Non-blind area PAL system design based on dichroic filter

Yujie Luo; Jian Bai; Xiangdong Zhou; Xiao Huang; Qun Liu; Yuan Yao

doi:10.1364/OE.24.004913

1. Introduction

All of the panoramic annular lens, fisheye lens and catadioptric system can realize the feature of imaging a wide field of view (FOV), even over 90°, which are mostly used in the satellite navigation system, robotic vision system and surveillance system, each with their merits and shortcomings [1]. The main advantages of PAL system are its compact size, small f-theta distortion and simple fabrication structure. In 1994, Canadian researcher Powell designed an infrared panoramic lens system which utilized two lens groups to project a full 360° cylindrical field of view onto a two-dimensional annular plane [2]. During the past two decades, other researchers endeavored lots of improved designs towards PAL system, for instance, extending the usage of PAL to visible and ultraviolet bands, introducing aspherical surface into the PAL system to shrink the blind area, adding several detectors on the image plane to get a high resolution picture, utilizing free-form surface to realize the zooming function, and so on [3–8]. However, there is still a fatal problem for us to conquer, the blind area.

According to the principle of flat cylinder perspective (FCP), while utilizing the PAL system, the existence of surface R₂ in Fig. 1(c) will obstruct the rays in front of this system, thus the pixels in the central part of detector cannot capture any ray, forming a round blind area [9]. And this problem directly weakens the efficiency of detector and limits the usage of PAL system. In order to make up the blind area on image plane, there must be the real object points conjugated to the image points in the central part of detector. With the purpose of looking for the conjugative object points, Chinese researcher Z. Huang proposed to coat a ring-shaped reflective film on surface R₂ of PAL block in 2012, which can make the rays with the conventional PAL FOV reflect and let the incident rays which usually have a small FOV in front of the system transmit into the PAL block through the hole in the central part of this film [10]. By this design, the blind area of typical PAL system can be made up. Besides, in 2015, researcher C. Gong proposed a new structure of panoramic system without central blindness based on a special aspherical lens [11]. And the essence of both methods mentioned above is the same that there is a ring-shaped film coated on a designated surface. However, there still mainly have two drawbacks about this structure: 1) it is difficult to coat a ring-shaped reflective film with smooth inner round boundary on a non-planar surface, and 2) the small size of this hole makes it harder to enlarge the front FOV and weakens the energy of the incident rays.

Fig. 1 Principle of FCP and ray-tracing in PAL. (a) FOV distribution, where Z represents the optical axis, $α$ and $β$ denote the minimal and maximal FOV respectively, while $θ$ indicates the orthogonal FOV to the optical axis. (b) Image plane. The imaging area of PAL system with FCP principle is a ring, the inner and outer solid circles are corresponding to the FOV $α$ and $β$ respectively, and the dashed circle represents the orthogonal FOV. The FOV $α$ and $β$ are expanded by this orthogonal FOV. (c) Typical structure of PAL system, where T₁, T₂ represent the transmitted surface 1 and transmitted surface 2, and R₁, R₂ represent the reflected surface 1 and reflected surface 2.

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In recent decades, the technique of film coating has obtained an extraordinary development, especially on the coating of wavelength-based film. Dichroic filter is a kind of selective film, which can make the rays of some specific wavelength bands reflect and make rays of other bands transmit [12]. In this paper, we propose to apply the technique of dichroic filter into PAL system, which can solve the problems mentioned above and even get some new features, for example, the dual-band imaging. Here we take the optical system of star-tracker as the prototype, and get an achievable design of dual-channel PAL system with different bands, which can confirm the feasibility of this structure and provide a new scheme to miniaturize the size of multi-channel star-tracker system.

This paper is organized as follows. Section 2 presents the application background and the detailed principle of non-blind area PAL system based on dichroic filter. Section 3 presents the design procedure step by step, including the design analysis and results. Section 4 concludes the optical system proposed in this paper and discusses the other application area of this kind of non-blind area PAL system.

