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Abstract
A novel UV-VIS-NIR imaging spectrometer prototype has been presented for the remote sensing of the coastal ocean by air. The concept is proposed for the needs of the observation. An advanced design has been demonstrated based on the Dyson spectrometer in details. The analysis and tests present excellent optical performances in the spectral broadband, easy and low cost fabrication and alignment, low inherent stray light, and high signal to noise ratio. The research provides an easy method for the coastal ocean observation.
© 2017 Optical Society of America
1. Introduction
The UV-VIS-NIR (ultraviolet-visible-near infrared) imaging spectrometer by air is one of the most important instruments for the coastal ocean observation. It can help researchers to obtain the characteristics and distributions of different substances in the environment of the coastal ocean by abundant spatial and spectral information. Besides the traditional spectrometer, the new technique such as snapshot spectral imaging is developing for the application [1].
The primary difficulty in the coastal ocean observation is that the water is an extremely dark target compared to land targets. In addition, water attenuates signal exponentially with depth, at different rates per wavelength. Therefore, it requires enough high SNR (Signal to noise ratio) for the instrument. Anymore, the load by air should have broad coverage, high spatial and spectral resolving abilities, and a compact volume.
The concentric spectrometers [2, 3] including Offner and Dyson forms are commonly adopted in the remote sensing of coastal ocean by air. PHILLS (Portable Hyper-Spectral Imager for Low-Light Spectroscopy) and MaRS (The Mapping Reflected-energy Sensor) used the Offner spectrometer. PRISM (Portable Remote Imaging Spectrometer) utilized the Dyson spectrometer [4–6].
The Dyson spectrometer owns better characteristics such as more compact volume, higher energy collection ability, and more excellent optical performances. However, the application of Dyson spectrometer is not as popular as the Offner spectrometer. Two reasons result in the situation. First, the slit and the imaging plane are too adjacent to the thick hemisphere lens in the traditional Dyson mounting. Secondly, the inherent stray lights influence the imaging quality heavily. These problems increase the cost and difficulty of the design, the manufacture, and the alignment of the spectrometer.
Many researchers have presented different studies to solve the problem. Montero-Orille [7,8] discussed the modified Dyson designs based on the Rowland circle concept. Wynne [9] and Zhang [10] brought more elaborate variants into the Dyson design to allow small air gaps in the axial direction. Warren [11] put a complex aspherical lens close to the grating to supply enough large axial air gaps. The Fery prism replacing the grating is another solution to solve the problem [12]. In contrast to the uniform dispersion by the grating, the dispersion ability of the prism is lower and decreases with wavelength increasing. Mouroulis [13,14] made great contributions to the application of the Dyson spectrometer. The prototype and flying instrument named PRISM have been produced and tested. However, the high precision of the design and the stringent stability specifications request the precise opto-mechanical system. It increases the cost and difficulty of the fabrication and alignment of the instrument.
The aim of paper is to supply a novel and rational Dyson spectrometer prototype by air for the coastal ocean observation. In Section 2, the remote sensing requests of coastal ocean and the concept of the instrument are presented. In Section 3, we present the new design of the optical system. The stigmatic condition and optimization method are studied for the advanced Dyson spectrometer, which owns large lateral and axial insertions of air gaps between the slit, the imaging plane and the hemisphere lens. In Section 4, the analysis of design results, the tolerances, the stray light, and SNR are presented. In Section 5, the tests of the prototype are presented. The analysis of experiments results verifies the feasibility of the design. The summary is presented in Section 6.
2. Requests of Coastal ocean observation and concept of instrument
NASA addresses four overarching questions for the ocean observation [15]: 1) marine ecosystems, 2) ocean biogeochemistry, 3) coastal habitats, and 4) hazards. For the coastal ocean spectroscopy application, the answer to these questions with consideration of science and societal urgency leads to four recommended integrated themes:
- (1) Separation of in-water constituents, e.g., organic and inorganic substances.
- (2) High temporal, spectral resolution and spatial resolution measurements of coastal phenomena and habitats.
- (3) Active assessments of plant physiology and the function of different groups of plants in aquatic ecosystem.
- (4) Environmental variability of the coastal ocean.
Figure 1 presents the essential substances in the coastal ocean which will reflect different wavelengths from the sunlight. By observing these targets and the radiances with the imaging spectrometer, the characteristics and distributions of these substances can be obtained. Spectral remote sensing reflectance R(λ) is calculated by [16]
where LO, rLS, and LP are the measured radiances of the ocean, reflected sky, and reference plank, respectively; and ρP is the known reflectance of the reference plank.The spectrum of primary targets for the scientific research distribute in a spectral broadband covering UV-VIS-NIR as Table 1.
