Focalization process of spherical concave diffraction gratings

Claim 2

In a spectrometric system including a first fixed member defining an entrance slit of finite area, a second fixed member defining an exit slit of finite area, a concave reflective diffraction grating having a selected radius of curvature, the center of said entrance slit presenting an entrance aperture which with the center of said grating defines an optical axis for incident radiation and the center of said exit slit presenting an exit aperture which with the center of said grating defines an optical axis for diffracted radiation, and means for rotating said grating about a fixed axis perpendicular to and passing through the intersection of said optical axes whereby successively to focus different wave lengths of incident radiation at said exit slit, the improvement wherein: said first member is located a distance r from said center of the grating and said second member is located a distance r' from said center of the grating such that r >m and r'>n where m and n are those distances at which the first and second members would be located to produce a zero sum of the object and image tangential focus for a system having its entrance slit, and consequently its entrance aperture, of negligible area the differences r - m and r' - n being such as to displace the Gaussian reference sphere of the system by an amount sufficient substantially to compensate for those aberrations introduced by said finite, non-negligible area of said entrance slit.

Claim 3

In a spectrometric system according to claim 1 wherein optical axes include an angle 2θ which is equal to the difference between the angles of incidence and diffraction.

Claim 4

In a spectrometric system including a concave reflective diffraction grating having a given radius of curvature, a given number of lines per mm and a given ruled area, and rotating about an axis tangent to its summit, and including a fixed entrance slit, the center of said entrance slit defining an entrance aperture and an optical axis for incident radiation with the center of said grating, and including a fixed exit slit, the center of said exit slit defining an exit aperture and an optical axis for diffracted radiation with the center of said grating, and means for rotating said grating about a fixed axis perpendicular to and passing through the intersection of said optical axes whereby successively to focus different wavelength at said exit slit, the improvement wherein: said entrance slit is located at a distance r from said center of the grating, said exit slit is located to a distance r' from said center of the grating, said optical axes include a fixed angle 2θ, said distances r and r' being equal to values determined for a mounting having a null aperture (i.e. values obtained by considering that the sum of the object and image tangential focus is null) said values being increased by an amount essentially equal to that required to achieve a displacement of the gaussian reference sphere in order to compensate the aberrations given by the concave grating in the considered amount, the value of said amount being then determined in function of said aberrations by image quality criterion.

Claim 5

In a spectrometric system including a concave reflective diffraction grating having a given radius of curvature, a given number of lines per mm and a given ruled area, and rotating about an axis tangent to its summit, and including a fixed entrance slit, the center of said entrance slit defining an entrance aperture and an optical axis for incident radiation with the center of said grating, and including a fixed exit slit, the center of said exit slit defining an exit aperture and an optical axis for diffracted radiation with the center of said grating, and means for rotating said grating about a fixed axis perpendicular to and passing through the intersection of said optical axes whereby successively to focus different wavelength at said exit slit, the improvement wherein: said entrance slit is located at a distance r from said center of the grating, said exit slit is located to a distance r' from said center of the grating, said optical axes include a fixed angle 2θ, said distances r and r' being equal to values determined for a mounting having a null aperture (i.e. values obtained by considering that the sum of the object and image tangential focus is null) said values being increased by an amount essentially equal to that required to achieve a displacement of the gaussian reference sphere in order to compensate the aberrations given by the concave grating in the considered amount, the value of said amount being then determined in function of said aberrations by image quality criterion.

Claim 6

A spectrometric system according to claim 3, characterized in that to each value of 2θ and for each value of the couple W and L, is associated a value of ε such that T + T' = ε and further that, to any value f' of the exit slit is associated a practical resolving power ##EQU37## where W and L respectively are the width and length of the ruled area of the grating, where T and T' respectively are the object tangential focal length and the image tangential focal length and ε represents second order aberrations introduced by said grating in imaging said entrance slit at said slit, f' is the width of the exit slit, N is the number of ruled lines per mm of the grating, λ is wavelength, β is the angle of diffraction and δ λ inst. is defect of residual instrument setting.