2. The principle of non-blind area PAL system based on dichroic filter

2.1 Application background

Star-tracker is an avionics instrument used to provide the absolute 3-axis attitude of a spacecraft utilizing star observations, which consists of an optical system and associated processing electronics. The processor has the capability to perform star identification utilizing an internal star catalog stored in firmware and to calculate the attitude quaternion autonomously [13]. The prototype of optical design in this paper is a kind of new dual-channel star-tracker on low Earth orbit (LEO) with the feature of imaging two different channels of FOV onto a single detector, which can dramatically reduce the size and weight of whole optical system compared with conventional two-channel system. In this design, one channel is used for getting the profile of Earth, and the other channel is used for observing the positions of stars far away from this system. Since this system is designated for spacecraft on LEO, the incident energy of Earth observing channel is much stronger than that from the stars observing channel. As a result, we select a relatively narrow bandwidth in ultraviolet band to observe the Earth profile, which is ranging from 350 nm to 360 nm. At the same time, we set the bandwidth of stars observing channel at visible band from 500 nm to 800 nm. On the other hand, considering the LEO is about 500 km to 2000 km above the earth, the FOV for observing the Earth profile must be at least ranging from 40°~80° [14].

2.2 The principle of non-blind area PAL system based on dichroic filter

Imaging a wide field of view with a blind area in the central part of image plane is the main feature of PAL system [15]. In this paper, we propose to apply the technique of dichroic filter into PAL system, utilizing the central blind area to image the front FOV, which can perfectly satisfy the conditions mentioned above. Different from the non-blind area PAL system with a ring-shaped reflective film, we coat the dichroic filter on surface R₂ of PAL block. The dichroic filter, also can be named as dichroic mirror, is a kind of color filter, which is designed to selectively pass the rays of a specific range of wavelengths while reflecting the rays of other wavelengths [16]. Compared with the conventional color filters, the light in the cut-off bands of dichroic filter will be reflected rather than absorbed, and this feature is the reason why the dichroic filter can be used in our design [12]. The main difference between the usage of dichroic filter and ring-shaped reflective film in this paper is shown in Fig. 2 and Fig. 3, in which the green lines represent the light in some band the dichroic filter transmits and the purple ones are in some other band the filter reflects. Here, we set the transmitted band at 500 nm to 800 nm for observing the stars, and the reflected band at 350 nm to 360 nm for observing the profile of Earth.

Fig. 2 The schematic diagram of non-blind area PAL system with a ring-shaped reflective film. The gray line on surface R₂ represents the ring-shaped reflective film, which can only let the front rays within the area of central hole pass through, and make the rays in any wavelength reflect at other parts of this film.

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Fig. 3 The schematic diagram of non-blind area PAL imaging system based on dichroic filter. The red line on surface R₂ represent the dichroic filter, which can let some band transmit and make some other band reflect. In this paper, the transmitted band is 500~800 nm, and the reflected band is 350~360 nm.

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The schematic diagram of non-blind area PAL imaging system based on dichroic filter is demonstrated in Fig. 3. According to the analysis above, the purple rays in Fig. 3 are corresponding to the conventional PAL imaging track, which will be reflected when hit the dichroic filter on surface R₂, while the green rays represent the front imaging track, which can pass through this surface directly. Consequently, the rays of both channels are converged by the relay lens group and imaged on the same detector. Compared with the non-blind area PAL system with a ring-shaped film, the structure demonstrated in this paper can obviously overcome the drawbacks mentioned above, which means the beams of front imaging channel are not limited by the area size of central hole, and will reduce the design difficulty, get a larger FOV result and derive more beam energy.

Also shown in Fig. 3, the central blind area in Fig. 1 is substituted by the green part which represents the imaging area of front imaging channel with some band the filter transmits, and the efficiency of detector is dramatically improved.

