Apparatus for carrying out spectral analysis of an optical light source using image detection and separation of spectral orders

Claim 3

An apparatus according to claim 1, wherein: the at least two refractive optical components, the diffractive gratings, the first imaging optical component and the second imaging optical component are arranged to produce a co-action to produce a substantially stigmatic image of the entrance aperture in at least one point on the detector unit.

Claim 4

An apparatus according to claim 2, wherein: the first imaging optical component and the second imaging optical component include mirrors having concave surface shapes.

Claim 5

An apparatus according to claim 3, wherein: the at least two refractive optical components include prismatic components having prismatic shape, and are arranged so that the wavelength dispersion of at least one refractive optical component opposes the wavelength dispersion of the other refractive optical components.

Claim 6

An apparatus according to claim 4, wherein: at least one prismatic component is arranged in the ray path between the first imaging optical component and the second imaging optical component.

Claim 7

An apparatus according to claim 4, wherein: the co-action to produce a substantially uniform distribution of the order spectra and the co-action to produce a substantially stigmatic image are achieved by positioning of the entrance aperture in relation to the first imaging component and by choice of the optical properties of the prismatic components.

Claim 8

An apparatus according to claim 5, wherein: the mirrors having concave surface shapes are mounted so that a plane of reflection of the mirrors containing a ray reflected in a central point of the mirror surface, both before and after said reflection, is substantially orthogonal to the direction defined by the wavelength dispersion of the diffraction grating at the mirrors, whereby to achieve stigmatic imaging the following first mathematical relation for achieving stigmatic imaging is satisfied by the quantities of the components of the spectral detector: ##EQU28## and where, R 21 =the radius of curvature of the curve of intersection between the surface of the second imaging optical component and its plane of reflection, R 22 =the radius of curvature of the curve of intersection between the surface of the second imaging optical component and the plane through the surface centre orthogonal to the plane of reflection, b=the tilt angle of the second imaging optical component, i.e., the angle between the direction of a ray through the second imaging optical component surface centre, and the normal to the surface through the centre, D CG =the total ray path of a central ray from the first imaging optical component to the diffraction grating, i=index denoting an i:th prismatic component in a sequence defined by the radiation when passing from the first imaging optical component to the second imaging optical component, where: i=K as index means that the quantity refers to a first integrated prismatic component, integrated with the first imaging optical component; i=F as index means that the quantity refers to a last integrated prismatic component, integrated with the second imaging optical component; i=1,2, . . . N as index means that the quantity refers to a sequence of N prismatic components positioned between the first imaging optical component and the second imaging optical component, D i =the total ray path of a central ray from said i:th prismatic component to the second imaging optical component, D GF =the total ray path of a central ray from the diffraction grating to the second imaging optical component, D CF =the total ray path of a central ray from the first imaging optical component to the second imaging optical component, N=the number of times that radiation passes prismatic components of the order sorter unit which are separate from the first imaging optical component and the second imaging optical component, n i =the refractive index of the optical material of the i:th prismatic components, α i =the angle of incidence, i.e. the angle between the direction of an incident ray and the normal to the first refracting surface of said i:th prismatic component, where α i has a positive sign if said ray is incident on the opposite side of said normal, in relation to the side that the edge of the prismatic component defines, δ i =an exit angle, i.e. the angle between the direction of a ray, that emerges after refraction in the second refracting surface of said i:th prismatic component, and the normal to said surface where δ i has a positive sign if said ray emerges on the opposite side of said normal, in relation to the side that the edge of the prismatic component defines, A i =the refractive angle of said i:th prismatic component, i.e. the angle between the optical surfaces of said component if both surfaces are refracting, and twice the value of said angle, if one of the surfaces is reflecting, α=the angle between the direction of the incident radiation and the normal to the grating surface, β=the diffraction angle, i.e. the angle between the direction of the ray emerging after diffraction, and the normal to the grating surface, r=the distance between the entrance aperture and the first imaging optical component, R 11 =the radius of curvature of the curve of intersection between the surface of the first imaging optical component and its plane of reflection, R 12 =the radius of curvature of the curve of intersection between the surface of the first imaging optical component and the plane through the surface centre orthogonal to the plane of reflection, and a=the tilt angle of the first imaging optical component, i.e. the angle between the direction of a ray through the first imaging optical component surface centre, and the normal to the surface through the centre.

