JPH0626024B2 - Optical head device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention is used for reproducing recorded signals from compact discs, video discs, etc., and recording, reproducing, and erasing information signals on optical discs, magneto-optical discs, etc. Optical head.

[Conventional technology]

The optical head used for reproducing recorded signals from compact discs, video discs, etc., recording, reproducing and erasing information signals on optical discs, magneto-optical discs, etc. is the most important and basic part of the optical recording system. is there. The optical head is desired to be small and lightweight in order to have a long life and high reliability, and to be compact, high transfer rate, and high access speed of the optical disk drive. Therefore, attempts are being made to replace the conventional bulk type optical component used in the focus error detection optical system with a thin film grating optical element such as a hologram or a simple grating.

FIG. 2 is a perspective view of an optical head for CD using a reflection hologram optical element which has been conventionally proposed. The light emitted from the semiconductor laser 1 which is a light source is specularly reflected by the reflection hologram optical element 2, guided to the converging lens 3, and condensed on the optical disc 4 which is an optical recording medium. The reflected light from the optical disc 4 becomes a convergent wave by the action of the converging lens 3 and re-enters the reflective hologram optical element 2. Since the reflection hologram optical element 2 is formed with a surface relief having a function of guiding the incident convergent wave to the photodetector 5 arranged in the vicinity of the semiconductor laser, the reflected light from the optical disc 4 is detected.
Can be detected with. The optical system for detecting the track error is omitted for the sake of clarity.

FIG. 3 schematically shows the relationship between the reflective hologram optical element 2 and the photodetector 5. In the figure, the reflection hologram optical element 2 is shown as seen from the semiconductor laser 1, and the photodetector 5 is seen from the light receiving surface side, that is, as seen from the reflection hologram optical element 2 side.
The light 6 incident on the reflection hologram element 2 (upper incident light) is converged on the first division line 8 on the left side of the second division line 7 of the photodetector 5, and the reflection hologram optical element 2 is exposed. The light 9 incident on the lower portion (lower incident light) is converged on the first dividing line 8 on the right side of the second dividing line 7 of the photodetector 5.

FIG. 4 schematically shows the spot shape on the photodetector when the defocus of the optical disc 4 occurs, and FIG. 4B shows the in-focus state. When the optical disc 4 is displaced toward the converging lens 3 (FIG. 4 (a)),
The light spot is composed of the first segment 10 and the fourth segment 10 of the photodetector 5.
It is incident on the segment 13. On the contrary, when the light is deviated in the direction away from the converging lens 3 (FIG. 4C), the light is incident only on the second segment 11 and the third segment 12 of the photodetector 5. Therefore, the focus error signal S _fe is given by S _fe = (V ₁ −V ₂ ) + (V ₄ −V ₃ ) where V _n (n = 1 to 4) is the output of each segment. In this focus error detection device, mainly the first
In order to detect a focus error from the difference in the light intensity of the dividing line 8 in the vertical direction, the photodetector and the first dividing line 8 of the light spot are
The relative positional deviation in the direction along the arrow does not affect the focus error detection operation unless either light spot crosses the second dividing line 7.

[Problems to be Solved by the Invention]

When the grating optical element such as a hologram is used, the biggest problem is the fluctuation of the oscillation wavelength of the semiconductor laser which is the light source. When the oscillation wavelength changes, the diffraction angle of the grating optical element changes accordingly. Therefore, in the conventional technique, in FIG. 2, the first dividing line 8 of the photodetector, the light emitting point 18 of the semiconductor laser 1 and the dividing line 21 of the reflective hologram optical element 2 are arranged so as to be in the same plane. That is, the second
By arranging A and A'shown in the same plane, the influence of the diffraction angle variation on the focus error detection operation is tried to be removed. However, it is only when the incident ray, the reflected ray and the diffracted ray to the hologram optical element are all in the same plane that the influence of the focus movement can be completely eliminated by the conventional solution. In this case, the convergence point moves in a direction having an angle with the first dividing line 8 of the photodetector 5, and as a result, problems such as deterioration of focus error signal strength and occurrence of focus error signal offset occur. It was Further, regarding the change in the spot shape on the photodetector when defocus occurs, as shown in FIG. 4, the defocus in the direction in which the optical disc 4 approaches and the defocus in the direction in which the optical disc moves away. On the other hand, the shape change that is symmetric with respect to the dividing line is only when the incident ray, the reflected ray, and the diffracted ray to the hologram optical element are all in the same plane. Otherwise, the shape change is symmetrical. However, this causes deterioration of the focus error signal strength.

