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We present an optical design for an airborne imaging spectrometer that addresses the unique constraints imposed by imaging the coastal ocean region. A fast (F/1.8) wide field system (36°) with minimum polarization dependence and high response uniformity is required, that covers the spectral range 350–1050 nm with 3 nm sampling. We show how these requirements can be achieved with a two-mirror telescope and a compact Dyson spectrometer utilizing a polarization-insensitive diffraction grating.
©2008 Optical Society of America
1. Introduction
Imaging spectroscopy in the visible and near infrared (VNIR) spectral region is acknowledged as an important technique for monitoring and understanding coastal ocean processes. It has been successfully used for example, to map phytoplankton distributions, seagrass leaf area index, as well as monitor algal blooms and coral health.1–3 In recent years, special-purpose airborne sensors have been built such as AAHIS4, PHILLS5, and CASI6, in addition to sensors that cover a broader spectral range such as AVIRIS7 or COMPASS8, which are used more typically over land targets.
The coastal ocean provides critical challenges to spectrometer system design:
- The reflectance of the target can vary from ~1% for dark water to over 90% for bright sand.
- The signal from the surface can be overwhelmed by atmospheric scatter, which is polarization-sensitive and wavelength-dependent.
- Spatial variation is of a relatively fine scale, below 1m, necessitating high spatial resolution and a concomitantly high degree of spectrometer response uniformity.
We show in this paper a powerful optical system design that responds to these challenges while at the same time maintaining a compact size that can ensure easy adaptability to different airborne platforms. It is also noted that in addition to high performance, the design utilizes a minimum number of optical elements, which is important in ensuring that the finished sensor can achieve its theoretical performance and retain stability in operation.
2. System considerations
The preferred sensor architecture for new sensors is the so-called pushbroom scan, in which the image of the spectrometer slit is projected on the ground and scanned forward with the aircraft motion. The width of the scan in the cross-track direction is the cross-track field of view (CFOV). The slit image is dispersed by a spectrometer utilizing a two-dimensional detector array that records spectral information in the direction perpendicular to the slit. We will follow here this pushbroom architecture, as it is well suited to the problem at hand.
Considering the previously stated conditions (1) and (2), it becomes evident that the optical design must have high collection aperture, as this will enable the system to observe dark targets with the requisite signal to noise ratio. However, the same property means that a lot of light will be collected over bright targets, potentially leading to detector saturation. There are two ways of addressing saturation: 1) utilize a detector with large pixel size (large number of electrons per full well), and 2) read out the detector rapidly. Both remedies may be required from a system design viewpoint; however, we are concerned here with the optical repercussions, which are as follows: First, we decide on a sensor CFOV of <40° which arises from considerations regarding ease of atmospheric correction not germane to this paper. From aircraft altitude and speed considerations, we can then decide on the approximate pixel angular subtense of ~1mrad. These two conditions already limit the number of pixels in the detector array. In order to proceed with exact numbers as an example, we settle on a real array of 640×480 pixels, with the long dimension in the cross-track (spatial) direction. This array is available with 27 µm square pixels; we will take it to be close to optimum from system design point of view, while at the same time noting that the optical design can be relatively easily scaled to a different focal length or number of pixels. Not all of the 480 pixels are needed (or used) in the spectral direction.
With respect to condition (2), it is important that the system response be polarization-independent. A level of <3% polarization sensitivity at 450 nm and <10% at 700 nm has been established as desirable.9 Finally, condition (3) implies minimization of spectrometer distortions (often called “smile” and “keystone”), as well as invariance of the spectral and spatial response functions through field and wavelength respectively. Levels below 10% have been established as desirable.10, 11 Condition (3) also implies either a reflective telescope or the complete absence of transverse chromatic aberration, since the latter can translate into an equivalent keystone error.
3. Design specifications and description
Based on all considerations stated up to this point, we present in Table 1 the specifications satisfied by the design to be presented. The terms SRF, CRF, and ARF stand for spectral response function, cross-track spatial response function, and along-track spatial response function respectively. FWHM is full width at half-maximum. Definition, computation, and examples of these response functions are given in ref. 12.