Claim 9

An apparatus according to claim 7, wherein: stigmatic imaging is achieved by applying the first mathematical relation for achieving stigmatic imaging in the following approximate form; ##EQU29##

Claim 10

An apparatus according to claim 7, wherein: all the prismatic components are mounted separately from the first imaging optical component and the second imaging optical component, whereby the first mathematical relation for achieving stigmatic imaging is applied with n K =n F =F K =F F =P K =P F =1.

Claim 11

An apparatus according to claim 7, wherein: the first integrated prismatic component is integrated with the first imaging optical component, while other prismatic components are mounted separately from the second imaging optical component, whereby the first mathematical relation for achieving stigmatic imaging is applied with n F =F F =P F =1.

Claim 12

An apparatus according to claim 7, wherein: the last integrated prismatic component is integrated with the second imaging optical component, while other prismatic components are mounted separately from the first imaging optical component whereby the first mathematical relation for achieving stigmatic imaging is applied with n K =F K =P K =1.

Claim 13

An apparatus according to claim 7, wherein: the spectral detector includes two prismatic components, the first prismatic component being integrated with the first imaging optical component and the second prismatic component being integrated with the second imaging optical component, whereby the first mathematical relation for achieving stigmatic imaging is applied in the following form; ##EQU30##

Claim 14

An apparatus according to claim 4, wherein: the mirrors having concave surface shapes are mounted so that a plane of reflection of the mirrors containing a ray reflected in a central point of the mirror surface both before and after reflection, is substantially parallel with the direction defined at the mirrors by the wavelength dispersion of the diffraction gratings whereby stigmatic imaging is achieved by satisfying the following second mathematical relation for achieving stigmatic imaging; ##EQU31## and where, R 21 =the radius of curvature of the curve of intersection between the surface of the second imaging optical component and the plane through the surface centre orthogonal to the plane of reflection, R 22 =the radius of curvature of the curve of intersection between the surface of the second imaging optical component and the plane through the surface centre orthogonal to the plane of reflection, b=the tilt angle of the second imaging optical component, i.e. the angle between the direction of a ray through the component surface centre, and the normal to the surface through said centre, D CG =the total ray path of a central ray from the first imaging optical component to the diffraction grating, D GF =the total ray path of a central ray from the diffraction grating to the second imaging optical component, D CF =the total ray path of a central ray from the first imaging optical component to the second imaging optical component, i=index denoting an i:th prismatic component in a sequence defined by the radiation when passing from the first imaging optical component to the second imaging optical component, where: i=K as index means that the quantity refers to a first integrated prismatic component integrated with the first imaging optical component; i=F as index means that the quantity refers to a last integrated prismatic component integrated with the second imaging optical component; i=1,2, . . . N as index means that the quantity refers to prismatic components positioned between the first imaging optical component and the second imaging optical component, D i =the total ray path of a central ray from the i:th prismatic component to the second imaging optical component, N=the number of times that radiation passes prismatic components of the order sorting means which are separate from the first imaging optical component and the second imaging optical component, n i =the refractive index of the optical material of the i:th prismatic component, α i =the angle of incidence, meaning the angle between the direction of an incident ray and the normal to the first refracting surface of said i:th prismatic components, where α i should have a positive sign if the ray is incident on the opposite side of said normal, in relation to the side that the edge of the prismatic component defines, δ i =the angle between the direction of a ray, that emerges after refraction in the second refracting surface of said i:th prismatic component, and the normal to said surface where δ i should have a positive sign if said ray emerges on the opposite side of said normal, in relation to the side that the edge of the prismatic component defines, A i =the refractive angle of the i:th prismatic component, i.e. the angle between the optical surfaces of the i:th prismatic component if both surfaces are refracting, and twice the value of the refractive angle, if one of the surfaces is reflecting, α=the angle between the direction of the incident radiation and the normal to the grating surface, β=the diffraction angle, i.e. the angle between the direction of the ray emerging after diffraction, and the normal to the grating surface, r=the distance between the entrance aperture and the first imaging optical component, R 11 =the radius of curvature of the curve of intersection between the surface of the first imaging component and its plane of reflection, R, 12 =the radius of curvature of the curve of intersection between the surface of the first imaging component and the plane through the surface centre orthogonal to the plane of reflection, and a=the tilt angle of the first imaging optical component, i.e. the angle between the direction of a ray through the component surface centre, and the normal to the surface through the centre.

