Chang Liu, Christoph Straif, Thomas Flügel-Paul, Uwe D. Zeitner, and Herbert Gross, "Comparison of hyperspectral imaging spectrometer designs and the improvement of system performance with freeform surfaces," Appl. Opt. 56, 6894-6901 (2017)

Hyperspectral-grating-based imaging spectrometer systems with F/3 and covering the visual–near-infrared (420–1000 nm) spectral range are investigated for monitoring Earth’s environmental changes. The systems have an entrance slit of 24 μm and a 6.5 nm spectral resolution. Both smile and keystone distortions are smaller than 20% of the pixel pitch. We benefit from the development in freeform technology and design 15 different systems with the help of off-axis aspheric and freeform surfaces. The potential of each system is explored with the help of nonspherical surfaces. Cross comparisons between different system types are summarized to give their advantages and disadvantages. In the end, detailed tolerancing of one selected system is presented to show the feasibility for fabrication.

Pantazis Mouroulis, Robert O. Green, and Daniel W. Wilson Opt. Express 16(12) 9087-9096 (2008)

References

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System Size (${\mathrm{mm}}^{3}$) ($\mathrm{x}\xb7\mathrm{y}\xb7\mathrm{z}$)

F

A

Grating Type

Angle (°)

Recomm.

Double TMA

M4, M5, M6

$<25\%$

$<5\%$

$130\times 200\times 300$

3

3

plane, reflection

14.11

0

Double TMA_TG

M4, M5, M6

$<8\%$

$<7\%$

$110\times 220\times 210$

3

3

plane, transmission

0

0

TMA+Schwarzschild

M4, M5

$<17\%$

$<10\%$

$100\times 250\times 400$

2

3

plane, transmission

0.43

0

TMA 1

—

$<30\%$

$<40\%$

$110\times 190\times 160$

0

3

plane, reflection

0

0

TMA 2

M2

$<5\%$

$<12\%$

$120\times 190\times 240$

1

2

plane, reflection

0

++

TMA 3

M1, M3

$<5\%$

$<20\%$

$80\times 110\times 150$

2

1

plane, reflection

0

+

TMA 4

M2, M3

$<14\%$

$<15\%$

$65\times 85\times 80$

2

1

plane, reflection

0

+

-+-TMA

—

$<8\%$

$<16\%$

$75\times 200\times 90$

0

3

plane, reflection

0

++

-+-TMA (integrated)

M3

$<1.5\%$

$<5\%$

$75\times 160\times 210$

1

2

plane, reflection

0

+

Folded TMA

M1, M2, M3

$<8\%$

$<7\%$

$40\times 150\times 210$

3

0

plane, reflection

0

0

Offner

—

$<3\%$

$<0.9\%$

$50\times 110\times 110$

0

2

convex, reflection

25.98

++

Schwarzschild

—

$<0.15\%$

$<0.25\%$

$50\times 160\times 140$

0

4

plane, reflection

17.73

++

Schwarzschild_TG

—

$<4\%$

$<8\%$

$50\times 180\times 120$

0

4

plane, transmission

0

+

Dyson 1

—

5%

8%

$35\times 45\times 110$

0

0

plane, transmission

20.18°

0

Dyson 2

lens rear surface

15%

5%

$25\times 45\times 110$

1

0

plane, transmission

20°

+

F location represents the locations of the freeform surfaces in each system, in which M is used to represent mirror. Keystone represents the keystone distortion, Smile represents the smile distortion, F represents the number of freeform surfaces, and A represents the number of aspheres. The last column gives recommendations of the systems based on the targeted application and the system performances. “0” means not recommended, “+” means somewhat recommended, and “++” means recommended.

Table 3.

Typical Tolerances According to the Usual Manufacturing Condition^{a}

Mirror

Surface form error

RMS 18 nm/PV 140 nm

Decenter

10 μm

Tilt

0.008°

Grating

Period

1 nm

Substrate surface irregularity

PV 250 nm*

The substrate surface irregularity is measured on a 6 in. (15.24 cm) mask blank.

Table 4.

