KR101523210B1 - Aberration analyzer of imaging spectrometer with a convex grating - Google Patents

Aberration analyzer of imaging spectrometer with a convex grating Download PDF

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KR101523210B1
KR101523210B1 KR1020140090429A KR20140090429A KR101523210B1 KR 101523210 B1 KR101523210 B1 KR 101523210B1 KR 1020140090429 A KR1020140090429 A KR 1020140090429A KR 20140090429 A KR20140090429 A KR 20140090429A KR 101523210 B1 KR101523210 B1 KR 101523210B1
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South Korea
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concave mirror
aberration
diffraction grating
convex
radius
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KR1020140090429A
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Korean (ko)
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김서현
장수
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삼성탈레스 주식회사
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
    • G01J3/12—Generating the spectrum; Monochromators
    • G01J3/18—Generating the spectrum; Monochromators using diffraction elements, e.g. grating
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M11/00—Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
    • G01M11/02—Testing optical properties
    • G01M11/0242—Testing optical properties by measuring geometrical properties or aberrations
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B5/00—Optical elements other than lenses
    • G02B5/18—Diffraction gratings
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations

Abstract

An aberration analyzer of imaging spectrometer with a convex grating is disclosed. The aberration analyzer of imaging spectrometer comprises: a first concave mirror to reflect light radiated from an object (slit); a convex grating equipped with an aperture stop to diffract light reflected by the first concave mirror; a second concave mirror to reflect light diffracted by the convex grating; and an aberration analyzer which includes a charge-coupled device detector to sense images shaped by light reflected by the second concave mirror. According to the aberration analyzer of imaging spectrometer with a convex grating, a concentric image spectrometer is composed of a convex grating and two concave mirrors, and by deriving and using a function of wavefront aberration converged to Gaussian Image wherein a number of light beams are scattered in the concentric image spectrometer, thereby initial design of the concentric image spectrometer having the least aberration can be performed more quickly and efficiently. Additionally, an effect of offsetting third-order aberration and fifth-order aberration may be obtained.

Description

Technical Field [0001] The present invention relates to an aberration analyzer using a spectroscope having a convex diffraction grating,

The present invention relates to an aberration analyzer, and more particularly, to an aberration analyzer using an image spectrometer having a reflection type convex diffraction grating.

An image spectrometer is a device that provides a spectral spectrum and two-dimensional images of the light emitted or absorbed by a material. Therefore, unlike ordinary spectroscopes, the spectroscopic slit is 10-20 mm long because it provides all spectroscopic images for a specific clock, not spectroscopic spectra for one point.

The spectroscope is composed of prism spectroscope, interference spectroscope, and grating spectroscope according to the principle of spectral separation. Grating spectroscopy is a spectroscope using a diffraction grating, and a long slit is required. .

In addition, when a reflection type diffraction grating is used, unlike a prism spectroscope, since there is no absorption of light by glass, it has good light efficiency and is suitable for visible light as well as infrared or ultraviolet ray spectroscopy.

Planar lattices, concave lattices, and stair lattices are mainly used for lattice spectroscopy, and convex lattices are rarely used.

In the case of a convex surface lattice, a basic function for designing the convex surface lattice is not disclosed.

It is an object of the present invention to provide an aberration analysis apparatus using a spectroscope having a convex diffraction grating.

The apparatus for analyzing an aberration using a spectroscope having a convex diffraction grating according to an embodiment of the present invention includes: a first concave mirror for reflecting light incident from an object (slit); A convex grating having an aperture stop for diffracting light reflected by the first concave mirror; A second concave mirror for reflecting the light diffracted by the convex diffraction grating; And an aberration analyzer including a charge-coupled device detector for sensing an image formed by the light reflected by the second concave mirror.

At this time, the convex diffraction grating r 2 may be formed with a grating groove of 100 lines / mm (lines / mm).

On the other hand, the first concave mirror r 1 is constituted by a radius of -294.1 mm, a distance (interval) to a convex diffraction grating of -144.1 mm, a semi-diameter (Sem-Dia) of 46 mm, The grating r 2 is composed of a radius of -150 mm, a distance (interval) to a concave mirror of 144.1 mm and a semi-diameter of 18 mm, and the second concave mirror r 3 , A radius of -294.1 mm, an average distance of -300.4 mm, and a semi-diameter of 44 mm.

According to the aberration analyzer using the spectroscope equipped with the above-described convex diffraction grating, a conical diffraction grating and two concave mirrors constitute a conical spectroscope, and in a conical spectroscope, a plurality of rays are scattered in a Gaussian image It is possible to more quickly and efficiently perform the initial design of the condenser having a minimum aberration by deriving a function of the converging wavefront aberration. Also, there is an effect that the third-order aberration and the fifth-order aberration are offset.