An object of the present invention is to provide an optical head having excellent temperature stability that solves the above problems.

[Means for Solving the Problems]

Means for Solving the Problems In order to solve the above problems, the means to be solved by the present invention include a light source, an imaging optical system for condensing light emitted from the light source onto an optical recording medium, a first dividing line and a second dividing line. A photodetector divided into at least three segments by lines,
At least a reflection-type grating optical element for guiding the reflected light reflected by the optical recording medium and having passed through the imaging optical system to the photodetector, wherein the reflection-type grating optical element emits light from the light source. The reflection-type grating optical element dividing line that intersects the optical axis of the emitted light divides the area into a first area and a second area, and the incident light on the first area of the reflection-type grating optical element is diffracted light to detect the light. On the second dividing line of the photodetector at a point (first converging point) on the first dividing line of the detector as incident light to the second region of the reflective grating optical element as diffracted light. Has the effect of converging to each point (second convergence point),
An intersection of the optical axis and the reflective grating optical element dividing line,
The light source, the reflective grating optical element, such that the first and second convergence points and the light emitting point of the light source are on the same plane.
An orthogonal coordinate system in which the photodetector is arranged, the reflecting surface of the reflective grating optical element is the XY plane, the intersection is the origin, and the axis passing through the origin and perpendicular to the XY plane is the Z axis. And the coordinates of the first convergence point are (x _1f , y _1f , z _1f ),
The coordinates of the second convergence point are (x _2f , y _2f , z _2f ), the coordinates of the light emitting point of the light source are (x _g , y _g , z _g ), and the oscillation wavelength of the light source at room temperature is λ ₁ age, , The first dividing line is the first convergence point (x
_1f , y _1f , z _1f ) and its direction cosine (B _1l , B
_1m , B _1n ) is abbreviation The second dividing line passes through the convergence point (x _2f , y _2f , z _2f ) and its direction cosine (B
_2l , B _2m , B _2n ) is abbreviation The reflection-type grating optical element dividing line is a straight line represented by, and the magnification of the imaging optical system is m _f , the dynamic range of focus error detection is ± α _d, and m = 2 · m _f ² · α _d x _f = (x _1f + x _2f ) / 2 y _f = (y _1f + y _2f ) / 2 z _f = (z _1f + z _2f ) / 2 α = x _f z _f z _g −x _g z _f ² − x _g y _f ² β ＝ y _f z _f z _g −y _g z _f ² −x _f ² y _g γ ＝ {x _f ² (y _f y _g -z _f z _g ) + y _f ² (x _f x _g -z _f z _g ) + z _f ² (x _f x _g -y _f y _g )} / z _f l _in ＝ {x _g (d _g + m) -x _h d _g } / DB ₁ m _in ＝ {Y _g (d _g + m) -y _h d _g } / DB ₁ DB ₁ = [d _g ² (d _g + m) ² −2d _g (d _g + m) (x _g x _h + y _g y _h ) + ^{_{(x h 2 + y h 2}} ) d g 2] 1/2 l out = l in - {(x g -x h) / DB 2 - (x f -x h) / DB 3} m out = m in -{(Y _g -y _h ) / DB _2- (y _f -y _h ) / DB ₃ } t _p = {x _h (z _f y _g -y _f z _g ) + y _h (x _f z _g -x _g z _f )} / {l _out (y _f z _g -z _f y _g ) + m _out (x _g z _f -x _f z _g ) + n _out (x _f y _g -x _g y _f )} x _p ＝ l _out・ t _p + x _h y _p ＝ m _out・ t _p + y _h z _p = when the _{n out · t p, x p} -x f: y p -y f: z p -z f = α: β: point on the reflection type grating optical element substantially satisfies γ the relationship (x _h ,
y _h , 0) and the coordinate origin are straight lines.

