Wayne R. McKinney and Christopher Palmer, "Numerical design method for aberration-reduced concave grating spectrometers," Appl. Opt. 26, 3108-3118 (1987)
A general method is described for the design of single concave grating optical systems. Proper parameter and variable sets are defined, and a straightforward technique leads to a final set of optimized variable values which minimize a merit function based on spectroscopic performance.
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Source Components of Power Series Terms, Second to Fifth Orders
The straight-grooved and holographic terms, Mij and Hij, are found via
and
, respectively.
is found from
by replacing α and r witn β and r′;
and
are found from
and
by replacing α, β, r, and r′ with γ, δ, rC, and rD, and the algebraic sign of the
terms is changed.
The zeroth-order term M00 vanishes when the source and image are at A and B, respectively, and the zeroth-order term H00 vanishes when the two recording sources are at C and D. The first-order terms M10 and H10 vanish when the grating equation is satisfied.
S and M stand for the spectrograph and monochromator examples, respectively. FWZH is the full width at zero height for a given image.
Tables (7)
Table I
Source Components of Power Series Terms, Second to Fifth Orders
The straight-grooved and holographic terms, Mij and Hij, are found via
and
, respectively.
is found from
by replacing α and r witn β and r′;
and
are found from
and
by replacing α, β, r, and r′ with γ, δ, rC, and rD, and the algebraic sign of the
terms is changed.
The zeroth-order term M00 vanishes when the source and image are at A and B, respectively, and the zeroth-order term H00 vanishes when the two recording sources are at C and D. The first-order terms M10 and H10 vanish when the grating equation is satisfied.
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