Abstract

Tandem gratings of double-dispersion mount make it possible to design an imaging spectrometer for the weak light observation with high spatial resolution, high spectral resolution, and high optical transmission efficiency. The traditional tandem Wadsworth mounting is originally designed to match the coaxial telescope and large-scale imaging spectrometer. When it is used to connect the off-axis telescope such as off-axis parabolic mirror, it presents lower imaging quality than to connect the coaxial telescope. It may also introduce interference among the detector and the optical elements as it is applied to the short focal length and small-scale spectrometer in a close volume by satellite. An advanced tandem Wadsworth mounting has been investigated to deal with the situation. The Wadsworth astigmatism-corrected mounting condition for which is expressed as the distance between the second concave grating and the imaging plane is calculated. Then the optimum arrangement for the first plane grating and the second concave grating, which make the anterior Wadsworth condition fulfilling each wavelength, is analyzed by the geometric and first order differential calculation. These two arrangements comprise the advanced Wadsworth mounting condition. The spectral resolution has also been calculated by these conditions. An example designed by the optimum theory proves that the advanced tandem Wadsworth mounting performs excellently in spectral broadband.

© 2012 Optical Society of America

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References

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  15. ZEMAX is a trademark of Zemax Development Corporation, Bellevue, Washington 98004, USA.

2011 (1)

2007 (1)

2004 (2)

2003 (1)

1995 (1)

1985 (1)

1979 (1)

1976 (1)

1975 (1)

1967 (1)

1950 (1)

1945 (1)

Bartoe, J. D. F.

Beasley, M.

Beutler, H. G.

Boone, C.

Brueckner, G. E.

Cruddace, R. G.

Cunningham, N.

Green, J.

Haber, H.

Huffman, R. E.

Hunter, W. R.

Kowalski, M. P.

Larrabee, J. C.

Leblanc, F. J.

Lin, G.-Y.

Longworth, J. W.

Nakada, M. P.

Nayyar, V. P.

Ogorzalek, B. S.

Onaka, T.

Poletto, L.

Qu, Y.

Rimington, N. W.

Schenkel, F. W.

Schieffer, S. L.

Schroeder, W. A.

Thomas, R. J.

Velzel, C. H. F.

Wang, S.-R.

Werner, W.

Wilkinson, E.

Wolfe, W. L.

W. L. Wolfe, Introduction to Imaging Spectrometers (SPIE Optical Engineering, 1997).

Yu, L.

Appl. Opt. (8)

J. Opt. Soc. Am. (5)

Other (2)

W. L. Wolfe, Introduction to Imaging Spectrometers (SPIE Optical Engineering, 1997).

ZEMAX is a trademark of Zemax Development Corporation, Bellevue, Washington 98004, USA.

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Figures (6)

Fig. 1.
Fig. 1.

Two principal tandem Wadsworth mountings. (a) Mounting is composed of two concave gratings of which curvature of radii and the ruling density are equal. (b) Mounting is composed of a plane grating and a concave grating of which the ruling density are equal.

Fig. 2.
Fig. 2.

Tandem Wadsworth mounting. G 1 is the first concave grating with the radius R 1 . G 2 is the second concave grating with the radius R 2 centered at N . O is the normal of G 1 , and N is the local normal of G 2 . The wavelength λ and the wavelength λ are presented in different lines. i and θ are the incident angle and the diffraction angle of G 1 , respectively, which satisfy the grating equation for the wavelength λ . i 1 is the incident angle of G 2 for the same wavelength λ . d PC is the distance between the local vertex A and C. m and s stand for the meridian and sagittal focal planes, respectively. d m CI and d s CI are the meridian and sagittal focal distances from the local vertex of G 2 to the imaging plane, respectively.

Fig. 3.
Fig. 3.

Diagram of the output of the advanced tandem Wadsworth spectrometer, showing the central ray λ and a ray with slightly different wavelength λ , of which displacement on the imaging plane is s .

Fig. 4.
Fig. 4.

Layout of advanced tandem Wadsworth mounting FUV imaging spectrometer.

Fig. 5.
Fig. 5.

RMS spot radius versus wavelength in different values of L G 1 G 2 .

Fig. 6.
Fig. 6.

MTF of the advanced tandem Wadsworth imaging spectrometer under central and marginal wavelengths in each field of view.

Tables (2)

Tables Icon

Table 1. Parameters of the FUV Imaging Spectrometer

Tables Icon

Table 2. General Characteristics of the FUV Imaging Spectrometer

Equations (27)