[Action]

Hereinafter, the operation of the present invention will be described in detail with reference to the drawings and mathematical formulas. FIG. 5 shows a reflective hologram optical element 27 for calculation.
FIG. 3 is a diagram showing the position of, the emission point 14 of the semiconductor laser, and the convergence point 15 of the light beam on the photodetector. The reflection-type hologram optical element 27 is on the XY plane. Considering an orthogonal coordinate system with the axis perpendicular to the XY plane as the Z axis, the light emitting point 14 of the semiconductor laser is set to (x _g , y _g , z _g ), And the position 15 of the convergence point of the light beam on the photodetector is (x _f , y _f , z _f ).

here, And The interference fringes recorded on the hologram optical element are due to the diverging spherical waves from these two points, and the phase transfer function thereof is given by the following equation.

Here, λ ₁ is the design wavelength of the reflective hologram optical element, and usually corresponds to the oscillation wavelength of the semiconductor laser at room temperature. Such reflection hologram optical element in a direction cosine with a phase transfer function _{(l in, m in, n} in) and light with the incident. Since the reflection type hologram optical element is considered here, the direction cosine of the incident light ray may be the direction cosine of the light ray regularly reflected by the surface of the reflection type hologram optical element. Now, assuming that the light emitted from the semiconductor laser is correctly focused on the optical disk, the return light from the optical disk becomes a wavefront having the light emitting point 14 of the semiconductor laser as a converging point, and the reflection hologram optical element. It is incident on 27. Thus the direction cosines of the incident light to the reflection type holographic optical element 27, the light passing through the origin _{l in = x g / d g} (4) m in = y g / d g (5) n in = z g / It becomes d _g (6). H.P., published from Applied Optics magazine, Volume 20, page 2081, published in 1981. W. HWHolloway
According to these documents, the direction cosine (l _out , m _out , n _out ) of the outgoing light beam that has been acted on by the hologram optical element is given by the following equation.

Here, λ ₂ is the oscillation wavelength of the laser during operation. Thus, the direction cosines _{(l in, m in, n} in) the light beam incident on origin is emitted under the action of the reflection type holographic optical element, the equation representing the output light beam, Here, the light receiving surface of the photodetector, wherein the point _{(x f, y f, z} f) , the origin and the point _{(x f, y f, z} f) Taking a plane perpendicular to the straight line connecting the, the equation becomes _{x f (x-x f)} + y f (y-y f) + z f (z-z f) = 0 (11). Therefore, the position on the photodetector of the light beam that has been diffracted by the holographic optical element, that is, the position of the light spot (x _pd , y _pd , z _pd ) can be calculated from equations (10) and (11) as x _pd = l _out・ d _f ² / A (12) y _pd = m _out・ d _f ² / A (13) z _pd = n _out・ d _f ² / A (14) A = x _f・ l _out + y _f・ m _out + z _f・ n _out (15) By using the equations (12) to (14), the direction cosine of the movement of the light spot near the design wavelength of the hologram optical element can be obtained from the derivative of λ ₂ when λ ₂ = λ ₁ .

Therefore, Therefore, the direction cosine of the movement of the light beam diffracted by the reflection type hologram optical element on the light receiving surface of the photodetector (B _l ,
B _m , B _n ) is Becomes Now, as a straight line (reference line) that serves as a reference on the light receiving surface of the photodetector, points (x _f , y _f , z _f ) on the photodetector and emission points (x _g , y _g , z _{g of the} semiconductor laser) ) And the plane including the three points of the origin and the line of intersection of the light receiving surface of the photodetector. The plane including the above three points is x (y _f z _g -y _g z _f ) -y (x _f z _g -x _g z _f ) + z (x _f y _g -x _g y _f ) = 0 (25 ), The direction vector (α, β,
γ) is α = x _f z _f z _g -x _g z _f ² -x _g y _f ² (26) β = y _f z _f z _g -y _g z _f ² -x _f ² y _g (27) γ = {X _f ² (y _f y _g −z _f z _g ) + y _f ² (x _f x _g -z _f z _g ) + z _f ² (x _f x _g −y _f y _g )} / z _f ( 28). Therefore, the angle θ formed by this reference line and the direction cosine (B _l , B _m , B _n ) of the movement of the light beam on the light receiving surface of the photodetector is calculated by calculating the inner product of these two vectors. It turns out that Therefore, when a straight line including (x _f , y _f , z _f ) and forming an angle θ with the direction vector (α, β, γ) is newly provided in the photodetector plane as a reference line, the light spot is λ ₁ It moves on this straight line with the wavelength fluctuation of the semiconductor laser having the center wavelength of. That is,
By using this straight line as the dividing line of the photodetector, it is possible to solve the problem in the focus error detecting operation which has been a problem in the conventional technique.