Table 1. Characteristic bands of the coastal ocean observation
The concept and key parameters of the hyper-spectral imaging sensor by air for our design are presented in Fig. 2. By the push-room observation, the imaging spectrometer obtains the multi-spectrum images along the track.
3. Design procedures for the spectrometer
The following important researches on the modified Dyson spectrometer will solve the problems referred in the introduction and make the instrument suitable for the further application.
3.1Stigmatic imaging analysis of the modified Dyson spectrometer
The biggest difference between our design and the previous researches is the location of the slit. As it shown in Fig. 3, the slit is no longer at the center of curvature as it in the traditional Dyson spectrometer. Besides a large axial air distance between the plane surface of the hemisphere lens and the slit, the slit also leaves a enough lateral air distance from the axis OX. The axis passes the central vertexes and the common curvature center O' of the concave grating and the hemisphere lens. This method produces enough air spaces among the slit, the detector and the lens, and makes the thickness of hemisphere lens decrease a lot. However, the traditional stigmatic condition for the Dyson spectrometer is also changed. Based on the Rowland circle concept, an improved analysis has been presented for the modified Dyson spectrometer.
Fig. 3 Optical path of the chief ray emerging from the center of the slit for an arbitrary wavelength in the advanced Dyson spectrometer. R1 is the radius of the convex surface of the hemispherical lens and Rg is the radius of the concave grating. S is the object point. IM and IS are the meridian and sagital imaging points, respectively. The common center of the convex surfaces of the hemisphere lens and the grating is O'. The angle (-i) and θ satisfy the grating equation sini + sinθ = mgλ, where m is the diffraction order as + 1, g is the grating ruling density, and λ is the selected wavelength. Astigmatism has been overstated on the right of the arrow.
The object point S, the common center O' and the imaging point I will locate in the same circle of the radius R1 in pink dash curve when the Rowland circle condition is satisfied. Coincidence of the stigmatic images only occurs when the angle δ = 0, which means the normal incidence on the imaging plane.
With the above discussion, we obtained Fig. 4 to analyze the stigmatic condition. The pair of angles ψ and ψ’ and the pair of angles φ and φ' satisfy the Snell's law. The object point S has a vertical off-axis distance d and the corresponding imaging point I has a vertical off-axis distance d’ from the axis OX.
Fig. 4 The optical path of an arbitrary wavelength of the chief ray emerging from the center of the slit is analyzed for the advanced stigmatic Dyson spectrometer.
The new coordinate system X’O1Y’ of which original point O1 locates on the incident point of the selected wavelength is built to apply Lobb’s study [17]. γ is the included angle of XO and X'O at the intersection point O'. With this transformation, the relationship between the two distances d and d’ of any ray as it passes through various media in a concentric segment of an optical system will satisfy
The relationship of angles could be expressed as
According to Fig. 4 and Snell's law, we have
where d’ can be derived from the Eq. (2) asWith the sine rule, we also have
The incident angle i and diffraction angle θ could be derived as
As it shown in Fig. 4, the following relationship of angles can be obtained.
According to the request of the spectral resolution, the ruling density g of the grating could be decided. We can choose the central wavelength of the broadband for the convenience of the calculation. The distance d can be set by the sizes of the slit and the detector mechanism at the beginning of the design. Substituting expressions (4), (5), (6), and (7) into Eq. (8), we will get the relationship between unknown R1 and Rg to make the system stigmatic. This relationship is the basic stigmatic condition of the advanced Dyson spectrometer.
3.2 Method of the extra aberrations correction for the spectrometer
The inherent pupil aberrations of the modified Dyson spectrometer can be restrained by the stigmatic condition in Section 3.1. It can be found that the axial air gaps between the slit, the imaging plane and the hemisphere lens don't play a role in the processing. In fact, the axial air gaps will primarily bring the extra spherical aberration and chromatic aberration.
