JP2001091402A - Composite declination computing method by computer for wedge prism and computer readable storage medium recording wedge prism composite declination computing program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a wedge prism composite declination computing method for easily computing a composite declination and its direction when a plurality of wedge prisms are combined with each other. SOLUTION: After declinations δ1, δ2 of a pair of wedge prisms 1, 2 and their rotation angles ψ1, ψ2 provided by means of encoders 5a, 5b are inputted, a computer computes a composite declination δT and a composite declination direction ψT for the combined wedge prisms 1, 2 according to the following expression: δT=√((δ1 cosψ1+δ2 cosψ2)2+(δ1 sinψ1+δ2 sinψ2)2 ψT=tan-1((δ1 sinψ1+δ2 sinψ2)/(δ1 cosψ1+δ2 cosψ2)).

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for calculating a combined deflection angle by a computer when a plurality of wedge prisms are combined.

[0002]

2. Description of the Related Art Wedge prisms for use in beam manipulation in optical systems are known. FIG.
1 shows a wedge prism 1. FIG. 2A shows a plan view of the wedge prism, and FIG. 2B shows a main section (a section perpendicular to the ridge line S) of the wedge prism 1. The wedge prism 1 is a thin prism lens having a small apex angle (wedge angle) w, and deflects the beam at a declination δ when the beam is vertically incident on the first surface of the wedge prism 1.

FIG. 7 shows beam deflection when two wedge prisms 1 and 2 are combined.
When the two wedge prisms 1 and 2 are arranged close to each other and the two wedge prisms 1 and 2 are separately rotated around the central axis, the beam is directed in an arbitrary direction inside a predetermined sharp cone. Can be deflected.

Here, by calculating a combined deflection angle δT and a combined deflection direction ΔT when two wedge prisms 1 and 2 are combined, it is possible to determine in which direction the beam is deflected.

[0005]

However, it is difficult to strictly determine the combined deflection angle δT and combined deflection direction ΔT when combined. This is because the light deflected by the wedge prism 1 enters the wedge prism 2 as a beam (skew beam) that is not within the main cross section. This is because the refraction of the skew beam is rather complicated.

Accordingly, an object of the present invention is to provide a method for calculating a combined deflection angle of a wedge prism that can easily calculate a combined deflection angle and a combined deflection direction when a plurality of wedge prisms are combined.

[0007]

Hereinafter, the present invention will be described. In addition, in order to facilitate understanding of the present invention, reference numerals in the accompanying drawings are added in parentheses, but the present invention is not limited to the illustrated embodiment.

To solve the above problems, the present inventor has
When calculating the combined deflection angle of the wedge prism using a computer, the wedge prism is a prism having a small apex angle, and the deflection angles δ1, δ2... Are minute, and the wedge prisms to be combined are arranged close to each other. Paying attention to this, the combined argument δT was calculated using a simple calculation formula. Specifically, the first aspect of the present invention is the invention in which each of the n wedge prisms (1, 2,..., N) has a declination δ1,
δ2, δ3,..., δn and angle detecting means (5a, 5
b), the rotation angles ψ1, ψ2, ψ3 of each of the n wedge prisms (1, 2,..., n)
,..., N, and a computer calculates a combined deflection angle δT when the n wedge prisms (1, 2,..., N) are combined using the following formula. , N) solved the above-mentioned problem.

ΔT = √ ((δ1cosψ1 + δ2cos)
ψ2 + ... + δncosψn) ² + (δ1sinψ1 + δ
2 sinψ2 +... + Δnsinψn) ² ) Further, according to a second aspect of the present invention, in the method for calculating a combined deflection angle of the wedge prisms (1, 2,..., N) according to the first aspect, The combined deflection direction ΔT when the wedge prisms (1, 2,..., N) are combined is calculated.

