a. The angular and linear intensity distributions Ib(ϕ), Ib(y), Ic(ϕ), and Ic(y) of the light line on the working plane can be measured by methods b and c, respectively.

Fig. 2
Fig. 2

Calculated Ia(ϕ), Ib(ϕ), and Ic(ϕ) and the corresponding ϕ ea , ϕ eb , and ϕ ec .

Fig. 3
Fig. 3

Calculated ϕ ea , ϕ eb , and ϕ ec as a function of ϕ ea .

Fig. 4
Fig. 4

Calculated Ib(y) and Ic(y) and the corresponding leb(w) and lec(w).

Fig. 5
Fig. 5

Measured Ib(y) and Ic(y) and the corresponding leb(w) and lec(w).

Equations (16)

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I y = exp - 2 y y e / 2 2 ,
I a ϕ = exp - 2 ϕ ϕ ea / 2 2 ,
ϕ ea = 2   tan - 1 y e 2 f ,
l a w = 2 w   tan ϕ ea 2 .
ϕ eb = 2   tan - 1 l eb w 2 w
ϕ ec = 2   tan - 1 l ec w 2 w .
Δ S a d / w .
Δ S b ϕ = cos ϕ Δ S a .
I b ϕ = Δ S b ϕ Δ S a exp - 2 ϕ ϕ ea / 2 2 = cos ϕ exp - 2 ϕ ϕ ea / 2 2 .
Δ S c ϕ = cos 2 ϕ Δ S a .
I c ϕ = Δ S c ϕ Δ S a exp - 2 ϕ ϕ ea / 2 2 = cos 2 ϕ exp - 2 ϕ ϕ ea / 2 2 .
Δ S a > Δ S b ϕ > Δ S c ϕ .
l a w > l eb w > l ec w ,
ϕ ea > ϕ eb > ϕ ec .
I b y = cos 2   tan - 1 y w exp - 2 tan - 1 y / w ϕ ea / 2 2 ,
I c y = cos 2 2   tan - 1 y w exp - 2 tan - 1 y / w ϕ ea / 2 2 ,

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