Further, the present invention solves the asymmetry of the spot shape change on the photodetector when defocus occurs, which is a problem in the conventional technique, by the following method. When the position of the optical disc is deviated from the image forming point of the light beam, the return light from the optical disc does not become the light beam which converges on the emission point 14 of the laser, but the optical disc is displaced in the direction away from the converging lens. At this time, the convergent position of the return light is shifted on the optical axis from the light emitting point of the laser toward the converging lens. On the contrary, when the optical disc is displaced in the direction of approaching the converging lens, the converging position of the return light is shifted on the optical axis in the direction away from the laser emission point to the converging lens. Here, the distance between the return light converging position and the laser emission point is m, the return light converging position is (x _g ′, y _g ′, z _g ′), and the point on the hologram optical element is (x _h , y _h , 0), the direction vector (L, M, N) of the line connecting (x _g ′, y _g ′, z _g ′) and (x _h , y _h , 0) is L = x _g (d _g + m) -x _h・ d _g (30) M ＝ y _g (d _g + m) -y _h・ d _g (31) N ＝ z _g (d _g + m) (32) Direction cosine of ray incident on (x _h , y _h , 0)
(l ′ _in , m ′ _in , n ′ _in ) is l ′ _in = L / B ′ ＝ {x _g (d _g + m) -x _h · d _g } / B ′ (33) m ′ _in ＝ M / B ′ ＝ {y _g (d _g + m) -y _h・ d _g } / B ′ (34) n ′ _in ＝ N / B ′ ＝ {z _g (d _g + m)} / B ′ ( 35) Becomes The direction cosines of the rays that are diffracted by the hologram optical element are (l ′ _out , m ′ _out , n ′ _out ) as in the above case. Becomes Here, λ ₂ = λ ₁ . The point (x _p , y _p , z) at which the ray having the direction cosine (l ′ _out , m ′ _out , n ′ _out ) intersects the light receiving surface of the photodetector through the point (x _h , y _h , 0). _p ), using equation (12), x _p = l ′ _out・ t _p + x _h (40) y _p ＝ m ′ _out・ t _p + x _h (41) z _p ＝ n ′ _out・t _p (42) t _p = {x _h (z _f y _g -y _f z _g ) + y _h (x _f z _g -x _g z _f )} / {l ' _out (y _f z _g −z _f y _g ) + m ′ _out (x _g z _f −x _f z _g ) + n ′ _out (x _f y _g −x _g y _f )} (43). Where x _p -x _f : y _p -y _f : z _p -z _f = α: β: γ (44) on the hologram optical element (x _h ′,
y _h ′, 0) exists. Therefore, this point (x _h ′, y _h ′,
The straight line connecting (0) and the origin may be the dividing line of the reflective hologram optical element. As can be seen from the equations (30) to (44), the point (x ′ _h , y ′ _h , 0) is a function of m, so that the equation (44) is satisfied only for a specific m. . In order to determine the dividing line of the hologram optical element, the m value may be determined from the desired dynamic range of focus error detection. If the magnification of the imaging optical system is m _f and the dynamic range of focus error detection is ± α _d , the m value is approximately given by m = 2 · m _f ² · α _d (45).

〔Example〕

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a perspective view for explaining an embodiment of the present invention. The semiconductor laser 1, the hologram optical element 27, the converging lens 3, and the photodetector 22 are used in the same manner as in the conventional example shown in FIG. 2, but their relative positions are different from those in the conventional case. In the description, the coordinate system used so far (the reflection hologram optical element is on the XY plane, and the center is the coordinate origin)
To use.

In the present embodiment, the angle formed by the incident ray and the specularly reflected ray is 90 degrees, and the first convergence point 16 on the photodetector 22 from the viewpoint of mounting.
(X _1f , y _1f , z _1f ), and the second convergence point 17 (x _2f , y
_2f , z _2f ), the midpoint (x _f , y _f , z _f ) of the line segment, the emission point (x _g , y _g , z _g ) 18 of the semiconductor laser 1, and the center of the reflective hologram optical element 27. (Coordinate origin 1
9) is arranged so as to be on the same plane (hereinafter referred to as the reference plane 20). here, And In order to remove the focal power of the reflection type hologram optical element 27 as much as possible and suppress the occurrence of longitudinal aberration due to wavelength fluctuation, d _1f = d _2f = d _g .