Claim 15

An apparatus according to claim 13, wherein: stigmatic imaging is achieved by applying the second mathematical relation for achieving stigmatic imaging in the following approximate form: ##EQU32##

Claim 16

An apparatus according to claim 7, wherein: component values for the refractive components of the order sorting means are chosen so that the following mathematical relation for achieving uniform distribution is satisfied, in order to achieve a substantially uniform distribution of the order spectra on the detector unit: ##EQU33## where δ N =the exit angle, i.e. the angle between the direction of a ray, that emerges after refraction in the second refracting surface of the N:th prismatic component, and the normal to said surface, the N:th prismatic component being the last of the prismatic components, in the sequence defined by the ray path, λ a =an arbitrarily chosen wavelength at which the first derivative in the mathematical relation is calculated, and λ b =a similarly chosen wavelength, different from λ a , at which the second derivative in the mathematical relation is calculated.

Claim 17

An apparatus according to claim 15, wherein: the wavelengths λ a and λ b are chosen to approximately coincide with those wavelengths, where a single prismatic component, used as order sorting means, results in the largest and the smallest distance between said order spectra on said detector unit, respectively.

Claim 18

An apparatus according to claim 1, wherein: the following mathematical relation for achieving full height utilization is satisfied for full utilization of the height of the sensitive surface of the detector unit; ##EQU34## where λ max =the longest wavelength in the wavelength range of the spectral detector, λ min =the shortest wavelength in the wavelength range of the spectral detector, δ N (λ max )=an exit angle for a ray with the wavelength λ max , δ N (λ min )=an exit angle for a ray with the wavelength λ min , H=the height of the sensitive surface in the direction orthogonal to the direction corresponding to the dispersion direction of the grating on the sensitive surface, h=the height of the image of the entrance aperture on the sensitive surface in the direction orthogonal to the direction corresponding to the dispersion direction of the grating on said surface, and f v eff =the effective focal distance used to calculate the size of the image on the focal surface, in the direction corresponding to the direction of the dispersion of the order sorter unit on said surface.

Claim 19

An apparatus according to claim 7, wherein: the last integrated prismatic component is integrated with the second imaging optical component, and component values for the refractive components of the order sorting means are chosen so that the following mathematical relation for achieving uniform distribution is satisfied, in order to achieve a substantially uniform distribution of the order spectra on the detector unit; ##EQU35## where δ F =the exit angle, i.e. the angle between the direction of a ray, that emerges after refraction in the second refracting surface of the F:th prismatic component, and the normal to said surface, the F:th prismatic component being the last integrated prismatic component, in the sequence defined by the ray path, λ a =an arbitrarily chosen wavelength at which the first derivative in the mathematical relation is calculated, and λ b =a similarly chosen wavelength different from λ a , at which the second derivative in the mathematical relation is calculated.

Claim 20

An apparatus according to claim 15, wherein: the exit angle δ N is calculated from the following mathematical recursion relation; ##EQU36## where index i relates to the i:th prismatic component in the ray path between the first imaging optical component and the second imaging optical component and index i+1 relates to the prismatic component following the i:th prismatic component in the ray path, and where further A' i+1 =the angle between the optical surfaces of the i:th and (i+1):st prismatic components adjacent to each other in the ray path, k i+1 =1 when the edge of the i+1:st prismatic component, points in the same direction as that of the i:th prismatic component, and k i+1 =2 when the edge of the i+1:st prismatic component, points in the opposite direction to that of the i:th prismatic component.

Claim 21

An apparatus according to claim 19, wherein: the mathematical recursion relation is applied in the following approximate form: δ.sub.i+1 A.sub.i+1 ·n.sub.i+1 (λ)-A.sub.i ·n.sub.i (λ)·(-1) .sup.k.sbsp.i+1 +α.sub.i ·(-1).sup.k.sbsp.i+1 +A'.sub.i+1 ·(-1).sup.k.sbsp.i+1.

Claim 22

An apparatus according to claim 7, wherein: planes of reflection for said mirror surfaces having concave surface shapes, are substantially orthogonal to the direction defined at the mirrors by the wavelength dispersion of said diffraction grating, and that said refractive components are mounted separately from said mirrors, whereby for the reduction of comatic aberration of the image on the sensitive surface of the detector unit, the following first mathematical relation for achieving reduction of comatic aberration is satisfied between the quantities of the components of the spectral detector; ##EQU37##

Claim 23

An apparatus according to claim 7, wherein: planes of reflection for said mirror surfaces having concave surface shapes, are substantially orthogonal to the direction defined at the mirrors by the wavelength dispersion of said diffraction grating, and the refractive components are integrated with each of said mirrors, whereby for the reduction of comatic aberration of the image on the sensitive surface of the detector unit, the following second mathematical relation for achieving reduction of comatic aberration is satisfied between the quantities of the components of the spectral detector; ##EQU38##

Claim 24

An apparatus according to claim 22, wherein: the first integrated prismatic component is integrated with the first imaging component while other prismatic components are mounted separately from the second imaging component, and the first mathematical relation for achieving stigmatic imaging and the second mathematical relation for achieving reduction of comatic aberration are applied with n F =1 and with α F =α F -α' F .