Table 1:. Design specifications
The optical system comprises a telescope and spectrometer module, both of which have been designed with a view to minimizing the number of optical surfaces and minimizing the angle of incidence on those surfaces. A solid model ray trace is shown in Fig. 1.
4. Telescope
A two-mirror unobscured telescope is utilized that achieves diffraction-limited performance (within 27 µm square) over a 36° field of view at F/1.8. The design is shown in Fig. 2. It comprises two oblate ellipsoids with a common axis of symmetry (conic constants of 6.00 and 0.185). The corresponding radii are -58.744 mm and 84.227 mm, and axial mirror separation is 58.744 mm.
The design is shown in telecentric mode, but to achieve telecentricity it is necessary to have a virtual aperture stop (12.617 mm behind the convex primary), as there are not enough degrees of freedom in a two-mirror design. There is also no field stop other than the spectrometer slit. The absence of real stops makes it necessary to pay careful attention to baffling both in the telescope and the spectrometer. However, this is not a prohibitive task.
Fig. 1. Apart from the protective window (omitted in this view for clarity), the optical system comprises two telescope mirrors, one fused silica lens/prism combination block, a concave diffraction grating, and an order-sorting filter in front of the detector (not shown). The long dimension of the system as shown is 25cm.
The ensquared energy is shown in Fig. 3 (all computations shown here have been performed with ZEMAX®). It assumes that a real, circular stop exists inside the spectrometer (which is at the grating location). For the telescope in isolation, the primary mirror acts as an oversized rectangular stop. Generally speaking, oversizing the telescope aperture has a beneficial effect in minimizing diffraction loss inside the spectrometer,12,13 although it also carries the potential for increased stray light.
The polarization performance of the telescope is shown in Fig. 4. These curves assume a protected aluminum coating (120 nm of SiO2). Aluminum coating is preferred to enable extension to 350 nm. Compared with a silver coating, it has lower overall transmittance, but as there are only two mirrors the effect is not severe. Further, the polarization difference for the Al coating appears mostly in the less critical region >700 nm.
Two-mirror telescopes based on the Schwarzschild form considered as inverted Cassegrain have been studied theoretically by Rosin14, who concentrated primarily on spherical mirror solutions, and also by Toyoda et al15. However, these methods were not found immediately useful to the problem at hand whether because of restrictions in the object and image locations or because of the pupil and obscuration conditions. We may note also that the telescope is not a strip-field system, as it has a considerable field of view in the perpendicular direction and may be usable for other applications.
We must add also a note regarding the use of refractive telescopes. As was noted earlier, transverse chromatic aberration (TCA) in the telescope translates into an equivalent keystone error. Since keystone must be controlled to a small fraction of a pixel, TCA must also be kept to an equivalent level of less than a few micrometers over a wide field and an unusually broad spectral range. Fisher and Welch16 investigated some fast and wide field achromatic designs for this purpose, but the TCA remained at an unacceptable level. Mouroulis17 showed wide field, telecentric designs with very small TCA over a broad band, but those designs could not be extended to an aperture as fast as F/1.8. Thus sensors that utilize refractive telescopes must account clearly for the TCA to a level that is exceptional by common optical design standards.
Fig. 3. Ensquared energy as a function of distance from centroid. The top three curves (that tend towards unity at 13.5 µm) are for the 350 nm wavelength and the bottom three are for the 1050 nm wavelength.
Fig. 4. Telescope transmittance in two orthogonal polarizations, for the worst-case field angle, and their normalized difference (yellow triangles).
5. Spectrometer
A ray trace of the spectrometer is shown in Fig. 5. It is of the Dyson form18 with a single fused silica lens and a concave grating. The Dyson relay was proposed as a fast point spectrometer by Mertz19, while Lobb20 showed a relatively slow imaging spectrometer design utilizing a cemented doublet but with unknown other properties. Lobb noted aberration limitations which led to the doublet design. However, those limitations are absent from our considerably faster design. To our knowledge this is the first time that a fast and uniform Dyson design is specifically optimized for the demanding ocean color applications.