1 is a schematic block diagram of an aberration analyzer using a spectroscope having a convex diffraction grating according to an embodiment of the present invention.
Figure 2 shows the effective f-number and function < RTI ID = 0.0 >

Figure 112014067297594-pat00001
Fig.

While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail to the concrete inventive concept. It should be understood, however, that the invention is not intended to be limited to the particular embodiments, but includes all modifications, equivalents, and alternatives falling within the spirit and scope of the invention. Like reference numerals are used for like elements in describing each drawing.

The terms first, second, A, B, etc. may be used to describe various elements, but the elements should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, the first component may be referred to as a second component, and similarly, the second component may also be referred to as a first component. And / or < / RTI > includes any combination of a plurality of related listed items or any of a plurality of related listed items.

It is to be understood that when an element is referred to as being "connected" or "connected" to another element, it may be directly connected or connected to the other element, . On the other hand, when an element is referred to as being "directly connected" or "directly connected" to another element, it should be understood that there are no other elements in between.

The terminology used in this application is used only to describe a specific embodiment and is not intended to limit the invention. The singular expressions include plural expressions unless the context clearly dictates otherwise. In the present application, the terms "comprises" or "having" and the like are used to specify that there is a feature, a number, a step, an operation, an element, a component or a combination thereof described in the specification, But do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, or combinations thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Terms such as those defined in commonly used dictionaries are to be interpreted as having a meaning consistent with the contextual meaning of the related art and are to be interpreted as either ideal or overly formal in the sense of the present application Do not.

Hereinafter, preferred embodiments according to the present invention will be described in detail with reference to the accompanying drawings.

1 is a schematic block diagram of an aberration analyzer using a spectroscope having a convex diffraction grating according to an embodiment of the present invention.

Referring to FIG. 1, an aberration analyzer (hereinafter, referred to as 'aberration analyzer') 100 using a spectroscope having a convex diffraction grating according to an embodiment of the present invention includes a first concave mirror A convex grating 120, a second concave mirror 130 and a charge-coupled device detector 140. The first and second concave mirrors 130,

The present invention is characterized in that a concentric imaging spectrometer using a convex diffraction grating 120 is used instead of a planar grating or a concave grating unlike the prior art. The present invention is very useful for initial designing the aberration analysis apparatus 100 using the convex diffraction grating 120 by inducing / deriving a function according to the convex diffraction grating 120.

In addition, the aberration analyzer 100 is configured to have a minimum aberration by canceling the third-order aberration and the fifth-order aberration.

First, the first concave mirror 110 may be configured to reflect light incident parallel thereto.

Next, the convex diffraction grating 120 may be configured to have an aperture stop that diffracts the light reflected by the first concave mirror 110.

The second concave mirror 130 may be configured to reflect the light diffracted by the convex diffraction grating 120.

The CCD sensor 140 may be configured to sense the image formed by the light reflected by the second concave mirror 130.

The preferred specifications of the first concave mirror 110, the convex diffraction grating 120, the second concave mirror 130, and the CCD detector 140 are as follows.

First, the convex diffraction grating 120 (r 2 ) may be configured to form a grating groove of 100 lines / mm (lines / mm).

At this time, the first concave mirror 110 (r 1 ) may be composed of a radius of -294.1 mm, a distance (interval) to a convex diffraction grating of -144.1 mm, and a semi-diameter of 46 mm. The convex diffraction grating 120 (r 2 ) is composed of a radius of -150 mm, a distance (interval) to the concave mirror of 144.1 mm and a semi-diameter of 18 mm, and the second concave mirror 130) (r 3 ) can be composed of a radius of -294.1 mm, an average distance of -300.4 mm, and a semi-diameter of 44 mm.

1, C is a common center between the convex diffraction grating 120 and the curved surfaces of the concave mirrors 110 and 130, V is an aperture stop 121, The straight line connecting C and V becomes the optical axis.

A plurality of light beams may be incident on the first concave mirror 110 from the object point O and reflected by the second concave mirror 130. The rays of rays that are diffracted by the convex diffraction grating 120 make the image O '.

Here, the O and O 'heights are

Figure 112014067297594-pat00002
,
Figure 112014067297594-pat00003
.

On the other hand, the tangent planes of the first concave mirror 110 and the second concave mirror 130 are parallel to the x axis and the y axis, respectively, and the z axis is perpendicular to the tangent plane thereof and parallel to the optical axis.

here,

Figure 112014067297594-pat00004
Is a coordinate at which the chief ray from the object point O intersects the j-th tangent plane. The path of the paraxial ray propagating from the object point O to the image point O 'is traceable in the yz plane of the j-th plane using Abbe's zero invariant.