Claim 25

An apparatus according to claim 22, wherein: the last integrated prismatic component is integrated with said second imaging component while other prismatic components are mounted separately from said first imaging optical component, and the first mathematical relation for achieving stigmatic imaging and the second mathematical relation for achieving reduction of comatic aberration are applied with n K =1 and with δ K =A K- α' K .

Claim 26

An apparatus according to claim 7, wherein: planes of reflection for the mirror surfaces having concave surface shapes, are substantially parallel to the direction defined at the mirrors by the wavelength dispersion of the diffraction grating, whereby for a reduction of comatic aberration of the image on the sensitive surface of the detector unit, the following third mathematical relation for achieving reduction of comatic aberration is satisfied between the quantities of the components of the spectral detector; ##EQU39##

Claim 27

An apparatus according to claim 1, wherein: optimal utilization of the sensitive surface of the detector unit is achieved by choosing parameters of the spectral detector so that the following mathematical relations for achieving optimal utilization are satisfied; ##EQU40## where λ max =the longest wavelength in the wavelength range of the spectral detector R r =the spectral resolving power of the spectral detector Δ= the distance on the sensitive surface of the detector unit corresponding to the spectral resolving power, D s =the width of the sensitive surface of the detector unit, in the direction that the dispersion of the diffraction grating defines on the sensitive surface, m min =the spectral order that the shortest wavelength λ min of the spectral detector is diffracted in, θ=the blaze angle, i.e. the angle between the normal to the grating surface and the normal to the groove facets, meaning the reflecting surfaces of the grooves on the grating surface, d=the distance between the lines or grooves on the grating surface, α=the angle between the direction of the incident radiation and the normal to the grating surface, and f h eff =the effective focal distance used to calculate the size of the image on the focal surface, in the direction corresponding to the direction of the dispersion of the grating on said surface.

Claim 28

An apparatus according to claim 17, wherein: the first imaging optical component and the second imaging optical component include mirrors having concave surface shapes; the at least two refractive optical components include prismatic components having prismatic shape, and are arranged so that the wavelength dispersion of at least one refractive optical component opposes the wavelength dispersion of the other refractive optical components; and planes of reflection of the mirror surfaces containing rays reflected in central points of the mirror surfaces are substantially orthogonal to the direction defined at the mirrors by the wavelength dispersion of the diffraction grating, whereby values of effective focal distances f v eff and f h eff are chosen so that the following first approximate mathematical relations for effective focal distances are satisfied; ##EQU41## where f=the distance between the second imaging optical component and the detector unit, f h eff =the effective focal distance used to calculate the size of the image on the focal surface, in the direction corresponding to the direction of the dispersion of the grating on said surface, R 21 =the radius of curvature of the curve of intersection between the surface of the second imaging optical component and its plane of reflection, R 22 =the radius of curvature of the curve of intersection between the surface of the second imaging optical component and the plane through the surface centre orthogonal to the plane of reflection, b=the tilt angle of the second imaging optical component i.e., the angle between the direction of a ray through the second imaging optical component surface centre, and the normal to the surface through the centre, i=index denoting an i:th prismatic component in a sequence defined by the radiation when passing from the first to the second imaging optical component, where: i=K as index means that the quantity refers to a first integrated prismatic component, integrated with the first imaging optical component: i=F as index means that the quantity refers to a last integrated prismatic component, integrated with the second imaging optical component: i=1.2, . . . N as index means that the quantity refers to prismatic components positioned between the first imaging optical component and the second imaging optical component, D i =the total ray path of a central ray from said i:th prismatic component to the second imaging optical component, and D GF =the total ray path of a central ray from the diffraction grating to the second imaging optical component.