Claim 7

A spectrometric system according to claim 1, characterized in that the rotation grating is associated with several exit slits.

Claim 8

A spectrometric system according to claim 1, characterized in that the image plane is chosen by taking into account not only the aberrations of the concave grating used but also aberrations resulting from the lighting conditions of said grating.

Claim 9

A spectrometric system according to claim 1, characterized in that the middles of the entrance and exit slits are in a plane containing the line normal to the grating and perpendicular to the direction of the grating lines and in that the entrance and exit slits have a fixed width, i.e. are independent of the wavelength λ determined so that there is no flux loss at the exit slit level.

Claim 10

A spectrometric system according to claim 2 characterized in that the value of angle θ of each grating is determined so that, for a given grating and for the object and image distances satisfying the relation T + T' = ε where T and T' respectively are the object tangential focal length and the image tangential focal length and ε represents second order aberrations introduced by said grating in imaging said entrance slit at said exit slit, the value of the width f' 1 of the exit slit, necessary to pick up all the flux corresponding to the practical resolution.

Claim 11

A spectrometric system according to claim 8, characterized in that two mountings with single grating rotation are associated in a "Z" mounting, the exit slit of the first serving as the entrance slit for the second mounting, and in that the first grating rotates in the direction of the entrance slit and the second rotates in the opposite direction (direction of the exit slit of the second mounting).

Claim 12

A focalization method for concave, reflective diffraction gratings having a curvature R wherein the dispersion and focus of different wavelengths of incident radiation are obtained with fixed entrance and exit slits and solely by rotation of the grating about a fixed axis, which comprises the steps of: a. relatively locating the entrance slit, the exit slit and the grating in fixed relation to define axes of incidence and diffraction lying in a plane perpendicular to the axis of rotation of the grating and passing through the center of the grating perpendicular to the rulings thereof; b. locating said axes of incidence and diffraction such that they include an angle 2θ equal to the difference between the angle of incidence α and the angle of diffraction β ; and c. locating said entrance and exit slits at distances from the grating respectively equal to r and r' such that: ##EQU38## where ε is a defect of focus balancing aberration terms of the second order providing a limited resolving power R p = 0.8 K N W o where K is the order of diffraction, N is the number of rulings per mm, and W o is the optimum ruled width of the grating computed on the basis of Strehl's criterion.

Claim 13

A focalization method for concave, reflective diffraction gratings having a curvature R wherein the dispersion and focus of different wavelengths of incident radiation are obtained with fixed entrance and exit slits and solely by rotation of the grating about a fixed axis, which comprises the steps of: a. relatively locating the entrance slit, the exit slit and the grating in fixed relation to define axes of incidence and diffraction lying in a plane perpendicular to the axis of rotation of the grating and passing through the center of the grating perpendicular to the rulings thereof; b. locating said axes of incidence and diffraction such that they include an angle 2θ equal to the difference between the angle of incidence α and the angle of diffraction β ; and c. locating said entrance and exit slits at distances from the grating respectively equal to r and r' such that: ##EQU38## where ε is a defect of focus balancing aberration terms of the second order providing a limited resolving power R p = 0.8 K N W o where K is the order of diffraction, N is the number of rulings per mm, and W o is the optimum ruled width of the grating computed on the basis of Strehl's criterion.

Claim 14

A focalization method for concave, reflective diffraction gratings having a radius of curvature R wherein the dispersion and focus of different wavelengths of incident radiation are obtained with fixed entrance and exit slits and solely by rotation of the grating about a fixed axis, which comprises the steps of: a. relatively locating the entrance slit, the exit slit and the grating in fixed relation to define axes of incidence and diffraction lying in a plane perpendicular to the axis of rotation of the grating and passing through the center of the grating perpendicular to the rulings thereof; b. locating said axes of incidence and diffraction such that they include an angle 2θ equal to the difference between the angle of incidence α and the angle of diffraction β ; and c. locating said entrance and exit slits at distances from the grating respectively equal to r and r' such that: ##EQU39## where ε is a defect of focus balancing aberration terms of the second order providing a limiting resolution < δ λ > and a corresponding limited practical resolving power ##EQU40##

