Plane diffraction grating based on surface normal rotation and its application to an optical system

A plane diffraction grating based on surface normal rotation according to the present invention is designed so that the profile of the grooves at a radial area is determined depending on a rotational position of the area about a rotational center defined as a foot of the rotational axis on the surface of the plane diffraction grating. An optical system such as a spectrometer or a monochromator according to the present invention uses such a plane diffraction grating, and requires a special arrangement. The optical system includes: a plane diffraction grating as described above; a mechanism for rotating the plane diffraction grating about the rotational axis; an incidence optical system for casting a converging beam of light on a point of the surface of the plane diffraction grating, where the point is set apart from the rotational center. As the diffraction grating is rotated about the rotational center, the point on which the incident converging beam of light is cast rotates about the rotation center, where the diffracting condition is optimized anywhere around the rotational center or for any scanning wavelength. The surface of the plane diffraction grating can be covered with a multiple-layer coating to improve diffraction efficiency. When such a multiple-layer is coated, the unit thickness of the multiple-layer coating at an area is also determined depending on the rotational position of the area about the rotational center.

The present invention relates to a spectrometer or a monochromator based on surface normal rotation, and to a plane diffraction grating optimized for use in such a spectrometer or a monochromator.

BACKGROUND OF THE INVENTION

In designing a diffraction grating employed in a spectrometer or a monochromator, the profile of the grooves should be designed so as to reveal the highest diffraction efficiency as much as possible. In a blazed type diffraction grating having a saw-like profile, for example, the blaze angle should be optimized, and in the laminar type diffraction grating having grooves of a rectangular profile, the depth of the grooves and the duty ratio should be optimized, to obtain the highest diffraction efficiency.

When such a diffraction grating is employed in a constant deviation angle monochromator in which wavelength scanning is done by rotating a diffraction grating about an axis parallel to the grooves of the diffraction grating, however, the diffraction efficiency is maximized only at a certain wavelength but is not maximized at the other wavelengths. Two methods have been proposed addressing the problem. In one of the methods, auxiliary mirrors are used to change the deviation angle according to the wavelength (M. Koike, “High resolution EUV monochromator/spectrometer,” U.S. Pat. No. 5,528,364). In the other method, the depth of the grooves of a laminar type diffraction grating is varied along the length of the groove, as shown in FIG.5. When the diffraction grating is rotated about the rotational axis A for wavelength scanning, the diffraction grating is shifted along the length of the groove (direction B) in synchronous with the rotational angle.

In any of the conventional methods, an auxiliary mechanism is needed besides that for rotating the diffraction grating. In the former case, for example, an appropriate mechanism is needed for properly arranging the auxiliary mirrors, and in the latter case, an appropriate mechanism is needed for moving the diffraction grating along the length of the grooves. In addition to that, a controller for synthesizing two mechanisms at high precision is required.

Another type of monochromator is proposed addressing the same problem in the U.S. Pat. No. 5,274,435, “Grating monochromators and spectrometers based on surface normal rotation” to M. C. Hettrick. In the monochromator, wavelength scanning is done by rotating the diffraction grating about an axis normal to the surface of the diffraction grating and standing at the incident point. In the patented monochromator also the diffraction efficiency is maximized at a certain wavelength, but is not maximized at the other wavelengths.

Thus a primary object of the present invention is to provide such a spectrometer or a monochromator based on surface normal rotation yielding the maximum diffraction efficiency at any wavelength. Another object of the present invention is to provide such a spectrometer with a minimized aberration. Still another object of the present invention is to provide a diffraction grating suited for use in such a spectrometer or a monochromator.

SUMMARY OF THE INVENTION

First, a plane diffraction grating based on surface normal rotation according to the present invention is designed so that the profile of the grooves at a radial area is determined depending on a rotational position of the area about a rotational center defined as a foot of the rotational axis on the surface of the plane diffraction grating.

The surface of the plane diffraction grating can be covered with a multiple-layer coating to improve reflectivity and then diffraction efficiency. When such a multiple-layer is coated, the unit thickness of the multiple-layer coating at a radial area is also determined depending on the rotational position of the area about the rotational center.

An optical system such as a spectrometer or a monochromator according to the present invention uses such a plane diffraction grating described above, and requires a special arrangement. The optical system includes:a plane diffraction grating as described above;a mechanism for rotating the plane diffraction grating about the rotational axis;an incidence optical system for casting a converging beam of light on an area of surface of the plane diffraction grating, where the area is set apart from the rotational center.

The diffraction grating is rotated at a rotational center. The off-axis area from the center of rotation is illuminated by the incident converging beam and optimized to maximize diffraction efficiency for the respective wavelength.

DETAIL DESCRIPTION OF THE EMBODIMENTS

FIG. 1shows an example arrangement of basic optical elements constituting a monochromator based on surface normal rotation embodying the present invention. Light beam passing through the entrance slit1is reflected by the concave mirror2so that the light beam is converted to a beam converging to the exit slit4. The converging incident light beam strikes the diffraction grating3and the diffracted light is focused at the exit silt4. The diffraction grating3is rotated by a grating rotating mechanism5.