FIG. 6 is a diagram showing a mutual relationship between each segment of the photodetector 22 and two regions of the reflection type hologram optical element 27. In the figure, a reflection hologram optical element 27
Shows the case seen from the semiconductor laser 1 and the photodetector 22 seen from the light receiving surface side, that is, the case seen from the reflection hologram optical element 27 side. The photodetector 22 is divided into three by a first dividing line 23 and a second dividing line 24. The first dividing line 23 passes through the first converging point 16 and forms an angle θ ₁ given by the expression (29) with respect to the intersection line of the reference plane 20 and the light receiving surface of the photodetector 22. Similarly, the second dividing line 24 passes through the second converging point 17, and an angle θ given by the equation (29) with respect to the intersection line of the reference plane 20 and the light receiving surface of the photodetector 22.
_{I am 2} . In such an arrangement, the semiconductor laser 1
The first convergence point 16 even if the oscillation wavelength λ _{1 of}
Since the light spot at the _first convergence point 17 moves at the angle of θ ₁ , the light spot at the second convergence point 17 moves at the angle of θ ₁ , and the light spot at the second convergence point 17 moves at the angle of θ ₂ . There is no effect such as offset of the focus error signal.

The area dividing line 28 of the reflective hologram optical element 27 is set so as to substantially satisfy the condition given by the above equation (47). In this embodiment, a converging lens with a magnification of 5.5 is used,
Since the dynamic range for focus error detection was designed to be ± 7 μm, the m value is m = 2 × 7 μm × 5.5 ₂ = 423.5 μm. M value given by this formula and the first convergence point 16
28 and the position of the second convergence point 17, 28 equations of the reflection hologram optical element dividing line satisfying the equation (44) are obtained for each position. In a normal case, the distance between the first convergence point and the second convergence point is sufficiently smaller than the distance between the reflection hologram optical element and each convergence point. Therefore, the obtained two straight lines are almost equal. Therefore, a straight line that satisfies the expression (44) is used as the dividing line 28 of the reflection-type hologram optical element with respect to the midpoint between the first convergence point and the second convergence point. In this case, the shape change is always asymmetric with respect to the dividing line, but the amount thereof is very small and has no influence on the focus error detection operation.

FIG. 7 schematically shows the shape of the light spot on the photodetector 22 when defocus occurs, and FIG. 7B shows the in-focus state. When the optical disc 4 is displaced in the direction of approaching the converging lens 3 (FIG. 7A), the light spot is incident only on the first segment 31 and the fourth segment 34 of the photodetector 22. On the contrary, when the optical disc 4 is displaced in the direction away from the converging lens 3 (FIG. 7 (c)), the light spot is the second spot of the photodetector.
It is incident only on the segment 32. Unlike the focus error signal S
_fe is given by S _fe = (V ₁ + V ₃ ) −V ₂ where the output of each segment is V ₁ , V ₂ , and V ₃ .

The optical head device is required to have a function of a track error detecting operation as well as a focus error detecting motion difference, but many known track error detecting methods can be applied to the optical head device according to the present invention. For example, the 1987 issue of the Japanese Journal of Applied Physics, Volume 26, Supplement 26-4, pages 131-134.
The method described in the article published by Yasuo Kimura et al. On the page can be used. Of course, it is also possible to use a known 3-beam method, push-pull method, or the like.

〔The invention's effect〕

According to the present invention, it is possible to provide an optical head device having an error detection characteristic that is very stable with respect to a wavelength variation of a light source. Further, the reflective grating optical element used in the present invention can be stably, mass-produced, and inexpensively by using a manufacturing process similar to the manufacturing process for manufacturing a semiconductor device. It is possible to provide.

