3.1. The Design of RS
According to the step width and the step orders in
Table 1, we determined that the RS’s object space FOV is a rectangular FOV that is 32 mm
× 32 mm. In chapter 1, we pointed out that the field depth of the rear imaging system must be greater than the maximum height difference caused by the stepped structure. The schematic diagram of the higher stepped micromirror is shown in
Figure 5. It can be seen that the maximum height difference is expressed as
d N2 = 1920 μm and that the field depth of RS is 1920 μm. The reference object plane should be set to O, and all of the object planes with the coordinates [−960 μm, 960 μm] must meet the image quality evaluation requirements after RS imaging.
The other part of the design index is determined by IFPA. The main parameters of IFPA are as follows: the f-number is expressed as
F# = 4, the cold stop is expressed as
Dcs = 5.1 mm, the number of pixels is 256 × 320, the size of a single pixel is
p = 30 μm and the distance from cold stop to the focal plane is
fDt = 19.8 mm. Therefore, the size of the RS image plane can be calculated as 7.68 mm × 7.68 mm. In order to suppress the influence of stray light in the mid-wave infrared band, the exit pupil of RS is designed to coincide with the cold stop of the detector, and the exit pupil distance (
EXPP) is equal to
fDt. The RS’s f-number is also equal to the IFPA’s, which is expressed as
F#RS = 4. The RS’s design index is shown in
Table 2.
In
Table 2, the
βRS represents the paraxial magnification of RS, which is calculated as
βRS = −7.68 mm/32 mm = −0.24. The
NARSO represents the object space
NA, which is calculated as
NARSO =
βRS/2
F#RS = 0.03. It is necessary to register each of the pixels from all of the interference image units for accurate spectrum reconstruction. However, when the FOV is large, the RS’ distortion aberration will lead to pixel registration dislocation. It is important that this distortion will be less than 0.1%. Therefore, we adopted a telecentric design to eliminate the RS’s distortion, something that required the entrance pupil distance (
ENPP) to be greater than 5 × 10
3 mm.
A SIIFTS works in the mid-wave infrared broadband, and an achromatic design is needed. We chose germanium and silicon as the design materials, and a refractive diffraction design was used for the second germanium lens. After optimization, the diffraction coefficients were determined to be A
1 = −43.749 and A
2 = −8.381. In addition, the astigmatic aberration caused by beam splitter and compensation plate was considered. The optimized RS results are shown in
Figure 6.
As shown in
Figure 6, image quality evaluations were provided for the object plane with coordinates of 960 μm and −960 μm. The root mean square (RMS) radius of the image spots is less than the radius observed for Airy spots, the distortion is less than 0.05%, and the MTF is better than 0.5 at 17 lp. When the
βRS = −0.241 and the
ENPP = 6.2 × 10
3 mm.
3.2. The Design of MS
MS consists of a collimator lens, a stop array and a lens array, as shown in
Figure 3. It is a relay subsystem that connects the stepped micromirrors with NIS or RSIS and can also realize DoA snapshot imaging. The collimator lens is used to modulate the incident light from each FOV of the target into parallel beams. The stop array is introduced to prevent lens array imaging crosstalk.
The lens array also adopts a telecentric design of the object space that is compatible with RS. Its image space
NA should be equal to
NARSO, which is expressed as
NALAI. The focal depth of the lens array must be greater than the RS’ field depth. The size of the lens array is decided by the size of the stepped micromirrors. The size and shape of the lens units should be the same as that of the phase modulation units mentioned in chapter 2 to ensure the one-by-one correspondence between the imaging channels and the spectral channels. That is, the lens unit is a square micro-lens with a side length of 4 mm. As shown in
Figure 3, the focal length of the lens array should be greater than the total length of the stepped micromirrors; otherwise, the subsystem’s layout will conflict with each other. In summary, it was possible to obtain the lens unit design index shown below (
Table 3).
In order to improve the spatial resolution and luminous flux, it is necessary to increase the FOV of the incident light beam and the aperture of the stop unit. We fully considered the tradeoff between the FOV of the incident light beam and the aperture of the stop unit in optical design, setting the FOV of the incident light beam to ω0 = 3.6°, and the aperture of the stop unit to 2 mm × 2 mm. The f-number of the lens unit was large, so it was easy to eliminate chromatic aberration. We chose silicon as the design material for the lens array.
Figure 7a is the layout of the combination of the stop unit and the lens unit. The optimized focal length of the lens unit is
fLA = 45 mm, and the exit pupil distance is
EXPPLA = 1 × 10
10 mm.
Figure 7b shows the spot diagram, and the focal depth of the lens array was calculated as Δ
z = 4
λ(
F#LA)
2 = 3980.608 μm, which is greater than the RS’s field depth.
The FOV of the collimator lens is equal to the lens unit’s, which is expressed as ω1 = 3.6°. The effective aperture of the collimator lens is expressed as Dc = × 32 = 45.3 mm. We set the focal length of the collimator lens to fc = 130 mm, and the primary imaging height of NIS or RSIS is calculated as hf = 2fctan (ω1/2) = 8.18 mm, that is, the maximum aperture of field stop is 8.18 mm. The collimator lens uses a combination of different materials, including germanium, silicon and zinc selenide, to achieve an achromatic design.