Curved Mirror Tolerances of the Double-Pass TMA System After Coupling M1 and M3^{a}

M1

M2

M3

Tilt around x axis (°)

−0.008

0.008

−0.01

0.01

P2

P2

Tilt around y axis (°)

−0.008

0.008

−0.01

0.01

P2

P2

Tilt around z axis (°)

−10

10

−0.1

0.1

P2

P2

Decenter in x axis (mm)

−0.012

0.012

−0.015

0.015

P2

P2

Decenter in y axis (mm)

−0.012

0.012

−0.015

0.015

P2

P2

Decenter in z axis (mm)

−0.01

0.01

−0.012

0.012

P2

P2

Surface irregularity (mm)

−0.0001

0.0001

−0.0026

0.0026

−0.0001

0.0001

Radius of curvature (fringe)

−1

1

−1

1

−2

2

P2 represents picking up from M2, which means all position tolerances of mirror 3 are the same as mirror 2.

System Size (${\mathrm{mm}}^{3}$) ($\mathrm{x}\xb7\mathrm{y}\xb7\mathrm{z}$)

F

A

Grating Type

Angle (°)

Recomm.

Double TMA

M4, M5, M6

$<25\%$

$<5\%$

$130\times 200\times 300$

3

3

plane, reflection

14.11

0

Double TMA_TG

M4, M5, M6

$<8\%$

$<7\%$

$110\times 220\times 210$

3

3

plane, transmission

0

0

TMA+Schwarzschild

M4, M5

$<17\%$

$<10\%$

$100\times 250\times 400$

2

3

plane, transmission

0.43

0

TMA 1

—

$<30\%$

$<40\%$

$110\times 190\times 160$

0

3

plane, reflection

0

0

TMA 2

M2

$<5\%$

$<12\%$

$120\times 190\times 240$

1

2

plane, reflection

0

++

TMA 3

M1, M3

$<5\%$

$<20\%$

$80\times 110\times 150$

2

1

plane, reflection

0

+

TMA 4

M2, M3

$<14\%$

$<15\%$

$65\times 85\times 80$

2

1

plane, reflection

0

+

-+-TMA

—

$<8\%$

$<16\%$

$75\times 200\times 90$

0

3

plane, reflection

0

++

-+-TMA (integrated)

M3

$<1.5\%$

$<5\%$

$75\times 160\times 210$

1

2

plane, reflection

0

+

Folded TMA

M1, M2, M3

$<8\%$

$<7\%$

$40\times 150\times 210$

3

0

plane, reflection

0

0

Offner

—

$<3\%$

$<0.9\%$

$50\times 110\times 110$

0

2

convex, reflection

25.98

++

Schwarzschild

—

$<0.15\%$

$<0.25\%$

$50\times 160\times 140$

0

4

plane, reflection

17.73

++

Schwarzschild_TG

—

$<4\%$

$<8\%$

$50\times 180\times 120$

0

4

plane, transmission

0

+

Dyson 1

—

5%

8%

$35\times 45\times 110$

0

0

plane, transmission

20.18°

0

Dyson 2

lens rear surface

15%

5%

$25\times 45\times 110$

1

0

plane, transmission

20°

+

F location represents the locations of the freeform surfaces in each system, in which M is used to represent mirror. Keystone represents the keystone distortion, Smile represents the smile distortion, F represents the number of freeform surfaces, and A represents the number of aspheres. The last column gives recommendations of the systems based on the targeted application and the system performances. “0” means not recommended, “+” means somewhat recommended, and “++” means recommended.

Table 3.

Typical Tolerances According to the Usual Manufacturing Condition^{a}

Mirror

Surface form error

RMS 18 nm/PV 140 nm

Decenter

10 μm

Tilt

0.008°

Grating

Period

1 nm

Substrate surface irregularity

PV 250 nm*

The substrate surface irregularity is measured on a 6 in. (15.24 cm) mask blank.

Table 4.

Curved Mirror Tolerances of the Double-Pass TMA System After Coupling M1 and M3^{a}

M1

M2

M3

Tilt around x axis (°)

−0.008

0.008

−0.01

0.01

P2

P2

Tilt around y axis (°)

−0.008

0.008

−0.01

0.01

P2

P2

Tilt around z axis (°)

−10

10

−0.1

0.1

P2

P2

Decenter in x axis (mm)

−0.012

0.012

−0.015

0.015

P2

P2

Decenter in y axis (mm)

−0.012

0.012

−0.015

0.015

P2

P2

Decenter in z axis (mm)

−0.01

0.01

−0.012

0.012

P2

P2

Surface irregularity (mm)

−0.0001

0.0001

−0.0026

0.0026

−0.0001

0.0001

Radius of curvature (fringe)

−1

1

−1

1

−2

2

P2 represents picking up from M2, which means all position tolerances of mirror 3 are the same as mirror 2.