An easy method to eliminate these aberrations is to introduce more lenses with more variables into the optical path. With the ray tracing calculation, a lot of groups of optimal solutions can be obtained but many of them will destroy the stigmatic condition. Therefore, we should raise the restrictions to maintain the concentricity of the grating and the hemisphere lens to keep the stigmatic condition. We split the hemisphere lens into three lenses as a new hemisphere lens and two spherical lenses, and make the composition of powers of these three lenses equal to the power of the original hemisphere lens. The method will keep the stigmatic conditions. The power of a lens is [18]
where Rlens1 and Rlens2 are the two radii of surfaces of the lens, n is the refractive index of the glass. The relationship of the power between the original hemisphere lens and the new three lenses is expressed aswhere Φo is the power of the original hemisphere lens, Φn is the power of new hemisphere lens, Φ1 is the power of the first spherical lens, Φ2 is the power of the second spherical lens, △n, 1 is the distance between the hemisphere lens and the lens 1, and △1, 2 is the distance between the lens 1 and the lens 2. When the axial air intervals allowed between the slit, the imaging plane and the lens are decided by the volumes of the mechanical mountings, the extra spherical aberrations and chromatic aberrations will be determined. By the ray tracing optimization and the added constraints, the parameters of the hemisphere lens and the two spherical lenses will be calculated to eliminate these aberrations.4. Results analysis for the spectrometer design
4.1Design results of the simulation
An optical ray tracing of the spectrometer identifying the design strategy in a broadband spanning 320 nm to 1000 nm has been presented in Fig. 5(a). The corresponding opto-mechanical system design is shown in Fig. 5(b).
A two-mirror Schwarzschild telescope produced by another institute will be in front of the spectrometer. The characteristics of the optical system are shown in Table 2.
Table 2. Characteristics of the spectrometer (including the telescope).
All the three lenses are made of fused silica of which the refractive index n is 1.456 for the selected wavelength 660nm. The weight of three lenses is lighter than the original hemisphere lens and the volume is more compact than the traditional Dyson spectrometer.
With the previous research and the simulation of ZEMAX, the results of the optimized system are in Fig. 6. Figures 6(a)-6(c) present the MTF (modulation transfer function) curves at the marginal and central wavelengths. The MTF in each field is larger than 0.55 at Nyquist frequency (38.5 lp/mm) of the CCD detector. Figure 6(d) presents that the RMS spots radii in all fields are lower than 5μm of the working waveband. These results prove that all imaging spots are completely enclosed in a square pixel of side 13μm of CCD, and the spatial resolutions in all the waveband keep high and uniform. As shown in Fig. 6(e), the max field curvature is shorter than 0.1 mm and the max distortion is lower than 0.812%. The target picture and the imaging of it are shown in Fig. 6(f). The above results prove that the design of the advanced Dyson spectrometer presents excellent optical performances.
Fig. 6 Optimized design results simulated by ZEMAX: (a) MTF curves of 320 nm; (b) MTF curves of 660 nm; (c) MTF curves of 1000 nm; (d) RMS spots radii distribution in the waveband, (e) Field curvature in millimeters and distortion in percent (the + Y expresses the half length of the slit and the unit is mm); Different colors in (a), (b), (c), (d) and (e) stand for the marginal and central fields of view. (f) The target is the left one. The spectral imaging is on the right. These images from top to bottom are corresponding to three wavelengths at 320 nm, 660 nm and 1000 nm, respectively.
4.2 Application analysis of the design
(1) The analysis of tolerances
The tolerances decide the difficulty and cost of the fabrication and alignment for the optical system. The software ZEMAX can provide the tolerance analysis ability. The tolerances are set up in Fig. 7. These values are common and loose in the actual optical system.
Fig. 7 The tolerances setting in the software ZEMAX before the calculation. The tolerances include the material, manufacture and alignment tolerances.
We utilize the geometric average MTF at the wavelength 660 nm as the nominal criterion. By the Monte Carlo calculation in ZEMAX, we found five offenders in Tab. 3 which have most effects on the MTF.
Table 3. Worst offenders influencing the optical system in the tolerance analysis
These five offenders are all about the hemisphere lens. Therefore, the fabrication and alignment precision for the hemisphere lens should be guaranteed. Anymore, the adjustment of the back focus is effective to increase MTF about 0.02.
By the final analysis, 90% MTF only decrease 0.046 and 80% MTF only decrease 0.037 for all tolerances concerned. The reductions are acceptable for the spectrometer. In conclusion, the designed spectrometer is not difficult for the fabrication and alignment of the prototype.
(2) The analysis of stray light
The stray lights of the Dyson spectrometer are mainly composed of two portions. The first one is dispersed rays in different orders diffracted by the grating. The second part results from the double reflections between each surface.
Figure 8 presents different orders of the light on the imaging plane simulated by ZEMAX. The 0 order and −1 order are out of the imaging plane and the slit. Therefore, they will not influence the imaging. The + 2 order light in 320~500nm falls on the imaging plane but leaves an axial distance of 0.5 mm. The distance is safe for the imaging, and the high antireflection coating (>98%) for the optical surfaces will block this order of light effectively.