Claim 15

A focalization method for concave, reflective diffraction gratings having a radius of curvature R wherein the dispersion and focus of different wavelengths of incident radiation are obtained with fixed entrance and exit slits and solely by rotation of the grating about a fixed axis, which comprises the steps of: a. relatively locating the entrance slit, the exit slit and the grating in fixed relation to define axes of incidence and diffraction lying in a plane perpendicular to the axis of rotation of the grating and passing through the center of the grating perpendicular to the rulings thereof; b. locating said axes of incidence and diffraction such that they include an angle 2θ equal to the difference between the angle of incidence α and the angle of diffraction β ; and c. locating said entrance and exit slits at distances from the grating respectively equal to r and r' such that: ##EQU39## where ε is a defect of focus balancing aberration terms of the second order providing a limiting resolution < δ λ > and a corresponding limited practical resolving power ##EQU40##

Claim 16

The method according to claim 10 wherein the width f of the entrance slit has the value ##EQU41## and the width f' of the exit slit has the value ##EQU42##

Claim 17

The method according to claim 11 wherein the width f of the entrance slit has a value ##EQU43## and the width f' of the exit slit has a value ##EQU44##

Claim 18

In a spectrometric system including a first fixed member defining an entrance slit of finite area, a second fixed member defining an exit slit of finite area, a concave reflective diffraction grating having a selected radius of curvature, the center of said entrance slit presenting an entrance aperture which with the center of said grating defines an optical axis for incident radiation and the center of said exit slit presenting an exit aperture which with the center of said grating defines an optical axis for diffracted radiation, and means for rotating said grating about a fixed axis perpendicular to and passing through the intersection of said optical axes whereby successively to focus different wave lengths of incident radiation at said exit slit, the improvement wherein: said first member is located a fixed distance r from said center of the grating and said second member is located at distance r' from said center of the grating, and said distances r and r' being such as to satisfy the fundamental focalization equation: T + T' = ε where T and T' respectively are the object tangential focal length and the image tangential focal length and ε represents a defect of focus balancing second order aberrations introduced by said grating in imaging said entrance slit at said exit slit.

Claim 19

In a spectrometric system including a first fixed member defining an entrance slit of finite area, a second fixed member defining an exit slit of finite area, a concave reflective diffraction grating having a selected radius of curvature, the center of said entrance slit presenting an entrance aperture which with the center of said grating defines an optical axis for incident radiation and the center of said exit slit presenting an exit aperture which with the center of said grating defines an optical axis for diffracted radiation, and means for rotating said grating about a fixed axis perpendicular to and passing through the intersection of said optical axes whereby successively to focus different wave lengths of incident radiation at said exit slit, the improvement wherein: said first member is located a fixed distance r from said center of the grating and said second member is located at distance r' from said center of the grating, and said distances r and r' being such as to satisfy the fundamental focalization equation: T + T' = ε where T and T' respectively are the object tangential focal length and the image tangential focal length and ε represents a defect of focus balancing second order aberrations introduced by said grating in imaging said entrance slit at said exit slit.

Claim 20

In a spectrometric system as defined in claim 14 wherein the width of said entrance slit equals ##EQU45## and the width of said exit slit equals ##EQU46## where K is the order of diffraction, N is the number of grating lines per mm, <δλ> is the limiting resolution, R p is practical resolving power equal to 0.8 K N W o where W o is the width of the ruled area of the grating, and α and β respectively are the angles of incidence and diffraction.

Claim 21

In a spectrometric system as defined in claim 14 wherein the width of said entrance slit equals ##EQU47## and the width of said exit slit equals ##EQU48## where λ is wavelength, W o is the width of the ruled area of the grating, and α and β respectively are the angles of incidence and diffraction.