The incident angle at the diffraction grating3is denoted as α, and the diffraction angle is denoted as β in FIG.1. The x-y-z coordinate system shown inFIG. 1places its origin at the point of incidence31of the principal ray of the incident light beam on the surface30of the diffraction grating3, where the x axis is normal to the surface30, the y axis is perpendicular to the grooves of the diffraction grating3, and the z axis is parallel to the grooves. The foot32of the rotation axis of the diffraction grating3(the point32is hereinafter referred to the “rotation center”) is set apart from the point of incidence31. The rotation axis is normal to the surface30of the diffraction grating3and is parallel to the x axis. The angle φ between the normal to the meridional plane (which includes the incident ray, the point of incidence30and the diffracting ray) and the z axis defines the rotational position of the diffraction grating3. The original position of the rotation (φ=0) is defined as the position where the grooves are perpendicular to the incident ray or perpendicular to the meridional plane.

FIG. 2shows the surface30of the diffraction grating3. The elongated area R1on the surface30is the area which the incident light beam illuminates when the rotational position of the diffraction grating is 0, and the elongated area R2is the area which the incident light beam illuminates when the rotational position is φ.

FIRST EXAMPLE

An example using a blazed type diffraction grating is first described referring to FIGS.2and3A-3C.FIG. 3Ashow the profile of the grooves of the diffraction grating in the area R1, in which the blaze angle is denoted as θ0, and the grating constant is denoted as d. Supposing the light diffracted by the area R1has the wavelength λ0, it is known that the diffraction efficiency in maximized for the light of wavelength λ0by setting the blaze angle θ0as follows:θ0=α+β2.(1)

In conventional blazed tape diffraction gratings, the blaze angle is the same throughout the entire surface30. When such a diffraction grating is used in the above described monochromator, the diffraction efficiency is not maximized for the light of wavelengths other than λ0(or at the position φ≠0). This is explained as follows: When the diffraction grating3is at the position φ (≠0) and the incident light beam illuminates the area R2, the profile of the grooves along the length of the area R2is as shown by FIG.3B. The light diffracted by the part R2of the surface30has the wavelength λ calculated asλ=λ0cos⁢⁢ϕ.(2)
As shown inFIG. 3B, the pitch dφof the grooves in the area R2for the rotational position φ is calculated asdϕ=dcos⁢⁢ϕ.(3)
So the area R2functions as a blazed type diffraction grating having the blaze angle θ0φcalculated byθ0⁢ϕ=sin-1⁡(sin⁢⁢θ01+tan2⁢ϕcos2⁢θ0).(4)
It is clear from the equation (4) that θ0φis smaller than θ0. As seen inFIG. 1, the incident angle α and the diffraction angle β remain constant while the diffraction grating3is rotated (or irrespective of the rotation angle φ). Thus the angle θ0φdoes not meet with the requirement of equation (1) for the maximum diffraction efficiency.

The present invention is to set the blaze angle θ100in the area R2large than the angle θ0in order to maximize the diffraction efficiency of the light diffracted by the area R2and having the wavelength λ. After an intensive study, the inventors revealed that the optimized blaze angle θ100in the radial area at the rotational position φ for the maximum diffraction efficiency for the light of wavelength λ is denoted as:θϕ=sin-1⁡(sin⁢⁢θ0⁢1+tan2⁢ϕ1+tan2⁢ϕsin2⁢θ0).(5)
By setting the blaze angle of the grooves in the area of the rotational position φ at the optimized blaze angle calculated above, the effective blaze angle in the area illuminated by the incident beam of wavelength λ becomes θ0, as shown in FIG.3C. Thus the diffraction efficiency is maximized for any scanning wavelength λ.

In conventional monochromators, the diffraction grating3is arranged so that the incident point31coincides with the rotational center32. In such an arrangement, the area around the incident point31(or the rotational center32) of the surface30of the diffraction grating3is always illuminated by the converging beam irrespective of the rotational position φ of the diffraction grating3. In this case it is impossible to optimize the blaze angle according to the rotational position φ.

The problem is addressed in the present invention by dislocating the incident point31from the rotational center32. In this arrangement the incident area centering the incident point31does not cover the rotational center32and shifts4on the surface30according to the rotational position of the diffraction grating3. Therefore it becomes possible to optimize the blaze angle at every location of the incident point31.

SECOND EXAMPLE

Another example using a blazed type diffraction grating is then described. The surface of the grooves of the diffraction grating3is covered with a multiple-layer coating to improve reflectivity and thus the diffraction efficiency. Suppose the unit thickness of the multiple-layer coating in the linear area R1at the rotational position φ=0 is db0. In order to improve the diffraction efficiency for the light of wavelength λ0, the unit thickness db0should satisfy the following Bragg equation:
mbλ0=2db0Rα0cos(α−θ0),  (6)
where Rα0is given by
Rα0=√{square root over (1−(2δ−δ2)/cos2α)},(7)
in which δ=1−n, where n is the average refractive index of the multiple-layer coating for wavelength λ0.