Consequently, the structure we propose in this paper has the advantages below:

• Coating a film on the whole area of surface R₂ of PAL block is much easier than coating a ring-shaped film with a smooth inner round boundary on the same surface, which can simplify the manufacture processing.
• Since the front imaging rays can transmit the surface R₂ of PAL block at any part of this filter, this design can get a better and more flexible optical result, for instance, a larger FOV and a larger entrance pupil.
• This filter can avoid the influence of local vignetting on surface R₂ of PAL block, which can help to reduce the impact of total vignetting on image plane in front imaging channel.
• According to the feature of dichroic filter, this design can realize the dual-band imaging and be used in the domain of dual-band imaging with a wide field of view.

3. Optical design

Since the signal of stars far away from this system is relatively weak and this system is used in both bands at 350~360 nm and 500~800 nm, we choose product CMV4000 manufactured by company CMOSIS as the detector, which can capture and image the rays in both bands with a high sensitivity, and set it as the image plane design model. According to its datasheet, the resolution of this product is 2048 (H) * 2048 (V) – 4MP, and the pixel size is 5.5 $\times$ 5.5 μm² [17]. The area of image plane can be calculated as the Eq. (1) below:

A r e a = [N (H) \times l (H)] \times [N (V) \times l (V)]

where N(H) and N(V) are the numbers of pixels in horizontal and vertical direction respectively, l(H) and l(V) are the lengths of one pixel in horizontal and vertical direction respectively. As a result, the imaging area of this detector is 11.26

\times

11.26 mm², and the maximal image height for us to design is about 5.63 mm.

Similar to the detector, because the rays of both channels will propagate in PAL and relay lens group, the optical materials of these lenses should be selected under the principle that all the materials of PAL and relay lenses can propagate the rays in both bands of 350~360 nm and 500~800 nm. In Table 1, we list the optical materials used in this design with their transmittance ratio, for example, the value 0.987 of H-BaK8 means that when the thickness of optical material H-BaK8 is 5 mm, the transmittance ratio of wavelength 355 nm is 0.987 [18].

Table 1. Transmittance of Optical Material

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On the other hand, the quality of this dichroic filter we try to use must be tested. Since the light source of spectrophotometer is parallel, the only way to test the quality of this film is coating it on a parallel plate. The test result of transmittance about the filter we use is shown in Fig. 4, which indicates that when the incident rays are orthogonal to this sample plate, the transmittance of the beam with wavelength between 350~360 nm is nearly close to 2%, while the beam between 500~800 nm is up above 80%.

Fig. 4 The transmittance of dichroic filter which reflects the beam with wavelength from 350 to 360 nm and transmits the beam with wavelength from 500 to 800 nm. The result is tested with the UV-VIS-NIR scanning spectrophotometer produced by SHIMADZU.

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As shown in Fig. 3, the visible rays of front imaging channel must propagate through the optical structure of PAL channel. Compared with conventional PAL channel, there is an additional correcting lens group in front imaging channel, which means designers can set more parameters to optimize the whole structure, so the design procedure can be divided into the following three steps:

• Setting the light source wavelength at 350~360 nm and designing an initial structure of PAL imaging system.
• Changing the source wavelength to 500~800 nm, fixing the parameters of PAL channel and adding a correcting lens group in front of PAL channel to enlarge the FOV of front imaging channel and converge the rays of this channel onto the image plane.
• Combining both channels and synchronously optimizing the whole structure to improve the imaging quality.

The image height control in PAL system with a wide FOV is different from other optical system. The relationship of theoretical image height, image focal length and object FOV can be expressed as the following Eq. (2).

y' = f' \times \tan θ

where

y'

is the image height,

f'

is the image focal length, and

θ

represents the object FOV of the optical system. However, this equation is not suitable for designing an optical system with a wide field of view, because when the FOV is approaching 90°, the value of

\tan θ

tends towards infinity, which means the image height also tends to infinity. In this paper, we introduce the linear distortion (f-theta distortion) to control the image height. Equation (3) shows the basic principle.

y' = f' \times θ

The connotation of the variables in Eq. (3) is the same as in Eq. (2). In Fig. 5, assumed the image focal length of PAL system is 3 mm, the blue line is under the rule of tan-function which indicates the image height will increase observably when the FOV increases, while the red line is linear and represents the image height with the f-theta distortion, which is suitable for the wide FOV optical system.