Fig. 8 Different orders of dispersed rays converging on the imaging plane. Three wavelengths are presented: 320 nm (blue), 660 nm (green), 1000 nm (red)
The reflection between each surface of optical elements will form different axial ghost images. If these ghost images locate too close to the CCD detector, they will affect the imaging. ZEMAX supplies the ghost reflection analysis in details to help us to obtain locations of every ghost image. The closest ghost is about 0.3166 mm away from the imaging plane, which is brought by the multi-reflection between the CCD detector and the grating. This distance is safe for the actual imaging. In conclusion, the problem of the inherent stray light can be greatly improved in our new design.
(3) The SNR analysis
The 1976 U. S. Standard Atmosphere profiles with an open ocean marine aerosol profile model are used for the calculation of radiance at the altitude of 1 km. By utilizing the MODTRAN with the zenith angle at 45° and other default models, we can simulate the radiation of targets in 320~1000 nm. With the parameters of the system, the simulated curve of SNR is shown in Fig. 9(b). It satisfies the requirements of the observation.
Fig. 9 (a) QE curves of the type of 4720 series of CCD detectors with three different coatings. We used the broadband coated one shown in the middle cash. (b) SNR curve simulation of our spectrometer in the waveband.
5. Performances tests procedure of the prototype
5.1 Prototype
A spectrometer prototype has been fabricated and tested on the previous research. The optical elements, the assembled prototype and the detector are shown in Fig. 10. The alignment of the prototype is easy. The following tests will prove the optical performances of the prototype.
5.2 Optical tests for spectral and spatial performances
The most important parameter of the prototype is the spectral resolution. Here we use the mercury lamp to be the light source because it owns precise isolated special lines. With a diffuse transmission plate, the mercury lamp illuminates the slit of the spectrometer uniformly, and we obtain the slit images of different spectral lines. By this common method, the spectral resolution of the prototype can be calculated with these slit images.
In Fig. 11(b), the interval between 546.1 nm and 435.8 nm covers 98 pixels on the CCD detector, which means one pixel covering about 1.125 nm. As we know, all the dispersed wavelengths in the working waveband will distribute uniformly on the CCD detector for the characteristics of the grating spectrometer. It means that the bandwidth of any wavelength will keep the same. The measured isolated spectral lines by the prototype in Fig. 11 also prove the point. The FHWM of 577.0 nm, 546.1 nm, 435.8 nm and 404.7 nm covers the same number of pixels as 3. Therefore, the corresponding bandwidth 3.375 nm (covering 3 pixels) could be considered as the spectral resolution of our prototype and satisfy the requests. Another function of the method is to calibrate the wavelengths on the CCD detector. It will help us to confirm the locations of different wavelengths. Anymore, the radiation calibration of the CCD detector and the spectrometer has also been completed before the performances tests. Therefore, the differences between the source and the spectral response including the radiation, the location and the resolution have been presented faithfully in the above figures and illustration. It proves the spectral reliability of our design.
Fig. 11 Spectral resolution of the prototype: (a) the slit image of the mercury lamp with isolated accurate spectral lines. (b) The radiation intensity in data of picture (a).
Figures 12 and 13 present the imaging ability of the prototype in the waveband. Because there is no telescope (not prepared) temporarily, we chose one camera of lenses with the matching parameters working in the visible waveband to be the telescope.
Fig. 12 Monochromatic images of the USAF resolution test target at three different wavelengths. (a) 440 nm, (b) 550 nm, and (c) 630 nm
A tungsten lamp has been chosen as the light source of the monochromator. The monochromatic light with bandwidth accuracy of 0.01 nm is obtained to illuminate the United States Air Force (USAF) resolution test target and the following collimator. The prototype observes this target and obtains the monochromatic images at three selected wavelengths in Fig. 12. The format of Nc expresses the resolved spatial frequency as
where k and m are the vertical and horizontal numbers in the USAF resolution test target respectively. According to the analysis of these images, the spatial frequencies that can be distinguished in all three images are identical as k = 5 and m = 2. As the description of the design results, the spatial resolutions under different wavelengths could be considered as nearly the same. The tests results prove our opinion. The resolved spatial frequency is calculated as 36.0 lp/mm which is close to the Nyquist frequency of the CCD detector (38.5 lp/mm). The equivalent spatial resolution is 0.5 mrad (0.5 m at the altitude 1 km). It can be considered as the spatial resolution of the spectrometer in all the waveband.Figure 13 presents the imaging of the far vision by the fused images in the waveband of 400~760 nm (limited by the telescope). We put the prototype on a precise rotating platform and utilize it to observe the far vision at a constant rotational speed. The excellent performances prove the imaging ability of the prototype in the working broadband. A comparison between the published works and our prototype has been presented in Table 4.
