Abstract

A new advanced optical design based on the Wadsworth mounting for a broadband stigmatic, coma-free practical spectrometer with high imaging quality is presented. By the addition of an inclined cylindrical lens with a wedge angle, the stigmatic imaging conditions in a broad waveband have been obtained by our analysis. An example which presents excellent optical performances over a spectral broadband of 380nm centered at 570nm has been designed to certify the analysis.

© 2015 Optical Society of America

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References

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2014 (1)

2013 (1)

2011 (1)

2010 (2)

2006 (1)

2004 (1)

2003 (1)

1979 (1)

1975 (1)

1970 (1)

1945 (1)

Bartoe, J. D. F.

Beasley, M.

Beutler, H. G.

Boone, C.

Brueckner, G. E.

Couce, B.

Cruddace, R. G.

Cunningham, N.

de la Fuente, R.

González-Núñez, H.

Green, J.

Hunter, W. R.

Kern, C.

Kowalski, M. P.

Lee, K.-S.

Lin, G. Y.

Montero-Orille, C.

Nakada, M. P.

Namioka, T.

Prieto-Blanco, X.

Qu, Y.

Rolland, J. P.

Seya, M.

Spielmann, C.

Thompson, K. P.

Wang, S. R.

Wilkinson, E.

Yu, L.

Zürch, M.

Appl. Opt. (4)

J. Opt. Soc. Am. (3)

Opt. Express (3)

Opt. Lett. (2)

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Figures (5)

Fig. 1
Fig. 1 Two Wadsworth mountings. (a) traditional Wadsworth mounting. i and θ are the incidence and diffraction angles for the grating with radius R. (b) advanced mounting with a cylindrical lens. The subscript m stands for meridian and s stands for sagittal.
Fig. 2
Fig. 2 Ray-tracing for an arbitrary 1st order diffraction wavelength in advanced Wadsworth spectrometer by a tilted cylindrical lens in meridian view, i is the incident angle to the grating.
Fig. 3
Fig. 3 The 1st order center diffraction wavelength tracing for the wedge angle calculation.
Fig. 4
Fig. 4 Residual coma in the design.
Fig. 5
Fig. 5 (a) Optimized layout of the broadband advanced Wadsworth spectrometer. (b) RMS spots radii versus wavelengths.

Tables (2)

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Table 1 Fixed Parameters of Advanced Mounting

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Table 2 Optimized Parameters of Advanced Wadsworth Mounting

Equations (28)

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{ r m = [ cosi+cosθ R cos 2 i r ] 1 cos 2 θ r s = [ cosi+cosθ R 1 r ] 1
{ r m =R cos 2 θ (cosi+cosθ) 1 r s =R (cosi+cosθ) 1
Δ= r s r m =R sin 2 θ (cosi+cosθ) 1
d cs d ' cs = d cs [ d cs f cs /( d cs + f cs ) ]
r ' m r m = n1 n t
{ r ' m = r m + n1 n t r ' s = r s [ d cs d cs f cs d cs + f cs ]
d cs 2 P d cs P f cs =0(P=Δ n1 n t)
d cs = P+ P 2 +4P f cs 2
L GC = r s d cs t=r ' s d ' cs t
α=γβθ
γ= tan 1 ( dd ' cs dH )= tan 1 ( dd ' cs dΔ dΔ dλ dλ dH )= tan 1 ( f cs 2 ( d cs + f cs ) 2 d d cs dΔ dΔ dλ dλ dH )
d d cs dΔ = 1 2 + P+2 f cs 2 P 2 +4P f cs
dΔ dλ = dΔ dθ dθ dλ =R sinθ cosi+cosθ (2cosθ+ sin 2 θ cosi+cosθ ) g cosθ
dH=dθ L GC
dλ dH = dλ dθ L GC = cosθ g( r s d cs t)
β= tan 1 ( dr ' m dH )= tan 1 ( dr ' s dH )
dr ' s dH = dr ' s dθ dθ dλ dλ dH =[ d r s dθ +( f cs d cs + f cs d cs f cs ( d cs + f cs ) 2 1) d d cs dΔ dΔ dθ ] dθ dλ dλ dH
d r s dθ =R sinθ (cosi+cosθ) 2
r s '= L GC +d ' cs +t= L GC +d' ' cs +t'
dr ' s dH = d L GC dH + dd ' cs dH + dt dH = d L GC dH + dd' ' cs dH + dt' dH
dd' ' cs dH dd ' cs dH + dt' dH dt dH =tanγ'tanγtanx=0
δ=α+x sin 1 ( nsin( sin 1 ( sinα n )+x ) )
tanγ'=tanγ+tanx=tan(γ+xδ)
Δp= 3 W 2 8R cosα[ tan θ 0 cosθ(cosi+cos θ 0 ) cos θ 0 (cosi+cosθ) ]× [ 1+ tan 2 θ( 1+ cosi cosi+cosθ ) ] 1/2
φ c = 3 8 (F#) 2 (r ' m ) 2 Rr ' s cosi·tanθ× [ 1+ tan 2 θ( 1+ cosi cosi+cosθ ) ] 1/2
{ sini= λ c g sini+sinθ=λg
sinθ=(λ λ c )g
dλ= cosi mg f 1 bcosζ

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