In the linear area R2of the rotational position φ(≠0), the unit thickness dbφof the multiple-layer coating for the improved diffraction efficiency for the wavelength λ is calculated as follows: When the rotational position of the diffraction grating3is φ, the angle between the incident ray and the normal to the surface of the groove and the angle between the normal and the diffraction ray are derived from equation (1):
α−θφ=−β+θφ.  (8)
From equation (8), the Bragg equation is denoted as:
mbλ=2dbφRαφcos(α−θ0),  (9)
where Rαφis given by
Rαφ=√{square root over (1−(2δφ−δ2φ)/cos2α)},(10)
in which δφ=1−nφ, where nφis the average refractive index of the multiple-layer coating for the light of wavelength λ.

Thus, by forming a multiple-layer coating having such unit thickness on the surface of the grooves of the diffraction grating3, the diffraction efficiency is improved anywhere on the surface30of the diffraction grating3and thus for any scanning wavelength λ.

THIRD EXAMPLE

The present invention is embodied in a monochromator using a laminar type diffraction grating. It is generally known (for example, K. H. Hellwege, Z. Phys. Vol. 106(1937), pp. 588-596) that the diffraction efficiency for the primary order diffraction light of wavelength λ0is maximized and the diffraction light of even-number orders are decreased by setting the depth h0of the grooves of the laminar type diffraction grating as:h0=λ02⁢(cos⁢⁢α+cos⁢⁢β).(11)
The wavelength λ corresponding to the rotational position φ of the diffraction grating3is given byλ=λ0cos⁢⁢ϕ.(12)
The optimal depth hφof the grooves in the linear area R2of the rotational position φ for maximizing the diffraction efficiency ishϕ=λ02⁢(cos⁢⁢α+cos⁢⁢β)⁢cos⁢⁢ϕ.(13)

By setting the depth of the grooves in the area R2at the optimal depth hφgiven above, the diffraction efficiency is always maximized irrespective of the rotational position of the diffraction grating3and for any scanning wavelength λ.

FOURTH EXAMPLE

Another example using a laminar type diffraction grating is then described. The surface of the grooves of the diffraction grating3is covered with a multiple-layer coating to improve the diffraction efficiency. In the present case, however, the angle of incidence and the angle of diffraction are different. Thus the multiple-layer coating should be formed to satisfy the generalized Bragg equation proposed by W. R. Warburton (Nucl. Instru. Meth., A291(1990), pp. 278-285). By the generalized Bragg equation, the optimal thickness db0of the multiple-layer coating for wavelength λ0(as in the area R1at the rotational position φ=0) is given by
mbλ0=db0(Rα0sinα+Rβ0sinβ),  (14)
where
Rα0=√{square root over (1−(2δ−δ2)/cos2α)}.Rβ0=√{square root over (1−(2δ−δ2)/cos2β)}.(15)
In equation (15), δ=1−n, n being the average refractive index of the multiple-layer coating for wavelength δ0.

Similarly, the optimal thickness dbφof the multiple-layer coating for wavelength λ in the area R2at the rotational position φ (≠0) is given by:
mbλ=dbφ(Rαφsinα+Rβφsinβ).  (16)
where
Rαφ=√{square root over (1−(2δφ−δ2φ)/cos2α)},Rβφ=√{square root over (1−(2δφ−δ2φ)/cos2β)},(17)
where δφ=1−nφ, nφbeing the average refractive index of the multiple-layer coating for wavelength λ.

By forming a multiple-layer coating having such unit thickness on the surface of the laminar grooves of the diffraction grating3, the diffraction efficiency if improved anywhere on the surface30of the diffraction grating3and thus for any scanning wavelength λ.

Finally, an example of producing a diffraction grating according to the present invention using the ion beam etching method is described referringFIG. 4. Aphoto-resist layer is coated on the etching surface of a substrate33and the pattern of the grooves is formed in the photo-resist layer. Then the etching surface is covered with a mask40having an opening41of a narrow sector, where the apex of the sector41is set at the rotational center34of the substrate33or the future diffraction grating. The angle φ between the center line of the opening41and the y axis of the substrate33(which is defined as perpendicular to the grooves) corresponds to the rotational position φ of the future diffraction grating3.

When ion beams are irradiated on the mask40with an appropriate etching condition, grooves having an appropriate profile (i.e., an appropriate blaze angle or an appropriate groove depth) according to the theory described above is formed in the opening41. Then the mask40is rotated about the rotational center34by the vertex angle of the narrow sector, shifting the opening41by the angle. Ion beams are irradiated on the mask40with another appropriate etching condition so that the grooves in the opening41are formed to have another appropriate profile corresponding to the rotational position of the opening41, or the linear area described before. Thus the diffraction grating3according to the present invention is produced when the opening41has swept the surface of the substrate33.