The correction of spatial resolution and distortion in imaging spectrometer systems is of great importance due to their significant impact on efficiency and quality. In this study, we analyze the corrective power of freeforms added at different positions in various spectrometer systems for high-performance requirements. The results show that the combination of a freeform prism and a second freeform close to the image has the best correction of distortion while preserving spot size.
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Boundary constraints: minimum edge thickness of glass/air (MNEG/MNEA)
15
MNEG
All surfaces
0.5
1
16
MNEG
All surfaces
0.5
1
RMS spot optimization (TRCX/TRCY: Transverse aberration x/y direction measured in image space with respect to the centroid.)
17
TRCX
Wavelength No.1
Sampling ray
0
Overall weight
18
TRCY
Wavelength No.1
Sampling ray
0
The target values here are regarding the example system shown in Table 2. Concerning the three aberration-related elements, according to the introduction in Section 2.B, ${\rm{Ws}}$, ${{\rm{Wk}}}$, and ${{\rm{Wr}}}$ are balanced to make sure not to degrade the spot size. Here only wavelength number 1 is illustrated as an example. The merit function operands applied for the other four sampling wavelengths are the same.
DIFF: calculate the difference between values of two given operands.
CONS: user-defined constant.
Tables (3)
Table 1.
Wavelength-dependent Improvement Factors for All Test Systems Using the Best Freeform Locationsa
Traditional Spectrometer
Warren Spectrometer
Modified Offner Spectrometer
Grism Spectrometer
1.78
14.4
5866
183
92.1
7.59
168
11.1
1.65
7.5
105
46
4.12
1.86
20.9
6.71
4.2
1.85
22.4
30.7
4.2
1.87
22.5
6.06
1
1.67
3.25
11.1
1
2.89
2.11
4.72
1.63
1.33
2.77
8.98
Freeform number
2
2
2
2
$\lambda {{1}}$ and $\lambda {{3}}$ are the edge wavelengths and the central wavelength is $\lambda {{2}}$.
Table 2.
Example 4: Lens Data of the Grism System with Freeform Combination , where the Lower Part Gives the Zernike Coefficients of the Two Freeform Surfaces
Boundary constraints: minimum edge thickness of glass/air (MNEG/MNEA)
15
MNEG
All surfaces
0.5
1
16
MNEG
All surfaces
0.5
1
RMS spot optimization (TRCX/TRCY: Transverse aberration x/y direction measured in image space with respect to the centroid.)
17
TRCX
Wavelength No.1
Sampling ray
0
Overall weight
18
TRCY
Wavelength No.1
Sampling ray
0
The target values here are regarding the example system shown in Table 2. Concerning the three aberration-related elements, according to the introduction in Section 2.B, ${\rm{Ws}}$, ${{\rm{Wk}}}$, and ${{\rm{Wr}}}$ are balanced to make sure not to degrade the spot size. Here only wavelength number 1 is illustrated as an example. The merit function operands applied for the other four sampling wavelengths are the same.
DIFF: calculate the difference between values of two given operands.
CONS: user-defined constant.
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