Figure 112014067297594-pat00005

The first order approximation can be traced using Snell's law for the m-th order diffracted ray at the j-th surface (j = 0-4).

Figure 112014067297594-pat00006

In Equation (2)

Figure 112014067297594-pat00007
Represents a refractive index in the object space (or image space) of the jth mirror, and has a positive value with respect to the z axis.

Figure 112014067297594-pat00008
Represents the z-coordinate of the local object belonging to the j-th mirror.
Figure 112014067297594-pat00009
Is the radius of the curved surface of the j-th mirror and is expressed as the z-coordinate of the center of the curved surface.
Figure 112014067297594-pat00010
Is the distance from the jth plane to the (j + 1) th plane and has a positive value in the z axis.
Figure 112014067297594-pat00011
Represents the angle of the ray incident on the jth plane and has a positive value when measured clockwise from the ray to the z axis. The grating spacing
Figure 112014067297594-pat00012
, ≪ / RTI >
Figure 112014067297594-pat00013
In
Figure 112014067297594-pat00014
to be. Similarly, the path of the paraxial beam in the xz plane is
Figure 112014067297594-pat00015
And
Figure 112014067297594-pat00016
To
Figure 112014067297594-pat00017
Can be tracked.

Assuming that the object point O is located in a plane containing the common focus C,

Figure 112014067297594-pat00018
.

Then, from equations (1) and (2), the ray from the object point O

Figure 112014067297594-pat00019
As shown in FIG. After being reflected in the spectroscope, finally converges to the point of the coordinates of the following equation (3).

Figure 112014067297594-pat00020

Here, the coordinates of the equation (3) correspond to the diffraction orders.

Spectrum Width

Figure 112014067297594-pat00021
The image size of the diffraction order m corresponding to the diffraction order m can be calculated by the following equation (4).

Figure 112014067297594-pat00022

In general, vignetting occurs at the starting point of an optical axis with a large angle at the non-axis object point. The extra rays below are reflected by the first concave mirror 110 to pass through the top of the second concave mirror 130 to be incident on the first concave mirror 110. Thus, the extra rays below the first concave mirror 110 must have at least an angle of inclination greater than the following equation (5).

Figure 112014067297594-pat00023

The excess light beams reflected from the first concave mirror 110 reach the bottom of the top of the second concave mirror 130 and when the first concave mirror 110 leaves the second concave mirror 110, Should pass below the bottom. Thus, the upper extra ray incident on the first concave mirror 110 should be smaller than the angle of inclination of the following equation (6).

Figure 112014067297594-pat00024

here,

Figure 112014067297594-pat00025
The
Figure 112014067297594-pat00026
or
Figure 112014067297594-pat00027
Lt; / RTI >
Figure 112014067297594-pat00028
or
Figure 112014067297594-pat00029
Has a relatively small value. For a finite conjugate point, the working f-number is given by: " (7) "

Figure 112014067297594-pat00030

On the other hand, a chief ray from an object point O off the axis has to be incident on the first concave mirror 110 with an angle of inclination of the following equation (8).

Figure 112014067297594-pat00031

Thus, the upper ray can pass through the center of the second concave mirror 130. Here, from equations (5) to (8)

Figure 112014067297594-pat00032
when,
Figure 112014067297594-pat00033
. In a pupil with vignetting, the chief ray is not the center ray of the bundle of stock rays. Main beam
Figure 112014067297594-pat00034
The angle of
Figure 112014067297594-pat00035
. Particularly in the system of the present invention
Figure 112014067297594-pat00036
It becomes telecentric.

The rays propagated from the object point O to the image point O 'through the system of the present invention are defined by the above-described equation (3), and the wavefront aberration and the fifth-order aberration are expressed by the following equation .

Figure 112014067297594-pat00037

here,

Figure 112014067297594-pat00038
And
Figure 112014067297594-pat00039
Is expressed by the following equation (10).

Figure 112014067297594-pat00040

Here, the coefficients of Equation (10) are expressed by the following Equation (11).

Figure 112014067297594-pat00041

In Equation (10) and Equation (11), when j = 0, 1,

Figure 112014067297594-pat00042
to be.
Figure 112014067297594-pat00043
The first term of the equation corresponds to a third linear astigmatism,
Figure 112014067297594-pat00044
The second term of the equation corresponds to the third order distortion.
Figure 112014067297594-pat00045
The first term corresponds to cubic astigmatism, and more generally corresponds to the olivine spherical aberration.
Figure 112014067297594-pat00046
The second and third terms are linear astigmatism and fourth-order distortion. The terms up to the other fifth of the aberration are completely eliminated in the system of the present invention. The aberration of the through-beam with respect to the image of the diffraction order m formed by the system of the present invention can be calculated by the following equation (12).