ΨT = tan ⁻¹ ((δ1 sinψ1 + δ2)
sinψ2 +... + δnsinψn) / (δ1cosψ1
+ Δ2cosψ2 +... + Δncosψn)) The invention according to claim 3 is a wedge prism (1,2).
Considering the case where two are combined, the pair of wedge prisms (1,2) and the pair of wedge prisms (1,2) acquired by the angle detection means δ1, δ2 and the angle detection means (5a, 5b). ) Each rotation angle ψ
Wedge prism (1,2) by a computer for inputting 1, ψ2 and calculating the combined deflection angle δT and combined deflection direction ψT when the pair of wedge prisms (1,2) are combined using the following formula. The above-described problem has been solved by the composite argument calculating method.

ΔT = √ ((δ1cosψ1 + δ2cos)
ψ2) ² + (δ1 sinψ1 + δ2 sinψ2) ² ) ψT = tan ⁻¹ ((δ1 sinψ1 + δ2 sinψ2)
/ (Δ1cosψ1 + δ2cosψ2)) Further, according to the invention of claim 4, the pair of wedge prisms (1, 2) have the declinations δ1, δ2 and the pair of wedge prisms (1) acquired by the angle detection means (5a, 5b). , 2) A procedure for inputting the respective rotation angles ψ1, ψ2, and a combined deflection angle δT and a combined deflection direction ψT when the pair of wedge prisms (1, 2) are combined are calculated based on the following formula. The above-described problem has been solved by a computer-readable recording medium that describes a program for causing a computer to execute a procedure and a procedure for outputting a combined deflection angle ΔT and a combined deflection direction ΔT.

ΔT = √ ((δ1cosψ1 + δ2cos)
ψ2) ² + (δ1 sinψ1 + δ2 sinψ2) ² ) ψT = tan ⁻¹ ((δ1 sinψ1 + δ2 sinψ2)
/ (Δ1cosψ1 + δ2cosψ2))

[0013]

FIG. 1 shows a prism unit in which a pair of wedge prisms is combined. The prism unit refracts a beam such as a laser beam emitted from a laser sighting device in an arbitrary direction. The prism unit includes a cylindrical case 3 and a pair of wedge prisms 1 rotatably provided in the case 3. , 2; motors 4a, 4b as drive units for individually rotating the wedge prisms 1, 2;
Encoders 5 and 5b as angle detecting means for digitally detecting the rotation angle of the camera. The motors 4a, 4b and the encoders 5a, 5b are integrated. The wedge prisms 1 and 2 are covered with a protective glass 6 to prevent dust and the like from adhering. A pair of prisms are centerline P
, Each of which rotates independently around the center line P
Incident from above.

FIG. 2 shows a main cross section of the combined wedge prisms 1 and 2. The wedge prisms 1 and 2 are thin, substantially cylindrical prism lenses having a small apex angle (wedge angle) w.

When the beam is deflected only by the wedge prism 1, assuming that the beam is vertically incident on the first surface of the wedge prism 1, the relationship between the deflection angle δ of the wedge prism 1 and the wedge angle w is represented by the following general formula. expressed.

[0016]

(Equation 1)

Assuming that w is small, δ−１ (n-1) w where n is the refractive index.

The two combined wedge prisms 1,
2 are of the same material and have the same wedge apex angle w.
When the two wedge prisms 1 and 2 are arranged close to each other so that the inclined surfaces are parallel, the beam that has passed through the wedge prisms 1 and 2 travels straight as if it passes through parallel glass. On the other hand, by separately rotating around the center lines of the wedge prisms 1 and 2, the laser light can be deflected in an arbitrary direction inside a predetermined sharp cone.