Table 4. Comparison of primary specifications.
6. Summary
To summarize, we present the reasonable and detailed research on an advanced Dyson broadband imaging spectrometer for the remote sensing of the coastal ocean by air. The concept of the instrument satisfies the requests of the observation. The innovative design provides better engineering applications. The fast imaging spectrometer prototype, which works in 320 nm~1000 nm, has enough air spaces for the opto-mechanical system, high optical performances with low stray light, low cost of the fabrication, and the easy alignment. The analysis of design and tests results of the prototype verifies the design. The new advanced spectrometer will be helpful for the coastal ocean observation.
Funding
National Natural Science Foundation of China (NSFC) (41504143); Youth Innovation Promotion Association CAS (2016203).
References and links
1. T. H. Tsai and D. J. Brady, “Coded aperture snapshot spectral polarization imaging,” Appl. Opt. 52(10), 2153–2161 (2013). [CrossRef] [PubMed]
2. J. Dyson, “Unit magnification optical system without Seidel aberrations,” J. Opt. Soc. Am. 49(7), 713–715 (1959). [CrossRef]
3. L. Mertz, “Concentric spectrographs,” Appl. Opt. 16(12), 3122–3124 (1977). [CrossRef] [PubMed]
4. C. Davis, J. Bowles, R. Leathers, D. Korwan, T. V. Downes, W. Snyder, W. Rhea, W. Chen, J. Fisher, P. Bissett, and R. A. Reisse, “Ocean PHILLS hyperspectral imager: design, characterization, and calibration,” Opt. Express 10(4), 210–221 (2002). [CrossRef] [PubMed]
5. C. Simi and E. Reith, “The Mapping Reflected-energy Sensor-MaRS: a New Level of Hyperspectral Technology,” Proc. SPIE 7457, 745703 (2009).
6. P. Mouroulis, B. E. Van Gorp, R. O. Green, M. Eastwood, D. W. Wilson, B. Richardson, and H. Dierssen, “The portable remote imaging spectrometer (PRISM) coastal ocean sensor,” in Imaging Appl. Opt. Technical Digest (OSA, 2012).
7. C. Montero-Orille, X. Prieto-Blanco, H. González-Núñez, and R. de la Fuente, “Two-wavelength anastigmatic Dyson imaging spectrometers,” Opt. Lett. 35(14), 2379–2381 (2010). [CrossRef] [PubMed]
8. C. Montero-Orille, X. Prieto-Blanco, H. González-Núñez, and R. de la Fuente, “Design of Dyson imaging spectrometers based on the Rowland circle concept,” Appl. Opt. 50(35), 6487–6494 (2011). [CrossRef] [PubMed]
9. C. G. Wynne, “Monocentric telescopes for microlithography,” Opt. Eng. 26(4), 300–303 (1987). [CrossRef]
10. Y. Zhang and Z. Wang, “Some developments for a unit magnification catadioptric optical system,” Appl. Opt. 34(7), 1203–1208 (1995). [CrossRef] [PubMed]
11. D. W. Warren, D. J. Gutierrez, and E. R. Keim, “Dyson spectrometer for high-performance infrared applications,” Opt. Eng. 47(10), 103601 (2008). [CrossRef]
12. L. Pei, B. Xiangli, Q. Lv, and X. Shao, “Optical system design of the Dyson imaging spectrometer based on the Fery prism,” Opt. Rev. 23(4), 695–702 (2016). [CrossRef]
13. P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design of a coastal ocean imaging spectrometer,” Opt. Express 16(12), 9087–9096 (2008). [CrossRef] [PubMed]
14. P. Mouroulis, R. O. Green, B. Van Gorp, L. B. Moore, D. W. Wilson, and H. A. Bender, “Landsat swath imaging spectrometer design,” Opt. Eng. 55(1), 015104 (2016). [CrossRef]
15. P. Bontempi, Earth's Living Ocean: 'The Unseen World': An advanced plan for NASA's Ocean Biology and Biogeochemistry Research, NASA, 2006.
16. T. Cui, J. Zhang, J. Tang, Y. Ma, and S. Qing, “Satellite retrieval of inherent optical properties in the turbid waters of the Yellow Sea and the East China Sea,” Chin. Opt. Lett. 8(8), 721–725 (2010). [CrossRef]
17. D. R. Lobb, “Theory of concentric designs for grating spectrometers,” Appl. Opt. 33(13), 2648–2658 (1994). [CrossRef] [PubMed]
18. M. Laikin, Lens design, 4th ed. (Academic, Taylor & Francis Group, 2006), Chap. 3.