Figure 112014067297594-pat00047

As can be seen from equation (11), the coefficient

Figure 112014067297594-pat00048
The
Figure 112014067297594-pat00049
Is from 1 to 4
Figure 112014067297594-pat00050
of
Figure 112014067297594-pat00051
Depends on the order.
Figure 112014067297594-pat00052
Wow
Figure 112014067297594-pat00053
end
Figure 112014067297594-pat00054
Gt; < RTI ID = 0.0 > 10, <
Figure 112014067297594-pat00055
Are important for image quality. As a result, an aberration-free image can be obtained in the following equation (13).

Figure 112014067297594-pat00056

Contrary,

Figure 112014067297594-pat00057
end
Figure 112014067297594-pat00058
, All the terms in Equation 10 cause blurring or deforming of the image. The linear astigmatism is expressed by the following equation (14)
Figure 112014067297594-pat00059
Wow
Figure 112014067297594-pat00060
Can be corrected.

Figure 112014067297594-pat00061

The distortion can be additionally controlled by the following equation (15).

Figure 112014067297594-pat00062

Figure 112014067297594-pat00063
end
Figure 112014067297594-pat00064
The common solution of Equation (14) and Equation (15) can be expressed as Equation (16). &Quot; (16) "

Figure 112014067297594-pat00065

Thus, the image is free of astigmatism or distortion.

Figure 2 shows the effective f-number and function < RTI ID = 0.0 >

Figure 112014067297594-pat00066
Fig.

2 (a) shows a working f-number, and FIG. 2 (b) shows a function

Figure 112014067297594-pat00067
≪ / RTI >
Figure 112014067297594-pat00068
Wow
Figure 112014067297594-pat00069
. here,
Figure 112014067297594-pat00070
to be.

It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention as defined in the following claims. There will be.

Claims (3)

A first concave mirror for reflecting light incident on an object (slit);
A convex grating having an aperture stop for diffracting light reflected by the first concave mirror;
A second concave mirror for reflecting the light diffracted by the convex diffraction grating;
And an aberration analyzer including a charge-coupled device detector for sensing an image formed by the light reflected by the second concave mirror,
Wherein the aberration analyzer comprises:
The image is configured to converge to coordinates by the following mathematical expression so as to eliminate linear astigmatism or distortion,
[Mathematical Expression]
Figure 112015030814376-pat00073

here,
Figure 112015030814376-pat00074
Is the y coordinate value of the object point O,
Figure 112015030814376-pat00075
Is the radius of curvature of the first concave mirror,
Figure 112015030814376-pat00076
Is the radius of curvature of the second convex diffraction grating,
Figure 112015030814376-pat00077
Is the radius of curvature of the second concave mirror,
The convex diffraction grating (r 2 )
A grating groove of 100 lines / mm (lines / mm) is formed and a radius of curvature of -150 mm, a distance to the concave mirror of 144.1 mm and a semi-diameter of 18 mm Respectively,
The first concave mirror (r 1 )
A radius of curvature of -294.1 mm, a distance (spacing) to a convex diffraction grating of -144.1 mm, and a semi-diameter of 46 mm,
The second concave mirror (r 3 )
A radius of curvature of -294.1 mm, an average distance of -300.4 mm, and a semi-diameter of 44 mm. The apparatus for analyzing aberration using a spectroscope having a convex diffraction grating. delete delete
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5880834A (en) * 1996-10-16 1999-03-09 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Convex diffraction grating imaging spectrometer
JPH11513134A (en) * 1996-06-07 1999-11-09 ザ・リージェンツ・オブ・ザ・ユニバーシティ・オブ・カリフォルニア Method of optimizing holographic optical system and monochromator configuration
JP3245189B2 (en) * 1991-05-10 2002-01-07 三井金属鉱業株式会社 Astigmatism correction type spectrometer
JP2010181413A (en) * 1998-04-29 2010-08-19 Headwall Photonics Inc Corrected concentric spectrometer

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP3245189B2 (en) * 1991-05-10 2002-01-07 三井金属鉱業株式会社 Astigmatism correction type spectrometer
JPH11513134A (en) * 1996-06-07 1999-11-09 ザ・リージェンツ・オブ・ザ・ユニバーシティ・オブ・カリフォルニア Method of optimizing holographic optical system and monochromator configuration
US5880834A (en) * 1996-10-16 1999-03-09 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Convex diffraction grating imaging spectrometer
JP2010181413A (en) * 1998-04-29 2010-08-19 Headwall Photonics Inc Corrected concentric spectrometer

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