Fig. 5 Difference between normal FOV-Image height relationship and image height with f-theta distortion

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In this paper, modern optical design software Zemax is engaged, which is capable to control the optimization procedure through merit function easily. And the design principle of image height control of both channels is demonstrated below:

{\begin{matrix} H_{3} = f_{P A L} \times θ_{H i g h} \\ H_{2} = f_{P A L} \times θ_{L o w} \\ H_{1} = f_{F r o n t} \times α \\ H_{2} > H_{1} \end{matrix}

where,

f_{P A L}

,

f_{F r o n t}

are the image focal length of PAL channel and front imaging channel, respectively,

θ_{H i g h}

,

θ_{L o w}

are the maximal and minimal FOV of PAL channel.

α

is the maximal FOV of front imaging channel,

H_{1}

is the image height corresponding to the maximal FOV of front imaging channel,

H_{2}

and

H_{3}

are the image height corresponding to the minimal and maximal FOV of PAL channel respectively. The last equation in Eqs. (4) indicates the maximal image height of front imaging channel must be less than the minimal image height in PAL channel to avoid the overlapping area of two channels on image plane.

With the purpose of figuring out the initial structure of PAL system, the FOV and image focal length $f_{P A L}$ must be confirmed firstly. In this design, we set the FOV ranging from 30° to 90° and calculate the approximate focal length of PAL as the Eq. (5) below:

f_{P A L} = H_{3} / θ_{H i g h}

The value of

H_{3}

in Eq. (3) is equal to the half of side length of detector. Consequently, the approximate image focal length is 3.58 mm. In Fig. 6, the layout of conventional PAL system is demonstrated, in which the red line represents the dichroic filter. And in software Zemax, we use the operand REAR to control the image height, which must be set at 1.94 mm precisely.

Fig. 6 The layout of conventional PAL imaging channel design

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During front imaging channel design procedure, we change the FOV to 0°~10°, set the source wavelength at 500~800 nm, fix the lenses parameters of PAL and relay lens group, and only set the parameters of correcting lens group as the variables. Additionally, in order to simplify the design complexity, we set the positions of stop in both channels at the same place. As the same as the design of PAL channel, the confirmed approximate focal length of this channel is 11.12 mm. And the layout of front imaging channel design is shown in Fig. 7.

Fig. 7 The layout of front imaging channel design

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At last, we combine both channels and synchronously optimize the whole structure. Fig. 8 shows the layout of this non-blind area PAL system. In this design, the overlapping area of both channels on surface R₂ is permitted, which provides more freedom for designers to get a flexible result, and is demonstrated in magnified area in the left side of Fig. 8. And the magnified area in the right side of Fig. 8 shows that there is no overlapping area of green and purple rays, which indicates one channel will not influence the other channel.

Fig. 8 The whole structure of non-blind area PAL system based on dichroic filter

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The optical parameters of both channels are listed in Table 2.

Table 2. Optical Parameters of Both Channels

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With the help of tolerancing tool in Zemax, we can deliver the result of tolerance analysis which is important to optical design. Considering the tolerance of lens decenter, lens tilt, lens curvature and lens thickness, in both channels, the most sensitive parameter is the decenter of the first lens behind PAL block, which shows that when the decenter of this lens from the optical axis by 0.04 mm, the average MTF will reduce by 0.255 and 0.033 at 100 lp/mm in PAL channel and front imaging channel respectively. And the imaging quality of both bands is not sensitive to other parameters.