FIG. 3 shows the refraction of the beam by the wedge prisms 1 and 2 in a coordinate system. The Z axis is set on the incident beam, that is, on the center line of the wedge prisms 1 and 2, and the XY plane is set on a plane orthogonal to the center line of the wedge prisms 1 and 2. Then, on the XY plane, the X axis is taken in the horizontal direction and the Y axis is taken in the vertical direction. As shown in this figure, when a beam is incident on the center line of the wedge prisms 1 and 2, the prism 1 deflects the beam, and the prism 2 further deflects the beam. Here, the deflection angle of the prism 1 is δ1, the polarization direction is ψ1, the deflection angle of the prism 2 is δ2, and the deflection direction is ψ2. Here, the polarization direction of the prism ψ
1, ψ2 is 0 when the deflection direction is located on the XZ plane.
The rotation angle from this position is represented by ψ1 and ψ2.
The deflection directions # 1 and # 2 are obtained from the rotation angles # 1 and # 2 of the wedge prisms 1 and 2, respectively. $ 1, $ 2
Is considered as the rotation angle of the wedge prisms 1 and 2, when the line connecting the thickest part and the thinnest part of the prism is horizontal (when it is located on the XZ plane),
Angles from this position are represented by ψ1 and ψ2.

The deflection angle δ of each of the wedge prisms 1 and 2
1, δ2 and the rotation angles ψ1, ψ2 of the wedge prisms 1, 2 obtained by the encoder are input to a computer, and the combined deflection angle δT and combined deflection direction ψT when combined are calculated by the computer. Here, since the wedge apex angle w is very small, it is assumed that both δ1 and δ2 are made small to simplify the calculation, and that the prism 1 and the prism 2 are close to each other. Then, the combined deflection angle δT and the combined deflection direction 偏向 T are the deflection vector (deflection angle δ1, deflection direction ψ
1) and the deflection vector (deflection angle δ2, deflection direction ψ2) in the case of only the prism 2 are displayed as vectors in the XY coordinate system, and the two vectors are calculated by adding them together.

FIG. 4A shows a deflection vector by the prism 1 and FIG. 4B shows a deflection vector by the prism 2. From this figure (a), the following formula is established for the prism 1.

[0022]

(Equation 2)

Further, the following calculation formula holds true for the prism 2 as well.

[0024]

(Equation 3)

From Expressions 2 and 3, the combined component δ in the X direction of the deflection vector when prism 1 and prism 2 are added
TX is represented by Equation 4 below.

[0026]

(Equation 4)

Similarly, the combined component δTY in the Y direction is represented by the following equation (5).

[0028]

(Equation 5)

Therefore, the combined deflection angle δT and the combined deflection direction ΔT are represented by the following equation (6).

[0030]

(Equation 6)

Here, the difference angle Δψ between the two prisms is given by Δψ =
Assuming that ψ1-ψ2, δT is expressed by the following equation 7.

[0032]

Equation 7

By using these formulas, the combined deflection angle δT and the combined deflection direction ΔT when combined can be easily calculated from the rotation angles of the two prisms.

When n wedge prisms are combined, similarly, the combined deflection angle δT and the combined deflection direction ΔT are calculated from the following equations.

[0035]

(Equation 8)

[0036]

[Equation 9]

The beam irradiation position (X0, Y0) on the XY plane at a distance L from the prism unit
Is calculated by X0 = L × δTX and Y0 = L × δTY.

FIG. 5 is a functional block diagram of a computer. First, the deflection angles δ1 and δ2 of the wedge prisms 1 and 2 are input from an input device such as a keyboard.
The inputted declination angles δ1 and δ2 are stored in the δ1 and δ2 storage files of the memory via the central processing unit. Next, the rotation angles ψ1 and ψ2 of the prism are input from angle detection means such as the encoders 5a and 5b. The input $ 1, $ 2 is temporarily stored in the # 1, $ 2 storage file of the memory via the central processing unit. Next, the central processing unit determines δ1,
δ1 and δ2 are obtained from the δ2 storage file and ψ1 and ψ2 are obtained from the ψ1 and ψ2 storage files, and the calculation of the above formula is executed, and the calculation results δT and ψT are output to the output device. Note that X, Y at a distance L from the prism unit
When calculating the irradiation position (X0, Y0) of the beam on the plane, the distance L is input from the input device, and the central processing unit executes the calculation of X0 = L × δTX and Y0 = L × δTY, and calculates Output the result to an output device.