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{ r m = [ ( cos i + cos θ ) / R cos 2 i / r ] 1 cos 2 θ r s = [ ( cos i + cos θ ) / R 1 / r ] 1 ,
{ d m CI = d PC r 1 m = R 2 cos 2 θ 1 ( cos i 1 + cos θ 1 ) 1 d s CI = d PC r 1 s = R 2 ( cos i 1 + cos θ 1 ) 1 .
| d m CI d s CI | = R 2 ( cos 2 θ 1 1 ) ( cos i 1 + cos θ 1 ) 1 = 0 .
d m CI = d s CI = R 2 ( cos i 1 + 1 ) 1 .
O A = O B 1 A B 1 = O B 2 A B 2 ,
{ A B 1 = [ L G 1 G 2 cos δ 1 , L G 1 G 2 sin δ 1 ] A B 2 = [ L G 1 G 2 cos δ 2 , L G 1 G 2 sin δ 2 ] ,
{ O B 1 = [ R 2 cos ( δ 1 i 1 ) , R 2 sin ( δ 1 i 1 ) ] O B 2 = [ R 2 cos ( δ 2 i 2 ) , R 2 sin ( δ 2 i 2 ) ] .
{ L G 1 G 2 cos δ 1 R 2 cos ( δ 1 i 1 ) = L G 1 G 2 cos δ 2 R 2 cos ( δ 2 i 2 ) L G 1 G 2 sin δ 1 R 2 sin ( δ 1 i 1 ) = L G 1 G 2 sin δ 2 R 2 sin ( δ 2 i 2 ) .
d i 1 d δ 1 = 1 L G 1 G 2 R 2 cos i 1 ,
d L G 1 G 2 d δ 1 = L G 1 G 2 tan i 1 .
C 2 C 1 = A C 1 A C 2 = ( A B 1 C 1 B 1 ) ( A B 2 C 2 B 2 ) .
C 2 C 1 = [ s · sin ( γ + δ 2 i 2 θ 2 ) , s · cos ( γ + δ 2 i 2 θ 2 ) ] ,
A C 1 = [ L G 1 G 2 cos δ 1 + L G 2 I cos ( i 1 + θ 1 δ 1 ) , L G 1 G 2 sin δ 1 L G 2 I sin ( i 1 + θ 1 δ 1 ) ] ,
A C 2 = [ L G 1 G 2 cos δ 2 + L G 2 I cos ( i 2 + θ 2 δ 2 ) , L G 1 G 2 sin δ 2 L G 2 I sin ( i 2 + θ 2 δ 2 ) ] .
{ s · sin ( γ + δ 1 i 1 θ 1 ) = L G 2 I cos ( i 1 + θ 1 δ 1 ) L G 2 I cos ( i 2 + θ 2 δ 2 ) L G 1 G 2 cos δ 1 + L G 1 G 2 cos δ 2 s · cos ( γ + δ 1 i 1 θ 1 ) = L G 2 I sin ( i 1 + θ 1 δ 1 ) + L G 2 I sin ( i 2 + θ 2 δ 2 ) L G 1 G 2 sin δ 1 + L G 1 G 2 sin δ 2 .
d L G 2 I d δ 1 = [ sin ( δ 1 i 1 ) cos ( δ 1 i 1 ) ] L G 1 G 2 L G 2 I [ L G 1 G 2 R ( cos i cos θ 1 ) cos θ 1 cos 2 i cos θ ] [ sin ( i 1 + θ 1 δ 1 ) + cos ( i 1 + θ 1 δ 1 ) ] [ cos ( i 1 + θ 1 δ 1 ) sin ( i 1 + θ 1 δ 1 ) ] cos i 1 .
d L G 2 I d δ 1 = L G 2 I i 1 d i 1 d δ 1 = R 2 sin i 1 ( 1 + cos i 1 ) 2 d i 1 d δ 1 = R 2 sin i 1 ( 1 + cos i 1 ) 2 ( 1 L G 1 G 2 R 2 cos i 1 ) .
L G 1 G 2 = tan γ · cos i 1 ( 1 + cos i 1 ) + sin i 1 2 tan γ ( 1 + cos i 1 ) + tan i 1 R 2 .
{ L G 1 G 2 = tan γ · cos i 1 ( 1 + cos i 1 ) + sin i 1 2 tan γ ( 1 + cos i 1 ) + tan i 1 R 2 L G 2 I = R 2 / ( 1 + cos i 1 ) 1 .
{ L G 1 G 2 = cos i 1 R 2 L G 2 I = R 2 / ( 1 + cos i 1 ) 1 .
d s d δ 1 = [ 1 + cos γ cos i 1 ( 1 + cos i 1 ) + sin γ sin i 1 cos i 1 ( 1 + cos i 1 ) 2 ] L G 1 G 2 R 2 sin i 1 sin γ ( 1 + cos i 1 ) 2 .
d s d δ 1 = R ( 1 + cos i 1 + cos 2 i 1 ) ( 1 + cos i 1 ) .
d δ 1 d s = d λ d s · d δ 1 d λ .
d δ 1 d λ = m d cos δ 1 ,
d λ d s = d δ 1 d s · d λ d δ 1 = ( 1 + cos i 1 ) R ( 1 + cos i 1 + cos 2 i 1 ) · d cos δ 1 m .
d s = f 2 cos ζ f 1 cos δ 1 b .
d λ = ( 1 + cos i 1 ) R 2 ( 1 + cos i 1 + cos 2 i 1 ) · d cos δ 1 m · d s = ( 1 + cos i 1 ) cos ζ ( 1 + cos i 1 + cos 2 i 1 ) · d f 2 m R 2 f 1 b .

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