4. Discussion

A non-blind area PAL system based on dichroic filter is designed in this paper. For PAL imaging channel, the FOV is the same as most typical PAL systems, ranging from 30°~90°. As shown in Fig. 9(a), the MTF values at 100 lp/mm of all fields can reach 0.65. At the same time, the distortion is under the principle of f-theta distortion and less than 4%, which is shown in Fig. 10(a). Figure 11(a) demonstrates the geometric encircled energy of PAL imaging channel, which indicates the 80% of beam energy is concentrated in a round spot with the radius of 4.5 mm on image plane. Also, the diagrams of ray fan are shown in Fig. 12 with the FOV of 30°, 60° and 90° respectively. For front imaging channel, the FOV is ranging from 0°~10°. As shown in Fig. 9(b), the MTF values can remain above 0.40. Figure 10(b) shows that the f-theta distortion in this channel is also less than 3%. The geometric encircled energy of this channel is also in a radius 4.5 mm circle on image plane. And in Fig. 13, the diagrams of ray fan with the FOV of 0°, 5° and 10° are presented. Compared with non-blind area PAL imaging system with a ring-shaped reflective film, this structure can reduce the design complexity and get a relatively larger entrance pupil in front imaging channel to let more energy of incident rays transmit into the system, which is useful towards a detector with a narrow dynamic range. In this paper, the optical system is designed for observation system on star-tracker. Besides, several components related and assembled on other parts are not discussed here, for instance, the light filter of 350~360 nm, the attenuation plate of UV-band, and the 45° mirror in front of PAL block. However, such a kind of structure or scheme is not only used in the domain of dual-band star-tracker system, but also on all the area of multi-band optical system with a wide FOV. For example, the technique of dichroic filter of transmitting VIS-band and reflecting NIR-band is also mature, and designers can substitute the dichroic filter by this filter to get some new application in navigation system or military equipment.

Fig. 9 MTF of both channels. (a) MTF of the conventional PAL imaging channel (Wavelength ranging from 350 to 360 nm). (b) MTF of the front imaging channel (Wavelength ranging from 500 to 800 nm).

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Fig. 10 Designs of both channels are under the principle of f-theta distortion. (a) F-theta distortion of conventional PAL imaging channel, which is less than 4% for all fields. (b) F-theta distortion of front imaging channel, which is less than 3% for all fields.

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Fig. 11 Diagram of geometric encircled energy. (a) The geometric encircled energy distribution of PAL imaging channel (UV-band), which indicates that 80% of the beam energy is concentrated in a radius 4.5mm circle with whole FOV on image plane. (b) The geometric encircled energy distribution of front imaging channel (VIS-band), which indicates that 80% of the beam energy is concentrated in a radius 4.5mm circle with whole FOV on image plane.

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Fig. 12 Transverse ray fan plot of PAL imaging channel, with the maximum scale of 20 μm.

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Fig. 13 Transverse ray fan plot of front imaging channel, with the maximum scale of 20 μm.

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Acknowledgments

I thank Prof. Jian Bai and our research group for their helpful discussion. This work was supported by State key laboratory of modern optical instrumentation of Zhejiang University.

References and links

1. Z. Huang, J. Bai, T. X. Lu, and X. Y. Hou, “Stray light analysis and suppression of panoramic annular lens,” Opt. Express 21(9), 10810–10820 (2013). [CrossRef] [PubMed]

2. I. Powell, “Design study of an infrared panoramic optical system,” Appl. Opt. 35(31), 6190–6194 (1996). [CrossRef] [PubMed]

3. S. Niu, J. Bai, X. Y. Hou, and G. G. Yang, “Design of a panoramic annular lens with a long focal length,” Appl. Opt. 46(32), 7850–7857 (2007). [CrossRef] [PubMed]

4. S. Thibault, “Panoramic lens applications revisited,” Proc. SPIE Vol. 7000, 70000L1–8(2008). [CrossRef]

5. E. J. Tremblay, D. L. Marks, D. J. Brady, and J. E. Ford, “Design and scaling of monocentric multiscale imagers,” Appl. Opt. 51(20), 4691–4702 (2012). [CrossRef] [PubMed]

6. T. Ma, J. Yu, P. Liang, and C. Wang, “Design of a freeform varifocal panoramic optical system with specified annular center of field of view,” Opt. Express 19(5), 3843–3853 (2011). [CrossRef] [PubMed]