[Brief description of drawings]

FIG. 1 is a perspective view for explaining an embodiment of the present invention, and FIG.
FIG. 1 is a perspective view of a conventional device, FIG. 3 and FIG. 4 are diagrams for explaining the conventional technique, FIG. 5 is a diagram for explaining the operation of the present invention, FIG. 6 and FIG. It is a figure for demonstrating the Example of this invention. 1 ... Semiconductor laser, 2 ... Reflective hologram optical element, 3 ... Converging lens, 4 ... Optical disk, 5 ... Photodetector, 6 ... Top incident light, 7 ... Second split line, 8 ......
1st parting line, 9 ... bottom incident light, 10 ... 1st segment, 11 ... 2nd segment, 12 ... 3rd segment, 13 ... 4th segment, 14, 18 ... Emission point,
15 ... Convergence point, 16 ... First convergence point, 17 ... Second
Convergence point, 19 ... Coordinate origin, 20 ... Reference plane, 21
...... Reflective hologram optical element dividing line, 22 ...... Photo detector, 23 ...... First dividing line, 24 ...... Second dividing line, 2
7 ... Reflective hologram optical element, 28 ... Reflective hologram optical dividing line, 31 ... First segment, 32 ...
2nd segment, 33 ... 3rd segment.

Claims (1)

[Claims] 1. A light source, an imaging optical system for condensing light emitted from the light source onto an optical recording medium, and light divided into at least three segments by a first dividing line and a second dividing line. A detector and at least a reflective grating optical element for guiding the reflected light reflected by the optical recording medium and passing through the imaging optical system to the photodetector, wherein the reflective grating optical element is It is divided into a first area and a second area by a reflective grating optical element dividing line that intersects the optical axis of the emitted light of the light source, and the incident light to the first area of the reflective grating optical element is diffracted light. A point on the first dividing line of the photodetector (first convergence point)
In addition, the incident light to the second region of the reflective grating optical element as diffracted light as a point on the second dividing line of the photodetector (
2 convergent point), respectively, the intersection of the optical axis and the reflective grating optical element dividing line, the first
1, the second converging point and the light emitting point of the light source are arranged so that the light source, the reflection-type grating optical element, the photodetector, and further, the reflection surface of the reflection-type grating optical element XY plane, the intersection is the origin, the orthogonal coordinate system with the axis passing through the origin and perpendicular to the XY plane as the Z axis is defined, and the coordinates of the first convergence point are (x _1f , y _1f , z _1f ). , The coordinates of the second convergence point
(x _2f , y _2f , z _2f ), the coordinates of the light emitting point of the light source are (x _g , y _g ,
z _g ), and the oscillation wavelength of the light source at room temperature is λ ₁ , Then, the first dividing line is the first convergence point.
(x _1f , y _1f , z _1f ) and its direction cosine (B _1l , B _1m , B _1n )
Stands for The second dividing line passes through the convergence point (x _2f , y _2f , z _2f ) and its direction cosine (B _2l , B _2m , B
_2n ) stands for The reflection-type grating degrading element dividing line is m = 2 · m _f ² 2 · α _d x, where the magnification of the imaging optical system is m _f and the dynamic range of focus error detection is ± α _{d. f} = (x _1f + x _2f ) / 2 y _f = (y _1f + y _2f ) / 2 z _f = (z _1f + z _2f ) / 2 α = x _f z _f z _g −x _g z _f ² −x _g y _f ² β = y _f z _f z _g −y _g z _f ² −x _f ² y _g γ = (x _f ² (y _f y _g −z _f z _g ) + y _f ² (x _f x _g −z _f z _g ) ＋ z _f ² (x _f x _g −y _f y _g )} / z _f l _in ＝ {x _g (d _g + m) −x _h d _g } / DB ₁ m _in ＝ {y _g (d _g + M) -y _h d _g } / DB ₁ DB ₁ = [d _g ² (d _g + m) ² −2d _g (d _g + m) (x _g x _h + y _g y _h ) + (x _h ² + y _h ² ) d _g ² ] ^1/2 l _out = l _in − {(x _g −x _h ) / DB ₂ − (x _f −x _h ) / DB ₃ } m _out = min _in − {(y _g −y _h ) / DB ₂ − (y _f −y _h ) / DB ₃ } t _p = {x _h (z _f y _g −y _f z _g ) ＋ y _h (x _f z _g −x _g z _f )} / {l _out (y _f z _g −z _f y _g ) ＋ m _out (x _g z _f −x _f z _g ) + n _out (x _f・ y _g −x _g y _f )} x _p ＝ l _out・ t _p ＋ x _h y _p ＝ m _out・ t _p ＋ y _h z _p ＝ n _out・when a _{t p + z h, x p} -x f: y p -y f: z p -z f = α: β: point on the reflection type grating optical element substantially satisfies γ the relationship (x _h,
An optical head device, which is a straight line connecting y _h , 0) and the origin of coordinates.