Figure 7c is the layout of the optimized collimator lens, and
Figure 7d shows the wavefront diagram of the light beam of the collimator lens at the edge of the FOV. The RMS wave aberration was 0.0178
λ, less than 0.05
λ. This proves that the collimator lens has good collimation. Additionally, the collimator lens is able to adopt an object space telecentric design whose entrance pupil distance is
ENPPc = 1 × 10
10 mm, and object space
NA is expressed as
NAco = 0.189 after optimization. The MS layout was determined by matching the collimator lens and the lens array, as shown in
Figure 8.
3.4. The Design of RSIS
A reflective optical system design is adopted to be the objective lens used for SIIFTS remote sensing applications. The large-aperture reflective telephoto optical system has the advantages of having no chromatic aberration, no secondary spectrum, a wide band range, etc. It is suitable for wide spectrum infrared imaging. The coaxial reflective optical system has the characteristics of central obscuration, a small receiving area and scattered central spot energy, among others, all of which reduce the detection ability. We adopted an off-axis three-mirror design to ensure that the RSIS was achromatic and to improve the luminous flux. Similar to NIS, RSIS is also an image space telecentric system. The image space NA of RSIS expressed as NARSISI should be equal to NANISI and have an image height of hR = hI.
The spatial resolution requirement of the SIIFTS is better than 0.3 m at 2000 m; that is, when the detection distance is
H = 2000 m, the spatial resolution
R should be less than 0.3 m. The size of a single pixel is
p = 30 μm, which corresponds to the height on the focal plane of the RSIS image, and is expressed as
dx = 30 μm ×
βNIS/
βRS = 0.032 mm. We set the focal length of RSIS to
fRSIS, where
H/fRSIS =
R/dx and
fRSIS =
Hdx/R = 2000 m × 0.032 mm/0.3 m = 213 mm; therefore, when the
fRSIS > 213 mm, the spatial resolution will be better than 0.3 m at 2000 m. The focal length of RSIS was set to
fRSIS = 300 mm. RSIS’s FOV of was calculated as
ωRSIS = arctan (
hI/2
fRSIS) = 0.75°. The design index is shown in
Table 5.
The off-axis three-mirror system is based on the coaxial reflective optical system.
Figure 10 shows a schematic diagram of the initial structure of a coaxial reflective optical system. The target is located at infinity, and the entrance pupil is on the primary mirror M
1, while M
2 and M
3 are the secondary mirror and the tertiary mirror, respectively. The mirror is usually a quadratic surface, and the quadratic coefficients are
e12,
e22 and
e32. We introduced the follow parameters: an obscuration ratio caused by the secondary mirror of
α1 =
l2/
f1’ ≈
h2/
h1, an obscuration ratio caused by the tertiary mirror of
α2 =
l3/
l2′ ≈
h3/
h2, a magnification of the secondary mirror is
β1 =
l2′/
l2 =
u2/
u2’ and a magnification of the tertiary mirror of
β2 =
l3′/
l3 =
u3/
u3′.
For the reflective system, the refractive index is
n1 =
n2′ =
n3 = 1,
n1′ =
n2 =
n3′ = −1, and
d1 and
d2 are the distances between the primary mirror, and the secondary mirror, and the distances between the secondary mirror and the tertiary mirror, respectively.
l3′ is the back intercept, where
d1 < 0,
d2 > 0,
l3′ < 0,
f′ is the focal length of the three-mirror off-axis subsystem, that is,
f′ =
fRSIS. The equation for the
d1,
d2 and
l3′ is as follows:
Assume that the radii of the primary mirror, the secondary mirror and the tertiary mirror are
r1,
r2 and
r3, respectively, as shown below:
The free variables of the three-mirror subsystem include
e12,
e22,
e32,
α1,
α2,
β1 and
β2, and the RSIS adopts the telecentric design of image space; that is, the image plane is flat. According to the third-order aberration theory, the spherical aberration S
I, the coma S
II, the astigmatism S
III, and the field curvature S
IV are all equal to 0:
The outline dimensions of the three mirrors can be determined by defining the three independent variables in the seven free variables above. The parameters of the initial structure can be calculated. The image space NA of the off-axis three-mirror subsystem is large. While shortening the lens barrel as much as possible, it is also necessary to ensure that there is no obscuration between the secondary mirror and the tertiary mirror, and the mechanical structure between RSIS and MS should be reasonably designed.
We set the distance between the secondary mirror and the primary mirror to be twice the distance between the secondary mirror and the tertiary mirror and ensured that the back intercept was slightly larger than the distance between the secondary mirror and the tertiary mirror, that is,
d2 = −1/2
d1,
l3′ = −1.2
d2, and the focal length was set to
d1 = −400 mm,
d2 = 200 mm,
l3′ = −240 mm, setting the focal length to
f′ = −300 mm. According to Formula (2),
α1 = 0.4,
α2 = 2,
β1 = 0.75,
β2 = 0.6. The quadratic coefficients
e12 = 1.197,
e22 = −1.929 and
e32 = −0.327 can be obtained by Formulas (3)–(6). The initial structure is shown in
Table 6.
The conic parameter is −
e2, and we optimized the initial structure and limited the operands, including the
NA, focal length and exit pupil distance. The parameters of the optimized RSIS are shown in
Table 7.
Figure 11a shows the FOV distribution, and
Figure 11b is the RSIS layout. The MTF of RSIS is shown in
Figure 11c, and the MTF of the full FOV is greater than 0.7 at 17 lp.
Figure 11d shows that the RMS radius of the image spots is less than 4 μm.