Fig. 5. Ray trace of the spectrometer. The slit is perpendicular to the plane of the drawing. The detector array is practically in contact with the order sorting filter (OSF). Note that the convergence angle of the rays inside the block appears to be less than F/1.8 because it is reduced by the refractive index of the material.
The two curved surfaces are spherical and have a common axis of symmetry. The axial separation between them is 11.536 mm. Radii are 53.693 mm and 165.0 mm respectively. The block thickness is 51.936 mm in the forward direction and 51.494 in the reverse, with an extra 1 mm OSF thickness. The slit is 1 mm in front of the block. The design utilizes near-normal angle of incidence on all but one surface thus reducing polarization effects. The reflecting surface of the prism utilizes total internal reflection (angle of 55°) which is 100% efficient for both polarizations. The size of the spectrometer is dictated more by the need to reduce polarization dependence than by optical performance. Specifically, as the spectrometer scales up in size, the required grating pitch becomes coarser and thus easier to correct for polarization. Note that the close proximity of detector and block requires some care in detector mounting. However, the required modified mount has been produced for a relatively small cost.
The spectrometer optical design achieves high response uniformity through field and wavelength as well as small spot size. The ensquared energy in a 27 µm pixel is shown in Fig. 6. It can be seen that the energy is tightly contained within a pixel, practically independent of field and wavelength. For this reason, the width of the spectrometer spectral and spatial response functions is dominated by the detector pixel response. Similarly, the variation of the spectral response function through field and of the spatial response function through wavelength at the design level is negligible, at the level of 1–3% of a pixel width (Table 1). The CRF variation with wavelength will probably be dominated by residual detector response variation, which, however, can be accounted for in optimization if known in advance.12 Geometric distortions are also very small (0.05 µm for “smile” and 0.7 µm for “keystone”).
6. Diffraction grating
The grating is an integral part of the spectrometer design as it is, at least in principle, the component most sensitive to polarization. The grating has a diameter of 63.5 mm and a sag of 2.982 mm. The frequency is 83 grooves/mm. Reduction in polarization sensitivity is achieved by sacrificing peak efficiency, though by a relatively small amount. The grating efficiency (in the -1 order) is shown in Fig. 7, computed through PCGrate®. A bare aluminum coating is assumed.
Fig. 6. Spectrometer ensquared energy as a function of distance from centroid. The legend gives the field (slit) position in mm, and the wavelength corresponding to each curve. The system is symmetric about the zero field point.
Fig. 7. Grating efficiency for two orthogonal polarizations. The normalized difference of the TE and TM polarizations (yellow triangles) is also shown. The light blue curve shows the difference that would have resulted from a fully blazed (sawtooth) profile, thus demonstrating the reduction in polarization sensitivity achieved with the triangular groove profile
Polarization-insensitive grating designs have been proposed before.21,22 These methods rely on control of groove corner rounding, on controlling the wavelength of peak efficiency of the TE and TM polarizations, and on using a partially flat or partially coated groove. They are concerned with finer grating pitch and narrower spectral band (<100 nm) typical of optical communication multiplexing applications. In our case, the grating is much coarser, but at the same time the band is wider than an octave, and the polarization variation must be much lower. An additional difference is that the polarization variation is more detrimental at the short wavelength end where the effect of atmospheric scatter is greater. We find that a simple triangular groove profile (shallow angle 1.2°, steep angle 10°) suffices to reduce the polarization sensitivity to acceptable levels. Fabrication techniques capable of producing a high quality grating of this type have been demonstrated using electron-beam23 and X-ray lithography24. The present grating design is well within the capabilities of these techniques.
The spectral response shown in Fig. 7 is advantageous for two reasons: 1) it is preferable to have maximum S/N in the blue end as that is the region where atmospheric scatter has the greatest effect, and 2) the efficiency of higher grating orders is substantially suppressed (pushed into the far UV), which is important for minimizing scatter and ghosts inside the spectrometer.