Such a method of calculating the combined deflection angle of the wedge prism is realized by a program, and the program is provided by being recorded on a recording medium.

[0040]

As described above, according to the present invention,
Deflection angles δ1, δ2, δ of each of n wedge prisms
3,..., Δn and the rotation angles ψ1, 1 of each of the n wedge prisms obtained by the n angle detection means.
ψ2, ψ3..., ψn are input, and the combined argument δT in the case where the n wedge prisms are combined is calculated using the above formula, so that the combined argument δT in the case where a plurality of wedge prisms are combined, The resultant deflection direction can be easily calculated.

[Brief description of the drawings]

FIG. 1 is a sectional view showing a prism unit.

FIG. 2 is a main sectional view showing a combined wedge prism.

FIG. 3 is a diagram showing refraction of a beam in an XYZ coordinate system.

FIG. 4 is a view showing a deflection vector ((a) in the figure shows a prism 1, and (b) in the figure shows a prism 2).

FIG. 5 is a functional block diagram of a computer.

FIG. 6 is a view showing a wedge prism (FIG. 6A is a plan view, and FIG. 6B is a main sectional view).

FIG. 7 is a perspective view showing deflection of a combined wedge prism.

[Explanation of symbols]

 1, 2 wedge prism 5a, 5b encoder (angle detection means)

Claims (4)

[Claims] 1. The declination angles δ1, δ2,..., Δn of each of the n wedge prisms and the rotation angle そ れ ぞ れ of each of the n wedge prisms obtained by the angle detection means.
.., Δn are input, and the computer calculates a combined argument δT when the n pieces of wedge prisms are combined using the following formula, and calculates a combined argument of the wedge prism by a computer. δT = √ ((δ1cosψ1 + δ2cosψ2 + ... + δ
ncosψn) ² + (δ1sinψ1 + δ2sinψ2
+ ... + δnsinψn) ² ) 2. The method for calculating a combined deflection angle of a wedge prism by a computer according to claim 1, wherein the combined deflection direction ΔT when the n wedge prisms are combined is calculated using the following formula. ψT = tan ⁻¹ ((δ1 sinψ1 + δ2 sinψ2 +
... + δnsinψn) / (δ1cosψ1 + δ2cos
{2 + ... + δncosψn)) 3. The declination angles δ1 and δ2 of each of the pair of wedge prisms and the rotation angles ψ1 and ψ2 of each of the pair of wedge prisms obtained by the angle detecting means are input, and the pair of wedge prisms are input using the following formula. A method for calculating a combined deflection angle of a wedge prism by a computer that calculates a combined deflection angle δT and a combined deflection direction ΔT when a wedge prism is combined. δT = √ ((δ1 cosψ1 + δ2 cosψ2) ² +
(Δ1 sinψ1 + δ2 sinψ2) ² ) ψT = tan ⁻¹ ((δ1 sinψ1 + δ2 sinψ2)
/ (Δ1cosψ1 + δ2cosψ2)) 4. A step of inputting the declination angles δ1, δ2 of each of the pair of wedge prisms and the rotation angles ψ1, ψ2 of each of the pair of wedge prisms obtained by the angle detecting means, and A computer-readable program that causes a computer to execute a procedure for calculating a combined deflection angle δT and a combined deflection direction ΔT when a pair of wedge prisms are combined, and a procedure for outputting the combined deflection angle δT and the combined deflection direction ΔT. Possible recording medium. δT = √ ((δ1 cosψ1 + δ2 cosψ2) ² +
(Δ1 sinψ1 + δ2 sinψ2) ² ) ψT = tan ⁻¹ ((δ1 sinψ1 + δ2 sinψ2)
/ (Δ1cosψ1 + δ2cosψ2))