7. Y. J. Luo, J. Bai, and Y. Yao, “Design of vari-focal panoramic annular lenses based on Alvarez surface,” Proc. SPIE 9272, 927216 (2014). [CrossRef]

8. I. Stamenov, I. P. Agurok, and J. E. Ford, “Optimization of two-glass monocentric lenses for compact panoramic imagers: general aberration analysis and specific designs,” Appl. Opt. 51(31), 7648–7661 (2012). [CrossRef] [PubMed]

9. I. Powell, “Panoramic lens,” Appl. Opt. 33(31), 7356–7361 (1994). [CrossRef] [PubMed]

10. Z. Huang, J. Bai, and X. Y. Hou, “Design of panoramic stereo imaging with single optical system,” Opt. Express 20(6), 6085–6096 (2012). [CrossRef] [PubMed]

11. C. Gong, D. W. Cheng, C. Xu, and Y. T. Wang, “Design of a novel panoramic lens without central blindness,” Proc. SPIE 9618, 961816 (2015). [CrossRef]

12. C. Kocher, C. Weder, and P. Smith, “Dichroic ultraviolet light filters,” Appl. Opt. 42(28), 5684–5692 (2003). [CrossRef] [PubMed]

13. C. C. Liebe, “Accuracy performance of star tracker – a tutorial,” IEEE Trans. Aerosp. Electron. Syst. 38(2), 587–599 (2002). [CrossRef]

14. E. R. Benton and E. V. Benton, “Space radiation dosimetry in low-Earth orbit and beyond,” Nucl. Instr. and Meth. in Phys. Res. B 184, 255–294 (2001).

15. L. J. Lu, X. Y. Hu, and C. Y. Sheng, “Optimization method for ultra-wide-angle and panoramic optical systems,” Appl. Opt. 51(17), 3776–3786 (2012). [CrossRef] [PubMed]

16. B. Lin, T. Y. Yu, D. Q. Liu, and F. S. Zhang, “Design and deposition of infrared/visible wide-band color separation filters,” Journal of Infrared Millim. Waves 23(5), 393–395 (2004).

17. Datasheet of Product CMV4000, CMOSIS.

18. Chinese CDGM optical glass products database.

	650nm		355nm
Material	$τ 5 m m$	$τ 10 m m$	$τ 5 m m$	$τ 10 m m$
H-BaK8	0.998	0.997	0.987	0.974
H-QK3L	0.999	0.998	0.995	0.991
BaF4	0.998	0.997	0.949	0.901
H-K9L	0.998	0.997	0.991	0.982

	PAL imaging channel	Front imaging channel
Wavelength	0.350~0.360 μm	0.500~0.800 μm
Field of view	30°~90°	0°~10°
Focal length	3.61 mm	11.15 mm
Diameter of entrance pupil	1.48 mm	4.51 mm
F/# number	2.44	2.47
RMS Spot radius	﹤6 μm	﹤4 μm

	650nm		355nm
Material	$τ 5 m m$	$τ 10 m m$	$τ 5 m m$	$τ 10 m m$
H-BaK8	0.998	0.997	0.987	0.974
H-QK3L	0.999	0.998	0.995	0.991
BaF4	0.998	0.997	0.949	0.901
H-K9L	0.998	0.997	0.991	0.982

	PAL imaging channel	Front imaging channel
Wavelength	0.350~0.360 μm	0.500~0.800 μm
Field of view	30°~90°	0°~10°
Focal length	3.61 mm	11.15 mm
Diameter of entrance pupil	1.48 mm	4.51 mm
F/# number	2.44	2.47
RMS Spot radius	﹤6 μm	﹤4 μm

Non-blind area PAL system design based on dichroic filter

Abstract

1. Introduction

2. The principle of non-blind area PAL system based on dichroic filter

2.1 Application background

2.2 The principle of non-blind area PAL system based on dichroic filter

3. Optical design

4. Discussion

Acknowledgments

References and links

Cited By

Figures (13)

Tables (2)

Equations (5)

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