7. Stray light control
Stray light control is essential in this type of system, especially at the short wavelength end where the effective signal is low. At the telescope level, a front baffle tube of appropriate length and a secondary baffle close to the window location (Fig. 2) suffice to remove any significant contributions. Stray light in the spectrometer can arise from reflections at the air/glass interfaces as well as reflection from the detector face. The required coatings are critical in controlling stray light, and therefore represent an integral part of the design. A peculiarity of this design is that light reflected from the detector face (as well as the OSF) can reach the grating and be diffracted back towards the detector in the second and third diffraction orders, thus creating a focused ghost (Fig. 8). This type of ghost can in principle be controlled by a linear variable bandpass OSF, however, such a multilayer filter is rather hard to produce and is typically limited to a band less than an octave wide. We specify below alternative, simpler coatings that achieve the same purpose. Table 2 summarizes the coating specifications for the various optical surfaces. The OSF is assumed to be a two-segment filter, with a transition around 600 nm.
Fig. 8. Example of ghosts arising from detector reflection. Three wavelengths are represented: 340 nm (blue), 600 nm (green) and 1050 nm (red). The positions marked “spectrum” show the desired first-order light, incident on and reflected from the detector (leftmost surface). The positions marked “2nd order ghost” represent light reflected from the detector that returns after being diffracted in second order by the grating. It can be seen that the 340 nm ghost falls outside the useful detector area, and the 600 nm just inside. The 600 nm and 1050 nm ghosts will not be rejected by a long-pass OSF, and hence must be controlled by antireflection (A/R) coatings.
With these specifications, the spectrometer can be expected to achieve a stray light intensity of <10-3 including ghosts. The focused ghosts shown in Fig. 8 owe their low intensity to the fact that the second and third orders have efficiencies only ~1–2% for most of the band. Actually, the second order retains some efficiency greater than 2% for wavelengths shorter than 470 nm, but as Fig. 8 shows, those ghosts fall outside the useful area of the detector. Thus the combination of the low detector/filter reflectance and the low efficiency of the 2nd and 3rd orders keep these focused ghosts to a level below 10-3. Stray light from the grating at or below 10-4 level has been achieved23. An additional way of removing detector ghosts is to displace the slit so that it lies entirely above or below the plane of symmetry. However, this effectively doubles the slit length, making the system harder to correct for aberration and increasing the angle of incidence. For these reasons, this otherwise desirable solution is not employed here.
Table 2. Coating specifications
Finally, we may note here that a separate OSF substrate is not needed in principle. The required OSF coatings can be deposited directly on the output face of the fused silica block, and the design can be readjusted slightly to provide additional detector clearance without any loss in performance. This solution is preferable in that it provides a simpler system and fewer interfaces, but these theoretical advantages are traded against the logistical difficulties of applying complex coatings at an exact location on a finished optical component against applying the coatings on several essentially disposable filter substrates and choosing the best performing ones. It is also possible to cement a separate filter to the fused silica block. These minor variations of the basic design do not alter the performance or conclusions.
8. Comparison with previous designs
We limit this comparison to sensors that specifically address ocean color, optimized in the visible/near infrared range. The comparison appears in Table 3 and shows that the design presented here provides order-of-magnitude improvement in uniformity (see smile and keystone error) while at the same time providing much higher light collection (see F-number comparison), enabling improved SNR.
Table 3. Comparison of specifications
9. Conclusions
We have presented a simple but powerful optical design that is optimized for airborne ocean color sensors, operating in the 350–1050 nm range. The design excels in providing high throughput (F/1.8), high uniformity of response (<5% of one pixel, with tolerances considered), low polarization sensitivity (2%), while also achieving a wide field of view (36°) and diffraction-limited performance within the detector pixel size. With only two telescope mirrors, one lens/prism block, the diffraction grating, one filter, and a protective window, the design also contains the minimum number of optical components possible. A broadband, polarization-insensitive diffraction grating has been described, and the necessary antireflection and other coatings have been specified for achieving low stray light.
Acknowledgment
The research described here was performed at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.
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