Claim 29

An apparatus according to claim 17, wherein: the first imaging optical component and the second imaging optical component include mirrors having concave surface shapes; the at least two refractive optical components include prismatic components having prismatic shape, and are arranged so that the wavelength dispersion of at least one refractive optical component opposes the wavelength dispersion of the other refractive optical components; and planes of reflection for the mirror surfaces containing rays reflected in central points of the mirror surfaces are substantially parallel to the direction defined at the mirrors by the wavelength dispersion of the diffraction grating, whereby values of effective focal distances f v eff and f h eff are chosen so that the following second approximate mathematical relations for effective focal distances are satisfied; ##EQU42## where f=the distance between the second imaging optical component and the detector unit, f h eff =the effective focal distance used to calculate the size of the image on the focal surface, in the direction corresponding to the direction of the dispersion of the (rating on said surface, R 21 =the radius of curvature of the curve of intersection between the surface of the second imaging optical component and its plane of reflection, R 22 =the radius of curvature of the curve of intersection between the surface of the second imagine optical component and the plane through the surface centre orthogonal to the plane of reflection, b=the tilt angle of the second imaging optical component, i.e., the angle between the direction of a ray through the second imaging optical component surface centre, and the normal to the surface through the centre, i=index denoting an i:th prismatic component in a sequence defined by the radiation when passing from the first to the second imaging optical component, where: i=K as index means that the quantity refers to a first integrated prismatic component, integrated with the first imaging optical component, i=F as index means that the quantity refers to a last integrated prismatic component, integrated with the second imaging optical component: i=1,2, . . . N as index means that the quantity refers to prismatic components positioned between the first imaging optical component and the second imaging optical component. D i =the total ray path of a central ray from said i:th prismatic component to the second imaging optical component, and D GF =the total ray path of a central ray from the diffraction grating to the second imaging optical component.

Claim 30

An apparatus according to claim 7, wherein: the first imaging optical component is a concave mirror having a spherical surface, and the first mathematical relation for achieving stigmatic imaging is applied with R 12 =R 11 =R 1 , with the notation R 1 denoting the radius of curvature of the spherical surface.

Claim 31

An apparatus according to claim 7, wherein: the second imaging optical component is a concave mirror having a spherical surface, and the first mathematical relation for achieving stigmatic imaging is applied with R 22 =R 21 =R 2 , with the notation R 2 denoting the radius of curvature of the spherical surface.

Claim 32

An apparatus according to claim 1, wherein: the at least two refractive optical components include prismatic components having prismatic shape, and are arranged so that the wavelength dispersion of at least one refractive optical component opposes the wavelength dispersion of the other refractive optical components, wherein: at least two of the prismatic components have prisms having surfaces which are joined so that the prisms have optical contact with each other.

Claim 33

An apparatus according to claim 1, wherein: the at least two refractive optical components include prismatic components having prismatic shape, and are arranged so that the wavelength dispersion of at least one refractive optical component opposes the wavelength dispersion of the other refractive optical components, wherein: at least one of the prismatic components has a reflecting optical surface.

Claim 34

An apparatus according to claim 1, wherein: the at least two refractive optical components include prismatic components having prismatic shape, and are arranged so that the wavelength dispersion of at least one refractive optical component opposes the wavelength dispersion of the other refractive optical components, wherein: at least one of the prismatic components is manufactured from the optical material lithium fluoride (LiF); and at least one other of the prismatic components with counteracting wavelength dispersion is manufactured from the optical material selected from the group of materials consisting of barium fluoride (BaF 2 ) and fused quartz.

Claim 35

An apparatus according to claim 1, wherein: the at least two refractive optical components include prismatic components having prismatic shape, and are arranged so that the wavelength dispersion of at least one refractive optical component opposes the wavelength dispersion of the other refractive optical components, wherein: at least one of the prismatic components is manufactured from the optical material with the notation LaK 31, or a material with similar dispersion properties; and at least one other of the prismatic components with counteracting wavelength dispersion is manufactured from the optical material with the notation SF 18, or a material with similar dispersion properties.

Claim 36

An apparatus according to claim 1, wherein: the light source is selected from the group of electrical light sources, consisting of arc discharges, sparks, flames and glow discharges.

Claim 37

An apparatus according to claim 1, wherein: the light source comprises: a lamp selected from the group of lamps consisting of halogen, arc and flash, and a vessel for liquid or gaseous samples, whereby the detector unit records the spectral absorbance or spectral fluorescence of the liquid or gaseous samples.

Claim 38

An apparatus according to claim 1, wherein: the light source is a plasma that has been generated either by electrical means or by laser light.

Claim 39

An apparatus according to claim 1, wherein: the light source is the sun or scattered light of the sun.

Claim 40

An apparatus according to claim 1, wherein: the light source is a combustion process selected from the group consisting of flames, explosions and fire involving gases, liquids and solids.